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http://studyadda.com/solved-papers/bcece-engineering/bcece-engineering-solved-paper-2007/341 | # Solved papers for BCECE Engineering BCECE Engineering Solved Paper-2007
### done BCECE Engineering Solved Paper-2007
• question_answer1) A body is projected at such angle that the horizontal range is three times the greatest height. The angle of projection is
A) ${{42}^{o}}8$
B) ${{53}^{o}}7$
C) ${{33}^{o}}7$
D) ${{25}^{o}}8$
• question_answer2) A gas bubble formed from an explosion under water oscillates with a period T proportional to ${{P}^{a}}{{d}^{b}}{{E}^{c}},$where P is pressure, d is the density of water and E is the total energy of explosion. The value of a, b, c are
A) $a=1,\,\,\,\,\,b=1,\,\,\,\,c=2$
B) $a=1,\,\,\,\,\,b=2,\,\,\,\,c=1$
C) $a=\frac{5}{6},$$b=\frac{1}{2},c=\frac{1}{3}$
D) $a=-\frac{5}{6},b=\frac{1}{2},c=\frac{1}{3}$
• question_answer3) A particle moving with a uniform acceleration travels 24 A and 64m in the first two consecutive interval of 4s each. Its initial velocity will be
A) 5 m/s
B) 3 m/s
C) 1 m/s
D) 4 m/s
• question_answer4) Two equal vectors have a resultant equal to either of them, then the angle between them will be
A) $~{{120}^{o}}$
B) $~{{110}^{o}}$
C) ${{60}^{o}}$
D) $~150{}^\circ$
• question_answer5) If the radius of earth of R then the height h at which the value of g becomes one fourth, will be
A) $~~\frac{R}{8}~~~$
B) $~~\frac{3R}{8}~~~$
C) $~~\frac{3R}{4}~~~$
D) $\frac{R}{2}$
• question_answer6) A body moves a distance of 10 m along a straight line under a action of 5 N force. If work done is 25 J, then angle between the force and direction of motion of the body will be
A) ${{75}^{o}}$
B) ${{60}^{o}}$
C) ${{45}^{o}}$
D) ${{30}^{o}}$
• question_answer7) If 150 J of heat is added to a system work done by the system is 110 J, the in internal energy will be
A) 40 J
B) 110 J
C) 150 J
D) 260 J
• question_answer8) Sum of the two binary numbers ${{(100010)}_{2}}$and ${{(11011)}_{2}}$is ${{(11011)}_{2}}$is
A) ${{(111111)}_{2}}$
B) ${{(101111)}_{2}}$
C) ${{(111001)}_{2}}$
D) ${{(111101)}_{2}}$
• question_answer9) What is the velocity of the bob of pendulum at its mean position, if it is a1 to vertical height of 10 cm? $(g=9.8\,m/{{s}^{2}})$
A) $2.2\text{ }m/s$
B) $1.8\text{ }m/s$
C) $1.4\text{ }m/s$
D) $0.6\text{ }m/s$
• question_answer10) A body cools from $60{{\,}^{o}}C$ to $50{{\,}^{o}}C$ in 1 the room temperature is$25{{\,}^{o}}C$ and assuming Newton law of cooling to hold g temperature of the body at the end of the next 10 min will be
A) $~45{{\,}^{o}}C$
B) $~42.85{{\,}^{o}}C$
C) $40{{\,}^{o}}C$
D) $~38.5{{\,}^{o}}C$
• question_answer11) At $27{}^\circ C$ a gas suddenly compressed such that its pressure becomes $\frac{1}{8}\text{th}$ of original pressure. The temperature of the gas will be $(\gamma =5/3)$
A) $-142{{\,}^{o}}C$
B) $300\,K$
C) $327{{\,}^{o}}C$
D) $420\,K$
• question_answer12) An ideal refrigerator has a freezer at a temperature of $-\text{ }13{{\,}^{o}}C.$ The coefficient of performance of the engine is 5. The temperature of the air (to which heat is rejected) will be
A) $325{{\,}^{o}}C$
B) 325 K
C) $~39{{\,}^{o}}C$
D) $320{{\,}^{o}}C$
• question_answer13) In a capacitor of capacitance $20\,\mu F$ the distance between the plates is 2 mm. If a dielectric slab of width 1 mm and dielectric constant 2 is inserted between the plates, then the new capacitance will be
A) $22\,\mu F$
B) $26.6\,\mu F$
C) $52.2\text{ }\mu \text{F}$
D) $~13\text{ }\mu \text{F}$
• question_answer14) An automobile spring extends 0.2 m for 5000 N load. The ratio of potential energy stored in this spring when it has been compressed by 0.2 m to the potential energy stored in a $10\,\mu F$ capacitor at a potential difference of 10000 V will be
A) 1/4
B) 1
C) 1/2
D) 2
• question_answer15) A solid metallic sphere has a charge + 3Q. Concentric with this sphere is a conducting spherical shell having charge - Q. The radius of the sphere is a and that of the spherical shell is $b(b>a).$What is the electric field at a distance $R(a<R<b)$from the centre?
A) $\frac{4Q}{2\pi \,{{\varepsilon }_{0}}{{R}^{2}}}$
B) $\frac{3Q}{4\pi \,{{\varepsilon }_{0}}{{R}^{2}}}$
C) $\frac{3Q}{2\pi \,{{\varepsilon }_{0}}{{R}^{2}}}$
D) $\frac{Q}{2\pi \,{{\varepsilon }_{0}}R}$
• question_answer16) Output $Y$is given by:
A) $(\bar{X}.\bar{Y}).Z$
B) $(X+Y)Z$
C) $(X+Y)\bar{Z}$
D) $\bar{X}.\bar{Y}+Z$
• question_answer17) In a network as shown in the figure, the potential difference across the resistance 2R is (the cell has an emf of E volts and has no internal resistance)
A) 2E
B) $\frac{4E}{7}$
C) $\frac{E}{7}$
D) $E$
• question_answer18) The resistance of a galvanometer coil is R, then the shunt resistance required to convert it into a ammeter of range 4 times, will be
A) 4R
B) $\frac{R}{3}$
C) $\frac{R}{4}$
D) $\frac{R}{5}$
• question_answer19) The instrument used by doctors for endoscopy works on the principle of
A) total internal reflection
B) reflection
C) refraction
D) none of the above
• question_answer20) A meter stick is held vertically with one end on the floor and is then allowed to fall. Assuming that the end on the floor the stick does not slip, the velocity of the other end when it hits the floor, will be
A) $10.8\text{ }m/s$
B) $~5.4\text{ }m/s$
C) $~2.5\text{ }m/s$
D) none of these
• question_answer21) If the coefficient of static friction between the tyres and road is 0.5, what is the shortest distance in which an automobile can be stopped when travelling at 72 km/h?
A) 50 m
B) 60 m
C) 40.8 m
D) 80.16 m
• question_answer22) A bullet fired at an angle of ${{30}^{o}}$ with the horizontal hits the ground 3 km away. By adjusting its angle of projection, can one hope to hit a target 5 km away. Assume the muzzle speed to be same and the air resistance is negligible
A) possible to hit a target 5 km away
B) not possible to hit a target 5 km away
C) prediction is not possible
D) none of the above
• question_answer23) Two springs of spring constant 1500 N/m and 3000 N/m respectively are stretched with the same force. They will have potential energy in ratio
A) 1 : 2
B) 2 : 1
C) 1 : 4
D) 4 : 1
• question_answer24) The elastic energy stored in a wire of Youngs modulus Y is
A) $\frac{\text{1}}{\text{2}}\text{Y}\,\text{ }\!\!\times\!\!\text{ }\,\text{stress}\,\text{ }\!\!\times\!\!\text{ strain}\,\text{ }\!\!\times\!\!\text{ }\,\text{volume}$
B) $\frac{{{\text{(stress)}}^{\text{2}}}\text{ }\!\!\times\!\!\text{ }\,\text{volume}}{\text{2Y}}$
C) $stress\times strain\times volume$
D) $Y\times \frac{{{(stress)}^{2}}}{volume}$
• question_answer25) A soap bubble A of radius 0.03 and another bubble B of radius 0.04 m are brought together so that the combined bubble has a common interface of radius r, then the value of r is
A) 0.24 m
B) 0.48 m
C) 0.12m
D) none of these
• question_answer26) An air bubble of radius ${{10}^{-2}}\,m$ is rising up at a steady rate of $2\times {{10}^{-3}}m/s$ through a liquid of density $1.5\times {{10}^{3}}kg/{{m}^{3}},$ the coefficient of viscosity neglecting the density of. air, will be $(g=10\,m/{{s}^{2}})$
A) 23.2 units
B) 83.5 units
C) 334 units
D) 167 units
• question_answer27) A Carnot reversible engine converts 1/6 of heat input into work. When the temperature of the sink is reduced by 62 K, the efficiency of Carnots cycle becomes 1/3. The temperature of the source and sink will be
A) $372\text{ }K,\text{ }310\text{ }K$
B) $~181\text{ }K,\text{ }150\text{ }K$
C) $~472\text{ }K,\text{ }410\text{ }K$
D) none of the above
• question_answer28) The ratio of the coefficient of thermal conductivity of two different materials is $5:3.$ If the thermal resistance of the rods of same thickness of these materials is same, then the ratio of the length of these rods will be
A) 3 : 5
B) 5 : 3
C) 3 : 4
D) 3 : 2
• question_answer29) Compressional wave pulses are sent to the bottom of sea from a ship and the echo is heard after 2 s. If bulk modulus of elasticity of water is $2\times {{10}^{9}}\text{ }N/{{m}^{2}}$and mean temperature is $4{{\,}^{o}}C,$ the depth of the sea will be
A) 1014 m
B) 1414 m
C) 2828 m
D) none of these
• question_answer30) Sound waves of $f=600\,Hz$fall normally on a perfectly reflecting wall. The shortest distance from the wall at which all particles will have maximum amplitude of vibration will be (speed of sound = 300 m/s)
A) $\frac{7}{8}m$
B) $\frac{3}{8}m$
C) $\frac{1}{8}m$
D) $\frac{1}{4}m$
• question_answer31) A pipe closed at one end produces a fundamental note of 412 Hz. It is cut into two pieces of equal length the fundamental notes produced by the two pieces are
A) $~824\text{ }Hz,\text{ }1648\text{ }Hz$
B) $~412\text{ }Hz,\text{ }824\text{ }Hz$
C) $~206\text{ }Hz,\text{ }412\text{ }Hz$
D) $216\text{ }Hz,\text{ }824\text{ }Hz$
• question_answer32) The refractive index of water and glycerine are 1.33 and 1.47 respectively. What is the critical angle for a light ray going from the later to the former?
A) $60{}^\circ 48$
B) $64{}^\circ 48$
C) $74{}^\circ 48$
D) None of these
• question_answer33) Lenses of power 3 D and -5D are combined to form a compound lens. An object is placed at a distance of 50 cm from this lens. Its image will be formed at a distance from the lens, will be
A) 25 cm
B) 20 cm
C) 30 cm
D) 40 cm
• question_answer34) If fringes width $\lambda =5.89\times {{10}^{-5}}$ mm is 0.431 mm and shift of white central fringe on introducing a mica sheet in one path is 1.89 mm. Thickness of the mica sheet will be $(\mu =1.59)$
A) $4.38\,\times {{10}^{-6}}m$
B) $5.38\,\times {{10}^{-6}}m$
C) $6.38\,\times {{10}^{-6}}m$
D) none of these
• question_answer35) A body is orbiting around earth at a mean radius which is two times as greater as the parking orbit of a satellite, the period of body is
A) 4 days
B) 16 days
C) $2\sqrt{2}$ days
D) 64 days
• question_answer36) A radioactive substance has half-life of 60 min. During 3 h, the fraction of the substance that has to be decayed, will be
A) 87.5%
B) 52.5%
C) 25.5%
D) 8.5%
• question_answer37) Voltage in the secondary coil of a transformer does not depend upon
A) frequency of the source
B) voltage in the primary coil
C) ratio of number of turns in the two coils
D) both (b) and (c)
• question_answer38) When n-p-n transistor is used as an amplifier
A) electrons move from emitter to base
B) electrons move from base to emitter
C) electrons move from collector to base
D) holes move from base to emitter
• question_answer39) $_{\text{7}}{{\text{N}}^{\text{14}}}$is bombarded with $_{2}H{{e}^{\text{4}}}.$ The resulting nucleus is $_{8}{{O}^{17}}$ with the emission of
A) neutrino
B) antineutrino
C) proton
D) neutron
• question_answer40) In the given figure the steady state current in the circuit is
A) Zero
B) 0.6 A
C) 0.9 A
D) 1.5 A
• question_answer41) The time of vibration of a dip needle vibration in the vertical plane in the magnetic meridian is 3 s. When the same magnetic needle is made to vibrate in the horizontal plane, the time of vibration is 3$\sqrt{2}$s. Then angle of dip will be
A) $90{}^\circ$
B) $60{}^\circ$
C) $45{}^\circ$
D) $30{}^\circ$
• question_answer42) The inductance of the oscillatory circuit of a radio station is 10 mH and its capacitance is 0.25 $\mu F$.Taking the effect of resistance negligible, wavelength of the broadcasted waves will be (velocity of light $=3.0\,\times {{10}^{8}}\,m/s,\,\pi =3.14$)
A) $9.42\,\times {{10}^{4}}\,m$
B) $18\,\times 8.\,{{10}^{4}}m$
C) $4.5\,\times {{10}^{4}}\,m$
D) none of these
• question_answer43) The ${{K}_{\alpha }}$ line of singly ionized calcium has a wavelength of 393.3 nm as measured on earth. In the spectrum of one of the observed galaxies, the spectral line is located at 401.8 nm. The speed with which this galaxy is moving away from us, will be
A) 7400 m/s
B) $32.\,4\times {{10}^{2}}m/s$
C) 6480 km/s
D) none of these
• question_answer44) In a common-base circuit of a transistor current amplification factor is 0.95. The base current when emitter current is 2 mA, will be
A) 0.2mA
B) 0.1mA
C) 0.002 mA
D) none of these
• question_answer45) Cathode rays of velocity ${{10}^{6}}\,m/s$ describe an approximate circular path of radius 1 m in an electric field 300 V/cm. If the velocity of the cathode rays are doubled. The value of electric field so that the rays describe the same circular path, will be
A) 2400 V/cm
B) 600 V/cm
C) 1200 V/cm
D) 12000 V/cm
• question_answer46) Light of wavelength $5000\overset{\text{o}}{\mathop{\text{A}}}\,$ falling on a sensitive surface. If the surface has received ${{10}^{-7}}J$ of energy, then the number of photons falling on the surface will be:
A) $5\times {{10}^{11}}$
B) $2.5\,\times {{10}^{11}}$
C) $3\times {{10}^{11}}$
D) none of these
• question_answer47) An X-ray machine is opearated at 40 kV. The short wavelength limit of continuous X-rays will be $(h=6.63\,\times {{10}^{-34}}\,Js,\,\,c=3\times {{10}^{8}}m/s,\,e=1.6\times {{10}^{-19}}C)$
A) $0.31\,\overset{\text{o}}{\mathop{\text{A}}}\,$
B) $0.62\,\overset{\text{o}}{\mathop{\text{A}}}\,$
C) $0.155\,\overset{\text{o}}{\mathop{\text{A}}}\,$
D) $0.62\,\overset{\text{o}}{\mathop{\text{A}}}\,$
• question_answer48) The wavelength of the first spectral line of sodium is $5896\,\overset{\text{o}}{\mathop{\text{A}}}\,$. The first excitation potential of sodium atom will be $(h=6.63\times {{10}^{-34}}\,Js)$
A) 4.2 V
B) 3.5 V
C) 2.1 V
D) None of these
• question_answer49) If 200 MeV energy is released in the fission of a single nucleus of $_{92}{{U}^{235}}$. How much fission must occur per second to produce a power of 1kW?
A) $3.125\,\times {{10}^{13}}$
B) $6.250\,\times {{10}^{13}}$
C) $1.525\,\times {{10}^{13}}$
D) None of these
• question_answer50) The energy supplied to calculate by state electricity board during an average November day was 40 mkh. If this energy could be obtained by the conversion of matter, how much mass will be annihilated?
A) 3.2 g
B) 6.4 g
C) 1.6 g
D) 2.5 g
• question_answer51) Which one of the following represents noble gas configuration?
A) $1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{10}},4{{s}^{2}}4{{p}^{6}}4{{d}^{10}},$$5{{s}^{2}},5{{p}^{6}}5{{d}^{6}},6{{s}^{2}}$
B) $1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{10}},4{{s}^{2}}4{{p}^{6}}4{{d}^{10}},$$5{{s}^{2}}5{{p}^{6}}5{{d}^{1}},6{{s}^{2}}$
C) $1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{10}},4{{s}^{2}}4{{p}^{6}}4{{d}^{10}}$$5{{s}^{2}}5{{p}^{6}}$
D) $1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{6}}3{{d}^{10}},4{{s}^{2}}4{{p}^{6}}4{{f}^{14}},$$5{{s}^{2}}5{{p}^{6}}5{{d}^{1}}$
• question_answer52) The number of unpaired electrons in $\text{Ni(CO}{{\text{)}}_{\text{4}}}$
A) 0
B) 1
C) 3
D) 4
• question_answer53) Nitrobenzene on treatment with zinc dust and aqueous ammonium chloride gives
A) ${{C}_{6}}{{H}_{5}}-N=N-{{C}_{6}}{{H}_{5}}$
B) ${{C}_{6}}{{H}_{5}}N{{H}_{2}}$
C) ${{C}_{6}}{{H}_{5}}NO$
D) ${{C}_{6}}{{H}_{5}}NHOH$
• question_answer54) Which one of the following is a correct statement?
A) All metal nitrates are insoluble in water
B) Solubility depends on temperature
C) All metal nitrates are soluble in water
D) All metal nitrates are soluble in alcohol
• question_answer55) Methyl $-\alpha -D-$glucoside and methyl$-\beta -D-$glucoside are
A) epimers
B) anomers
C) enantiomers
D) conformational diastereomers
• question_answer56) Which one of the following shows maximum value of paramagnetic behaviour?
A) ${{[Sc{{(CN)}_{6}}]}^{3-}}$
B) ${{[Co{{(CN)}_{6}}]}^{3-}}$
C) ${{[Fe{{(CN)}_{6}}]}^{4-}}$
D) ${{[Cr{{(CN)}_{6}}]}^{3-}}$
• question_answer57) Carbolic acid is
A) $~HCOOH$
B) $~C{{H}_{3}}COOH$
C) $~{{C}_{6}}{{H}_{5}}COOH$
D) $~{{C}_{6}}{{H}_{5}}OH$
• question_answer58) The solubility product of $BaC{{l}_{2}}$ is $4\times {{10}^{-9}}.$ Its solubility in mol/L is
A) $4\times {{10}^{-3}}$
B) $4\times {{10}^{-9}}$
C) $1\times {{10}^{-3}}$
D) $1\times {{10}^{-9}}$
• question_answer59) Which one can differentiate between ${{C}_{2}}{{H}_{5}}OH$ and$C{{H}_{3}}OH$?
A) ${{H}_{2}}O$
B) $N{{a}_{2}}C{{O}_{3}}+{{I}_{2}}$
C) $N{{H}_{3}}$
D) $HCl$
• question_answer60) Zinc and cold dil. $HN{{O}_{3}}$ reacts to produce
A) NO
B) $N{{O}_{2}}$
C) $N{{H}_{4}}N{{O}_{3}}$
D) $ZnN{{O}_{3}}$
• question_answer61) For the reaction, ${{H}_{2}}+{{I}_{2}}2HI,$the equilibrium concentration of ${{H}_{2}},{{I}_{2}}$and HI are 8.0, 3.0 and 28.0 mol/L respectively. The equilibrium constant is
A) 28.34
B) 32.66
C) 34.78
D) 38.88
• question_answer62) Tincture of iodine is
A) aqueous solution bf ${{I}_{2}}$
B) solution of ${{I}_{2}}$ in aqueous $KI$
C) alcoholic solution of ${{I}_{2}}$
D) aqueous solution of $KI$
• question_answer63) The chemical formula of plaster of Paris is
A) $CaS{{O}_{4}}.\frac{1}{2}{{H}_{2}}O$
B) $CaS{{O}_{4}}.{{H}_{2}}O$
C) $CaS{{O}_{4}}.2{{H}_{2}}O$
D) $CaS{{O}_{4}}.3{{H}_{2}}O$
• question_answer64) Which one of the following has square planar structure?
A) ${{[Ni{{(CN)}_{4}}]}^{2-}}$
B) $[Ni{{(CO)}_{4}}]$
C) ${{[NiC{{l}_{4}}]}^{2-}}$
D) All of the above
• question_answer65) The oxidation number of chromium in potassium dichromate is
A) + 2
B) + 4
C) + 6
D) + 8
• question_answer66) The electronic configuration of most electronegative element? is
A) $1{{s}^{2}},2{{s}^{2}}2{{p}^{5}}$
B) $1{{s}^{2}},2{{s}^{2}}2{{p}^{4}},3{{s}^{1}}$
C) $1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{1}}3{{p}^{1}}$
D) $1{{s}^{2}},2{{s}^{2}}2{{p}^{6}},3{{s}^{2}}3{{p}^{5}}$
• question_answer67) The molecular formula ${{C}_{3}}{{H}_{9}}N$cannot represent
A) ${{1}^{o}}$amine
B) ${{2}^{o}}$amine
C) ${{3}^{o}}$amine
D) quaternary salt
• question_answer68) The bond length between $C-C$bond in $s{{p}^{2}}$hybridized molecule is
A) $1.2\overset{\text{o}}{\mathop{\text{A}}}\,$
B) $1.39\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,$
C) $1.33\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,$
D) $~1.54\text{ }\overset{\text{o}}{\mathop{\text{A}}}\,$
• question_answer69) The energy ratio of a photon of wavelength $\text{3000 }\overset{\text{o}}{\mathop{\text{A}}}\,$and $\text{6000 }\overset{\text{o}}{\mathop{\text{A}}}\,$is
A) 1 : 1
B) 2 : 1
C) 1 : 2
D) 1 : 4
• question_answer70) Gas equation $PV=nRT$is obeyed by ideal gas in
B) isothermal process
C) both (a) and (b)
D) none of the above
• question_answer71) Clemmensens reduction of ketones is carried out in
A) $LiAl{{H}_{4}}$in ${{H}_{2}}O$
B) glycol and KOH
C) $Zn-Hg$and $HCl$
D) ${{H}_{2}}$and $Pd$catalyst
• question_answer72) The planar structure of $B{{F}_{3}}$can be explained by the fact that $B{{F}_{3}}$ is
A) $sp-$hybridized
B) $s{{p}^{2}}-$hybridized
C) $s{{p}^{3}}-$hybridized
D) $s{{p}^{3}}d$hybridized
• question_answer73) Reduction of aniline with acetyl chloride in presence of $\text{NaOH}$produce
A) aniline hydrochloride
B) acetanilide
C) p-chloroaniline
D) a red dye
• question_answer74) Which of the following compounds has the highest boiling point?
A) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}Cl$
B) $C{{H}_{3}}C{{H}_{2}}C{{H}_{2}}C{{H}_{2}}Cl$
C) $C{{H}_{3}}CH(C{{H}_{3}})C{{H}_{2}}Cl$
D) ${{(C{{H}_{3}})}_{3}}CCl$
• question_answer75) An unknown compound D first oxidized to aldehyde and then acetic acid by a dilute solution of ${{K}_{2}}C{{r}_{2}}{{O}_{7}}$and ${{H}_{2}}S{{O}_{4}}.$The compound D is
A) $C{{H}_{3}}OH$
B) ${{C}_{2}}{{H}_{5}}OH$
C) $C{{H}_{3}}C{{H}_{2}}COOH$
D) $C{{H}_{3}}C{{H}_{2}}CHO$
• question_answer76) Which of the following is not possible?
A) $n=2,\,l=1,m=0$
B) $n=2,\,l=0,m=-1$
C) $n=3,\,l=0,m=0$
D) $n=3,\,l=1,m=-1$
• question_answer77) A gas expands isothermally against a constant external pressure of 1 atm from a volume of $10\,d{{m}^{3}}$to a volume of $20\,d{{m}^{3}}.$ It absorbs 300 J of thermal energy from its surroundings. The $\Delta U$is
A) $-312\,J$
B) $+\,123J$
C) $-213\,J$
D) $+\,231\,J$
• question_answer78) Phenol is more acidic than alcohol because
A) phenol is more soluble in polar solvents
B) alcohol does not lose hydrogen atom
C) phenoxide ion is stabilized by resonance
D) phenoxide ion do not exhibit resonance
• question_answer79) The element having highest electron affinity
A) bromine
B) iodine
C) fluorine
D) chlorine
• question_answer80) Bakelite is prepared by the reaction between
A) phenol and formaldehyde
B) urea and formaldehyde
C) ethylene and glycol
D) tetramethylene and glycol
• question_answer81) Which one of the following is a conjugated protein?
A) Phosphoprotein
B) Glycoprotein
C) Chromoprotein
D) All of the above
• question_answer82) Iodine test is shown by
A) glucose
B) starch
C) glycogen
D) polypeptide
• question_answer83) A fruity smell is obtained by the reaction of ethanol with
A) $~C{{H}_{3}}COC{{H}_{3}}~~~~~~~$
B) $PC{{l}_{5}}$
C) $C{{H}_{3}}COOH$
D) $C{{H}_{3}}CHO$
• question_answer84) Cyanide process is used for extraction of
A) Ag
B) Ni
C) Pt
D) Zn
• question_answer85) An acid solution of 0.005 M has a pH of 5. The degree of ionization of acid is
A) $0.1\times {{10}^{-2}}$
B) $0.2\times {{10}^{-2}}$
C) $0.5\times {{10}^{-4}}$
D) $0.6\times {{10}^{-6}}$
• question_answer86) Which metal gives hydrogen gas on heating with hot concentrated alkali?
A) Ag
B) Ni
C) Zn
D) Cu
• question_answer87) The conversion of ethyl chloride into diethyl ether takes place by
A) Williamsons synthesis
B) Perkins reaction
C) Wurtz reaction
D) Grignard reaction
• question_answer88) $CHC{{l}_{3}}+{{C}_{6}}{{H}_{5}}N{{H}_{2}}+3NaOH\xrightarrow{{}}A$ $+\,3B\,+3C$ In the above reaction, the product A is
A) chlorobenzene
B) phenyl isocyanide
C) phenyl cyanide
D) phenyl chloride
• question_answer89) A gas is found to have a formula ${{[CO]}_{x}}.$Its vapour density is 70, the $x$ is
A) 3.0
B) 3.5
C) 5.0
D) 6.5
• question_answer90) Which of the following is used as purgative?
A) $HgS$
B) $H{{g}_{2}}C{{l}_{2}}$
C) $HgC{{l}_{2}}$
D) $ZnS{{O}_{4}}$
• question_answer91) Least stable oxide of chlorine is
A) $C{{l}_{2}}O$
B) $Cl{{O}_{2}}$
C) $C{{l}_{2}}{{O}_{7}}$
D) $Cl{{O}_{3}}$
• question_answer92) The sides of safety matches contains
A) red phosphorus + sand powder
B) ${{P}_{4}}{{S}_{3}}$
C) $C{{a}_{3}}{{(PO)}_{4}}+\text{glass}\,\text{pieces}$
D) $KCl{{O}_{3}},KN{{O}_{3}},$ sulphur + antimony
• question_answer93) Chemically aspirin is known as
A) salicylic acid
B) salicylaldehyde
C) 2-acetoxybenzoic acid
D) phenyl salicylate
• question_answer94) Gun metal is
A) $Cu+Zn$
B) $Cu+Sn+Zn$
C) $Cu+Sn$
D) $Zn+Sn$
• question_answer95) Which cannot be oxidized by${{H}_{2}}{{O}_{2}}$?
A) $N{{a}_{2}}S{{O}_{3}}$
B) $PbS$
C) $KI$
D) ${{O}_{3}}$
• question_answer96) The gas not absorbed by coconut charcoal is
A) He
B) Ne
C) Ar
D) Kr
• question_answer97) KI and $CuS{{O}_{4}}$solutions on mixing produce
A) $C{{u}_{2}}{{I}_{2}}+{{K}_{2}}S{{O}_{4}}$
B) $C{{u}_{2}}{{I}_{2}}+{{I}_{2}}+{{K}_{2}}S{{O}_{4}}$
C) $Cu{{I}_{2}}+{{K}_{2}}S{{O}_{4}}$
D) $Cu{{I}_{2}}+{{I}_{2}}+{{K}_{2}}S{{O}_{4}}$
• question_answer98) Vitamin ${{B}_{12}}$contains
A) Co
B) Mn
C) Mg
D) Fe
• question_answer99) Water glass is
A) glass made of water
B) sodium silicate
C) calcium formate
D) pyrex glass
• question_answer100) Purification of alumina takes place by
A) Bosch process
B) Halls process
C) Hoopes process
D) Quartation process
• question_answer101) If $f(x)=f(a-x)$ and $g(x)+g(a-x)=2,$then the value of $\int\limits_{0}^{a}{f(x)g(x)dx}$ is
A) $\int_{0}^{a}{f(x)dx}$
B) $\int_{0}^{a}{g(x)dx}$
C) $\int_{0}^{a}{[g(x)-f(x)]dx}$
D) $\int_{0}^{a}{[g(x)+f(x)]dx}$
• question_answer102) The differential equation of the family of the curves ${{x}^{2}}+{{y}^{2}}-2ax=0$is
A) ${{x}^{2}}-{{y}^{2}}-2ax=0$
B) ${{y}^{2}}-{{x}^{2}}=2xyy$
C) ${{x}^{2}}+{{y}^{2}}+2y=0$
D) none of the above
• question_answer103) A body falls freely from the top of a tower and during the last second of its flight it falls $\frac{\text{5}}{\text{9}}\text{th}$of the whole distance. The height of the tower and time of motion are respectively
A) 44.1 m and 3s
B) 44.1m and 5s
C) 4.41 m and 3s
D) none of the above
• question_answer104) The sum of the series $\frac{1}{2}+\frac{3}{4}+\frac{7}{8}+\frac{15}{16}+...$upto $n$ term is
A) $n-1+\frac{1}{{{2}^{n}}}$
B) $n+\frac{1}{{{2}^{n}}}$
C) $2n+\frac{1}{{{2}^{n}}}$
D) $n+1+\frac{1}{{{2}^{n}}}$
• question_answer105) The equation of the plane passing through the mid point of the line of join of the points (1, 2, 3) and (3, 4, 5) and perpendicular to it is
A) $x+y+z=9$
B) $x+y+z=-9$
C) $2x+3y+4z=9$
D) $2x+3y+4z=-9$
• question_answer106) The equation of the circle concentric to the circle $2{{x}^{2}}+2{{y}^{2}}-3x+6y+2=0$ and having area double the area of this circle, is
A) $8{{x}^{2}}+8{{y}^{2}}-24x+48y-13=0$
B) $16{{x}^{2}}+16{{y}^{2}}+24x-48y-13=0$
C) $16{{x}^{2}}+16{{y}^{2}}-24x+48y-13=0$
D) $8{{x}^{2}}+8{{y}^{2}}+24x-48y-13=0$
• question_answer107) The domain of the function $f(x)=\frac{{{\cos }^{-1}}x}{[x]}$is
A) $[-1,0)\cup \{1\}$
B) $[-1,1]$
C) $[-1,1)$
D) none of these
• question_answer108) Let $f(x)=\left\{ \begin{matrix} \frac{\tan x-\cot x}{x-\frac{\pi }{4}}, & x\ne \frac{\pi }{4} \\ a, & x=\frac{\pi }{4} \\ \end{matrix} \right.$ the value of a so that $f(x)$ is continuous at$x=\frac{\pi }{4}$
A) 2
B) 4
C) 3
D) 1
• question_answer109) If e and e are the eccentricities of hyperbolas$\frac{{{x}^{2}}}{{{a}^{2}}}-\frac{{{y}^{^{2}}}}{{{b}^{2}}}=1$ and its conjugate hyperbola, then the value of $\frac{1}{{{e}^{2}}}+\frac{1}{e{{}^{2}}}$is
A) 0
B) 1
C) 2
D) none of these
• question_answer110) The value of the$\int_{{}}^{{}}{\frac{\sin x+\cos x}{3+\sin 2x}}dx$is
A) $\frac{1}{4}\ln \left( \frac{2-\sin x+\cos x}{2+\sin x+\cos x} \right)+c$
B) $\frac{1}{2}\ln$$\left( \frac{2+\sin x}{2-\sin x} \right)+c$
C) $\frac{1}{4}\ln$$\left( \frac{1+\sin x}{1-\sin x} \right)+c$
D) none of the above
• question_answer111) If forces of magnitude 12 kg-wt, 5 kg-wt and 13 kg-wt act at a point are in equilibrium, then the angle between the first two forces is
A) $~{{30}^{o}}$
B) $~{{90}^{o}}$
C) $~{{60}^{o}}$
D) ${{45}^{o}}$
• question_answer112) For a party 8 guests are invited by a husband and his wife. They sit in a row for dinner. The probability that the husband and his wife sit together is
A) $\frac{2}{7}$
B) $\frac{2}{9}$
C) $\frac{1}{9}$
D) $\frac{4}{9}$
• question_answer113) If${{I}_{m}}\left( \frac{z-1}{2z+1} \right)=-4,$then locus of z is
A) ellipse
B) parabola
C) straight line
D) circle
• question_answer114) The equation $(x-b)(x-c)+(x-a)(x-b)$$+\,(x-a)(x-c)=0$ has all its roots
A) positive
B) real
C) imaginary
D) negative
• question_answer115) The sum of coefficients of the expansion${{\left( \frac{1}{x}+2x \right)}^{n}}$is 6561. The coefficient of term independent of $x$ is
A) $16\,{{\,}^{8}}{{C}_{4}}$
B) $^{8}{{C}_{4}}$
C) $^{8}{{C}_{5}}$
D) none of these
• question_answer116) The area enclosed between the curves $y=x$ and $y=2x-{{x}^{2}}$is (in sq. unit)
A) $\frac{1}{2}$
B) $\frac{1}{6}$
C) $\frac{1}{3}$
D) $\frac{1}{4}$
• question_answer117) There are 12 white and 12 red balls in a bag. Balls are drawn one by one with replacement from the bag. The probability that 7th drawn ball is 4th white is
A) $\frac{1}{4}$
B) $\frac{1}{8}$
C) $\frac{1}{2}$
D) $\frac{1}{3}$
• question_answer118) In an ellipse the angle between the lines joining the foci with the positive end of minor axis is a right angle, the eccentricity of the ellipse is
A) $\frac{1}{\sqrt{2}}$
B) $\frac{1}{\sqrt{3}}$
C) $\sqrt{2}$
D) $\sqrt{3}$
• question_answer119) If $|\vec{a}|=3,\,\,\,|\vec{b}|=5$and $|\vec{c}|=4$then and $\vec{a}+\vec{b}+\vec{c}=0,$ then the value of $\vec{a}+\vec{b}+\vec{c}=0,$then the value of $\vec{a}.\vec{b}\,+\,\vec{b}.\vec{c}$is equal to
A) 0
B) -25
C) 25
D) none of these
• question_answer120) The equation of a line is$6x-2=3y-1=2z-2.$The direction ratios of the line are
A) 1, 2, 3
B) 1, 1, 1
C) $\frac{1}{3},\frac{1}{3},\frac{1}{3}$
D) $\frac{1}{3},\frac{-1}{3},\frac{1}{3}$
• question_answer121) For the circuit shown below, the Boolean polynomial is
A) $(\tilde{\ }p\vee q)\vee (p\vee \tilde{\ }q)$
B) $(\tilde{\ }p\wedge p)\wedge (\tilde{\ }q\wedge q)$
C) $(\tilde{\ }p\wedge \tilde{\ }p)\wedge (q\wedge p)$
D) $(\tilde{\ }p\wedge q)\vee (q\wedge \tilde{\ }q)$
• question_answer122) The value of $\int_{{}}^{{}}{\frac{dx}{x+\sqrt{x-1}}}$is
A) $\log (x+\sqrt{x-1})+{{\sin }^{-1}}\left( \sqrt{\frac{x-1}{x}} \right)+c$
B) $\log (x+\sqrt{x-1})+c$
C) $\log (x+\sqrt{x-1})-\frac{2}{\sqrt{3}}{{\tan }^{-1}}$
D) $\left( \frac{2\sqrt{x-1}+1}{\sqrt{3}} \right)$ none of the above
• question_answer123) If $y={{\sin }^{-1}}\frac{x}{2}+{{\cos }^{-1}}\frac{x}{2},$then the value of $\frac{dy}{dx}$is
A) 1
B) -1
C) 0
D) 2
• question_answer124) In Boolean algebra, the unit element 1
A) has two values
B) is unique
C) has at least two values
D) none of the above
• question_answer125) On one bank of river there is a tree. On another bank, an observer makes an angle of elevation of ${{60}^{o}}$ at the top of the tree. The angle of elevation of the top of the tree at a distance 20 m away from the bank is 30?. The width of the river is
A) 20 m
B) 10 m
C) 5 m
D) 1 m
• question_answer126) The magnitude of cross product of two vectors is $\sqrt{3}$times the dot product. The angle between the vectors is
A) $\frac{\pi }{6}$
B) $\frac{\pi }{3}$
C) $\frac{\pi }{2}$
D) $\frac{\pi }{4}$
• question_answer127) If ${{D}_{r}}=\left| \begin{matrix} r & 1 & \frac{n(n+1)}{2} \\ 2r-1 & 4 & {{n}^{2}} \\ {{2}^{r-1}} & 5 & {{2}^{n-}}-1 \\ \end{matrix} \right|,$then the value of $\sum\limits_{r=0}^{n}{{{D}_{r}}}$is
A) 0
B) 1
C) $\frac{n(n+1)(2n+1)}{6}$
D) none of these
• question_answer128) If$\left| \begin{matrix} -12 & 0 & \lambda \\ 0 & 2 & -1 \\ 2 & 1 & 15 \\ \end{matrix} \right|=-360,$then the value of $\lambda$is
A) $-1$
B) $-2$
C) $-3$
D) $4$
• question_answer129) If $A=\left[ \begin{matrix} 1 & x \\ {{x}^{2}} & 4y \\ \end{matrix} \right]$and $B\,=\left[ \begin{matrix} -3 & 1 \\ 1 & 0 \\ \end{matrix} \right]$adj.$A+B=\left[ \begin{matrix} 1 & 0 \\ 0 & 1 \\ \end{matrix} \right],$ then the value of $x$and $y$are
A) 1, 1
B) $\pm \,1,1$
C) $1,0$
D) none of these
• question_answer130) If ${{\tan }^{-1}}\frac{1-x}{1+x}=\frac{1}{2}{{\tan }^{-1}}x,$then values of $x$is
A) $\frac{1}{2}$
B) $\frac{1}{\sqrt{3}}$
C) $\sqrt{3}$
D) 2
• question_answer131) If ${{x}^{2/3}}-7{{x}^{1/3}}+10=0$then, the value of $x$ is
A) $\{125\}$
B) $\{8\}$
C) $\phi$
D) $\text{ }\!\!\{\!\!\text{ 125,8 }\!\!\}\!\!\text{ }$
• question_answer132) The value of \underset{\alpha \to 0}{\mathop{\lim }}\,\frac{\begin{align} & \cos e{{c}^{-1}}(sec\alpha )+co{{t}^{-1}}(tan\alpha ) \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,+co{{t}^{-1}}\cos (si{{n}^{-1}}\alpha ) \\ \end{align}}{\alpha }is
A) 0
B) $-1$
C) $-2$
D) 1
• question_answer133) If the second term in the expansion${{\left[ \sqrt[13]{a}\frac{a}{\sqrt{{{a}^{-1}}}} \right]}^{n}}$is $14{{a}^{5/2}},$ then the value of $\frac{{{\,}^{n}}C{{\,}_{3}}}{{{\,}^{n}}{{C}_{2}}}$is
A) 4
B) 3
C) 12
D) 6
• question_answer134) One of the diameter of the circle ${{x}^{2}}+{{y}^{2}}-12x+4y+6=0$ is given by
A) $~x+y=0$
B) $~x+3y=0$
C) $x=y$
D) $3x+2y=0$
• question_answer135) Point D, E are taken on the side BC of the triangle ABC, such that $BD=DE=EC.$If $\angle BAD=x,\angle DAE=y,\angle EAC=z,$ then the value of $\frac{\sin (x+y)\sin (y+z)}{\sin x\sin \,z}$ is equal to
A) 1
B) 2
C) 4
D) none of these
• question_answer136) The number of real solution of${{\tan }^{-1}}\sqrt{x(x+1)}+{{\sin }^{-1}}\sqrt{{{x}^{2}}+x+1}=\frac{\pi }{2}$is
A) zero
B) one
C) two
D) infinite
• question_answer137) The equation ${{\sin }^{-1}}x-{{\cos }^{-1}}x={{\cos }^{-1}}\left( \frac{\sqrt{3}}{2} \right)$ has
A) no solution
B) unique solution
C) infinite number of solution
D) none of the above
• question_answer138) In a $\Delta ABC,\,a,c,A$are given and ${{b}_{1}},{{b}_{2}}$are two values, if the third side b such that ${{b}_{2}}=2{{b}_{1}}$then sin A is equal to
A) $\sqrt{\frac{9{{a}^{2}}-{{c}^{2}}}{8{{a}^{2}}}}$
B) $\sqrt{\frac{9{{a}^{2}}-{{c}^{2}}}{8{{c}^{2}}}}$
C) $\sqrt{\frac{9{{a}^{2}}+{{c}^{2}}}{8{{a}^{2}}}}$
D) none of these
• question_answer139) A variable chord is drawn through the origin to the circle ${{x}^{2}}+{{y}^{2}}-2ax=0.$The locus of the centre of the circle drawn on this chord as diameter is
A) ${{x}^{2}}+{{y}^{2}}+ax=0$
B) ${{x}^{2}}+{{y}^{2}}-ax=0$
C) ${{x}^{2}}+{{y}^{2}}+ay=0$
D) ${{x}^{2}}+{{y}^{2}}-ay=0$
• question_answer140) If $1,{{a}_{1}},{{a}_{2}},...,{{a}_{n-1}}$are the n roots of unity, then the value of $(1-{{a}_{1}})(1-{{a}_{2}})(1-{{a}_{3}})......(1-{{a}_{n-1}})$ is equal to
A) $\sqrt{3}$
B) $\frac{1}{2}$
C) $n$
D) 0
• question_answer141) Let a, b, c be real. If $a{{x}^{2}}+bx+c=0$has two real roots $\alpha$and$\beta ,$where $a<-1$and $\beta >1,$then $1+\frac{c}{a}+\left| \frac{b}{a} \right|$is
A) $<0$
B) $>0$
C) $\le 0$
D) none of these
• question_answer142) Number of divisiors of the form $(4n+2),n\ge 0$ of the integer 240 is
A) 4
B) 8
C) 10
D) 3
• question_answer143) The expression ${{\{x+{{({{x}^{3}}-1)}^{1/2}}\}}^{5}}$$+\,{{\{x-{{({{x}^{3}}-1)}^{1/2}}\}}^{5}}$ is a polynomial of degree
A) 5
B) 6
C) 7
D) 8
• question_answer144) Let a, b, c be positive and not all equal, the value of the determinant $\left| \begin{matrix} a & b & c \\ b & c & a \\ c & a & b \\ \end{matrix} \right|$is
A) $\text{+}\,\text{ve}$
B) $-\text{ve}$
C) zero
D) none of these
• question_answer145) $\underset{h\to 0}{\mathop{\lim }}\,\frac{{{(a+h)}^{2}}\sin (a+h)-{{a}^{2}}\sin a}{h}$is equal to
A) $2a\,\sin \,a$
B) ${{a}^{2}}\cos \,a$
C) ${{a}^{2}}\cos a+2a\,\,\sin \,a$
D) none of these
• question_answer146) If $f(x)=x(\sqrt{x}+\sqrt{x+1}),$then
A) $f(x)$is continuous but not differentiable at $x=0$
B) $f(x)$ is differentiable at $x=0$
C) $f(x)$is not differentiable at $x=0$
D) none of these
• question_answer147) If $y$is a function of $x$and $\log (x+y)=2xy,$ then the value of $y(0)$is equal to
A) 1
B) -1
C) 2
D) 0
• question_answer148) The angle between the tangent drawn from the point (1, 4) to the parabola ${{y}^{2}}=4x$is
A) $\frac{\pi }{6}$
B) $\frac{\pi }{4}$
C) $\frac{\pi }{3}$
D) $\frac{\pi }{2}$
• question_answer149) If $y=a\log x+b{{x}^{2}}+x$has its extremum value at $x=-1$and $x=2,$then
A) $x=-1$and $x=2,$
B) $a=2,\,b=-\frac{1}{2}$
C) $a=2,=-\frac{1}{2}$
D) none of the above
• question_answer150) The value of $\int_{{}}^{{}}{\frac{dx}{{{x}^{2}}{{({{x}^{4}}+1)}^{3/4}}}}$is
A) $-\frac{{{({{x}^{4}}+1)}^{1/4}}}{x}+c$
B) $\frac{{{({{x}^{4}}+1)}^{1/4}}}{x}+c$
C) zero
D) none of the above | 2017-06-26 03:30:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.989924430847168, "perplexity": 5257.848550451378}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320669.83/warc/CC-MAIN-20170626032235-20170626052235-00439.warc.gz"} |
https://diabetesjournals.org/care/article/30/3/542/25594/Clinical-Depression-Versus-Distress-Among-Patients | OBJECTIVE—We sought to determine differences between structured interviews, symptom questionnaires, and distress measures for assessment of depression in patients with diabetes.
RESEARCH DESIGN AND METHODS—We assessed 506 diabetic patients for major depressive disorder (MDD) by a structured interview (Composite International Diagnostic Interview [CIDI]), a questionnaire for depressive symptoms (Center for Epidemiological Studies Depression Scale [CESD]), and on the Diabetes Distress Scale. Demographic characteristics, two biological variables (A1C and non-HDL cholesterol), and four behavioral management measures (kilocalories, calories of saturated fat, number of fruit and vegetable servings, and minutes of physical activity) were assessed. Comparisons were made between those with and without depression on the CIDI and the CESD.
RESULTS—Findings showed that 22% of patients reached CESD ≥16, and 9.9% met a CIDI diagnosis of MDD. Of those above CESD cut points, 70% were not clinically depressed, and 34% of those who were clinically depressed did not reach CESD scores ≥16. Those scoring ≥16, compared with those <16 on the CESD, had higher A1C, kilocalories, and calories of saturated fat and lower physical activity. No differences were found using the CIDI. Diabetes distress was minimally related to MDD but substantively linked to CESD scores and to outcomes.
CONCLUSIONS—Most patients with diabetes and high levels of depressive symptoms are not clinically depressed. The CESD may be more reflective of general emotional and diabetes-specific distress than clinical depression. Most treatment of distress, however, is based on the depression literature, which suggests the need to consider different interventions for distressed but not clinically depressed diabetic patients.
Patients with diabetes and comorbid depressive symptoms, compared with patients with diabetes alone, have increased functional impairment, more hospital days and days off of work (1,2), poorer glycemic control (3), poorer self-management behavior (4), increased health care use and costs (5), and a higher risk of morbidity and mortality (6,7). Clearly, the co-occurrence of diabetes and depression has significant implications for clinical outcomes, disease management, health care costs, and patient health and well-being.
The way depression is measured in clinical studies of diabetes, however, takes a number of different forms, and it is not at all clear whether each method similarly assesses depression and whether different methods uniformly classify patients. We may be identifying very different groups of patients by each method.
The gold standard for assessment of clinical depression is a standardized, structured patient interview that yields clinical diagnoses that conform with Diagnostic and Statistical Manual of Psychiatric Disorders, 4th edition (DSM-IV) criteria. The most frequently used interview schedules are the Structured Clinical Interview for DSM (8), the Composite International Diagnostic Interview (CIDI) (9), and the Mini International Neuropsychiatric Interview (10). Unfortunately, these interviews are time-consuming and expensive to administer, which often adds to patient burden, and, because of cost, they are rarely used to screen for depression among patients with diabetes.
The most widely used method of depression assessment is self-administered questionnaires, e.g., Beck Depression Inventory (11), the Center for Epidemiological Studies Depression (CESD) scale (12), and the Patient Health Questionnaire-9 (13). These scales are easy to use, inexpensive, and user-friendly. However, most do not directly address clinical diagnostic criteria; rather, they consist of a list of emotional symptoms that are endorsed by the respondent as present or absent during a specified time period. The time period, however, varies across scales: The CESD and the Beck Depression Inventory ask about symptoms occurring during the last week, and the Patient Health Questionnaire-9 refers to the last 2 weeks. Most scales have cut points based on summed symptom scores, above which “likely depression” is suggested. However, studies (14,15) employed different cut points: ≥16 or ≥22 on the CESD.
Many studies (14,16) add diagnostic interviews to confirm DSM-IV diagnoses for those patients who reach clinical criteria on questionnaire measures, but this method can create a verification bias (17): A patient who is false negative on the questionnaire never reaches the interview stage. Also, the number of patients diagnosed with a depressive disorder using an interview is far lower than the number who reach a cut point on a questionnaire (3), although many studies (18) rely on questionnaire methods alone when linking depression to poor diabetes outcomes. For example, in a recent meta-analysis (19), 11.4% of patients reached criteria for a depressive disorder using interview methods, whereas 31.0% had significantly elevated depressive symptoms using questionnaire methods.
Although there are considerable data (14) about the sensitivity and specificity of questionnaire and diagnostic interview measures of depression, two related questions of clinical concern remain and are the subject of this study. First, among patients with diabetes, are there differences between those with positive scores only on depression symptom questionnaires versus only on diagnostic interviews? Second, are the clinical implications of high symptom scores the same as clinical depression with respect to their linkages with diabetes distress, self-management, and biological markers? If not, what do symptom questionnaires actually measure? Given the importance of depression in diabetes care, these questions address what the two methods of assessment actually measure and the clinical implications of each.
This report is based on the first of a three-wave longitudinal study of diabetes and depression. To assure a diverse, multiethnic community sample, patients were recruited from several San Francisco Bay area medical groups and diabetes education centers. Inclusion criteria included patients with type 2 diabetes who were aged 21–75 years, could fluently read and speak English or Spanish, and had no severe diabetes complications and no diagnosis of active psychosis or dementia. All patients received a letter from their respective health facilities, cosigned by a facility and project representative, informing them of the project and that they would receive a phone call from the project office if one of the following two opt-out procedures was not initiated: return postcard or 800-number phone call. A screening phone call followed, and, for eligible patients, an appointment was made in the patient’s home, our office, or a community setting to explain the project in detail, collect informed consent, and begin assessment. Patients received a 1.5-h home visit that included questionnaires, physical measurements, interviews, a 150-item mail-back questionnaire, and a visit to a community laboratory for collection of blood and urine specimens. All materials were prepared in English and Spanish, and research assistants were fluent in both languages. The project was approved by the Committee on Human Research at the University of California San Francisco and at each participating facility.
The following patient characteristics were included: age, sex, education, BMI, number of comorbidities (from a list of 25), self-identified ethnicity, years since diagnosis, diabetes treatment (i.e., diet/exercise, oral medication, or insulin), and use of psychotropic medication.
Two measures of depression were used for all patients. The CIDI is a structured interview including a set of modules that assess different groups of DSM-IV psychiatric diagnoses (9). We included the depressive disorders module that yields time of last diagnosis of major depressive disorder (MDD) being within the last month (Dx1), between 1 and 6 months (Dx2), or between 6 and 12 months (Dx3). Research assistants were trained by a registered CIDI trainer to criterion, and they scored standardized protocols over time to prevent drift. The CESD is a 20-item questionnaire (α = 0.89) that assesses depressive symptoms over the previous 7 days (12). Cut points of ≥16 and ≥22 were used to define “likely depression” (14,15). Prevalence comparisons between our sample and community rates were based on data from the National Comorbidity Survey Replication (20,21). Also using the CIDI, the National Comorbidity Survey Replication study assessed a stratified national sample of 9,090 community respondents in 2001 and 2002. Last, we included a measure of diabetes-specific emotional distress. The Diabetes Distress Scale (DDS) is a 17-item scale that assesses distress associated with emotional burden, care regimen, interpersonal factors, and physician care (α = 0.93) (22,23). Each item is rated on a six-point scale, ranging from “not a problem” to “a very serious problem.”
Six dependent variables were included. Two diabetes-related biological measures were A1C and non-HDL cholesterol. Four behavioral management measures included three dietary indexes, derived from the Block 2000 Brief Food Frequency Questionnaire (Block Dietary Data Systems, Berkeley, CA): average kilocalories consumed per day, average calories of saturated fat as a percentage of total calories consumed per day, and average number of fruit and vegetable servings per day (see Block et al. [24] for psychometric data). Physical activity was assessed by the International Physical Activity Questionnaire (IPAQ) (25). This scale reflects the number of minutes of activity per week at each of three activity levels (walking, moderate, or vigorous), each weighted by a measure of energy expenditure with multiples of resting metabolic rate for each activity for a 60-kg person (light = 3.3, moderate = 4.0, and vigorous = 8.0).
### Data analysis
Univariate comparisons between patients with and without a CIDI diagnosis of a MDD and by CESD of likely depression were undertaken using χ2 tests and Student’s t tests. ANCOVA was used to estimate the effects of CIDI, CESD scores ≥16, and their interaction on the six dependent variables. The effects of nine covariates, and their interactions with the primary variables, were evaluated to prevent their potential effects from obscuring the relationships among the primary variables. Multiple regression was used to assess the impact of distress on these relationships, and tests for multicolinearity and corrections for multiple statistical tests were also undertaken. The analyses were completed using SPSS 11.0 and SAS 9.1.
Screening identified 640 eligible patients, and 506 patients completed data collection (79.0%). There were no significant differences between eligible patients who participated and eligible patients who initially refused or later dropped out in terms of age, sex, ethnicity, marital status, education, years since diagnosis, and number of comorbidities.
The sample was ethnically and socially diverse, with large SDs around most mean values (Table 1). Average age was 57.8 years, average time since diabetes diagnosis was 8.2 years, and average A1C was 7.2%. Nineteen patients (4.0%) received a CIDI Dx1, 16 (3.0%) a Dx2, and 15 (2.9%) a Dx3 diagnosis of MDD (total n = 50, 9.9%). The comparable past-year National Comorbidity Survey Replication rate was 6.6%, suggesting a 50% higher rate of past-year MDD for patients with diabetes than suggested by community samples.
Because the recency of diagnosis of the last MDD episode might have been related to the primary study variables, we conducted a time-trend analysis among the three CIDI time-of-diagnosis groups (Dx1, Dx2, and Dx3), with demographic, disease status, control, and outcome variables. A priori estimates of differences among the three groups found that to detect an average difference of 0.5 SD required an n = 17 per group for a power = 0.80. No analysis reached statistical significance, although there was a non-significant trend on the IPAQ: Dx1 patients reported a lower level of physical activity than Dx2 and Dx3 patients. Patients in all three CIDI groups were highly symptomatic on the CESD, with 78, 63, and 53% scoring ≥16 in groups Dx1–3, respectively, compared with patients without MDD (18%). Because we noted no significant differences among these three patient groups, we combined them into a single group of MDD patients who had an episode within the last year. This combined group was used in subsequent analyses.
Of the 506 patients, 113 (22.0%) scored ≥16, and 75 (15.0%) scored ≥22 on the CESD. Among the 113 patients with CESD scores ≥16, only 33 (29.2%) received a past-year CIDI diagnosis of MDD; among the 75 patients with CESD scores ≥22, only 23 (30.7%) received a similar CIDI diagnosis. Conversely, of the 50 patients receiving a CIDI MDD diagnosis, 33 (66.0%) scored ≥16, and 23 (46.0%) scored ≥22 on the CESD. This means that 70% of patients above the CESD cut points did not meet CIDI criteria for MDD and that 30–50% of those with a CIDI diagnosis were not above CESD cut points.
Of the 50 patients with MDD, 31 (62.0%) were taking psychotropic medication; of those scoring ≥16 and ≥22 on the CESD, the rates were 48 (42.5%) and 35 (46.7%), respectively (90% antidepressants, 8% anti-anxiety, and 2% antipsychotics). Thus, far more patients with a CIDI diagnosis were taking psychotropic medications compared with those above the CESD cut points.
Among the patient characteristics listed in Table 1, differences between those with MDD and those without occurred for ethnicity, BMI, number of comorbidities, and psychotropic medication. Far fewer Asian- and African-American patients had MDD than members of other ethnic groups, and those with MDD had a higher BMI, more comorbidities, and took psychotropic medication more often than those without MDD. Significant differences between those with and without likely depression in patients with CESD scores ≥16 and ≥22 occurred for five variables: patients with elevated CESD scores were significantly younger, less educated, of lower income, had more comorbid conditions, and were more likely to take psychotropic medications.
### Relationships with behavioral and biological markers
Student’s t tests compared those who met versus those who did not meet CESD scores ≥16 or ≥22 and CIDI criteria on each of the six biological and behavioral variables (Table 2). Results for the patients with CESD scores ≥16 and ≥22 were quite similar, with four of the six comparisons statistically significant: those who scored above the CESD cut points had higher A1C, higher kilocalories and saturated fat calories, and less physical activity (IPAQ). No significant differences occurred for any of the six tests comparing those with and without MDD. Thus, CESD scores ≥16 and ≥22 were significantly linked to biological and behavioral markers, whereas a CIDI diagnosis of MDD was not.
To assess the main and interactive effects of CESD and CIDI diagnoses on each of the six dependent variables, two-by-two ANCOVAs were used. Controls for patient sex, years since diagnosis, age, BMI, number of comorbid conditions, education, ethnicity, diabetes medications, and use of psychotropic medication were included because of the significant findings reported in Table 1. Since results for patients with CESD scores ≥16 and ≥22 were similar, we reviewed only those with CESD scores ≥16 (yes/no) by CIDI (yes/no) findings. Controlling both for covariates and CIDI diagnosis, scoring ≥16 on the CESD was significantly and independently related to higher A1C (F = 10.93, P < 0.001), higher kilocalories (F = 23.66, P < 0.001), and lower IPAQ scores (F = 4.26, P = 0.04). Conversely, controlling for both the covariates and patients with CESD scores ≥16, having a CIDI diagnosis of MDD yielded nonsignificant findings in each analysis. With the covariates included, and controlling for both the CESD and the CIDI, we then tested the interaction between having a CESD score ≥16 and CIDI diagnoses on the six dependent variables. None of the six interaction terms were statistically significant. We also tested interaction terms for patient sex and use of psychotropic medication in all equations. None reached statistical significance.
### Relationships with diabetes-specific distress
The differences between the CIDI and CESD findings led us to hypothesize that the CESD may be measuring something other than clinical depression, perhaps something akin to a general level of emotional distress. To explore this hypothesis, we constructed six multiple regression equations. Each included the same nine control variables used in the two-by-two ANCOVAs described above (to assure that any between-group differences were not due to differences in the proportion of patients within the control subgroups), as well as CIDI diagnosis of MDD (yes/no), the continuous CESD score, and the DDS continuous score. Continuous CESD and DDS scores were used because negative mood and emotional distress were considered continuous and not dichotomous variables. The dependent variable in each equation was one of the six behavioral or biological markers. Our goal in these equations was to observe the independent associations of MDD, CESD, and DDS with respect to each of the six diabetes markers. Tests for multicolinearity were negative.
The zero-order correlation between DDS versus CESD and MDD was 0.48 (P < 0.001) and 0.16 (P < 0.001), respectively. No CIDI-MDD regression coefficient reached significance in any of the six equations, nor was the interaction between DDS and CESD or DDS and MDD significant in any equation (Table 3). DDS scores independently reached or approached significance in four of the six equations: A1C (B = 0.23, P < 0.001), non-HDL cholesterol (B = 4.94, P < 0.06), kilocalories (B = 168.10, P < 0.001), and fruit and vegetable servings (B = 0.41, P < 0.03). CESD scores reached or approached significance in only two equations: fruit and vegetable servings (B = −0.04, P < 0.04) and IPAQ (−37.90, P < 0.04). Both CESD and DDS coefficients were significant only in the equation with fruit and vegetable servings. Thus, once DDS was added to these analyses, the initial univariate associations between CESD and the dependent variables (A1C, kilocalories, and saturated fat calories) were no longer significant. The independent and shared associations of the CESD and DDS with each other and with diabetes management variables (from both the ANCOVAs and multiple regression analyses) suggested that the CESD reflected diabetes-specific and perhaps other forms of general emotional distress but not clinical depression.
The analyses yielded five major findings. First, we found CIDI prevalence rates of last diagnosis of MDD within the past year and CESD likely depression similar to other studies of diabetes (19,26,27) that used diverse, community samples: 9.9% for MDD and 22.0% for likely depression. This suggests substantive differences in the prevalence of depression based on assessment measure: CESD rates of likely depression are twice as high as CIDI rates of MDD, and rates of MDD are 50% higher than those found among community samples (20,21). Second, >70% of those with CESD scores ≥16 or ≥22 are not clinically depressed, according to the CIDI, whereas about one-third of those receiving a CIDI diagnosis of MDD do not score above a CESD cut point. Thus, a substantial number of patients who receive a diagnosis on one depression measure do not receive a diagnosis on the other. These results are unrelated to use of psychotropic medication, even though 62% of patients with MDD and 42% of those who met criteria on the CESD take psychotropic medication (27).
Third, among patients with diabetes, there were relatively few significant differences between those with MDD and those without in terms of patient characteristics: far fewer Asian- and African-American patients and more non-Hispanic white patients received a CIDI diagnosis of MDD compared with patients from other ethnic groups, and those with MDD had a higher BMI, more comorbidities, and more often take psychotropic medications. However, patients who met criteria on the CESD, compared with those who did not, were younger, less educated, had a lower family income, and had more comorbidities. Thus, the CESD, compared with the CIDI, seems to be more sensitive to or reflective of the stresses associated with other interrelated chronic health conditions, socioeconomic factors, and, perhaps, access to care issues.
Fourth, being above a cut point on the CESD was more strongly associated with deficits in diabetes-related behavioral and biological variables than receiving a CIDI diagnosis of MDD. This finding occured in comparisons that included other potentially confounding covariates. These findings suggest that patients with diabetes who reach criteria for MDD may be considerably different from those who report elevated levels on the CESD; the CESD discriminates between patients based on demographic and diabetes-related behavioral and biological variables, whereas the CIDI alone does not. Fifth, the CESD was significantly associated with the DDS, and the CESD and DDS displayed both shared and independent linkages with behavioral and biological markers.
Three factors may explain the discrepancy between our findings and those of some other studies. First, regarding the relatively low rates of clinical depression found in this study, we used a diverse community sample, not one gathered at a specialty clinic or health facility. Recent meta-analyses (19) suggest that the prevalence of MDD among patients with diabetes is substantially lower in community settings, closely matching the level found in this report. Community samples may also have lower rates of severity than other samples. The percentage of patients who scored above CESD cut points (22.0%) is also at levels reported in other studies (18,19).
Second, our depression assessment was not staged, thus reducing potential sampling bias. Third, there are differences between the time frames covered by the two measures: past-year time of diagnosis for the CIDI and past-week time of diagnosis for the CESD. It may have been that patients who met criteria on the CIDI experienced their depression earlier in the previous year and were no longer depressed at time of assessment. However, a trend analysis for time of diagnosis within the past year showed no differences in patient demographics, disease status, behavioral, or biological variables for Dx1, Dx2, and Dx3. Furthermore, Dx1, Dx2, and Dx3 patients remained highly symptomatic at time of assessment, and 62% remained on medication. Thus, time of diagnosis within the last year is a possible but unlikely explanation for our findings.
What is particularly striking among the current findings is that the 70% of patients who scored above CESD cut points but who were not clinically depressed displayed significant deficits in behavioral and biological markers, deficits often considered to be a function of clinical depression. What, then, does the CESD measure if it is not a screening surrogate for DSM-IV MDD? Our results suggest that the CESD may be a broader, more heterogeneous measure of negative mood or emotional distress than a measure of depressive affect alone. Findings from two previous meta-analytic reports (3,19) suggest that the items of the CESD reflect symptoms of anxiety, subclinical depression, substance use, and general distress. Another report (28) demonstrated that the CESD is as good a screening tool for other Axis I disorders as it is for dysphoria. Items such as fatigue and irritability also may be symptoms of hyperglycemia. Others outside the diabetes arena (29,30) have long argued that scales like the CESD are really measures of emotional distress, not clinical depression. They have shown that even when severity is controlled those with and without clinical depression differ on the CESD in significant ways: The clinically depressed endorse items reflecting depressed mood, anhedonia, and suicidality, whereas the nonclinically depressed but distressed score high on items reflecting hypochondriasis and insomnia. Future research should explore how reliable and coherent subsets of CESD items are linked to diabetes-specific outcomes.
Given the significant correlation between the CESD and the DDS (r = 0.48) and the findings from the analyses with behavioral and biological markers, we suggest that the CESD may, at least in part, reflect both general psychological distress and diabetes-specific distress in ways that are qualitatively different from clinical depression and are more related to struggles with life circumstances, including dealing with a demanding chronic disease like diabetes. The diabetes-specific component of negative mood and emotional distress may reflect not only general dysphoria around the disease and its management, but also distress associated with general health, comorbidities, regimen adherence, and other diabetes-related health care, economic, social, and family difficulties.
This is not to say that the prevalence of clinical depression is not elevated in diabetes or that depression among these patients is not a serious clinical condition worthy of concern and treatment in its own right; rather, we suggest only that a far larger number of other, nonclinically depressed patients display a high level of distress and that a significant amount of this distress is related to diabetes and its management. In fact, scoring high on the CESD is more related to these markers than receiving a diagnosis of MDD alone. This may explain why even successful treatments for clinical depression among patients with diabetes have little or no effect on diabetes management (16,27,31); they were based on studies of MDD, and the distress substantively linked to biological and behavioral disease management variables may not have been directly addressed.
Our proposed distinction between clinical depression, general emotional distress, and diabetes-specific distress has two major implications for clinical care. First, considerable research (32) has identified a highly differentiated subset of negative emotions that are linked to coronary artery disease and often co-occur with diabetes: hopelessness, pessimism, rumination, anxiety, and anger/hostility. Understanding patients’ qualitative experiences of general and diabetes-specific distress should provide a greater understanding of the specific affective processes that are involved with poor behavioral disease management, rather than generically labeling the culprit as depression when, in fact, most of these patients are not clinically depressed.
A second implication is that patients with diabetes who are significantly distressed but who are not clinically depressed, and this includes 70% of those who score ≥16 on the CESD, may not profit from interventions that are derived from studies of the clinically depressed. Instead, addressing the personal, health-related, and social causes of their distress, including diabetes-specific distress with problem-solving or coping interventions, may be more meaningful and effective than initiating treatments specifically directed at clinical depression.
Several limitations may affect these findings. First, the diversity of the sample prevented a full examination of subgroup variations among the relationships reported. Second, the data reported are cross sectional, and implications about causation can only be inferred. Third, we did not explore the potential impact of other Axis I disorders, such as general anxiety or panic disorders, which have additional implications for treatment.
We have shown that 70% of patients with diabetes who reach high levels of negative mood and psychological distress, as measured by the CESD, are not clinically depressed. Yet, both general and diabetes-specific distress are significantly related to behavioral and biological diabetes outcomes, and distress is more common and more impactful than clinical depression alone. Most treatments for general and disease-specific distress, however, are derived from the depression treatment literature. New research should focus on identifying the impact of specific negative emotions, such as has been done in the coronary artery disease literature, and on clarifying the roles of both general and diabetes-specific distress so that the mechanisms of influence can be more fully understood and appropriate interventions developed.
Table 1—
Sample description
Total samplePatients with CESD scores ≥16Patients with CESD scores ≥22CIDI
n = 506 n = 113 n = 75 n = 50
≥16 <16 ≥22 <22 MDD No MDD
Male/female subjects 218 (43)/288 (57) 41 (36)/72 (64) 176 (45)/212 (55) 25 (33)/50 (67) 192 (45)/239 (55) 20 (40)/30 (60) 198 (43)/258 (57)
Age (years) 57.83 ± 9.86 55.38 ± 10.13* 58.4 ± 9.7 55.53 ± 0.96 58.1 ± 9.8 56.90 ± 9.11 57.9 ± 9.9
Education (years) 14.57 ± 3.33 13.72 ± 3.62* 14.8 ± 3.2 13.49 ± 3.71* 14.8 ± 3.2 14.56 ± 3.62 14.6 ± 3.3
Family income ($1,000) 52.68 ± 36.37 42.11 ± 38.28* 55.4 ± 35.0 40.23 ± 39.93* 54.6 ± 35.1 52.89 ± 40.91 52.8 ± 35.9 BMI (kg/m232.73 ± 7.74 33.80 ± 8.11 32.5 ± 7.6 33.95 ± 8.55 32.6 ± 7.6 35.52 ± 8.81* 32.4 ± 7.6 Psychiatric medications 105 (20.8) 48 (42.7)* 57 (14.8) 35 (46.7)* 70 (16.5) 31 (62)* 74 (16.3) Comorbidities 3.8 ± 2.5 4.9 ± 2.97* 3.6 ± 2.3 5.3 ± 2.85* 3.6 ± 2.4 5.6 ± 2.79* 3.7 ± 2.4 Years with diabetes 8.1 ± 7.5 8.7 ± 7.3 7.9 ± 7.6 8.0 ± 6.6 8.2 ± 7.7 8.4 ± 7.0 8.1 ± 7.6 Medication Diet/exercise 84 (16.6) 13 (11.6) 72 (18.0) 10 (13.0) 75 (17.1) 6 (12.0) 77 (16.9) Oral 346 (68.2) 78 (68.8) 267 (68.3) 51 (67.0) 294 (68.5) 36 (72) 311 (68.1) Insulin 76 (15.0) 22 (19.6) 54 (13.7) 14 (19.0) 62 (14.8) 8 (16) 68 (15.0) Ethnicity Asian American 85 (16.8) 15 (18.1) 69 (81.9) 7 (8.4) 77 (91.6) 3 (3.5) 82 (96.5) African American 104 (20.5) 21 (20.6) 82 (79.4) 15 (14.7) 88 (85.3) 5 (4.9) 98 (95.1) Hispanic 98 (19.3) 29 (29.3) 71 (70.7) 24 (24.2) 76 (75.8) 11 (11.1) 88 (88.9) Non-Hispanic white 185 (36.7) 42 (22.7) 144 (77.3) 24 (13.0) 162 (87.0) 25 (13.4) 161 (86.6) Other 34 (6.7) 6 (18.8) 27 (81.3) 5 (15.6) 28 (84.4) 6 (18.2) 27 (81.8) Total samplePatients with CESD scores ≥16Patients with CESD scores ≥22CIDI n = 506 n = 113 n = 75 n = 50 ≥16 <16 ≥22 <22 MDD No MDD Male/female subjects 218 (43)/288 (57) 41 (36)/72 (64) 176 (45)/212 (55) 25 (33)/50 (67) 192 (45)/239 (55) 20 (40)/30 (60) 198 (43)/258 (57) Age (years) 57.83 ± 9.86 55.38 ± 10.13* 58.4 ± 9.7 55.53 ± 0.96 58.1 ± 9.8 56.90 ± 9.11 57.9 ± 9.9 Education (years) 14.57 ± 3.33 13.72 ± 3.62* 14.8 ± 3.2 13.49 ± 3.71* 14.8 ± 3.2 14.56 ± 3.62 14.6 ± 3.3 Family income ($1,000) 52.68 ± 36.37 42.11 ± 38.28* 55.4 ± 35.0 40.23 ± 39.93* 54.6 ± 35.1 52.89 ± 40.91 52.8 ± 35.9
BMI (kg/m232.73 ± 7.74 33.80 ± 8.11 32.5 ± 7.6 33.95 ± 8.55 32.6 ± 7.6 35.52 ± 8.81* 32.4 ± 7.6
Psychiatric medications 105 (20.8) 48 (42.7)* 57 (14.8) 35 (46.7)* 70 (16.5) 31 (62)* 74 (16.3)
Comorbidities 3.8 ± 2.5 4.9 ± 2.97* 3.6 ± 2.3 5.3 ± 2.85* 3.6 ± 2.4 5.6 ± 2.79* 3.7 ± 2.4
Years with diabetes 8.1 ± 7.5 8.7 ± 7.3 7.9 ± 7.6 8.0 ± 6.6 8.2 ± 7.7 8.4 ± 7.0 8.1 ± 7.6
Medication
Diet/exercise 84 (16.6) 13 (11.6) 72 (18.0) 10 (13.0) 75 (17.1) 6 (12.0) 77 (16.9)
Oral 346 (68.2) 78 (68.8) 267 (68.3) 51 (67.0) 294 (68.5) 36 (72) 311 (68.1)
Insulin 76 (15.0) 22 (19.6) 54 (13.7) 14 (19.0) 62 (14.8) 8 (16) 68 (15.0)
Ethnicity
Asian American 85 (16.8) 15 (18.1) 69 (81.9) 7 (8.4) 77 (91.6) 3 (3.5) 82 (96.5)
African American 104 (20.5) 21 (20.6) 82 (79.4) 15 (14.7) 88 (85.3) 5 (4.9) 98 (95.1)
Hispanic 98 (19.3) 29 (29.3) 71 (70.7) 24 (24.2) 76 (75.8) 11 (11.1) 88 (88.9)
Non-Hispanic white 185 (36.7) 42 (22.7) 144 (77.3) 24 (13.0) 162 (87.0) 25 (13.4) 161 (86.6)
Other 34 (6.7) 6 (18.8) 27 (81.3) 5 (15.6) 28 (84.4) 6 (18.2) 27 (81.8)
Data are means ± SD or n (%). Significance levels based on Student’s t test or χ2 test compared between those with and without a diagnosis on the designated scale.
*
P < 0.001;
P < 0.05;
P < 0.01.
Table 2—
Student’s t test compared between those who reached and did not reach criteria on the CIDI or score ≥16 or ≥22 on the CESD
CESD score (cut point 16)CESD score (cut point 22)CIDI
≥16 <16 ≥22 <22 MDD No MDD
A1C 7.58 ± 1.73 7.16 ± 1.33 7.55 ± 1.7 7.20 ± 1.38 7.06 ± 1.30 7.28 ± 1.45
Non-HDL cholestorol 144.85 ± 52.95 136.50 ± 45.37 138.80 ± 54.43 138.24 ± 45.98 144.54 ± 53.79 137.74 ± 46.80
Kilocalories 1,636.30 ± 819.74 1,294.40 ± 608.54 1,661.10 ± 844.38 1,317.40 ± 627.15 1,385 ± 632.13 1,367.10 ± 678.64
Saturated fat calories (%) 12.7 ± 3.54* 11.86 ± 3.54 13.0 ± 3.97§ 11.86 ± 3.46 12.75 ± 4.07 11.9 ± 3.49
Fruit and vegetable servings (n5.45 ± 3.39 5.39 ± 3.32 5.25 ± 3.27 5.43 ± 3.34 5.63 ± 3.47 5.38 ± 3.31
Exercise level (IPAQ) 1,970.80 ± 2,637.1* 2,565.80 ± 2,704.2 1,732.40 ± 2,622.7§ 2,695.50 ± 2,697.60 2,280.40 ± 2,591.0 2,432.30 ± 2,701.8
CESD score (cut point 16)CESD score (cut point 22)CIDI
≥16 <16 ≥22 <22 MDD No MDD
A1C 7.58 ± 1.73 7.16 ± 1.33 7.55 ± 1.7 7.20 ± 1.38 7.06 ± 1.30 7.28 ± 1.45
Non-HDL cholestorol 144.85 ± 52.95 136.50 ± 45.37 138.80 ± 54.43 138.24 ± 45.98 144.54 ± 53.79 137.74 ± 46.80
Kilocalories 1,636.30 ± 819.74 1,294.40 ± 608.54 1,661.10 ± 844.38 1,317.40 ± 627.15 1,385 ± 632.13 1,367.10 ± 678.64
Saturated fat calories (%) 12.7 ± 3.54* 11.86 ± 3.54 13.0 ± 3.97§ 11.86 ± 3.46 12.75 ± 4.07 11.9 ± 3.49
Fruit and vegetable servings (n5.45 ± 3.39 5.39 ± 3.32 5.25 ± 3.27 5.43 ± 3.34 5.63 ± 3.47 5.38 ± 3.31
Exercise level (IPAQ) 1,970.80 ± 2,637.1* 2,565.80 ± 2,704.2 1,732.40 ± 2,622.7§ 2,695.50 ± 2,697.60 2,280.40 ± 2,591.0 2,432.30 ± 2,701.8
Data are means ± SD.
*
P < 0.05;
P < 0.10;
P < 0.001;
§
P < 0.01.
Table 3—
Unstandardized regression coefficients in MR equations
Independent variablesDependent variables
A1CNon-HDL cholesterolKilocaloriesSaturated fat calories (%)Fruit and vegetable servingsIPAQ
Controls
MDD −0.19 4.24 −200.9* 0.13 0.24 35.86
CESD 0.00 −0.21 5.73 0.02 −0.04 −37.90
DDS 0.23§ 4.63* 168.1§ 0.25 0.41 −33.45
R 0.46 0.26 0.37 0.43 0.28 0.30
P 0.001 0.01 0.001 0.001 0.002 0.001
Independent variablesDependent variables
A1CNon-HDL cholesterolKilocaloriesSaturated fat calories (%)Fruit and vegetable servingsIPAQ
Controls
MDD −0.19 4.24 −200.9* 0.13 0.24 35.86
CESD 0.00 −0.21 5.73 0.02 −0.04 −37.90
DDS 0.23§ 4.63* 168.1§ 0.25 0.41 −33.45
R 0.46 0.26 0.37 0.43 0.28 0.30
P 0.001 0.01 0.001 0.001 0.002 0.001
Controls included sex, years with diabetes, age (years), BMI, number of comorbidities, years of education, ethnicity (non-Hispanic white versus other), diabetes medications (diet/exercise, oral, insulin), and psychotropic medication (yes/no).
*
P < 0.10;
P < 0.05;
P < 0.01;
§
P < 0.001.
This research was supported by grants DK062732 and DK061937 from the National Institute of Diabetes, Digestive, and Kidney Disease. The following medical groups and diabetes education centers collaborated in this research: Alta Bates Diabetes Education Center, Brown and Toland Medical Group, CA Pacific Diabetes Education Center, Hill Physicians Medical Group, Marin IPA, St. Luke’s Diabetes Education Center, St. Mary’s Medical Center, and University of California San Francisco Hospital and Clinics.
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The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked “advertisement” in accordance with 18 U.S.C Section 1734 solely to indicate this fact. | 2022-10-03 01:20:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22519421577453613, "perplexity": 10875.483735131575}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337371.9/warc/CC-MAIN-20221003003804-20221003033804-00416.warc.gz"} |
https://puzzling.stackexchange.com/questions/99976/lgbt-speeddating | # LGBT+ SpeedDating
Congratulations!
You are now the lucky franchise owner of 'SpeedDating Inc'.
We are the number one organiser of speed-dating events in WhereverYouAre.
We would love for you to start organizing new events in your town, we think it certainly has potential.
And with the advent of pride month, we are doing a 'rainbow special'.
Normally, you would organise a heterosexual speed-dating evening as follows:
1. Provide a numbered placeholder to each table.
3. Every turn, ask the men to go to the table that is one higher than their current number (except for whoever is sitting at the highest numbered table, they will move to table 1)
This system guarantees that all men will see all the women. And above all, it's very easy to explain. After all, these men will be here all evening, drinking some beers in between. You do not want complicated 'move to' rules.
Now, for rainbow events we've hit a bit of a snag.
If you use the same system as for the heterosexual people, half the men (for instance those doing the moving around) will never see half the men.
Your job is to figure out an easy to explain system, that will enable same-sex speed-dating.
Here is a simple answer for an odd number of people $$n$$. Obviously, on each round one person will have to sit out the round.
Label the two seats at the $$k$$th table with the numbers $$k$$ and $$n+1-k$$. The seat labeled $$\frac{n+1}{2}$$ sits on its own at the last table.
Between each round, everybody moves to the next numbered seat, and the person on seat $$n$$ moves to seat $$1$$.
The differences between the seat numbers at the tables are all distinct, and when you include a plus or minus sign they represent all possible values modulo $$n$$ , so there will be no repeats.
If $$n$$ is even, place one person on an extra seat at the last table and apply the above method on the remaining $$n-1$$ people. That person stays seated, and automatically pairs up with whoever would otherwise have to sit out the round.
(Thanks to hexomino for this part)
Here is a picture for the $$n=8$$ case:
• For $n$ even you can just get one person to sit at an "outside table" for the whole night. Then the person who would have to sit out in the $n-1$ case just sits at the "outside table" instead. Jul 15 '20 at 14:06
• @hexomino Doh! That makes perfect sense. Thanks. Jul 15 '20 at 14:09
• Funnily enough, I've thought about this question in a completely different context before - organising a fixture list in a sports league - and I find your strategy is a great one to go for. +1 Jul 15 '20 at 14:09
To extend Jaap's answer for an even number of people:
Arrange all the people on the two sides of a long table, which you can simulate with several tables side-by-side for adequate physical distancing. (Why do we call it social distancing, by the way?) Everyone is now dating the person opposite them.
To prepare for the other rounds,
Choose one person sitting at one end of the table. That person never moves.
Then, after every round,
everyone else moves one chair to the left. Like so:
This should be easy enough to implement.
To see that this works, we first check the pairings for the person starting in chair P. That seems to work trivially. For the person in seat 1, the pairings will be 10-8-6-4-2-11-9-7-5-3-P, which is what's desired. Finally, since everyone else sits at seat 1 at some point, they'll have the same pairings, only time-shifted and re-labeled.
(Disclaimer: this is not my own invention, it's how go players pair round-robin blitz tournaments.) | 2021-10-16 03:11:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 11, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.369783490896225, "perplexity": 1101.2659705975177}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323583408.93/warc/CC-MAIN-20211016013436-20211016043436-00159.warc.gz"} |
https://ctan.org/tex-archive/macros/latex/contrib/preprint | # Directory macros/latex/contrib/preprint
Preprint Collection: (May 2013)
~~~~~~~~~~~~~~~~~~~~
This directory contains some packages written by Patrick W. Daly. The
primary distribution site is:
http://www.mps.mpg.de/software/latex/localtex/localltx.html
I (Arash Esbati) mentioned balance.sty in comp.text.tex, was invited
to put in on CTAN, asked Patrick W. Daly for permission, wrote this
Legal stuff:
~~~~~~~~~~~~~~~~~~~~
The copyright holder of these packages is Patrick W. Daly. They can be
redistributed and/or modified under the terms of the LaTeX Project Public
License Distributed from CTAN archives in directory
macros/latex/base/lppl.txt; either version 1 of the License, or any later
version.
Important note:
~~~~~~~~~~~~~~~~~~~~
Unfortunately, the author of these packages doesn't have the time for
further development, bug fixes, "wishes" etc. Hence, they are provided
"as is". If you run into problems, you are on your own.
Brief description:
~~~~~~~~~~~~~~~~~~~~
1. authblk.sty: (version 1.3 from 2001/02/27)
A LaTeX2e package to redefine the \author command to work as normal or
to allow a footnote style of author/affiliation input.
2. balance.sty: (version 4.3 from 1999/02/23)
When writing a document with LaTeX two-column mode, the columns on the
last page, or those before a \cleardoublepage command, will be of
unequal height. balance.sty solves this problem by modifying the output
routines in two-column mode.
3. figcaps.sty: (version 4.7 from 1999/02/23)
This package allows the figure captions to be collected throughout the
paper and printed on a separate page at the end. The figures themselves
will not appear in the text. This is for purposes of a manuscript for
submission. Similarly, tables are not printed in the text, but are
outputted at the end, after the figure captions. This package may
optionally be used with the longtable environment defined in the package
of the same name.
4. fullpage.sty: (version 1.1 from 1999/02/23)
This package sets all 4 margins to be either 1 inch or 1.5 cm, and
specifies the page style.
5. sublabel.sty (version 4.5 from 1999/02/23)
The macros in this package allow all counters to be subnumbered, as for
example 4a, 4b, 4c, simply by bracketting the objects to be so numbered
with appropriate on/off commands. They will work with any user-defined
counters too.
6. appendix.sty: (version 2.2 from 2005/10/30)
Adding this package redefines \appendix so that main counters for
figures, tables, equations are subnumbered under the appendix. The
plate counter is also subnumbered. A \noappendix command is included so
that things like bibliographies may be called after the appendix with
\section*. This package is only useful with article documentclass for
obvious reasons.
N.B.: This package is not available on CTAN due to a name clash. You
have to fetch it from the site mentioned above.
Installation:
~~~~~~~~~~~~~~~~~~~~
Just run LaTeX on (package).ins, which generates (package).sty. If you
want the documentation as a dvi, run LaTeX on (package).dtx, otherwise use
the provided format. Move the .sty-files to a directory where LaTeX looks
for the input files. Update your file name database and you're done.
Happy TeXing!
Arash Esbati
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https://steelmartbhatkal.com/r2mur/a151f8-complex-addition-and-subtraction-worksheets | Subtraction Worksheets On this page you will find: a complete list of all of our math worksheets relating to shapes.Choose a specific addition topic below to view all of our worksheets in that content area. See more ideas about preschool worksheets, preschool, kindergarten worksheets. Intuitively, it seems apparent that when we add these two complex numbers, then the sum will be obtained by adding the real parts separately and the imaginary parts separately: \begin{align}{z_1} + {z_2}& = \left( {{x_1} + i{y_1}} \right) + \left( {{x_2} + i{y_2}} \right)\\&= \left( {{x_1} + {x_2}} \right) + \left( {i{y_1} + i{y_2}} \right)\\& = \left( {{x_1} + {x_2}} \right) + i\left( {{y_1} + {y_2}} \right)\end{align}. You will find addition lessons, worksheets, homework, and quizzes in each section. Math Worksheets For Grade 5 Addition And Subtraction Word Problems. Find $${z_1} + {z_2}$$ and $${z_1} - {z_2}$$. 'Grab em all' to review a student's prowess at solving them. Grade 1 Math Addition And Subtraction Worksheets. ${z_1} = 2 - 3i,\,\,\,{z_2} = - 3 + 4i$. simple-mixed-arithmetic Download Image «« Previous Wallpaper Next Wallpaper »» Wallpaper Name : Addition and Subtraction … The worksheets in this section have different levels of complexity, including adding a single digit number to a two digit number, two digit plus two digit addition, three digit plus two digit addition, addition of three digit numbers and addition of the three values. You will understand this better at a later stage. Plunge into practice with our addition and subtraction worksheets featuring oodles of exercises to practice performing the two basic arithmetic operations of addition and subtraction. Children will practice addition to 10 and subtraction within 10 in two different layouts. Time to move on to subtraction! Study Addition And Subtraction Of Complex Numbers in Numbers with concepts, examples, videos and solutions. Mar 23, 2020 - Explore Haylley Perez's board "Preschool worksheets" on Pinterest. You will understand this better at a later stage. Example 1. Explore. Math Worksheets For Grade 2 Addition And Subtraction Word Problems. Check my answers: Email my answers to my teacher . Understanding addition and subtraction related to decimals is a bit complex. Number Line Subtraction Sheet 2. 1st Grade Math Worksheets Addition And Subtraction. ${z_1} = 2 - 3i,\,\,\,{z_2} = - 3 + 4i$. In Key Stage 1, pupils learn the basics of adding and subtracting numbers. Free Addition and Subtraction Math Worksheet. Access FREE Addition And Subtraction Of Complex Numbers Interactive Worksheets! By the end of Year 1, they are expected to know addition and subtraction symbols, addition and subtraction facts up to 20, and solve simple one-step problems. 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Adding and Subtracting Complex Numbers Simplify. You will find addition lessons, worksheets, homework, and quizzes in each section. Addition and Subtraction Math Worksheets Suitable for First Grade and Second Grade. Find $${z_1} + {z_2}$$ and $${z_1} - {z_2}$$. Click on an objective for related worksheets and resources. 29 scaffolded questions that start relatively easy and end with some real … But before we hop on to that discussion, let’s see what decimals mean. Estimating Sums and Differences. This assortment of addition and subtraction worksheets in column and horizontal formats features up to 7-digit numbers. Solve simple addition sums using given number lines. Relationship Between Addition And Subtraction - Recognise And Use The Inverse Relationship Between Addition Inverse Relationships Inverse Relationships Between Addition And Subtraction Worksheet Relationship Between Addition And Subtraction printable worksheets. Main content: Addition and subtraction Other contents: Add to my workbooks (1) Download file pdf Embed in my website or blog Add to Google Classroom Add to Microsoft Teams Share through Whatsapp: Link to this worksheet: Copy: nramsey Finish!! Our grade 2 subtraction worksheets provide the practice needed to master basic subtraction skills. Some of the worksheets for this concept are Multiplication and division, Mixed word problems, Mixed operations word problems, Website e mail tim, Year 2 maths addition and subtraction workbook, Sample work from, Practice workbook grade 2 pe, Ace your math test reproducible work. One can also consider decimals … Review and practice addition and subtraction with this free printable worksheets for kids. Print and use these christmas addition subtraction math worksheets. Math Worksheets For Grade 4 Addition And Subtraction Word Problems . In mathematics, we often encounter word problems ranging from basic problems … Intuitively, it seems apparent that when we add these two complex numbers, then the sum will be obtained by adding the real parts separately and the imaginary parts separately: \begin{align}{z_1} + {z_2}& = \left( {{x_1} + i{y_1}} \right) + \left( {{x_2} + i{y_2}} \right)\\&= \left( {{x_1} + {x_2}} \right) + \left( {i{y_1} + i{y_2}} \right)\\& = \left( {{x_1} + {x_2}} \right) + i\left( {{y_1} + {y_2}} \right)\end{align}. Pinterest. \begin{align}{z_1} + {z_2}& = \left( {2 - 3i} \right) + \left( { - 3 + 4i} \right)\\& = \left\{ {2 + \left( { - 3} \right)} \right\} + i\left\{ {\left( { - 3} \right) + 4} \right\}\\& = - 1 + i\end{align}, \begin{align}{l}{z_1} - {z_2} &= \left( {2 - 3i} \right) - \left( { - 3 + 4i} \right)\\&= \left\{ {2 - \left( { - 3} \right)} \right\} + i\left\{ {\left( { - 3} \right) - 4} \right\}\\& = 5 - 7i\end{align}, Addition and Subtraction of Complex Numbers, Addition and Subtraction of complex Numbers. Let's subtract the following 2 complex numbers $(8 + 6i ) \red{-}(5 + 2i)$ Step 1. Addition Subtraction Multiplication And Division Practice - Displaying top 8 worksheets found for this concept.. Note that adding two complex numbers yields a complex number - thus, the Complex Set is closed under addition. 21 Posts Related to 1st Grade Math Addition And Subtraction Worksheets Pdf. It can also be used as an assessment or quiz. 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The teachers are often needed to offer these worksheets to the entire class to verify the students’ strength and fundamental maths know-how. The real and imaginary parts add / subtract separately because they are in perpendicular directions. They cover 2nd grade topics ranging from basic subtraction facts to subtracting in columns with regrouping. 21 Posts Related to Math Worksheets For Grade 3 Addition And Subtraction Word Problems. Free Printable Math Addition And Subtraction worksheets for kids to help them learn and practice their concepts related to Addition And Subtraction. Addition and Subtraction Worksheets KS1. Tout l'ensemble est sur le . Grade 4 Math Worksheets Addition And Subtraction . Save and Download Math Addition And Subtraction worksheets for kids pdf. Have you mastered the addition facts? Video Tutorial on Subtracting Complex Numbers. Similarly, upon subtracting these two numbers, we have: \begin{align}{z_1} - {z_2}&= \left( {{x_1} + i{y_1}} \right) - \left( {{x_2} + i{y_2}} \right)\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,&= \left( {{x_1} - {x_2}} \right) + \left( {i{y_1} - i{y_2}} \right)\\&= \left( {{x_1} - {x_2}} \right) + i\left( {{y_1} - {y_2}} \right)\end{align}. You can Practice, check answers and Upload your sheets for free using SchoolMyKids Worksheets for Kids. More information... People also love these ideas. Cancel: Text box style: Font: Size: px. The decimal number is used to represent a number that has greater precision in comparison to integers or whole numbers. Math Worksheets For Grade 3 Addition And Subtraction… Note: The second half of the video focuses on subtracting complex numbers so if you already understand adding just skip to the middle. Subtraction Worksheets for Math Practice! Complex Numbers Worksheets On this page you will find: a complete list of all of our math worksheets relating to complex numbers. Make your child a Math Thinker, the Cuemath way. addition-subtraction-practice-second-grade Download Image. Number Line Addition Sheet 2. Solve the subtraction sums as quickly as possible using the ‘counting back’ strategy. 15. All of these worksheets will practice a students place value and regrouping skills thoroughly. Count Back Worksheet. Integer Addition And Subtraction - Integer Addition And Subtraction Range Adding Integers Subtracting Integers Worksheet Free Math Worksheet printable worksheets. This provides great extra practice for kids. There are many subtraction exercises in these worksheets that you can choose. Worksheet with answer key on adding and subtracting complex numbers. It is also closed under subtraction. It is also closed under subtraction. This provides great extra practice for kids. Note that adding two complex numbers yields a complex number - thus, the Complex Set is closed under addition. Hence, the students must be encouraged to practice the addition and subtraction worksheets to improve their maths basic. Addition and subtraction form the basis of every calculation, no matter how simple or complex. Log in. Study Addition And Subtraction Of Complex Numbers in Numbers with concepts, examples, videos and solutions. Free Addition and Subtraction Math Worksheet – Free Printable Worksheet. You may select up to 30 addition problems per worksheet. Free worksheet(pdf) and answer key on adding and subtracting complex numbers. Year 3 Addition & Subtraction. Table Addition 2nd Grade Math Worksheets Voici Montessori Coloring Pages French Math Activities Mental Calculation Mathematical Practices. Presenting a mixed review of addition and subtraction of single-digit, 2-digit, 3-digit, 4-digit and 5-digit numbers, each pdf practice set is designed to suit the learning needs of elementary school children. Font color Background color … Simple addition and subtraction worksheets for your winter math in kindergarten or first grade! Grade 3 Math Addition And Subtraction Worksheets Pdf. No login required. Math Worksheets Grade 3 Addition … Solve problems, including missing number problems, using number facts, place value, and more complex addition and subtraction Provide year 3 students with a range of problem-solving opportunities using our addition and subtraction maths worksheets, activities and investigations. Choose a specific addition topic below to view all of our worksheets in that content area. addition and subtraction regrouping worksheet Download Image. Voici un ensemble complet pour travailler et évaluer les tables d'additions et de soustractions en classe. Number Line Subtraction Sheet 1. 1) (−i) + (6i) 2) (−6i) − (6i) 3) (−4i) − (5i) 4) (−3i) + (3 + 5i) 5) (−2i) + (5i) 6) (3i) + (4i) 7) (−6 − 2i) + (6 − 5i) 8) (−5 + 3i) − (4 − 5i) 9) (5 + 6i) + (2 − 7i) 10) (6 − 8i) − (4i) + 7 11) (3 − 4i) − (−5 + 7i) 12) (5 + 3i) − (−2 − 5i) 13) (5 − 6i) + (5i) + (7 + 6i) 14) (−7 + 7i) − (−7 � Grab some of these … Grade 2 subtraction worksheets. This is a fantastic bundle which includes everything you need to know about the problems involving addition and subtraction across 30 in-depth pages. Consider two complex numbers $${z_1}$$ and $${z_2}$$, given by: ${z_1} = {x_1} + i{y_1}, \quad {z_2} = {x_2} + i{y_2}$. Make your child a Math Thinker, the Cuemath way. All math worksheets below are dynamically generated. \begin{align}{z_1} + {z_2}& = \left( {2 - 3i} \right) + \left( { - 3 + 4i} \right)\\& = \left\{ {2 + \left( { - 3} \right)} \right\} + i\left\{ {\left( { - 3} \right) + 4} \right\}\\& = - 1 + i\end{align}, \begin{align}{l}{z_1} - {z_2} &= \left( {2 - 3i} \right) - \left( { - 3 + 4i} \right)\\&= \left\{ {2 - \left( { - 3} \right)} \right\} + i\left\{ {\left( { - 3} \right) - 4} \right\}\\& = 5 - 7i\end{align}, Addition and Subtraction of Complex Numbers, Addition and Subtraction of complex Numbers. Consider two complex numbers $${z_1}$$ and $${z_2}$$, given by: ${z_1} = {x_1} + i{y_1}, \quad {z_2} = {x_2} + i{y_2}$. These numbers are written with a dot within them. digit-plus-minus-addition-and-subtraction-with-some-math-worksheets-regrouping-digits Download Image. Mixed Addition and Subtraction. They are perfect for the January snowman theme in your classroom or for some extra practice at home. 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These are ready-to-use Problems Involving Addition and Subtraction with this free printable for. | 2021-05-18 10:50:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 8, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.30604419112205505, "perplexity": 3123.692146811536}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989819.92/warc/CC-MAIN-20210518094809-20210518124809-00430.warc.gz"} |
https://www.maplesoft.com/support/help/maplesim/view.aspx?path=componentLibrary/signalBlocks/sources/real/Constant | Constant
Generate constant signal of type Real
Description The Constant component has a real Real output equal to parameter $k$.
Equations $y=k$
Connections
Name Description Modelica ID $y$ Real output signal y
Parameters
Name Default Units Description Modelica ID k $1$ $1$ Constant output value k
Modelica Standard Library The component described in this topic is from the Modelica Standard Library. To view the original documentation, which includes author and copyright information, click here. | 2022-08-17 01:07:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41927558183670044, "perplexity": 6809.190692065187}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882572833.78/warc/CC-MAIN-20220817001643-20220817031643-00565.warc.gz"} |
http://tug.org/pipermail/macostex-archives/2011-March/046660.html | # [OS X TeX] Memoir Figures in Margin with Captions and Proper Float Numbers
David Arnold dwarnold45 at suddenlink.net
Sun Mar 13 22:48:07 CET 2011
Alan,
Thanks, that worked. I did have to use the TeX Live Utility to update memoir.
David.
On Mar 13, 2011, at 1:51 PM, Alan Munn wrote:
> On Mar 13, 2011, at 4:23 PM, David Arnold wrote:
>
>> All,
>>
>> I am using the memoir package and I'd like to put some of my figure environments in the margin, with captions, and numbered in concurrence with the floats in the main body.
>>
>> Does anyone know how to do this?
>
>
> Memoir provides a \marginfigure environment for this. I haven't used it, but it seems to do what you want.
>
> Alan
>
> --
> Alan Munn
> amunn at gmx.com
>
>
>
>
> ----------- Please Consult the Following Before Posting -----------
> TeX FAQ: http://www.tex.ac.uk/faq
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> | 2018-06-19 09:03:13 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9959290623664856, "perplexity": 10229.084478548024}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267861981.50/warc/CC-MAIN-20180619080121-20180619100121-00093.warc.gz"} |
http://mathhelpforum.com/math-topics/72111-when-population-doubled.html | # Math Help - when the population is doubled
1. ## when the population is doubled
In a certain population the annual birth rate and annual death rate are 3.94% and 1.94% respectively.Find the number of years in which the population is doubled assuming that there is no immigration and emigration ?
now what i've tried is this
let x be the total population today
now we want 2x population
now we know that
total population in n years = total population born in n years - total population die in n years
=> 2x =x (1.0394)^n -x (1.0194)^n [ i've used the formula of compund interest which is derive by using a geometric series]
now what ???
after taking x common and canceling it , what should i do ?
2. You forgot to add x. You start with say 100 people, if you subtracted 1.02 of 100 from 1.04 of 100, you would have lost most of your population, so you need to add on x because that is the starting number, and the rest of your formula is just the increase.
$2x = x + x(1.0394^n) - x(1.0194^n)$
$x = x(1.0394^n) - x(1.0194^n)$
$1 = 1.0394^n - 1.0194^n$
$1 + 1.0194^n = 1.0394^n$
This is as much as I can help you. I hope I have helped a bit, maybe you can take it from here?
3. Originally Posted by LordMaximus
In a certain population the annual birth rate and annual death rate are 3.94% and 1.94% respectively.Find the number of years in which the population is doubled assuming that there is no immigration and emigration ?
now what i've tried is this
let x be the total population today
now we want 2x population
now we know that
total population in n years = total population born in n years - total population die in n years
=> 2x =x (1.0394)^n -x (1.0194)^n [ i've used the formula of compund interest which is derive by using a geometric series]
now what ???
after taking x common and canceling it , what should i do ?
$\frac{dP}{dt} = \frac{3.94}{100} P - \frac{1.94}{100} P = \frac{P}{50}$.
Therefore $P = P_0 e^{t/50}$.
Solve $2 P_0 = P_0 e^{t/50} \Rightarrow 2 = e^{t/50}$ for t.
4. You are making this too difficult! If the annual birth rate is 3.94% and the annual death rate is 1.94% then the population is increasing at 3.94- 1.94= 2% per year (that's where mr. fantastic got his "P/50"). With problems that talk about "doubling" or "half life" I prefer NOT to use "e" like mr. fantastic did. The fact that the rate of increase is a constant tells us there IS a specific time until doubling and we can write the population at year t as $P(t)= P(0)2^{t/T}$ where P(0) is the population at t=0 and T is the time to double. Because the annual increase is 2%, P(1)= P(0)+ 0.2P(0)= 1.02P(0).
From the previous formula, $P(1)= P(0)2^{1/T}$ and setting those equal and cancelling P(0) on both sides of the equation, [tex]2^{1/T}= 1.02[/itex]. Solve that equation for T. Of course, you would use logarithms to solve that equation just as you would for $e^{t/50}= 2$ in mr fantastic's method. | 2015-04-27 02:02:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 10, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7856839895248413, "perplexity": 1022.5507195306209}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1429246656965.63/warc/CC-MAIN-20150417045736-00258-ip-10-235-10-82.ec2.internal.warc.gz"} |
http://physics.stackexchange.com/questions/79411/simularity-transformation-of-heisenberg-xxz-hamiltonian | # Simularity transformation of Heisenberg XXZ Hamiltonian
I am considering the Heisenberg XXZ Hamiltonian: $$H(\Delta, J) = J\sum_{i=1}^L\left(\sigma^x_i\sigma^x_{i+1} + \sigma^y_i\sigma^y_{i+1} + \Delta \sigma^z_i\sigma^z_{i+1} \right)$$ Apparently, one can show: $$-H(-\Delta) = UH(\Delta)U^{-1}$$, where $U=\Pi_{m=1}^{M/2}\sigma_z^{2m}$ is a unitary transformation. I am having some trouble showing this. Of course the transformation commutes with the z-Pauli matrices and using $(\sigma^z)^{\dagger} = \sigma_z$ and $(\sigma_z)^2 = \textrm{id}$ this term is unchanged. However, I am left with mix terms for the first and second term.
Furthermore, my reference claims that because of this simularity transformation, $J$ can be omitted if $-\infty<\Delta<\infty$. I don't really see how this follows from the simularity transform.
Any help is much appreciated!
-
I don't see how you get mixed terms. Your $U$ acts on every other site. For instance (as operators acting on different sites commute) $$\ldots+ U \sigma^{2i}_x \sigma^{2i+1}_x U^{-1} +\ldots= \ldots \sigma^{2i}_z \sigma^{2i}_x \sigma^{2i}_z \sigma^{2i+1}_x \ldots=\ldots i \sigma^{2i}_y \sigma^{2i}_z \sigma^{2i+1}_x \ldots=\ldots-\sigma^{2i}_x \sigma^{2i+1}_x\ldots,$$ and similarly for the Pauli $y$-matrices.
$J$ can be omitted because it is not zero compared to $\Delta$ and you can divide (rescale) the Hamiltonian by $J$ and absorb it into $\Delta/J \rightarrow \Delta'$. If $\Delta \rightarrow \infty$ then you just recover the Ising model. Remember, this transformation is unitary, which means it's just a change of basis in Hilbert space. It can't change anything "physically" and that tells us that it's only the relative $\pm$ - sign between $J$ and $\Delta$ that is physical. | 2015-08-01 22:26:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8389708995819092, "perplexity": 272.64742719285124}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-32/segments/1438042988922.24/warc/CC-MAIN-20150728002308-00028-ip-10-236-191-2.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/126835/for-complex-z-find-all-solutions-to-z-6-i3-27/126836 | # For complex $z$, find all solutions to: $(z - 6 + i)^3 = -27$
For complex $z$, find all solutions to: $(z - 6 + i)^3 = -27$
I reasoned that for this to be true, $z - 6 + i$ must be $= -3$
$\therefore z - 3 + i = 0$
$z = 3 - i$
However, there are two more solutions provided for this problem and I am not sure how to get to them. What is the standard method for solving something like this to ensure that all answers are produced?
-
The equation $u^3=-27$ has three solutions $u$ in $\mathbb C$. Can you describe them? Hint: polar representation of complex numbers and de Moivre's formula.
Once this is done, you will see that the equation $(z-6+\mathrm i)^3=-27$ has three solutions as well, and you will be able to write them down (one of them is $3-\mathrm i$, of course).
-
$(z - 6 + i)^3 = -27$ is of the form $u^3=(-3)^3$, which can be factored over $\mathbb{C}$ as:
$$u^3-(-3)^3=(u-(-3))(u^2+u(-3)+(-3)^2)=(u+3)(u^2-3u+9)$$
One root is $u=-3$.
The other two roots, one can get after solving quadratic equation $u^2-3u+9=0$.
-
First Try to find all the cube roots of $-27$.(Or whatever it is that is relevant to your problem)
To do this you write down Complex numbers in their Polar form. Or in the form
$$z=r(\cos\theta+\text{i}\sin\theta)$$ Where $\theta$ is the argument of $z$ and $r$ its modulus or norm (or its length (on the Argand Diagram) in simple terms). Finding out the cube roots of $-27$ is not a very difficult thing to do. But for this you require the knowledge of de Moivre's Theorem. It deals with computing powers of complex numbers. It says (for now, just trust the equation and move along:) I will not give you a proof here) $$r(\cos\theta+\text{i}\sin\theta)^n=r^n(\cos n\theta+\text{i}\sin n\theta)\tag{1}$$ How do you use this to find the cube roots? Well, Just assume that for some $u\in \mathbb C$ with argument $\alpha$ and modulus $q$, $$[q(\cos\alpha+\text{i}\sin\alpha)]^3=-27$$ Or, from the result of de Moivre's Theorem, $$q^3(\cos 3\alpha+\text{i}\sin 3\alpha)=-27(\cos 0+\text i \sin0)\tag{2}$$ Equation $(2)$ suggests that
$q^3=-27 ~~~~~\implies~ q=\sqrt[3]{-27}=-3$, and
$3\alpha=0~~~~~~~~~\implies3\alpha=0, 2\pi ~\text{or}~ 4\pi\implies~\alpha =0 ,~ \frac23\pi~~\text{or} ~~\frac43\pi~$
You now have three sets of possible values for $\alpha$ which is, if you remember, the argument of you cube roots of $-27$ and as given in your answer, has three values that it can take. [Note that for all three $\alpha$s, the value for the modulus of the roots $($or $q)$ is always the same ($-3$). This is where your problem came about. (You didd not consider other possible roots)]
So now, we have found all values that a complex number, say $u$ can take where $$u^3=-27$$ And your question asks you to find the solution to the equation $$(z - 6 + \text i)^3 = -27$$
Notice the similarity? They are in similar forms right? So it would be fair to say that
$$~~~~~~~~~~~~~~u=(z - 6 + \text i)$$ $$\implies z=u+6-\text i \tag{3}$$ From this you easily get 3 values for $z$ (using the three solutions for $u$ that we got earlier on)
Note: During the last step, you need to change solutions for $u$ from their Polar form to the usual $a+b\text i$ format. The reason should be apparent from $(3)$
Hope it helps!
-
$z^3-(18-3i)z^2+(105-36i)z-(171-107i)=0$
Since one solution $z_0$ is already known I'd rather divide that expression by $z-z_0$ and end up with a quadratic equation than use that formula. – user20266 Apr 1 '12 at 10:52 | 2014-03-07 21:21:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.923686146736145, "perplexity": 156.45119624565734}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1393999650916/warc/CC-MAIN-20140305060730-00080-ip-10-183-142-35.ec2.internal.warc.gz"} |
http://math.stackexchange.com/questions/293134/is-this-a-transitive-relation | # Is this a transitive relation?
$$A = \{foo, bar\}$$
$$R_1 = \{(foo, foo)\}$$
$$R_2 = \{(foo, bar)\}$$
Is $R_1$ transitive on $A$? My gut tells me yes, but I'm not sure if transitivity requires $3$ elements.
What about $R_2$? foo R2 bar ^ foo R2 bar => foo R2 bar?
-
Yes, it’s transitive. If it weren’t, you’d be able to find $a,b,c\in A$, not necessarily distinct, such that $\langle a,b\rangle\in A$, $\langle b,c\rangle\in A$, and $\langle a,c\rangle\notin A$, and you can’t: the only way to get $\langle a,b\rangle\in A$ and $\langle b,c\rangle\in A$ is to set $a=b=c=\text{foo}$, in which case $\langle a,c\rangle$ is in $A$.
-
Transitivity requires three elements, but they need not be distinct. This is one of the many reasons why mathematicians are considered strange by laypeople. We say three, but we really mean three, two or one.
-
The relation $R$ is transitive if whenever $(a,b)\in R$ and $(b,c)\in R$ then $(a,c)\in R$.
Since $R$ is a singleton there is only one pair so $\newcommand{\foo}{\mathbf{foo}}(\foo,\foo)\in R$ as well $(\foo,\foo)\in R$ and indeed $(\foo,\foo)\in R$.
-
Yes it is transitive.
Proof :
defination of Transitivity :if ( aRb and bRC )then { aRc}
here (foo, foo) is aRb..where a=foo and b=foo .
Since there is nothing to represent bRc, the condition ( aRb and bRC ) is false
defination of if...then
By the defination of if...then , we can say when p is false the answer is true as can be seen from the image.
THUS , The Given Relation is Transitive :)
- | 2015-08-31 22:35:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9403877854347229, "perplexity": 643.1984054395786}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644068098.37/warc/CC-MAIN-20150827025428-00020-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://www.mathxplain.com/calculus-1/indefinite-integral/summary-problem-for-rational-functions | Contents of this Calculus 1 episode:
Integrating rational functions, Partial fractions, First type partial fractions, Second type partial fractions, Decompose it into partial fractions, Factorization, Linear denominator, Non-factorable quadratic denominator, f’/f and arctan forms, Polynomial division.
Text of slideshow
Here is a summary problem where we can see all important steps.
Bad news. First, we need polynomial division, because the degree of the numerator must be less than the degree of the denominator.
This polynomial division is just like long division we learned in elementary school.
Like 25:7=3 and the remainder is 4.
In other words
Polynomial division is just like this.
quotient remainder
Here comes the polynomial division:
Everything is OK so far.
But this is not the end, yet.
We multiply the quotient with the divisor,
and subtract that from the dividend.
And then we divide again, and repeat this until the degree of the dividend becomes less than that of the divisor.
Hey, it is less now, so we are done.
We integrate the first two members, and then we proceed to the fraction where the degree of the numerator is less than that of the denominator.
Again, we need to factorize the denominator into linear and irreducible quadratic factors. First, we factor out x2.
Then we check whether the remaining quadratic part could be factorized. The answer is no. It is because there is no real solution to the equation.
On the other hand, x2 can be factorized.
Now come the decomposing into partial fractions.
If the denominator contains a square of some ax+b linear polynomial, then we decompose into partial fractions, such that
the denominator of one of the partial fractions is ax+b,
and the other is (ax+b)2.
Now we have to figure out the numerators. The denominator of the first fraction seems to be linear, so the numerator is some A.
The denominator of the second fraction is a square of a linear expression, so the numerator here is also some A, but since A is already used, let's call it B.
Finally, the denominator of the third fraction is a quadratic polynomial, so its numerator should be in the form of Ax+B, but since A and B are already used, Cx+D will do.
Now we calculate the values of A, B, C and D.
We multiply by the denominators.
Next, expand the parentheses.
And then we check how many x3 terms, x2 terms, x terms and constants are on the right side.
Because there are exactly the same on the left side as well.
The first two terms are very easy to integrate.
The third term becomes this:
The first term, as we wanted, f’/f, while the second term leads to arctangent.
And then it is done.
Finally, one more example:
First of all, we need to factorize the denominator into linear or irreducible quadratic factors. The factorization isn't trivial at all, because the denominator does not have a real root. The product form:
Then:
The factors in the denominator will be the denominators of the partial fractions. Since both factors are irreducible quadratic expressions, it seems we will get a sum of two Type II partial fractions:
Next, we move on to finding A, B, C, and D.
Multiplication:
and then conversion
finally the usual system of equations:
The solutions: , thus
We will integrate the two fractions separately.
The first fraction:
This will turn into a linear substitution of arctgx:
The second fraction, due to symmetry reasons:
The solution of the problem is the sum of the expressions found before:
Let's not forget though, that the method of integrating rational functions should be regarded as the last resort, and used only when all other methods failed to work. This latter problem was solved earlier, somewhat faster, using S4!
# Summary problem for rational functions
17
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Integrating rational functions, Partial fractions, First type partial fractions, Second type partial fractions, Decompose it into partial fractions, Factorization, Linear denominator, Non-factorable quadratic denominator, f’/f and arctan forms, Polynomial division.
Let's see this
Calculus 1 episode | 2020-07-13 07:32:49 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9522024989128113, "perplexity": 630.0679727280784}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-29/segments/1593657143354.77/warc/CC-MAIN-20200713064946-20200713094946-00286.warc.gz"} |
https://socratic.org/questions/58e6a87511ef6b3999334e28 | # Question 34e28
Apr 8, 2017
You need 0.0678 mol of ${\text{Cl}}_{2}$.
Given: Mass of $\text{KI}$ and the chemical equation.
Find: Mass of ${\text{Cl}}_{2}$.
Strategy:
The central part of any stoichiometry problem is to convert moles of something to moles of something else.
(b) We can use the molar mass of $\text{KI}$ to find the moles of $\text{KI}$.
(c) We can use the molar ratio from the equation to convert moles of $\text{KI}$ to moles of ${\text{Cl}}_{2}$.
${\text{moles of KI" stackrelcolor(blue)("molar ratio"color(white)(Xl))(→) "moles of Cl}}_{2}$
Our complete strategy is:
${\text{Mass of KI"stackrelcolor (blue)("molar mass"color(white)(Xl))(→) "moles of KI"stackrelcolor (blue)("molar ratio"color(white)(Xl))( →) "moles of Cl}}_{2}$
Solution
(a) The balanced equation is
${\text{Cl"_2 + "2KI" → "2KCl" + "I}}_{2}$
(b) Calculate moles of $\text{KI}$
22.5 color(red)(cancel(color(black)("g KI"))) × ("1 mol KI")/(166.00 color(red)(cancel(color(black)("g KI")))) = "0.1355 mol NH"_3
(c) Calculate moles of ${\text{Cl}}_{2}$
The molar ratio of ${\text{Cl}}_{2}$ to $\text{KI}$ is ("1 mol Cl"_2)/("2 mol KI")"#.
${\text{Moles of Cl"_2 = 0.1355color(red)(cancel(color(black)("mol KI"))) × ("1 mol Cl")/(2 color(red)(cancel(color(black)("mol KI")))) = "0.0678 mol Cl}}_{2}$ | 2020-01-20 04:24:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 17, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.700296938419342, "perplexity": 8810.201652522383}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250597230.18/warc/CC-MAIN-20200120023523-20200120051523-00358.warc.gz"} |
http://mymathforum.com/algebra/344299-1-2-0-x-not-0-a.html | My Math Forum 1=2 or 0/x NOT = 0
Algebra Pre-Algebra and Basic Algebra Math Forum
May 23rd, 2018, 03:00 AM #1 Newbie Joined: May 2018 From: United Kingdom Posts: 1 Thanks: 1 1=2 or 0/x NOT = 0 I have either proved that 1=2, 0/x for a value of x not equal to 0... Or I have made a mistake. I started with e^i*pi=-1 I then squared both sides to get: e^2*i*pi=1 Taking the log of both sides allows me to remove the power and multiply by the log for: 2*i*pi*log(e)=log(1) S1) 2*i*pi*log(e)=0 To extract the value of i, sqrt(-1), I divide both sides by 2*pi*log(e) i=0/2*i*pi*log(e) 0/x=0 i=0 sqrt(-1)=0 Square both sides for: -1=0 +2 both sides: 1=2 Help... Thanks from v8archie
May 23rd, 2018, 03:17 AM #2 Global Moderator Joined: Oct 2008 From: London, Ontario, Canada - The Forest City Posts: 7,879 Thanks: 1087 Math Focus: Elementary mathematics and beyond Your mistake lies in applying logarithmic identities which apply to real numbers to a complex number. Not all of these identities are necessarily true for complex numbers. See here for more information.
May 23rd, 2018, 03:21 AM #3 Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 Your error is when you take the logarithm of a complex number. A complex number can be written in polar form as $\displaystyle re^{i\theta}= re^{i(\theta+ 2\pi n)}$ since "$\displaystyle e^{i\theta}= \cos(\theta)+ i\sin(\theta)$" is periodic with period $\displaystyle 2\pi$. Taking the logarithm, $\displaystyle \ln(re^{i(\theta+ 2n\pi)}= \ln(r)+ i(\theta+ 2n\pi)$ for n any integer. That is, ln is multivalued. Last edited by skipjack; May 23rd, 2018 at 05:45 AM.
May 23rd, 2018, 03:31 AM #4
Math Team
Joined: Dec 2013
From: Colombia
Posts: 7,445
Thanks: 2499
Math Focus: Mainly analysis and algebra
Quote:
Originally Posted by keylewer I have either proved that 1=2, 0/x for a value of x not equal to 0... Or I have made a mistake.
This is great, thank you. Too many are unwilling to admit that they might have erred.
May 23rd, 2018, 01:37 PM #5 Global Moderator Joined: May 2007 Posts: 6,607 Thanks: 616 A simple way to look at it is $e^{2\pi i}=1=e^0$, but $2\pi i\ne 0$. Thanks from JeffM1
Tags 0 or x, broken, e^i*pi, oops
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Contact - Home - Forums - Cryptocurrency Forum - Top | 2018-10-17 21:10:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8626764416694641, "perplexity": 3274.3162357487895}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583511216.45/warc/CC-MAIN-20181017195553-20181017221053-00255.warc.gz"} |
https://physics.aps.org/synopsis-for/10.1103/PhysRevLett.112.165901 | Synopsis: Amber Does Not Act Its Age
$110$-million-year-old amber samples surprisingly retain the same thermodynamic properties as much younger amorphous solids.
Amber is a vitrified resin valued for its beauty and the intriguing specimens occasionally trapped within it. Now, scientists are studying ancient amber samples to determine how their glasslike properties change with time. Amber is a unique example of a glass because it has “hyperaged,” i.e., has undergone thermodynamic stabilization for millions of years—a process that is impossible to replicate in a lab.
Conventional, nonhyperaged glasses characteristically exhibit a so-called boson peak—an enhancement in the density of vibrational states over that expected for a crystalline solid. As reported in Physical Review Letters, Miguel Ramos at the Autonomous University of Madrid, Spain, and his collaborators used $110$-million-year-old Spanish amber samples to investigate how the boson peak changes as the amber samples are subjected to thermal annealing, which effectively de-ages them. Previous studies suggested that the strength of the boson peak diminished with annealing, although the samples that were tested had only cooled for moderately short laboratory time scales.
Ramos and his team measured the specific heat of several amber samples, comparing specimens of pristine hyperaged amber, samples that had been annealed at temperatures below and around their glass transition temperature, and “rejuvenated” amber that had been heated well above its glass transition temperature. The annealed samples represented glasses with partially erased thermal histories, while the rejuvenated amber had had its $110$-million-year cooling cycle effectively erased. The authors found that the specific heats of all the samples were identical within the experimental errors for temperatures below $1$ kelvin. This finding implies that the boson peak and other thermodynamic properties remain fossilized in the glass—much like a trapped insect—and are unchanged by more than $100$ million years of aging. – Katherine Kornei
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A new analysis technique allows researchers to extract atomic-resolution holographic images of materials using a transmission electron microscope. Read More » | 2018-04-26 09:36:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 5, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5051347613334656, "perplexity": 4506.630894275382}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-17/segments/1524125948125.20/warc/CC-MAIN-20180426090041-20180426110041-00058.warc.gz"} |
http://mathoverflow.net/questions/40742/symmetric-functions-in-type-b-and-type-d?sort=newest | # Symmetric functions in type B and type D
It is well known that the symmetric groups have a very nice and explicit representation theory. This is in particular true when one works with the collection of all symmetric groups simultaneously, in which case the ring of virtual representations is the ring of symmetric functions. This has many advantages: it allows one to reduce hard questions in representation theory to formal combinatorial manipulations with symmetric functions; there is a lot of extra structure like inner product, outer product, and plethysm; it leads directly to the general theory of λ-rings, etc...
From the point of view of Coxeter groups there are two other infinite families of groups that seem natural to study from the same point of view, i.e. Bn and Dn. Is there an analogue of the theory of symmetric functions in this situation, i.e. a "nice" (i.e. highly structured and purely combinatorial) description of their rings of virtual representations?
-
If you want something like the Frobenius map from the ring of characters (with induced product) of $\bigcup_n S_n$ to the ring of symmetric functions, then something like this exists for any wreath product $G \wr S_n$, namely there is a Frobenius map from the ring of characters of $\bigcup_n G \wr S_n$ into a tensor product of copies of the ring of symmetric functions, one for each conjugacy class of $G$. And there's an inner product and Schur functions, power sum, etc. This is explained in Appendix B of Macdonald's Symmetric Functions and Hall Polynomials.
So this takes care of type B ($G = {\bf Z}/2$) but I'm not sure about type D.
- | 2014-03-12 06:01:21 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6109581589698792, "perplexity": 100.99596678818324}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-10/segments/1394021389272/warc/CC-MAIN-20140305120949-00044-ip-10-183-142-35.ec2.internal.warc.gz"} |
https://engineering.stackexchange.com/questions/23282/converting-grams-of-fuel-per-kwh-of-energy | # Converting grams of fuel per kWh of energy
Is there a database showing how many grams of a particular fuel generates how many Kilowatt hours of electricity?
• Google "levelized cost of electricity". The fuel cost and energy conversion efficiency are two of the primary drivers of LCoE. The size and engineering of the plant have a lot to do with final number, so you can expect a range of about a factor of three for many types of fuel. Lazard has published very detailed breakdowns of LCoE for many years. These include the fuel cost percentage of levelized cost Aug 17, 2018 at 14:20
• This is the Lazard document I was thinking of. I was about to walk out the door when I wrote the above comment. Lazard’s Levelized Cost of Energy Analysis, version 11.0. Some of the price and conversion numbers are on page 19. But look at the entire presentation. This is how it's done. Aug 17, 2018 at 19:20
The burning of the fuel generates thermal energy, i.e. hot gases.
The energy what it generates is the heat of combustion. Its ideal value is well known, depends mainly in the binding energy of the of the fuel and the combustion products.
Here comes the first problem: the burning is typically not perfect and it depends significantly on the circumstances (mainly temperature, pressure).
All the motors, generators, power plants convert this energy to electrical energy. It happens typically by the conversion to mechanical energy (typically rotating parts), and then the mechanical is converted to electrical energy.
All energy conversion using a different path have typically a very bad efficiency, typically below $20\%$.
The conversion of the thermal energy to mechanical or electrical energy is subject of the Second law of thermodynamics. It is the same Law which says that
• heat moves always from the warmer body to the colder, never back
• you can't build a ship which would cool the water of the sea and using its energy to move
• more technically, the maximal efficiency is $\frac{T_2-T_1}{T_2}$, for example if the $1000K$ burning products are cooled down to $300K$, then the maximal efficiency is $\approx 70\%$.
The conversion of the mechanical energy to electrical energy is much easier, because (ideally) there is no heat exchange, it happens by coils in generators, the efficiency is typically over $90\%$.
Practical generators have an efficiency between $30\%$ and $70\%$, depending on the circumstances.
Find the burning heat of the fuel (anywhere, it is public data), and find the efficiency of the device which burns it. After that, you need only some multiplications. | 2022-08-18 05:27:57 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7304888367652893, "perplexity": 751.601902385762}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-33/segments/1659882573163.7/warc/CC-MAIN-20220818033705-20220818063705-00463.warc.gz"} |
https://dsp.stackexchange.com/questions/47471/why-is-second-order-gaussian-called-laplacian-gaussian | # Why is second-order Gaussian called Laplacian Gaussian?
We usually use Laplacian of Gaussian as the filter for edge detection or blob detection. But the filter itself is essentially a second order Gaussian. So why do we call it Laplacian of Gaussian? Is there some other meanings behind it?
• HINT: A second order of what operation on a Gaussian? – A_A Feb 28 '18 at 11:41
## 2 Answers
Applying a Gaussian filter is a linear operation, also taking any type of derivative (finite difference) like Laplacian are also linear operations. Now considering the order of applying these operations doesn't matter (a property of convolution), you could combine them in many different ways, e.g. take Laplacian at first then take Gaussian or Gaussian first and Laplacian next, also you could apply Gausian on Laplacian or Laplacian on Gaussian and find a LoG Kernel, then apply the obtained Kernel on image once, which is more efficient in number of computations.
• More efficient in number of operations, but also much more precise. With the LoG you compute the exact Laplacian of the blurred image, rather than a finite difference approximation of the Laplacian. – Cris Luengo May 29 '18 at 18:15
I think it's calles LoG because as you wrote you take the second derivation of the gaussian filter.
A laplace operation is a derivation in 2 (or more) dimensions . In 2 dimensions it's what you do when creating the kernel. You derive the Gausskernel with the laplacian operation.
For more details on the laplacian operator see laplace operator wolfram alpha. | 2019-12-08 03:23:05 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8138654828071594, "perplexity": 814.6216625355663}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540504338.31/warc/CC-MAIN-20191208021121-20191208045121-00033.warc.gz"} |
https://www.taylorfrancis.com/books/9781315154473/chapters/10.1201/9781315154473-2 | chapter 1
Cantor and Peano type functions
ByGilbert W. Bassett Jr., Roger Koenker
Pages 20
It is widely known that one of the first set-theoretical results of Cantor was his discovery of the existence of a bijection between the set R of all real numbers and the corresponding product set R 2 = R × R $\mathbf{R}^{2} = \mathbf{R} \times \mathbf{R}$ (i.e., the Euclidean plane). For a time, Cantor did not believe that such a bijection exists and even wrote to Dedekind about his doubts in this connection. Of course, Cantor already knew of the existence of a bijection between the set N of all natural numbers and the product set N 2 = N × N $\mathbf{N}^2 = \mathbf{N} \times \mathbf{N}$ . A simple way to construct such a bijection is the following. We first observe that a function f : N → N \ { 0 } $f : \mathbf{N} \rightarrow \mathbf{N} \setminus \{0\}$ , defined by the formula f ( n ) = n + 1 $f(n) = n + 1$ for all n ∈ N $n \in \mathbf{N}$ , is a bijection between N and the set of all strictly positive natural numbers. Then, for each integer n > 0 $n> 0$ , we have a unique representation of n in the form n = 2 k ( 2 l + 1 ) $n = 2^{k}(2l + 1)$ , where k and l are some natural numbers. Now, define a function g : N \ { 0 } → N × N $g : \mathbf{N} \setminus \{0\} \rightarrow \mathbf{N} \times \mathbf{N}$ by the formula g ( n ) = ( k , l ) $g(n) = (k,l)$ for all n ∈ N \ { 0 } $n \in \mathbf{N} \setminus \{0\}$ . One can immediately check that g is a bijection, which also gives the corresponding bijection between N and N × N $\mathbf{N} \times \mathbf{N}$ . | 2019-10-14 01:24:10 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9150845408439636, "perplexity": 148.60065800640325}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986648481.7/warc/CC-MAIN-20191014003258-20191014030258-00116.warc.gz"} |
https://codingbobby.xyz/projects/chaotic-shapes/arn%C3%A9odo/ | # Arnéodo Attractor
In 1979 and a follow-up work in 1981, the physicist Alain Arnéodo who researches on fields like chemical chaos and fractal growth defined together with two colleagues a new type of chaotic systems1,2. This was done through a geometrical proof of Shil’nikov’s theorem which constrains a specific form of differential system so that their orbits become unstable.
The original set was:
$\dot{x} = \varrho\,x - \omega\,y + P(x,y,z)$ $\dot{y} = \omega\,x + \varrho\,y + Q(x,y,z)$ $\dot{z} = \lambda\,z + R(x,y,z)$
Where $$\lambda > -\varrho > 0$$.
## Renders
Differential system:
$\dot{x} = y$ $\dot{y} = z$ $\dot{z} = \alpha\,z - \beta\,x - \gamma\,y - x^3$
Constants:
$\alpha = -1$ $\beta = -5.5$ $\gamma = 3.5$
With different constants:
$\alpha = -0.45$ $\beta = -0.8$ $\gamma = 1.1$
1. P. Coullet, C. Tresser and A. Arneodo , 1979. "Transition to stochasticity for a class of forced oscillators". Phys. Lett. 72(4-5). doi:10.1016/0375-9601(79)90464-X
2. A. Arneodo, P. Coullet and C. Tresser , 1981. "Possible New Strange Attractors With Spiral Structure". Commun. Math. Phys. 79. doi:10.1007/BF01209312
🕸 💍 | 2022-12-08 03:52:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7401463985443115, "perplexity": 7372.647422416639}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711232.54/warc/CC-MAIN-20221208014204-20221208044204-00258.warc.gz"} |
http://www.all-science-fair-projects.com/science_fair_projects_encyclopedia/Doppler_effect | # All Science Fair Projects
## Science Fair Project Encyclopedia for Schools!
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# Doppler effect
The Doppler effect is the apparent change in frequency or wavelength of a wave that is perceived by an observer moving relative to the source of the waves. For waves, such as sound waves, that propagate in a wave medium, the velocity of the observer and the source are reckoned relative to the medium in which the waves are transmitted. The total Doppler effect may therefore result from both motion of the source and motion of the observer. Each of these effects is analyzed separately.
The effect was first proposed by Christian Andreas Doppler in 1842 in the monograph Über das farbige Licht der Doppelsterne und einige andere Gestirne des Himmels (On the colored light of the binary star and other stars). The hypothesis was tested for sound waves by the Dutch scientist Christoph Hendrik Diederik Buys Ballot in 1845. He confirmed that the sound's pitch was higher as the sound source approached him, and lower as the sound source receded from him. Hippolyte Fizeau discovered independently the same phenomenon on electromagnetic waves in 1848 (in France, the effect is sometimes called "effet Doppler-Fizeau").
It is important to realize that the frequency of the sounds that the source emits does not actually change. To understand what happens, consider the following analogy. Someone throws one ball every second in your direction. Assume that balls travel with constant velocity. If the thrower is stationary, you will receive one ball every second. However, if he is moving towards you, you will receive balls more frequently than that because there will be less spacing between the balls. The converse is true if the person is moving away from you. So it is actually the wavelength which is affected; as a consequence, the perceived frequency is also affected.
If the moving source is emitting waves with an actual frequency f0, then an observer stationary relative to the medium detects waves with a frequency f given by:
$f = f_0 \frac {v}{v - v_{s, r}}$
where v is the speed of the waves in the medium and vs, r is the speed of the source with respect to the medium (positive if moving towards the observer, negative if moving away) radial to the observer.
A similar analysis for a moving observer and a stationary source yields the observed frequency (the observer's velocity being represented as vo):
$f = f_0 \left(1 + \frac {v_0}{v} \right)$
The first attempt to extend Doppler's analysis to light waves was soon made by Fizeau. In fact, light waves do not require a medium to propagate and the correct understanding of the Doppler effect for light requires the use of the Special Theory of Relativity. See relativistic Doppler effect.
Contents
## Applications
### Everyday
The siren on a passing emergency vehicle will start out higher than its stationary pitch, slide down as it passes, and continue lower than its stationary pitch as it receedes from the observer. Astronomer John Dobson explained the effect thus:
"The reason the siren slides is because it doesn't hit you."
In other words, if the siren approached you directly, the pitch would remain constant (as vs, r is only the radial component) until the vehicle hit you, and then immediately jump to a new lower pitch. The difference between the higher pitch and rest pitch would be the same as the lower pitch and rest pitch. Because the vehicle passes by you, the radial velocity does not remain constant, but instead varies as a function of the angle between your line of sight and the siren's velocity:
$v_{s, r}=v_s\cdot \cos{\theta}$
where vs is the velocity of the object (source of waves) with respect to the medium, and θ is the angle between the object's forward velocity and the line of sight from the object to the observer.
### Astronomy
The Doppler effect for light has been of great use in astronomy. It has been used to measure the speed at which stars and galaxies are approaching to, or receding from us, i.e. the radial velocity. This is used to detect that an apparently single star is, in fact, a close binary and even to measure the speed of rotation of stars and galaxies.
The use of the Doppler effect for light in astronomy depends on the fact that the spectra of stars are not continuous. They show absorption lines at well defined frequencies that are correlated with the energies required to excite electrons in various elements from one level to another. The Doppler effect is recognizable in the fact that the absorption lines are not always at the frequencies that are obtained from the spectrum of a stationary light source. Since blue light has a higher frequency than red light, the spectral lines from an approaching astronomical light source show a blueshift and those of receding sources show a redshift.
Amongst the nearby stars, the largest radial velocities with respect to the Sun are +308 km/s (BD-15°4041 , also known as LHS 52, 81.7 light-years away) and -260 km/s (Woolley 9722 , also known as Wolf 1106 and LHS 64, 78.2 light-years away). Positive radial velocity means the star is receding from the Sun, negative that it is approaching.
The redshift effect that shows remote galaxies seem to be moving away from us is not caused by the Doppler effect, although many laymen believe it is. This effect is caused by the expansion of the universe, which is subtly different, and can be used to estimate the age of the universe (see redshift and Hubble's Law).
### Temperature measurement
Another use of the Doppler effect which is found mostly in astronomy, is the estimation of the temperature of a gas which is emitting a spectral line. Due to the thermal motion of the gas, each emitter can be slightly red or blue shifted, and the net effect is a broadening of the line. This line shape is called a Doppler profile and the width of the line is proportional to the square root of the temperature of the gas, allowing the Doppler-broadened line to be used to measure the temperature of the emitting gas.
The Doppler effect is also used in some forms of radar to measure the velocity of detected objects. A radar beam is fired at a moving target - a car, for example, as radar is often used by police to detect speeding motorists - as it recedes from the radar source. Each successive wave has to travel further to reach the car, before being reflected and re-detected near the source. As each wave has to move further, the gap between each wave increases, increasing the wavelength. In some situations, the radar beam is fired at the moving car as it approaches, in which case each successive wave travels a lesser distance, decreasing the wavelength. In either situation, calculations from the Doppler effect accurately determine the car's velocity.
### Medical imaging
An echocardiogram can within certain limits produce accurate assessment of the direction of blood flow and the velocity of blood and cardiac tissue at any arbitrary point using the doppler effect. One of the limitations is that the ultrasound beam should be as parallel to the blood flow as possible. Velocity measurements allows assessment of cardiac valve areas and function, any abnormal communications between the left and right side of the heart, any leaking of blood through the valves (valvular regurgitation), and calculation of the cardiac output.
However, "Doppler" has become synonymous with "velocity measurement" in medical imaging. But in many cases it is not the frequency shift (Doppler shift) of the received signal that is measured, but the phase shift (when the received signal arrives).
Velocity measurements of blood flow is also used in other fields of medical ultrasonography, such as obstetric ultrasonography and neurology.
### Flow measurement
Instruments such as the Laser Doppler Velocimeter (LDV), and Acoustic Doppler Velocimeter (ADV) have been developed to measure velocities in a fluid flow. The LDV and ADV emit a light or acoustic beam, and measure the doppler shift in wavelengths of reflections from particles moving with the flow. This technique allows non-intrusive flow measurements, at high precision and high frequency. | 2013-05-23 13:29:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 3, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6595309972763062, "perplexity": 603.5517797564421}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703317384/warc/CC-MAIN-20130516112157-00086-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://ssconlineexam.com/onlinetest/ssc-cgl-tier-1/english-comprehension/ec-test-92 | # ssc cgl tier 1 :: english comprehension :: ec test 92
## Home ssc cgl tier 1 / english comprehension Questions and Answers
1 .In Question , out of the four alternatives, choose the one which can be substituted for the given words/sentences and indicate it by blackening the appropriate oval in the Answer Sheet.
An imaginary name assumed by an author for disguise
Pseudonym
Pen - name
Nick name
Homonym
2 . In Question , four alternative are given for the Idiom/Phrase in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase and mark it in the Answer Sheet.
To lose one's bearings
to become sick and tired
to lose one's strength
to be uncertain of one's position
to become hopeless
3 . In Question , four alternative are given for the Idiom/Phrase in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase and mark it in the Answer Sheet.
To see eye to eye
to be annoyed
to be unhappy
to be incomplet
to agree
4 . In Question , four alternative are given for the Idiom/Phrase in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase and mark it in the Answer Sheet.
To pick holes
to cut some part of an item
to find some reason to quarrel
to find fault
to destroy something
5 . In Question , four alternative are given for the Idiom/Phrase in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase and mark it in the Answer Sheet.
Bon voyage
in absence
in presence
free journey
a good journey to you
6 . In Question , four alternative are given for the Idiom/Phrase in the sentence. Choose the alternative which best expresses the meaning of the Idiom/Phrase and mark it in the Answer Sheet.
To strain every nerve
to make utmost efforts
to feel weak and tired
to be dilligent workers
to be methodical in work
7 . In Question, in the following passages some of the words have been left out. Read the passages carefully and choose the correct answer to each question out of the four alternative and fill in the blanks
The millions of people from different parts of the world, who have settled in America, have all contributed something to American English. Though in the main ...$(1)$...to the new ways of life they ...$(2)$...in the new country, they could not help leaving some ...$(3)$...of their language of English....$(4)$...drawing upon these many elements which make ... $(5)$ ... American culture, Americans have made their kind of English a melting pot in miniature
$(1)$
confining
connecting
confirming
conforming
8 . In Question, in the following passages some of the words have been left out. Read the passages carefully and choose the correct answer to each question out of the four alternative and fill in the blanks
The millions of people from different parts of the world, who have settled in America, have all contributed something to American English. Though in the main ...$(1)$...to the new ways of life they ...$(2)$...in the new country, they could not help leaving some ...$(3)$...of their language of English....$(4)$...drawing upon these many elements which make ... $(5)$ ... American culture, Americans have made their kind of English a melting pot in miniature
$(2)$
acquired
traced
sought
found
9 . In Question, in the following passages some of the words have been left out. Read the passages carefully and choose the correct answer to each question out of the four alternative and fill in the blanks
The millions of people from different parts of the world, who have settled in America, have all contributed something to American English. Though in the main ...$(1)$...to the new ways of life they ...$(2)$...in the new country, they could not help leaving some ...$(3)$...of their language of English....$(4)$...drawing upon these many elements which make ... $(5)$ ... American culture, Americans have made their kind of English a melting pot in miniature
$(3)$
identity
element
mark
sign
10 . In Question, in the following passages some of the words have been left out. Read the passages carefully and choose the correct answer to each question out of the four alternative and fill in the blanks
The millions of people from different parts of the world, who have settled in America, have all contributed something to American English. Though in the main ...$(1)$...to the new ways of life they ...$(2)$...in the new country, they could not help leaving some ...$(3)$...of their language of English....$(4)$...drawing upon these many elements which make ... $(5)$ ... American culture, Americans have made their kind of English a melting pot in miniature
$(4)$
by
in
on
from | 2022-01-26 15:24:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34463250637054443, "perplexity": 2675.0996714056605}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320304954.18/warc/CC-MAIN-20220126131707-20220126161707-00180.warc.gz"} |
https://deepai.org/publication/distributed-parameter-estimation-in-randomized-one-hidden-layer-neural-networks | DeepAI
# Distributed Parameter Estimation in Randomized One-hidden-layer Neural Networks
This paper addresses distributed parameter estimation in randomized one-hidden-layer neural networks. A group of agents sequentially receive measurements of an unknown parameter that is only partially observable to them. In this paper, we present a fully distributed estimation algorithm where agents exchange local estimates with their neighbors to collectively identify the true value of the parameter. We prove that this distributed update provides an asymptotically unbiased estimator of the unknown parameter, i.e., the first moment of the expected global error converges to zero asymptotically. We further analyze the efficiency of the proposed estimation scheme by establishing an asymptotic upper bound on the variance of the global error. Applying our method to a real-world dataset related to appliances energy prediction, we observe that our empirical findings verify the theoretical results.
• 6 publications
• 38 publications
02/22/2019
### On Parameter Estimation of Hidden Ergodic Ornstein-Uhlenbeck Process
We consider the problem of parameter estimation for the partially observ...
08/11/2015
### Are Slepian-Wolf Rates Necessary for Distributed Parameter Estimation?
We consider a distributed parameter estimation problem, in which multipl...
09/10/2013
### Exponentially Fast Parameter Estimation in Networks Using Distributed Dual Averaging
In this paper we present an optimization-based view of distributed param...
03/30/2020
### Supplementary Material for CDC Submission No. 1461
In this paper, we focus on the influences of the condition number of the...
03/30/2020
### On Effects of Condition Number of Regression Matrix upon Hyper-parameter Estimators for Kernel-based Regularization Methods
In this paper, we focus on the influences of the condition number of the...
09/23/2018
### On the Information in Extreme Measurements for Parameter Estimation
This paper deals with parameter estimation from extreme measurements. Wh...
11/10/2016
### Distributed Estimation and Learning over Heterogeneous Networks
We consider several estimation and learning problems that networked agen...
## I Introduction
Supervised learning is a fundamental machine learning problem, where given input-output data samples, a learner aims to find a mapping (or function) from inputs to outputs [1]
. A good mapping is one that can be used for prediction of outputs corresponding to previously unseen inputs. Recently, deep neural networks have dominated the task of supervised learning in various applications, including computer vision
[2], speech recognition [3], robotics [4], and biomedical image analysis [5]. These methods, however, are data hungry and their application to domains with few/sparse labeled samples remains an active field of research [6]. An alternative effective method for supervised learning is shallow architectures with one-hidden-layer. This architecture was motivated by the classical results of Cybenko [7] and Barron [8], showing that (under some technical assumptions) one can use sigmoidal basis functions to approximate any output that is a continuous function of the input. These results later motivated researchers to develop algorithmic frameworks to leverage shallow networks for data representation. The seminal work of Rahimi and Recht is a prominent point in case [9]. In their approach, the nonlinear basis functions are selected using Monte-Carlo sampling with a theoretical guarantee that the approximated function converges asymptotically with respect to the number of data samples and basis functions.
The problem of function approximation in supervised learning (both in shallow and deep neural networks) is often formulated via empirical risk minimization [1], which amounts to solving an optimization problem over a high-dimensional parameter. Due to the computational challenges associated with high-dimensional optimization, an appealing solution turns out to be decentralized training of neural networks [10]. On the other hand, recent advancement in distributed computing within control and signal processing communities [11, 12, 13, 14, 15, 16] has provided novel decentralized techniques for parameter estimation over multi-agent networks. In these scenarios, each individual agent receives partially informative measurements about the parameter and engages in local communications with other agents to collaboratively accomplish the global task. A crucial component of these methods is a consensus protocol [17], allowing collective information aggregation and estimation. Distributed algorithms gained popularity due to their ability to handle large data sets, low computational burden over agents, and robustness to failure of a central agent.
Motivated by the importance of distributed computing in high-dimensional parameter estimation, in this paper, we consider distributed parameter estimation in randomized one-hidden-layer neural networks. A group of agents sequentially obtain low-dimensional measurements of the parameter (in various locations at different randomized frequencies). Despite the parameter being partially observable to each individual agent, the global spread of measurements is informative enough for a collective estimation. We propose a fully distributed update where each agent engages in local interactions with its neighboring agents to construct iterative estimates of the parameter. The update is akin to consensus+innovation algorithms in the distributed estimation literature [11, 13, 18].
Our main theoretical contribution is to characterize the first and second moments of the global estimation error. In particular, we prove that the distributed update provides an asymptotically unbiased estimator of the unknown parameter when all the randomness is expected out, i.e., the first moment of the global error converges to zero asymptotically. This result also allows us to characterize the convergence rate and derive an optimal innovation rate to speed up the convergence. We further analyze the efficiency of the proposed estimation scheme by establishing an asymptotic upper bound on the variance of the global error. We finally simulate our method on a real-world data related to appliances energy prediction, where we observe that our empirical findings verify the theoretical results.
## Ii Problem Statement
Notation: We adhere to the following notation table throughout the paper:
set for any integer
transpose of vector
identity matrix of size
vector of all ones with dimension
vector of all zeros
-norm operator
-th largest eigenvalue of matrix
expectation operator
spectral radius of matrix
trace operator
is positive semi-definite
The vectors are in column format. Boldface lowercase variables (e.g., ) are used for vectors, and boldface uppercase variables (e.g., ) are used for matrices.
### Ii-a One-Hidden-Layer Neural Networks: The Centralized Problem
Let us consider a regression problem of the form
y=f(x)+v,
where is the output, is the input, and is a the noise term with zero mean and constant variance. The objective is to find the unknown mapping (or function) based on available input-output pairs . Various regression methods assume different functional forms to approximate
. For example, in linear regression, the input-output relationship is assumed to follow a linear model.
In this work, we focus on one-hidden-layer neural networks [7], where the approximated function is a nonlinear function of the input, and
ˆf(x)=M∑l=1θlϕ(x,ωl), (1)
where is called a basis function (or feature map) parameterized by . In the above model, the parameters and are unknown and should be learned from data (i.e., input-output pairs). The underlying intuition behind this model is that the feature map transforms the original data from dimension to , where often time we have . Since the new space has a higher dimension, it provides more flexibility for approximation of the unknown function (as opposed to a linear model that is restrictive). It turns out that approximations of form (1) are dense in the space of continuous functions [7], i.e., they can be used to approximate any continuous function (on the unit cube).
However, from an algorithmic perspective, learning both and is computationally expensive. For a nonlinear feature map (e.g., cosine feature map), the problem is indeed non-convex and thus hard to solve. An alternative approach was proposed in [9] where one-hidden-layer neural networks are thought as Monte-Carlo approximations of kernel expansions. In particular, if we assume that
is a random variable with a support
, the corresponding kernel can be obtained via [19]
k(x,x′)=∫Ωϕ(x,ω)ϕ(x′,ω)dτ(ω). (2)
Hence, if are independent samples from , the approximated kernel expansion corresponds to (1) and learning becomes a convex optimization problem with a modest computational cost. are then called random features in this model.
One such example is using cosine feature map to approximate a Gaussian kernel with unit width. In this case, (1) will be as follows
ˆf(x)=M∑l=1θl√2cos(ν⊤lx+bl), (3)
where
come from a multi-variate Gaussian distribution
and
come from a uniform distribution
. In this paper, we will focus on the approximated function of form (3) and propose a distributed algorithm for learning the parameter .
### Ii-B Local Measurements in Multi-agent Networks
The proposed scenario in the previous section was centralized in the sense that the estimation task was done only by one agent that has all the data . In this section, we propose an iterative distributed scheme where we have a network of agents, each of which has access to a subset of data. In particular, agent has access to only data points at each iteration.
###### Assumption 1
Without loss of generality, we assume each agent observes the same number of data points at each time, i.e., throughout the paper.
This assumption is only for the sake of presentation clarity. Our main results can be extended to the case where different agents have various numbers of measurements.
Now, in the distributed model, the observation matrix at time will be as follows
Hi,t=⎡⎢⎣ϕ(x1,i,t,ω1,i,t)…ϕ(x1,i,t,ωM,i,t)………ϕ(xc,i,t,ω1,i,t)…ϕ(xc,i,t,ωM,i,t)⎤⎥⎦, (4)
with any agent having access to . We then have the following measurement model
yi,t=Hi,tθ+vi,t,
where is the unknown parameter that needs to be learned, and denotes the observation noise at agent . The above local measurement model can be interpreted as iteratively collecting low-dimensional measurements of parameter at different locations using distinct frequencies.
We follow the general assumptions of zero mean and constant variance on the noise term, i.e., we have and . We further denote by the estimate of for agent at time .
### Ii-C Multi-agent Network Model
The interactions of agents, which in turn defines the network, is captured with the matrix . Formally, we denote by , the -th entry of the matrix . When , agent communicates with agent . We assume that is symmetric, doubly stochastic with positive diagonal elements. The assumption simply guarantees the information flow in the network. Alternatively, from the technical point of view, we respect the following hypothesis.
###### Assumption 2
(connectivity) The network is connected, i.e., there is a path from any agent to another agent .
The assumption implies that the Markov chain
is irreducible and aperiodic, thus having a unique stationary distribution, i.e.,
is the unique (unnormalized) left eigenvector corresponding to
. It also entails that is unique, and the other eigenvalues of are less than unit in magnitude [20].
### Ii-D Distributed Estimation Update
To construct an iterative estimate of the parameter , each agent at time performs the following distributed update
^θi,t+1 =n∑j=1Pij^θj,t+αH⊤i,t(yi,t−Hi,t^θi,t), (5)
where is the step size. The update is akin to consensus+innovation schemes in the distributed estimation literature [11, 13, 18], and we analyze this update in Section III in the context of one-hidden-layer neural networks. Intuitively, the first part of the update (consensus) allows agents to keep their estimates close to each other, and the second part (innovation) takes into account the new measurements.
## Iii Main Theoretical Results
In this section, we provide our main theoretical results. We show that the local update (5) is an asymptotically unbiased estimator of the global parameter . Based on this result, we characterize the optimal step-size to obtain the fastest convergence rate. We then prove that the asymptotic second moment of the collective estimation error is bounded.
### Iii-a First Moment
Let us define the local error for each agent as
ei,t≜^θi,t−θ. (6)
Subtracting from both sides of the local update (5), we can write the iterative local error process as follows
(7)
Stacking the local errors in a vector, we denote the global error by
et≜[e⊤1,t,…,e⊤n,t]⊤. (8)
We now characterize the global error process with the following proposition.
###### Proposition 1
Given Assumptions 1-2, the expected global error can be expressed as an LTI system that takes the form
E[et]=QE[et−1],
where
Q=P⊗IM−αcIMn, (9)
and denotes the Kronecker product. The expectation is taken over the stochasticity of and .
The proof of proposition 1 is given in the Appendix. It shows that the agents will collectively generate estimates of the parameter that are asymptotically unbiased as long as the spectral radius of is less than 1.
### Iii-B Step Size Tuning
According to Proposition 1, the convergence rate depends on the choice of the step size. If one wants to speed up the convergence rate of the process, it is necessary to shrink the spectral radius of as much as possible. This corresponds to solving the following problem
α⋆=argminα>0{max{|λ1(Q)|,|λMn(Q)|}}. (10)
According to Assumption 2, is the unique (un-normalized) eigenvector of the matrix associated with , because . It is then immediate that
λ1(Q)=1−αc. (11)
On the other hand, we have that
λMn(Q)=λn(P)−αc. (12)
Plotting and in terms of , we can notice that the optimal would occur exactly where , in which case we have the following relationship
αc−λn(P)=1−αc⇒α⋆=1+λn(P)2c. (13)
Plugging the optimal step size (13) into (11) and (12), we get
|λ1(Q)|=|λMn(Q)|=1−λn(P)2,
and achieve the fastest convergence rate. This result suggests that when is close to one, we have the fastest convergence rate. Since is the smallest eigenvalue of , this would also imply that other eigenvalues are close to one in this scenario since . Intuitively, this indicates that is close to identity and agents have high self-reliance, i.e., they do not rely highly on their neighbors. Indeed, since otherwise the connectivity constraint is violated. Notice that in this paper, we are not concerned with network design, i.e., we assume that is given, and we can choose based on (13) accordingly.
### Iii-C Asymptotic Second Moment
To capture the efficiency of the collective estimation, we should also study the variance of the error, which (asymptotically) amounts to the second moment in view of Proposition 1. In the next theorem, we present an asymptotic upper bound on the second moment for a feasible range of step size .
###### Theorem 2
Given Assumptions 1-2, and the further assumption that and , the expected second moment of the estimation error is bounded as follows
limt→∞E[e⊤tet]≤αMnσ2v2−αc(M+1),
for any . The expectation is taken over the stochasticity of random features and observation noise .
The proof of theorem 2 is given in the Appendix. It shows that the (asymptotic) expected second moment of the estimation error is bounded by a finite value that scales linearly with respect to the number of agents for a certain range of step size . It also suggests that the optimal step size in (13) will work whenever .
## Iv Numerical Experiments
We now provide empirical evidence in support of our algorithm by applying it to a regression dataset on UCI Machine Learning Repository. In this dataset, the input includes a number of attributes including temperature in kitchen area, humidity in kitchen area, temperature in living room area, humidity in laundry room area, temperature outside, pressure, etc.. The regression model aims at representing appliances energy use in terms of these features. More details about this dataset can be found in [21] as well as the UCI Machine Learning Repository. We randomly choose 16000 observations out of its 19735 observations for our simulation.
We consider observation matrices of form (4), where the bases are cosine functions as follows
ϕ(x,ω)=ϕ(x,ν,b)=√2cos(x⊤ν+b), (14)
as described in section II-A where come from a multi-variate Gaussian distribution and come from a uniform distribution . Without loss of generality, we set , i.e., we use five basis functions in the approximation model (3). One can consider other values for and perform cross-validation to find the best one, but this is outside of the scope of this paper, as our focus is on estimation rather than model selection.
Network Structure: We consider a network of agents. Each agent has access to observation matrix with data points at time . Also, each agent is connected to agents (with a circular shift for any number outside of the range ). The matrix is such that agent is connected to itself with weight , connected to agents with weight , and connected to agents with weight . The smallest eigenvalue of our network is less than , so according to the step size constraint in Theorem 2, we can use the optimal step size (13) for this simulation. Therefore, the step size is set to be as in (13).
Benchmark: Since this dataset is from real-world and the ground truth value is unknown, we consider the solution of the centralized problem as the baseline. The local error at time is then calculated as the difference between local estimates and the centralized estimates as given in (6). We run update (5) for iterations such that the process reaches a steady state. To verify our results, we need to repeat the update process using Monte-Carlo simulations on random features to estimate the expectations.
Performance: We visualize the error process in Proposition 1 by presenting the plot of norm- of the expected global error, i.e., the norm- of given in Proposition 1 at . The vertical axis in Fig. 1 represents the average global error obtained by repeating Monte-Carlo simulations to form an estimate of the expected global error. The horizontal axis shows the number of Monte-Carlo simulations indexed by where . As the number of Monte-Carlo simulations increases, the norm- of the average global error will converge to the norm- of the expected global error in Proposition 1. As we can observe, the estimation of the expected global error converges to zero verifying that agents form asymptotically unbiased estimators of the parameter.
We next plot the expected norm- square of global error, i.e., given in Theorem 2 at . The vertical axis in Fig. 2 represents the norm- square of the global error averaged over Monte-Carlo simulations. The horizontal axis shows the number of Monte-Carlo simulations index by where . As the number of Monte-Carlo simulations increases, the average norm- square of the global error will converge to the expected norm- square of the global error in Theorem 2. The expected norm- square of the global error is upper bounded by according to Theorem 2 for this simulation set up and as we can observe, the average norm- square of global error is always less than verifying the accuracy of the upper bound in Theorem .
## V Conclusion
In this paper, we considered a distributed scheme for parameter estimation in randomized one-hidden-layer neural networks. A network of agents exchange local estimates of the parameter, formed using partial observations, to collaboratively identify the true value of the parameter. Our main contribution is to characterize the behavior of this distributed estimation scheme. We showed that the global estimation error is asymptotically unbiased and its second moment is finite under mild assumptions. Interestingly, our results shed light on the interplay of step size and network structure, which can be used for optimal design in practice. We verified this empirically by applying our method to a real-world data. Future directions include studying the estimation problem when the parameter has some dynamics [22] or the random frequencies are generated from a time-varying distribution. Due to the non-stationary nature of the problem in these two cases, the theoretical analysis becomes challenging and interesting to explore.
## Appendix
For presentation clarity, we use the following definitions in the proofs:
Ut ≜diag[H⊤1,tH1,t,…,H⊤n,tHn,t] Ei,t ≜H⊤i,tvi,t Et ≜[E⊤1,t,…,E⊤n,t]⊤. (15)
### V-a Proof of Proposition 1
To prove Proposition 1, we first need to show that
E[H⊤i,tHi,t]=cIM, (16)
for any . Recall that where and , and thus
E[ϕ(x,ω)]=0,
since cosine is a periodic function. Therefore, we can conclude that for any and ,
E[ϕ(x,ω)ϕ(x′,ω′)]=E[ϕ(x,ω)]E[ϕ(x′,ω)]=0, (17)
whenever is independent from . Notice that given the observation model (4), the -th entry of the matrix can be written as
[H⊤i,tHi,t]pq=c∑j=1ϕ(xj,i,t,ωp)ϕ(xj,i,t,ωq). (18)
When , we have according to (17); otherwise, , since for any we have
E[ϕ2(x,ωp)]=k(x,x)=exp(−∥x−x∥22)=e0=1.
Hence, , entailing that
E[Ut]=cIMn, (19)
in view of (15). Following the lines of the proof of Lemma 1 in [18], the error process can be expressed as the following
et+1=Q′tet+αEt, (20)
where
Q′t=P⊗IM−αUt. (21)
Taking expectation over random features on both sides and noting (19), we have
Q≜E[Q′t]=P⊗IM−αE[Ut]=P⊗IM−αcIMn.
Recalling (15), we can also immediately see from the zero-mean assumption on the noise that for every . Combining this with above and returning to (20) will finish the proof of Proposition 1.
### V-B Proof of Theorem 2
To prove Theorem 2, we first need to show a recursive relationship for the error process based on (20) where
E[e⊤t+1et+1] =E[(Q′tet+αEt)⊤(Q′tet+αEt)] (22) =E[e⊤tQ′t⊤Q′tet]+α2E[E⊤tEt] ≤ρ(E[Q′t⊤Q′t])E[e⊤tet]+α2E[E⊤tEt] =λ1(E[Q′t⊤Q′t])E[e⊤tet]+α2E[E⊤tEt],
where we used the fact , resulting in zero cross-terms in the second line. To further bound , let us recall (21). As and are both symmetric and , we have that
E[Q′t⊤Q′t]=E[(P⊗IM)(P⊗IM)−αUt(P⊗IM) −(P⊗IM)αUt+α2U2t] =(P⊗IM)(P⊗IM)−2αc(P⊗IM)+α2E[U2t].
Now, we apply Lemma 3 to bound above as
E[Q′t⊤Q′t] +α2(M+1)c2IMn =P2⊗IM−2αc(P⊗IM) +α2(M+1)c2IMn =(P2−2αcP)⊗IM+α2(M+1)c2IMn.
Then, the largest eigenvalue of can be bounded as follows
λ1(E[Q′t⊤Q′t]) (23) ≤λ1((P2−2αcP)⊗IM+α2(M+1)c2IMn) =λ1(P2−2αcP)+α2(M+1)c2.
Now, let denote the kernel matrix formed with measurements at agent at time where its -th entry is . Recalling (15), we can then bound the additive term in the recursive relation (22) as follows
α2E[E⊤tEt]= α2E[n∑i=1E⊤i,tEi,t] (24) = α2E[n∑i=1v⊤i,tHi,tH⊤i,tvi,t] = α2ME[n∑i=1v⊤i,tKi,tvi,t] = α2Mn∑i=1Tr[Ki,tE[vi,tv⊤i,t]] = α2Mn∑i=1Tr[Ki,t]σ2v=α2cMnσ2v.
Letting
Φa ≜λ1(P2−2αcP)+α2(M+1)c2 Φb ≜α2cMnσ2v, (25)
and using (23) and (24), we can re-write the recursive relation in (22) as
E[e⊤t+1et+1]≤ΦaE[e⊤tet]+Φb. (26)
We can find the feasible range of through the inequality which ensures that the recursive process (26) will converge.
First, we have the following fact
λ1(P2−2αcP)=max{1−2αc,λ2n(P)−2αcλn(P)}.
One can show that when and otherwise.
For the case when , we have the following
Φa<1 ⟺ 1−2αc+α2c2(M+1)<1 ⟺ α2c2(M+1)<2αc ⟺ α<2c(M+1).
Therefore, given , we have that
E[e⊤t+1et+1] ≤ΦaE[e⊤tet]+Φb ≤ΦtaE[e⊤1e1]+Φb(Φt−1a+...+Φa+1) =ΦtaE[e⊤1e1]+Φb(1−Φta)1−Φa.
This upper bound will converge to as , and noting definitions of and in (25), we derive the upper bound in the statement of Theorem 2.
For the case when , we have the following
Φa<1 (27) ⟺ λ2n(P)−2αcλn(P)+α2c2(M+1)<1 ⟺ (λ2n(P)−1)−2αcλn(P)+α2c2(M+1)<0.
Considering the LHS of the last line in (27) as a quadratic function of , one can show that
αc<2λn(P)+√4(M+1)−4Mλ2n(P)2(M+1),
must be true for (27) to hold. Therefore, the following must be true as well
2λn(P)+√4(M+1)−4Mλ2n(P)2(M+1) (28) >1+λn(P)2 ⟺ (2−(M+1))λn(P) +√4(M+1)−4Mλ2n(P) −(M+1)>0.
Viewing the LHS of (28) as a function of , one can immediately verify that the function is always non-positive for any as long as . Therefore, contradicts . The only feasible region for is , finishing the proof of Theorem 2.
### V-C Statement and Proof of Lemma 3
###### Lemma 3
Under same assumptions as Theorem 2,
E[U2t]⪯c2(M+1)IMn, (29)
where is defined in (15).
In the proof, we omit the time index and agent index for presentation clarity, i.e., we denote by , by for any , and by for any , respectively. We will show that is a diagonal matrix and all of its diagonal entries are upper bounded by .
Let us start by observing that the -th entry of the matrix (for any agent) can be written as
M∑j=1(c∑k=1ϕ(ωp,xk)ϕ(ωj,xk)c∑k′=1ϕ(ωj,xk′)ϕ(ωq,xk′)), (30)
We now consider a single term in the previous summation:
ϕ(ωp,xk)ϕ(ωj,xk)ϕ(ωj,xk′)ϕ(ωq,xk′), (31)
and analyze its expectation case by case.
Case 1: and ( and ).
Since and are independent, the expectation of the product of these two functions is zero as previously discussed in (17), so (31) would be zero.
Case 2: and ( or ).
In this case, three out of four product terms in (31) will include or . Then, the expectation of the other term will be zero again as cosine is periodic. Thus, the expectation of (31) will still be zero.
Case 3: and .
Now, (31) will become a product of two expectations of unbiased approximates of the kernel function in view of (2). Thus, the expectation of (31) will become which is less than 1. There are terms of this form in (30), which implies that it is upper bounded by .
Case 4: .
In this case, (31) becomes
ϕ2(ωq,xk)ϕ2(ωq,xk′).
So, the expectation of (31) with will become the following where and :
E[ϕ2(ωq,xk)ϕ2(ωq,xk′)] =4 E[cos2(ν⊤qxk+bq)cos2(ν⊤qxk′+bq)] =E[(cos(ν⊤q2xk+2bq)+1)(cos(ν⊤q2xk′+2bq)+1)] =E[1+cos(ν⊤q2xk+2bq)cos(ν⊤q2xk′+2bq)] +E[cos(ν⊤q2xk+bq)] +E[cos(ν⊤q2xk′+bq)] =E[1+cos(ν⊤q2xk+2bq)cos(ν⊤q2xk′+2bq)]≤2,
simply because cosine is bounded by 1, and its integral over is equal to zero. Notice that there are terms like above for every , and thus for a specific , the summation of term (31) where is upper bounded by .
We can then conclude that the expectation of term (30) is nonzero only for , and the diagonal entries of are upper bounded by . Recalling the definition of from (15) and combining it with the fact that
E[H⊤i,tHi,tH⊤i,tHi,t]⪯(M+1)c2IM,
concludes the proof.
## Acknowledgments
We gratefully acknowledge the support of Texas A&M Triads for Transformation (T3) program.
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• [22] S. Shahrampour, S. Rakhlin, and A. Jadbabaie, “Online learning of dynamic parameters in social networks,” in Advances in Neural Information Processing Systems, 2013. | 2023-02-09 11:33:59 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.848967969417572, "perplexity": 654.9294740069573}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764499966.43/warc/CC-MAIN-20230209112510-20230209142510-00697.warc.gz"} |
http://tex.stackexchange.com/questions/67178/function-arguments-in-algorithmicx | # Function arguments in algorithmicx
I have a question about function arguments in the algorithmicx package. The following code works:
\documentclass{article}
\usepackage{algpseudocode}
\usepackage{algorithm}
\begin{document}
\begin{algorithm}
\begin{algorithmic}[5]
\Function{f}{$\tau$ , $\delta$}
%\Function{f}{$\overrightarrow{\tau}$, $\overrightarrow{\delta}$}
\State etc
\EndFunction
\end{algorithmic}
\end{algorithm}
\end{document}
But if I change the arguments to:
\Function{f}{$\overrightarrow{\tau}$ , $\overrightarrow{\delta}$}
I get an apparently unrelated error:
! Illegal parameter number in definition of \@gtempa.
Do you know any solutions or workarounds for this situation?
-
Please edit your question so the code is a full document using any packages. I tried \usepackage{algorithmicx} but got ! Undefined control sequence. l.11 \Function – David Carlisle Aug 14 '12 at 20:11
@DavidCarlisle I edited the question with a complete example code; I hope that's OK. – Gonzalo Medina Aug 14 '12 at 20:16
thanks! that's better:-) – David Carlisle Aug 14 '12 at 20:17
I'm sorry for the incomplete example, and thank you for the edit. – Rares T Aug 15 '12 at 10:17
If in doubt, try \protect...
\Function{f}{$\protect\overrightarrow{\tau}$, $\protect\overrightarrow{\delta}$}
"If in doubt, try \protect...". I will add this to my list of memorable quotes. – Boris Aug 14 '12 at 21:55 | 2015-07-08 00:07:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9550081491470337, "perplexity": 6098.482842080869}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375635143.91/warc/CC-MAIN-20150627032715-00190-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://schoollearningcommons.info/question/is-1-3-a-zero-of-p-2-cube-3-swuare-6-7-eplaon-23214033-75/ | ## is 1/3 a zero of p(x) = 2x cube + 3x swuare – 6x + 7 explaon
Question
is 1/3 a zero of p(x) = 2x cube + 3x swuare – 6x + 7 explaon
in progress 0
4 weeks 2021-08-13T06:54:13+00:00 1 Answer 0 views 0
1. Step-by-step explanation:
no | 2021-09-17 18:42:29 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8291059732437134, "perplexity": 7099.678367617298}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780055775.1/warc/CC-MAIN-20210917181500-20210917211500-00139.warc.gz"} |
https://github-wiki-see.page/m/GEOS-ESM/MAPL/wiki/PFIO%3A-a-High-Performance-Client-Server-I-O-Layer | Introduction
GEOS-5 related applications (such as GEOSgcm, GEOSctm, GEOSldas, GCHP, etc.) produce a lot of output files that consist of several file collections that individually have their own set of fields and are created at different time frequencies (every hour, three hours, etc.). As the model resolution increases, the amount of data generated significantly grows, and may become overwhelming for the file system especially if one processor is in charge of reading in or writing out all files. Running applications on more nodes increases the aggregate memory bandwidth and flops/s but does not necessary improve the I/O performance.
PFIO, a subcomponent of the MAPL package, is a parallel I/O tool that was designed to facilitate the production of model netCDF output files (organized in collections) and to efficiently use available resources in a distributed computing environment. PFIO asynchronously creates output files therefore allowing the model to proceed with calculations without waiting for the I/O tasks to be completed. This allows the applications to achieve achieve higher effective write speeds, and leads to a decrease of the overall model integration time. The goal of PFIO is for models to spend more time doing calculations instead of waiting on I/O activity.
Typically, with PFIO, the available nodes (cores) are split into two groups:
• The computing nodes that are reserved for model calculations. The nodes contain cores that are called Clients.
• The I/O nodes that are grouped to form the PFIO Server. For reading files, we use the name Iserver and when we create outputs, we use instead Oserver. In this presentation, we will focus only on the Oserver.
All the file collections to be generated by the MAPL HISTORY (MAPL_History) gridded component are routed through the PFIO server that will distribute the output files to the I/O nodes based on the user's configuration set at run time (we will explain more how to configure PFIO). In its basic configuration, the compute nodes and I/O nodes can overlap. In such a case, PFIO is set to run the standard-like Message Passing Interface (MPI) root processor configuration (where IO are completed before calculations resume). This default is efficient at low resolution and/or with few file collections.
In this document, we explain when and how to configure the PFIO Server to run on separate resources. We also provide general recommendations on how to properly configure the PFIO Server in order to get the best possible performance. It is important to note that it is up to users to run their application multiple times to determine the optimal PFIO Server configuration.
Types of Oserver
Simple Server or MpiServer Class
This particular configuration can be seen as the case where there is no distinction between the compute nodes and the IO nodes.
The PFIO Server runs on the same MPI resources as the application. Each time HISTORY is executed, it will not return until the process of writing the data into files (at that particular HISTORY execution) is completed. All the data aggregation and writing is done on the same MPI tasks as the rest of the application. The model calculations cannot proceed until all output procedures for that step are finished. There is no asynchrony or overlap between computations and outputs in this case.
Internally, here are the different PFIO Server steps:
• The Clients send the data to Oserver.
• All processors in Oserver would coordinate to create different shared memory windows for different collections.
• The processors use one-sided MPI_PUT to send the data to the shared memory.
• Different collections are written by different processors. Those writing processors are distributed among nodes as evenly as possible.
• All the other processors have to wait for the writing processors to finish their jobs before responding to Clients’ next round of requests.
This configuration of PFIO is suitable when the model runs at low resolutions or if there are a few file collections to produce. If you are for instance running GEOS AGCM at c24/c48/c90 resolution for development purposes with a modest HISTORY output on 2 or 3 nodes, there is no need to dedicate any extra resources for the PFIO Server.
Command Line
If executable_file is the executable file, we can issue the regular mpirun (same for mpiexec) command:
mpirun -np npes executable_file
where npes is the number of processors. In this case, the MpiServer is used as Oserver. The Client processes are overlapping with Oserver processes. The Client and Oserver are sequentially working together. When Client sends data, it actually makes a copy, then the Oserver takes over the work, i.e., shuffling data and writing data to the disk. After MpiServer is done, the Client moves on.
MultiGroupServer Class
For exploiting asynchronous output when using HISTORY, we recommend using the MultiGroupServer option for the PFIO Server. With PFIO Server, the model (or application) does not write the data to the disk directly. Instead the user launches the application on more MPI tasks than is needed for the application. The extra MPI tasks are dedicated to running the the PFIO Server. When the user chooses the MultiGroupServer option, the server is itself split into a frontend and backend. Only the backend actually writes to disk.
The frontend of the server functions as a memory buffer. When HISTORY decides it is time to write, the data is processed if necessary (regridding for example) to the final form. Then the data is forwarded from the application MPI ranks to the "front end" of the server which is on a different set of MPI ranks. As soon as the data is forwarded the model continues.
Once all the data has been received by the frontend of the server, the data is forwarded to the backend on yet a different set of MPI ranks. In the currently implementation each collection to be written is forwarded to a single processor on the backend based on what are available. Note that some may still be writing from the previous write request. That's fine as long as there are still some resources on the backend available. Also note that this implies a collection must fit in a single node memory.
PFIO follows these steps in the execution of the MultiGroupServer option:
• The Oserver is divided into frontend and backend.
• When the frontend receive the data, its root process asks backend‘s root (or head) for an idle process for each collection. Then it broadcasts the info to the other frontend processes.
• When the frontend processors forward (MPI_SEND) the data to the backend ( different collections to different backend processors), they get back to the clients without waiting for the actual writing.
Command Line
There are many options to configure the Oserver.
n1 processes for the model and n2 processes for the MpiServer
mpirun -np npes executable_file –npes_model n1 --npes_output_server n2
• Note that $npes$ is not necessary equal to $n1+n2$.
• The client (model) will use the minimum number of nodes that contain $n1$ cores.
• For example, if each node has n processors, then $npes = \lceil \frac{n1}{n} \rceil \times n + n$.
• If --isolate_nodes is set to false (by default, it is true), the oserver and client can co-exist in the same node, and $npes = n1 + n2$.
• --npes_output_server n2 can be replaced by --nodes_output_server n2. Then the $npes = \lceil \frac{n1}{n} \rceil \times n + n2 \times n$.
n1 processes for the model and n2 processes for the MultiGroupServer
mpirun -np npes executable_file –npes_model n1 --npes_output_server n2 --oserver_type multigroup --npes_backend_pernode n3
• For each node of oserver, $n3$ processes are used as backend.
• For example, if each node has $n$ cores, then $npes = \lceil \frac{n1}{n} \rceil \times n + n2 \times n$.
• The frontend has $n2 \times (n-n3)$ processes and the backend has $n3 \times n$ processes.
• The frontend has $\lceil \frac{n2}{n} \rceil \times (n-n3)$ processes and the backend has $n3 \times n$ processes.
Passing a vector of oservers
mpirun -np npes executable_file –npes_model n1 --npes_output_server n2 n3 n4
• The command creates $n2$-node, $n3$-nodes and $n4$-nodes MpiServer.
• The oservers are independent. The client would take turns to send data to different oservers.
• If each node has $n$ processors, then $npes = \lceil \frac{n1}{n} \rceil \times n + (n2+n3+n4) \times n$.
• Advantage: Since the oservers are independent, the client has the choice to send the data to the idle oserver.
• Disavantage: Finding an idle oserver is not easy.
Passing a vector of oservers and the MultiGroupServer
mpirun -np npes executable_file –npes_model n1 --npes_output_server n2 n3 n4 --oserver_type multigroup --npes_backend_pernode n5
• The command creates $n2$-node, $n3$-nodes and $n4$-nodes MultiGroupServer.
• The oservers are independent. The client would take turns to send data to different oservers.
• If each node has $n$ processors, then $npes = \lceil \frac{n1}{n} \rceil \times n + (n2+n3+n4) \times n$.
• Each oserver has $n2 \times n5$, $n3 \times n5$, and $n4 \times n5$ backend processes respectively.
MpiServer using one-sided MPI_PUT and shared memory
mpirun -np npes executable_file –npes_model n1 --npes_output_server n2 --one_node_output true
• The option --one_node_output true makes it easy to create n2 oservers and each is one-node oserver.
• It is equivalent to --nodes_output_server 1 1 1 1 1 ... with n2 “1”s.
--fast_oclient true
• After the client sends history data to the Oserver, by default it waits and makes sure all the data is sent even it uses non-blocking isend. If this option is set to true, the client copies the data before non-blocking isend. It waits and cleans up the copies next time when it re-uses the Oserver.
Profiling Features of PFIO
PFIO has an internal profiling tool that collects the time spent on its operations. To turn on the tool, users need to add the command line option --with_io_profiler. At the end of the run (based on the Oserver), the following timing statistics will be provided:
• Inclusive: all time spent between start and stop of a given timer.
• Exclusive: all time spent between start and stop of a given timer _except_ time spent in any other timers.
• o_server_front:
• --wait_message: Time while the front ends is waiting for the data from application.
• --add_Histcollection: Time for adding history collections.
• --receive_data: The total time Frontends receive data from applications.
• ----collection_i: The time Frontends receive collection_i.
• --forward_data: The total time Frontends forward data to Backend.
• ----collection_i: The time Frontends forward collection_i.
• --clean up: The time finalizing o-server.
Note that the timing statistics for --receive_data and --forward_data are created for each collection.
Recommendations
For the best performance, users should try different configurations of PFIO for a specific run. They will generally find that after several trials they will hit a limit where the wall-clock time does not decrease despite adding more resources. By doing several tests, users will identify the particular configuration that reduces I/O bottlenecks and minimizes the overall computing time.
In general, there is a "reasonable" estimated configuration for users to start with. If you run a model requiring NUM_MODEL_PES of cores, each node has NUM_CORES_PER_NODE, the total number of history collections is NUM_HIST_COLLECTION, then
$$MODEL\_NODE = \frac{NUM\_MODEL\_PES}{NUM\_CORES\_PER_NODE}$$
$$O\_NODES = \frac{NUM\_HIST\_COLLECTION + 0.1 \times NUM\_MODEL\_PES}{NUM\_CORES\_PER\_NODE}$$
$$NPES\_BACKEND = \frac{NUM\_HIST\_COLLECTION}{O\_NODES}$$
$$TOTAL\_PES = (MODEL\_NODE + O\_NODES)\times NUM\_CORES\_PER\_NODE$$
All above number should round up to an integer.
The run command line would look like
mpirun -np TOTAL_PES ./GEOSgcm.x --npes_model NUM_MODEL_PES --nodes_output_server O_NODES --oserver_type multigroup --npes_backend_pernode NPES_BACKEND
Exercising PFIO
PFIO Programming
PFIO handles netCDF files and therefore follows the netCDF steps to create files. However, the processes in PFIO are simpler because it works only with variable names instead of variable identifier (as in netCDF). Here are the key features code developers need to know while programming with PFIO:
• Only variable names are passed along when creating and writing out fields.
• The file metadata is created once and stored in a collection identifier (integer). At any time in the code (before the data are written out), any attribute or value can be modified.
• Only local variables are passed to PFIO routines.
Step 1: Collection Creation
During the initialization stages, we need to create the file metadata and store it in a collection identifier. Two PFIO derived types variables are used to perform the necessary operations:
type(FileMetadata) :: fmd ! stores metadata
Type(Variable) :: v ! stores variable information
Define Dimensions
call fmd%add_dimension('lon', IM_WORLD, rc=status)
Define Dimension Variable
v = Variable(type=PFIO_REAL32, dimensions='lon')
Define Variable
Note how the dimension information is passed to define the variable.
v = Variable(type=PFIO_REAL32, dimensions='lon,lat,lev,time')
Set File Attribute
call fmd%add_attribute('Convention', 'COARDS')
call fmd%add_attribute('Title', 'Sample code to test PFIO')
call fmd%add_attribute('HISTORY', 'File written by PFIO vx.x.x')
Create File Collection
Now we need to
hist_id = o_clients%add_hist_collection(fmd)
All the above operations are done during initialization procedures.
Step 2: Passing Data to PFIO
When we are ready to write the data out, PFIO only needs to have the the collection identifier (hist_id), the file name and the local variable (containing the data). Two calls are necessary:
ref = ArrayReference(local_temp)
call o_clients%collective_stage_data(hist_id, TRIM(file_name), &
'temperature', ref, &
start = [i1,j1,k1,1], &
global_start = [1,1,1,record_id], &
global_count = [IM_WORLD,JM_WORLD,KM_WORLD,1])
Here, ArrayReference takes the local data and transforms it to a PFIO pointer object. 'i1', 'j1andk1 are local domain starting indices with respected to the global domain.
Example with a Standalone Code
The PFIO source code comes with a standalone test program:
MAPL/Tests/pfio_MAPL_demo.F90
that exercises the features of PFIO. This program is written to mimic the execution steps of MAPL_Cap and can be used as reference to use PFIO in a non-GEOS application. It writes several time records of 2D and 3D arrays. The compilation of the program generates the executable named pfio_MAPL_demo.x.
If we reserve 2 haswell nodes (28 cores in each), run the model on 28 cores and use 1 MultiGroup with 5 backend processes, then the execution command is:
mpiexec -np 56 pfio_MAPL_demo.x --npes_model 28 --oserver_type multigroup --nodes_output_server 1 --npes_backend_pernode 5
• The frontend has $28-5=23$ processes and the backend has $5$ processes.
Performance Analysis
We create a collection that contains:
• one 2D variable (IMxJM)
• one 3D variable (IMxJMxKM)
Three (3) 'daily' files are written out and each of them contains six (6) time records. We measure the time to perform the IO operations. Note that no calculations are involved here. We only do the array initialization.
We run the model (with IM=360, JM=181, KM=72 and 5 Backend) by turning on the PFIO profiling tool:
mpiexec -np 56 \$MAPLBIN/pfio_MAPL_demo.x --npes_model 28 --oserver_type multigroup --nodes_output_server 1 --npes_backend_pernode 5 --with_io_profiler
The profiling tool generated the report:
=============
Name Inclusive % Incl Exclusive % Excl Max Excl Min Excl Max PE Min PE
i_server_client 0.324201 100.00 0.324201 100.00 0.520954 0.245613 0016 0023
Final profile
=============
Name Inclusive % Incl Exclusive % Excl Max Excl Min Excl Max PE Min PE
o_server_front 0.357244 100.00 0.053738 15.04 0.881602 0.013470 0000 0002
--wait_message 0.047207 13.21 0.047207 13.21 0.052244 0.040038 0011 0013
--add_Histcollection 0.003346 0.94 0.003346 0.94 0.005641 0.000294 0002 0007
--receive_data 0.194778 54.52 0.000496 0.14 0.000696 0.000367 0013 0019
----collection_1 0.194282 54.38 0.194282 54.38 0.421234 0.113870 0013 0021
--forward_data 0.057849 16.19 0.017939 5.02 0.051281 0.000058 0020 0018
----collection_1 0.039910 11.17 0.039910 11.17 0.048129 0.030721 0018 0019
--clean up 0.000325 0.09 0.000325 0.09 0.000529 0.000244 0009 0017
IM=360 JM=181 KM=72 and 5 Backend
In the table below, we report the Inclusive time for the two main IO components as the number of backend PEs per node varies:
Number of Backend PEs/node i_server_client o_server_front
1
2 1.186932 1.813097
3 0.291334 1.216281
4 0.259511 0.296956
5 0.324201 0.357244
IM=720 JM=361 KM=72
with 5 Backend PEs/node
=============
Name Inclusive % Incl Exclusive % Excl Max Excl Min Excl Max PE Min PE
i_server_client 1.050624 100.00 1.050624 100.00 1.515223 0.822786 0015 0025
Final profile
=============
Name Inclusive % Incl Exclusive % Excl Max Excl Min Excl Max PE Min PE
o_server_front 1.250806 100.00 0.128693 10.29 2.737311 0.008478 0000 0012
--wait_message 0.108261 8.66 0.108261 8.66 0.130712 0.081595 0008 0022
--add_Histcollection 0.003061 0.24 0.003061 0.24 0.004589 0.001020 0004 0002
--receive_data 0.789012 63.08 0.000642 0.05 0.000909 0.000484 0013 0019
----collection_1 0.788370 63.03 0.788370 63.03 1.568300 0.406615 0013 0021
--forward_data 0.221412 17.70 0.102570 8.20 0.378546 0.000081 0021 0018
----collection_1 0.118842 9.50 0.118842 9.50 0.145169 0.090811 0013 0021
--clean up 0.000367 0.03 0.000367 0.03 0.000552 0.000256 0004 0012
`
In the table below, we report the Inclusive time for the two main IO components as the number of backend PEs per node varies:
Number of Backend PEs/node i_server_client o_server_front
1
2 3.378511 5.795466
3 0.977153 6.262224
4 1.009190 1.203735
5 1.050624 1.250806
Examples of the Implementation of PFIO in non-GEOS Application
Land Information System
The Land Information System (LIS) is a software framework for high performance terrestrial hydrology modeling and data assimilation developed with the goal of integrating satellite and ground-based observational data products and advanced modeling techniques to produce optimal fields of land surface states and fluxes. In LIS, model calculations are embarrassedly parallel and the I/O procedures are done by the root processor. As we increase the number of cores to integrate LIS, IO dominates and the overall timing performance significantly deteriorates. In addition, LIS has only one HISTORY collection mainly consisting of 2D fields.
PFIO has been implemented in LIS to reduce the IO time as model resolution and the number of cores increase. To achieve it:
• MAPL was compiled and used as an external library for LIS.
• A new module was written to create necessary subroutines that include PFIO statements for the creation of the LIS HISTORY.
• The ability to create virtual HISTORY collections was introduced to take advantage of the capabilities of PFIO. This virtual collection feature is critical in LIS because in general calculations are completed well before the production of a collection is done.
• Preprocessing directives were introduced in the code to be able to use the PFIO option or not.
• At compilation users could select to compile LIS without (falls back to the LIS original code) or with PFIO. This setting was important to code developers who still want to use LIS in platforms where MAPL is not available.
Here are some preliminary results:
• LIS/PFIO produces files bitwise identical to the original version of the code.
• LIS/PFIO requires less computing resources to achieve the same wall-clock time as the original LIS.
• Using virtual collections (set at run time) significantly improve the IO performance. | 2022-10-01 21:32:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27166232466697693, "perplexity": 4416.931740743864}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030336921.76/warc/CC-MAIN-20221001195125-20221001225125-00024.warc.gz"} |
https://caphuuquan.com/sudoku-solver-part-1-grid-detection/ | # Building a simple SUDOKU Solver from scratch - Part 1: Grid Detection & Digit Extraction
Hi, today I’m gonna explain how to build a simple SUDOKU Solver taken from image step-by-step. You can see the demo of SUDOKU Solver in the GIF image below.
To build this program, we will go through 4 main steps.
1. SUDOKU Grid Detection and Digit Extraction
2. Recognize Number with Support Vector Machine (SVM)
3. Solving SUDOKU with Backtracking Algorithm
4. Completing the simple SUDOKU Solver
This program was built by Python 2.7 and OpenCV 2.4.13 so before you want to follow this post, please install Python 2.7 and OpenCV 2.4.13 Update: Since some people asked me to modify the code to work with OpenCV 3.x, please refer to this link if you’re using OpenCV 3.x SUDOKU_OpenCV3
## 1. SUDOKU Gird Detection and Digit Extraction
The most important thing to solve a SUDOKU board from images is detecting SUDOKU grid (or line). I found many ways to extract digit from SUDOKU on the internet, but I saw this article (http://jponttuset.cat/solving-sudokus-like-a-pro-1/) is the smartest and easy way to extract digit from SUDOKU board. I took the idea from that guy and re-implement myself with Python. Let’s get started!
We will use a famous and simple technique called Hough Line Transform to detect lines on the image. If you’re not familiar with Hough Line Transform, please check out my previous article about Hough Line Transform
Note: We can visit this website to print any SUDOKU images for practicing: http://show.websudoku.com/
From an RGB frame captured from the webcam, we will convert it to a grayscale image. After that, extract edges using Canny Edge detection and then apply Hough Line Transform to detect lines. We use cv2.HoughLines() with $$\rho$$ unit equal to $$2$$ and minimum length of line to be detected is $$300$$ pixels. It means increasing the accumulator by $$2$$ when a point is satisfied and consider to be a line when the minimum value in the accumulator is $$300$$. The result will look like this:
Fig. 1. Line detection using Hough Line Transform
The next step is looking for intersections between these lines. When we know the intersection points, we can extract every block that contains SUDOKU digit.
Hmm … Look at that! There are too many lines. Synonymous with there are some redundant lines (some lines are overlapped each other).
But wait, we already know the distance of each line to the origin. It means we can easily remove the overlapped lines if the distance between these lines is close to each other.
Let’s say we will remove the redundant lines if the distance between these lines is less than $$10$$. Firstly, let’s sort these line increasingly by the distance ($$\rho$$) and then check the distance of every $$2$$ lines. If the distance is less than $$10$$, remove the second line.
You can read the following code
# HOW TO USE
# Use this with a printed SUDOKU Grid
# Press ESC key to Exit
import cv2
import numpy as np
ratio2 = 3
kernel_size = 3
lowThreshold = 30
cv2.namedWindow("SUDOKU Solver")
vc = cv2.VideoCapture(0)
if vc.isOpened(): # try to get the first frame
else:
rval = False
while rval:
# Preprocess image, convert from RGB to Gray
sudoku1 = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
sudoku1 = cv2.blur(sudoku1, (3,3))
# Apply Canny edge detection
edges = cv2.Canny(sudoku1, lowThreshold, lowThreshold*ratio2, kernel_size)
# Apply Hough Line Transform, return a list of rho and theta
lines = cv2.HoughLines(edges, 2, cv2.cv.CV_PI /180, 300, 0, 0)
if (lines is not None):
lines = lines[0]
lines = sorted(lines, key=lambda line:line[0])
# Define the position of horizontal and vertical line
pos_hori = 0
pos_vert = 0
for rho,theta in lines:
a = np.cos(theta)
b = np.sin(theta)
x0 = a*rho
y0 = b*rho
x1 = int(x0 + 1000*(-b))
y1 = int(y0 + 1000*(a))
x2 = int(x0 - 1000*(-b))
y2 = int(y0 - 1000*(a))
# If b > 0.5, the angle must be greater than 45 degree
# so we consider that line as a vertical line
if (b>0.5):
# Check the position
if(rho-pos_hori>10):
# Update the position
pos_hori=rho
cv2.line(frame,(x1,y1),(x2,y2),(0,0,255),2)
else:
if(rho-pos_vert>10):
pos_vert=rho
cv2.line(frame,(x1,y1),(x2,y2),(0,0,255),2)
# Show the result
cv2.imshow("SUDOKU Solver", frame)
key = cv2.waitKey(20)
if key == 27: # exit on ESC
break
vc.release()
cv2.destroyAllWindows()
Now, the result looks better than before.
Fig. 2. SUDOKU Grid after removing redundancy lines
Next, we will find the intersection points based on those lines. Just to recap again, every line is satisfied this equation: $$\rho=x\cos \theta+y\sin \theta$$ (1)
We have $$\rho$$ and $$\theta$$ for each line, so it’s easy to find the intersection between 2 lines by solving linear equations. In this post, I use the $$linalg$$ library in Numpy to find the intersection points. You can check out this link to see how to use $$linalg$$ in Python: https://docs.scipy.org/doc/numpy/reference/generated/numpy.linalg.solve.html
Just change a bit of code and found the intersection points like this
Fig. 3. Intersection points detection
If we have those points, we also can extract the bouding boxes of the digit number in the SUDOKU board.
Fig. 4. Bounding block for each digit
Here is the code for digit number extraction
# HOW TO USE
# Use this with a printed SUDOKU Grid
# Press ESC key to Exit
import cv2
import numpy as np
ratio2 = 3
kernel_size = 3
lowThreshold = 30
cv2.namedWindow("SUDOKU Solver")
vc = cv2.VideoCapture(0)
if vc.isOpened(): # try to get the first frame
else:
rval = False
while rval:
# Preprocess image, convert from RGB to Gray
sudoku1 = cv2.cvtColor(frame, cv2.COLOR_BGR2GRAY)
sudoku1 = cv2.blur(sudoku1, (3,3))
# Apply Canny edge detection
edges = cv2.Canny(sudoku1, lowThreshold, lowThreshold*ratio2, kernel_size)
# Apply Hough Line Transform, return a list of rho and theta
lines = cv2.HoughLines(edges, 2, cv2.cv.CV_PI /180, 300, 0, 0)
if (lines is not None):
lines = lines[0]
lines = sorted(lines, key=lambda line:line[0])
# Define the position of horizontal and vertical line
pos_hori = 0
pos_vert = 0
# Create a list to store new bundle of lines
New_lines = []
# Store intersection points
Points = []
for rho,theta in lines:
a = np.cos(theta)
b = np.sin(theta)
x0 = a*rho
y0 = b*rho
x1 = int(x0 + 1000*(-b))
y1 = int(y0 + 1000*(a))
x2 = int(x0 - 1000*(-b))
y2 = int(y0 - 1000*(a))
# If b > 0.5, the angle must be greater than 45 degree
# so we consider that line as a vertical line
if (b>0.5):
# Check the position
if(rho-pos_hori>10):
# Update the position
pos_hori=rho
# Saving new line, 0 is horizontal line, 1 is vertical line
New_lines.append([rho,theta, 0])
else:
if(rho-pos_vert>10):
pos_vert=rho
New_lines.append([rho,theta, 1])
for i in range(len(New_lines)):
if(New_lines[i][2] == 0):
for j in range(len(New_lines)):
if (New_lines[j][2]==1):
theta1=New_lines[i][1]
theta2=New_lines[j][1]
p1=New_lines[i][0]
p2=New_lines[j][0]
xy = np.array([[np.cos(theta1), np.sin(theta1)], [np.cos(theta2), np.sin(theta2)]])
p = np.array([p1,p2])
res = np.linalg.solve(xy, p)
Points.append(res)
if(len(Points)==100):
for i in range(0,9):
for j in range(0,9):
y1=int(Points[j+i*10][1]+5)
y2=int(Points[j+i*10+11][1]-5)
x1=int(Points[j+i*10][0]+5)
x2=int(Points[j+i*10+11][0]-5)
# Saving extracted block for training, uncomment for saving digit blocks
# cv2.imwrite(str((i+1)*(j+1))+".jpg", sudoku1[y1: y2,
# x1: x2])
cv2.rectangle(frame,(x1,y1),
(x2, y2),(0,255,0),2)
# Show the result
cv2.imshow("SUDOKU Solver", frame) | 2022-06-28 23:49:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44072604179382324, "perplexity": 4301.937220932358}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103619185.32/warc/CC-MAIN-20220628233925-20220629023925-00708.warc.gz"} |
http://mathoverflow.net/feeds/question/116469 | AS Cohen Macaulay algebras and dualizing complexes - MathOverflow most recent 30 from http://mathoverflow.net 2013-05-19T06:45:35Z http://mathoverflow.net/feeds/question/116469 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/116469/as-cohen-macaulay-algebras-and-dualizing-complexes AS Cohen Macaulay algebras and dualizing complexes Pablo Zadunaisky 2012-12-15T17:46:17Z 2012-12-15T22:17:12Z <p>Let $A$ be an $\mathbb N$-graded algebra such that $A_0 = k$ is a field. This are usually called graded connected algebras. </p> <p>One can define a torsion functor with respect to the ideal $\mathfrak m = \bigoplus_{i \geq 1} A_i$, setting for any graded $A$ module $M$</p> <p>$$\Gamma_{\mathfrak m}(M) = \{m \in M | A_{\geq i}m = 0 \mbox{ for } i \gg 0 \} \cong \varinjlim_i Hom_A(A/A_{\geq i},M).$$</p> <p>The derived functors of $\Gamma_{\mathfrak m}$ are the local cohomology functors with respect to $\mathfrak m$, and are denoted by $H^i_\mathfrak m$. As in the commutative case, there is a natural isomorphism $$H_\mathfrak m(-) \cong \varinjlim Ext_A^i(A/A_{\geq i}, -)$$</p> <p>We say $A$ is</p> <ul> <li><p>AS Cohen Macaulay if there is a natural number $n$ such that $H_\mathfrak m^i (A) = H_\mathfrak m(A^{op}) = 0$. Let us call $n$ the local dimension of the module $A$ (I'm not sure this is standard notation)</p></li> <li><p>AS Gorenstein if it has finite injective dimension $n$ both as a right and left module, and furthermore $Ext_A^n(k,A) = k$, once again on both sides.</p></li> </ul> <p>This are generalizations of ye olde condition of regularity for graded connected algebras introduced by Artin and Schelter, hence the AS. If $A$ is commutative and noetherian, then they are equivalent to their AS-less counterparts. (Maybe you can drop the noetherian hypothesis on this, but I'm not sure.)</p> <p>We have the usual implication chain </p> <blockquote> <p>AS regular $\Rightarrow$ AS Gorenstein $\Rightarrow$ AS Cohen Macaulay.</p> </blockquote> <p>By Groethendick's vanishing theorem, if $A$ is a noetherian Cohen Macaulay algebra of local dimension $n$, then $H^i_\mathfrak m \equiv 0$ for $i > n$.</p> <p><strong>Question 1</strong>: Is this result still true for noncommutative noetherian AS Cohen Macaulay algebras? </p> <p>The result is true for noetherian AS Gorenstein algebras, as explained in <a href="http://www.ams.org/mathscinet/search/publdoc.html?arg3=&co4=AND&co5=AND&co6=AND&co7=AND&dr=all&pg4=AUCN&pg5=TI&pg6=PC&pg7=ALLF&pg8=ET&r=1&review_format=html&s4=Yekutieli&s5=Serre&s6=&s7=&s8=All&vfpref=html&yearRangeFirst=&yearRangeSecond=&yrop=eq" rel="nofollow">this paper</a> by Yekutieli and Zhang, Corollary 4.3. The argument comes basically from the fact that AS Gorenstein algebras have balanced dualizing complexes, almost by definition. This brings me to my</p> <p><strong>Question 2</strong>: Are there AS Cohen Macaulay algebras <em>without</em> (balanced or unbalanced) dualizing complexes?</p> <p>Thanks!</p> | 2013-05-19 06:45:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9253592491149902, "perplexity": 1560.7806854558905}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368696384181/warc/CC-MAIN-20130516092624-00051-ip-10-60-113-184.ec2.internal.warc.gz"} |
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CATEGORY: Blog [back]
TOPIC: Physics of the Observer - Call for Proposals and Program Launch [refresh]
FQXi Administrator Brendan Foster wrote on Oct. 27, 2015 @ 16:33 GMT
And now, we’d like to announce the beginning of an ambitious new program, investigating Physics of the Observer.
We’re asking you to take a long hard look at yourself — and to think about what it means to be an "observer". Many problems in physics and cosmology implicitly or explicitly include this idea of an observer. But a tendency within physics to focus on objective phenomena and avoid subjectivity has led to a general avoidance of discussing exactly what an observer is. Not only has this habit avoided an intrinsically universal question, it has led to a situation in which many thinkers implicitly employ different meanings of "observer" in their work. They are then not able (or willing) to confront the impact of their definition on the questions they face.
In addition, the development of physics in the 20th century has led to a peculiar sort of polarization in thinking about the observer. Prior to the development of quantum mechanics, the observer was largely seen as irrelevant, as physics was about objective reality, by definition observer-independent. Quantum mechanics directly contradicted this view, requiring a much more nuanced understanding of the observation process and creating a lasting controversy between those embracing the observer’s role and those opposing its place.
As with previous FQXi programs on the Nature of Time, the Physics of Information, and the on-going Physics of What Happens, we believe that focusing the attention of the research community will start to bring us closer to “seeing” the solution to these problems.
Like our past programs, this one will feature support for foundational physics research, an international conference, essay and video contests, plus articles, blog posts, and the ever popular FQXi podcast. In addition, this program will for the first time also have a research component directly organized and coordinated by FQXi and its personnel.
First, let us announce the launch of our next Large Grant round. We will award a total of US$2.0M for projects examining Physics of the Observer. We welcome applications related to physics, cosmology, and closely related fields, such as neuroscience, philosophy, biophysics, complex systems, computer science, mathematics, and more. Questions to think about include: 1. What does being an observer mean? The term 'observer' is used in contexts as varied as quantum foundations, biophysics, neuroscience and cognitive science, artificial intelligence, philosophy of consciousness, relativity, and cosmology. What are the properties or attributes that a system must have in order to constitute an ‘observer’ in these varying contexts? 2. What sort of physical systems have the requisite properties for those systems to construe various types of observers? In a spectrum from most simple to most complex physical structures, which systems constitute observers? 3. Are there interesting questions, to which the answers depend on how we think of observers? Initial proposals are due on January 20, 2016. You can find full details about the RFP and more examples of questions on the website here. If you have any questions on this, please contact us at mail@fqxi.org. The second major component of the Physics of the Observer program will foster a multidisciplinary network or researchers supported by centers in the Boston area and in the San Francisco Bay area. These two “B-Area” centers will be organized by FQXi Scientific Director Max Tegmark at MIT in Boston, and FQXi Associate Scientific Director Anthony Aguirre and Joshua Deutsch at the University of California - Santa Cruz. Supplementing previous experience in cosmology, gravity, quantum foundations, etc., Deutsch brings a powerful foundation in quantum mechanics, condensed matter, statistical mechanics, and biophysics to the team. Tegmark has been recently active in neuroscience research, and Aguirre & Tegmark have also been in deep-learning mode (get it?) regarding machine intelligence, in relation to work with the Future of Life Institute. With visitor programs and local meetings, the B-Area centers will attempt to generate somewhat coherent research programs in both areas, and personnel from the B-area centers will come together for two dedicated workshops. Please stay tuned for future updates about FQXi contests, our 2016 conference, and all the other great content on the website. Here’s looking at you. this post has been edited by the forum administrator report post as inappropriate Steve Dufourny wrote on Oct. 27, 2015 @ 16:54 GMT Hello Mr Foster Super news for FQXi,Happy to see that fqxi lives and will live :) But a little suggestion if I can it could be well if FQXi improved the number of articles even short about many things. Here is some ideas Astrobiology,Spaceship and engeniering architecture,dark matter and dark energy,Universal entropy principle and its steps of disponible énergies,gravitation and gravitons ,and his and that. Congratulations FQXi in allcase Regards report post as inappropriate Ronald Denzil Pearson wrote on Oct. 27, 2015 @ 20:47 GMT Observers are Earth based for this experiment The new experiment uses one of three instruments invented to enable the speed of a probe to be measured from the local vacuum. They all depend on the magnetic effect of moving electric charge. The proposal aims to provide a new form of space exploration: measuring the velocity structure of the quantum vacuum throughout the solar system.... view entire post report post as inappropriate Amrit Srecko Sorli wrote on Oct. 27, 2015 @ 21:16 GMT I publish a paper "On the origin of the Observer" in 2014. Interesting subject. yours Amrit report post as inappropriate Amrit Srecko Sorli wrote on Oct. 28, 2015 @ 17:22 GMT The final result of this research is that observer has origin in consciousness. Now 2 millions will be spend and at the end no significant result will be achieved. I’m sure no one will mention what I say at the beginning. HOW THAT? The same was with time, no result on time research was given. At the end of research Dr.Barbour publish a paper on arxiv on time which is nothing new. He tried not to use symbol t in his paper.....but this is not the point.....Why FQXI give money only researchers which are employed in established institutions? Do they think no independent researcher can give progress to physics? Dear Editors of FQXI, you are wrong…..at the moment physics progress is happening outside of established physics where still old paradigm is prevailing. Standard model has no power to explain mass, gravity and dark energy. Will establishment need 100 years more to get what we know for years already. This is really dark night of the physics. Wake up dear editors, wake up. Yours Amrit Sorli attachments: 4_On_the_origin_of_the_observer.pdf, sorli_CV.pdf this post has been edited by the author since its original submission report post as inappropriate kevin l bootes replied on Dec. 9, 2015 @ 12:26 GMT [ This bracket-delimited edit added Dec 10 to more clearly distinguish FQXi from conventional physics funding agencies: In addressing the funding challenges facing unconventional research proposals at NSF-style, establishment agencies being specifically* addressed by the breathtakingly unconventional Physics of the Observer RFP, ] Mr. Sorli makes a very perceptive point: established... view entire post this post has been edited by the author since its original submission report post as inappropriate Amrit Srecko Sorli replied on Dec. 15, 2015 @ 14:24 GMT Kevin thank you for this support. I'm independent researcher doing research on time, gravity, cosmology, bijective epistemology for years with no financial support. But I have results. Sure money from FQXI would be well-come, but if you are not part of established institution you are "officially" not scientist. This is sad and we should left behind a stereotype that PhD means science. Not at all, see articles on arxive, most of them are just hypothetical "hocus-pocus". report post as inappropriate kevin l bootes replied on Dec. 16, 2015 @ 01:47 GMT Hi Amrit - We're in exactly the same position, doing same work. But watch out! I don't believe in photons or other point particles, wave-particle duality, singularities, big bangs, inflation, static black holes (but certainly gravitational collapse), wormholes, gravity waves, dark matter or energy (apart from electromagnetically describable but unobservable forms like radio waves'... view entire post report post as inappropriate Joe Fisher wrote on Oct. 29, 2015 @ 16:36 GMT The real unique Universe am infinite as can be confirmed by a real sensible person's real observation. The unreal finite abstract universe misinformation provided by mindless credentialed professors of finite abstract quantum guesswork are not observable. Joe Fisher, Realist report post as inappropriate Eckard Blumschein wrote on Oct. 30, 2015 @ 02:18 GMT Hint ++++ report post as inappropriate Tung Ten Yong wrote on Oct. 30, 2015 @ 08:28 GMT In the previous grant (Physics of Events) my proposal was to investigate the definition of event by explicitly taking into account the role of observer in Physics. I am happy to see that now the status of observer is the topic of the grant. this post has been edited by the author since its original submission report post as inappropriate Steve Agnew wrote on Oct. 31, 2015 @ 03:05 GMT There are two very different observers of objects in the universe; an objective observer sees objects as they really are and a subjective observer feels an object’s relative phase coherence. As a result, an objective observer sees action as it really is and agrees with other observers about common properties. Even if an observer affects a measurement, as long as others agree to the observer effect, the observer remains objective. A subjective observer’s relative feeling about an action phase coherence no other observer can measure or know. While an objective observer agrees with other observers about the objective properties of an object, including an observer effect, a subjective observer’s phase relative to an object depends on the unique lifetime of experience and development for that observer. report post as inappropriate John R. Cox replied on Oct. 31, 2015 @ 16:07 GMT I am the only observer of anything. At least I admit it. jrc this post has been edited by the author since its original submission report post as inappropriate Steve Dufourny replied on Oct. 31, 2015 @ 16:16 GMT :) me I see like observer many balls,spheres,bubububbles,spheroids,tori,bobobobowls everywhere, publication finished !Short but very clear no:) report post as inappropriate Steve Agnew replied on Nov. 1, 2015 @ 18:03 GMT There are therefore two very different personalities for observers; objective Cartesian and subjective relational. A Cartesian observer views an object on a distinct path through Cartesian space and interacting little with other objects. A relational observer views an object with purpose and interacting strongly with other objects and so the relations among other objects, especially their phases, determines the object’s future more than the object’s immediate trajectory. The objective Cartesian observer tends to focus on the object properties and how the object moves and not so much why. A subjective relational observer tends to focus on the object relations with other objects, especially phase coherence, and why the object moves, not so much how. report post as inappropriate Gary D. Simpson wrote on Oct. 31, 2015 @ 16:32 GMT I observe. Therefore, I am. Gary Simpson Houston,Tx report post as inappropriate kevin l bootes replied on Dec. 9, 2015 @ 12:36 GMT I observe observing. Therefore, I am Universe. report post as inappropriate Georgina Woodward wrote on Nov. 1, 2015 @ 00:34 GMT Pentcho, All, the wavelength of the incoming wave is not changed. The sensory output of the observer encountering the wave is, due to how it is encountered. It differs from the input. What is experience is not a replica of what exists externally but a new 'reality' that is formed from both the nature of the stimulus and the measurement process-I.E.how it is encountered. The mistake is that thinking before and after measurement are the same phenomenon. this post has been edited by the author since its original submission report post as inappropriate Don Limuti replied on Nov. 1, 2015 @ 04:06 GMT Hi Georgina, I translate your post as saying that the observer is a person X (or intelligence) that makes measurements (on inputs) by way of their senses. I agree that this is the essence of the observer! And would add that the observed measurements can be indirect via instruments (which can be a chain of further people and instruments) the output of which ultimately provide inputs to person X's senses. Did I understand you correctly? And of course the people in the chain would be reliable people like those involved in FQXi.org :) And the instruments would all be traceable to Amazon :) Glad to see you still active in the blogs. Don Limuti report post as inappropriate Georgina Woodward wrote on Nov. 1, 2015 @ 05:00 GMT Hi Don, Yes it sounds to me that we are on the same wavelength- I agree about intermediate instruments. These can be reality interfaces altering the input received by them into a different kind of output prior to receipt by the "Primary Reality Interface" the human sensory system. Eg. The beep of a photo-multiplier, or the line on an oscilloscope. The case of information in books is interesting because one is not dealing merely with the formation of seen images but also with the meaning associated with those images necessary for reading and understanding, requiring prior learning. All, in the image Pentcho linked a person is shown. Though it could be any organism or AI with at least proto-vision via a photo-receptor. In the case of a person the light input chemically alters the pigment of the cone cells that are stimulated and that can cause an electrical impulse to be sent to the brain where further processing occurs leading to an experienced output. As soon as interaction with the retina occurs the part of the light wave that was input ceases to be and new outputs are formed. To think the final observed output is still a light wave, because it is mentally associated with the light wave input is naive realism. The change from external reality to observed image reality begins with the processing of the input information by the reality interface, which for a human is its visual system. report post as inappropriate Amrit Srecko Sorli wrote on Nov. 1, 2015 @ 08:07 GMT observer know how to develop device for antigravity report post as inappropriate H.H.J. Luediger wrote on Nov. 6, 2015 @ 12:08 GMT The new theme of the FQXi program – the observer – can be seen as focusing many previous themes in a single point the other name of which is the measurement problem. The notion of observer, however, has so far played a folkloristic role in an intra-physical debate on the measurement problem at best, because ‘observing’ in physics has generally been taken to mean incontrovertible sensuous judgment of an observer-independent reality. A child, however, when shown around a nuclear power plant, cannot observe the nuclear power plant, but only walls, floors, pipes, flashing lights, and a water basin. Nor is it given to an ignorant spectator to make much sense of the game called cricket :) – observation is not merely Hume’s ‘looking at and rule finding’. Rather must the observer bring something to the (to be) observed that is of a categorically different nature than the (to be) observed itself in the sense of Einstein’s: only the theory decides what can be observed. Hence the new theme’s title Physics of the Observer cements precisely that perspective on the matter that has been in the way of making progress for almost a century, i.e. the banalisation of Heisenberg’s ‘cut’. Regards report post as inappropriate Thomas Howard Ray replied on Nov. 6, 2015 @ 13:41 GMT " ... in the sense of Einstein’s: only the theory decides what can be observed." Precisely. This is what confuses people who insist on using the meaning of 'observer' as a convention. By removing the necessity to assume a preferred reference frame, Einstein removed the role of brain-mind to process information digitally. this post has been edited by the author since its original submission report post as inappropriate Georgina Woodward replied on Nov. 6, 2015 @ 20:47 GMT Good post H.H.J. An AI that has learned to identify objects and an organism that has learned brings that knowledge to extract 'meaning' from sensory (or data) input giving the potential for further understanding and or prediction. An inanimate measuring or detection object does not do that but only measures, or merely detects, and produces an output of which it has no awareness/can not identify. The 'reality' output depends in part on the processing conducted by the organism or AI. Inceptionism going deeper into neural networks report post as inappropriate Georgina Woodward replied on Nov. 6, 2015 @ 21:39 GMT Tom , Einstein started out on his theory with a dream about different relative observations of cows jumping in response to a shock from an electric fence. It was a dream about human observers and what they see (relative perception). The theory has developed such that it is possible to theoretically calculate what will be seen in different co-ordinate frames and to switch between frames to calculate what other observers would see. Because of this objective ability to switch frames by calculation (objective calculation not subjectively generated ) it has been imagined that an actual object capable of 'seeing' can be substituted by any object such as a nail. However the nail is incapable of seeing and so the output of sensory data processing that would be obtained for that coordinate system does not exist for the nail in actual fact. Though the sensory data is encountered it is not converted into a space-time output. The role of the output reality fabricating observer, which could be an organism or AI or a simpler reality interface can not really be removed. Without reducing the theory to one that is purely theoretical and not representative of what actually happens. Un-received unprocessed EM radiation provides no information. What is observed is the (space-time)output, not what is existing externally un-received. All of the images seen or calculated to be seen, trains, clocks, galaxies etc. are output image realities not un-received sensory data and not substantial source objects made of atoms. Yes the calculations seem to work and they are objective but they are not modelling a reality interface, or organism or AI, independent process. (A reality interface, in this context, is a material or device or sensory system able to convert input from external reality into a different kind of output.) report post as inappropriate Amrit Srecko Sorli wrote on Nov. 6, 2015 @ 21:47 GMT observer is beyond the brain and yeyond the mind and beyond the time. OBSERVER IS NOW. report post as inappropriate Steve Agnew wrote on Nov. 7, 2015 @ 18:48 GMT continued from...Steve Agnew replied on Nov. 7, 2015 @ 18:51 GMT If someone argues that there is only one kind of observer and one kind of reality, that would mean their opinion and feelings are facts and facts are their opinion and feelings. In this case, there would not be any difference between objective and subjective reality. Since my experience has been that there are great differences of opinion and feeling among people about the nature of a tree, but all agree that there is a tree. Denying that does not make any sense. this post has been edited by the author since its original submission report post as inappropriate Steve Agnew replied on Nov. 7, 2015 @ 19:03 GMT It therefore does not make any sense to redefine the objective color red by mixing that objective notion up with the subjective feeling about a red object. I can look at a beautiful red tree in the Fall and am confident that nearly everyone who sees that tree will also call it red. However, my feeling about the beauty of such a red tree in the Fall is mine alone. To argue otherwise does not make sense. report post as inappropriate Robert H McEachern replied on Nov. 8, 2015 @ 14:54 GMT And nearly everyone that pricks their finger on the thorn of a red rose will feel pain. But neither the color red nor the pain are an objective property of the rose bush - they are both just your nervous system's generated response (a virtual reality of sorts) to your encounter with the rose. Neither the color nor the pain flowed into your body, from the rose, they were both entirely generated internally, in response to encountering something from the rose, that was neither colorful nor painful. Rob McEachern report post as inappropriate Thomas Howard Ray replied on Nov. 8, 2015 @ 15:03 GMT Rob, Excellent. And the basis of a feedback theory that covers all possible varieties of complicated events and phenomena. report post as inappropriate Lorraine Ford wrote on Nov. 9, 2015 @ 01:13 GMT What is observed? Answer: The universe/reality from a particular point of view. There are no abstractly-existing “frames of reference”, there are only the frames of reference/points of view of real things: particles, atoms, molecules, single-cell living things, and multi-cell living things. What is observation? Answer: Observation is just the apprehension of various categories of... view entire post report post as inappropriate Georgina Woodward replied on Nov. 9, 2015 @ 05:11 GMT Hi Lorraine, an interesting post. For me demonstrating clearly why it is important for physics to decide definitively what does and does not constitute an observer. Or to have an accepted differentiation of the term observer such as with alphabetic attachment There are significant differences between most basic response to an input of a simple element of reality -compared to a reality interface, that outputs a different kind of information to the input, -compared to higher level analysis and attachment of associations, such as name and other information that requires prior learning of AI , neural network, or brain. There is also significant difference of all of those kinds of (maybe) observers with a theoretical observer that amounts to nothing more than carrying out a quantum calculation as if observation has occurred, or imposing an observer reference frame in order to conduct a relativity calculation. Re.your comment:Quote: "All of reality observes i.e. subjectively apprehends/experiences information about self and the rest of reality. “Consciousness”/subjective experience of information is NOT something new, unique and special that only occurs in higher-level living things." If by apprehend you mean to understand or perceive, which is a standard meaning, then I don't agree. I think consciousness requires a certain level of complexity in order to have awareness and understanding rather than just unaware response. Though consciousness too is a word with different connotations for different people. Also in need of standardization or formal differentiation within science, especially with ongoing research into the perception of neural networks and AI development. report post as inappropriate Eckard Blumschein wrote on Nov. 9, 2015 @ 08:25 GMT Georgina, Do you think the Woodward effect relates to the question of observer? I am rather interested in how the SR's notion "observer" arose. ++++ report post as inappropriate Georgina Woodward replied on Nov. 9, 2015 @ 12:06 GMT Hi Eckard, Am I being asked whether the (James F.) Woodward hypothesis might involve the local accelerated frame as observer of the large scale distribution of matter? Yes it seems to me from what I have just read that maybe that is what the hypothesis entails. There is a Wikipedia article, "Observer(special relativity)" that explains the mathematical observer reference frame used in SR and its historical development. report post as inappropriate Eckard Blumschein replied on Nov. 9, 2015 @ 21:20 GMT Yes Georgina, Identical sentences in at least two articles are telling rather than explaining us something confusing: "it does not make sense to speak of an observer (in the special relativistic sense) having a location. Also, an inertial observer cannot accelerate at a later time, nor can an accelerating observer stop accelerating." I also looked for the history of Maxwell's equation. I was in particular interested in the contributions by Heaviside, Gibbs, and Hertz but I didn't find anything. Tom and Steve A refused to comment on how Lorentz understood the notion observer. Maybe, I am just too stupid? ++++ report post as inappropriate Georgina Woodward replied on Nov. 9, 2015 @ 23:20 GMT Hi Eckard, if the observer is in an inertial frame of reference it is the frame of an observer moving at a steady velocity, not accelerating. What will be seen if the position of the observer person or device is changing and affecting the output that will be observed. Re quote "an inertial observer cannot accelerate at a later time, nor can an accelerating observer stop accelerating" Taking a guess I think that means that in order to be an inertial observer it can not be accelerating and to be an accelerating observer the observer must be accelerating. If either changed their behaviour they would not meet the requirements of their classification. It seems to me that Lorentz considered observers in different inertial reference frames (Ie moving observers in motion relative to each other) that were not within space time but time and space as his work on transformations preceded special relativity but was later adapted by Einstein. Though the transformations are objective and can be applied as linear matrices they are in real world physics, rather than mathematics alone, in no way independent of the observer device or organism as the thing being calculated is what the observer's would see. IMHO In the real universe, rather than the mathematics alone, without having an device or organism capable of converting EM input into output there is no seen. That rings alarm bells for me when I read about transformations of appearance when the relative motions are of inanimate matter alone. Sometimes the ends of conversations get 'lost' due to the way the site works and sometimes questions are not easy, or are time consuming, to answer. Those are more likely explanations for the lack of replies I should think. this post has been edited by the author since its original submission report post as inappropriate Lorraine Ford wrote on Nov. 9, 2015 @ 22:23 GMT Hi Georgina, Surely, you have to look at what seemingly must be happening at a REALLY fundamental level of reality, before you start discussing higher-level reality? I’m saying that there is no mysterious ABSTRACT apprehension of what-there-is-to-know at a fundamental level in the universe (like laws-of-nature and fundamental information like mass, charge and spin). I’m saying that what-there-is-to-know is apprehended (i.e. somehow, grasped/known/experienced) by REAL things: particles, atoms and molecules. The fundamental information is clearly the foundation of complex consciousness/observation. I’m saying that subjective experience/consciousness is not something inexplicable that arises ex nihilo, and only for complex living things. I’m saying that the apprehension of what-there-is-to-know is clearly ABSOLUTELY NECESSARY to the universe, because there is no ABSTRACT comprehension of what-there-is-to-know: there are only real things, like particles, available to apprehend what-there-is-to-know. Cheers, Lorraine report post as inappropriate Georgina Woodward replied on Nov. 10, 2015 @ 00:08 GMT Hi Lorraine, No I don't. I don't think that reduction-ism provides all the answers when it comes to what is output from the information input to organisms, neural networks and AI and how 'object' identification, understanding and knowledge occur. The components of the observing system and processes can be broken down, I agree; However to produce the outputs, perception of objects; object recognition and association of related information; understanding and knowledge, requires a certain level of scale and organisation including that obtained via learning or training. The output being emergent products of and consequences of the function of the complex system. That is, novel emergent organisation, not identified in the interactions of far simpler systems of atoms or particles, lacking the requisite complexity and organisation. report post as inappropriate Lorraine Ford replied on Nov. 10, 2015 @ 00:23 GMT Georgina, you've got yourself mixed up. Though the outcomes of complexity cannot necessarily be predicted, NOTHING NEW ever "emerges" out of complexity. That is a complete furphy. Lorraine report post as inappropriate Robert H McEachern replied on Nov. 10, 2015 @ 00:38 GMT There is a huge difference between reacting to the immediate presence of other things, and reacting to one's created prediction of some future presence of other things. The ability to make such predictions is something new, that arises out of some types of complexities. Rob McEachern report post as inappropriate Lorraine Ford wrote on Nov. 10, 2015 @ 00:58 GMT Rob, mathematical models show that nothing new emerges out of complexity. Georgina is seemingly talking about magical mystery woo-woo emergence. Lorraine report post as inappropriate Robert H McEachern replied on Nov. 10, 2015 @ 15:32 GMT Models can only show that which their premises enable. Other premises show other things. Complexity is all about the information content of the premises - the subsequent math is of little consequence. Rob McEachern this post has been edited by the author since its original submission report post as inappropriate Lorraine Ford wrote on Nov. 10, 2015 @ 02:15 GMT Hi Georgina, OK, you seem to agree that no new rules and no new parameter types can emerge out of complexity alone. But there can be no "progress" in a complex system without the introduction of new rules and new parameters. New superficial arrangements in a complex system are represented by new numerical values for existing parameters. But you have got the problem that seemingly nothing is holding the new arrangements in place. Lorraine report post as inappropriate Frank Martin DiMeglio wrote on Nov. 11, 2015 @ 23:34 GMT The ultimate unification of physics balances being AND experience. There is no getting around this. Outer space is fully invisible and involves full inertia. The Earth/ground is fully visible and involves the experience of full gravity. The space between (and in the MIDDLE of) these spaces necessarily constitutes a MIDDLE distance in/of space consistent with invisible and visible space in fundamental equilibrium and balance. Indeed, notice the balanced attraction and repulsion. This space involves half gravity and half inertia. Given full inertia, space disperses. Given full (or all) gravity, space collapses. report post as inappropriate Lorraine Ford wrote on Nov. 12, 2015 @ 00:17 GMT Rob, Talking about complex systems that might be like our (single) universe (i.e. not complex systems like the Mandelbrot Set): 1. You are right in that an EXTERNAL OBSERVER of a mathematically modelled complex system might see superficial lumps and bumps and islands that come and go. These lumps and bumps merely correspond to a different set of number values for the parameters of the system. But the whole system, including this set of number values for the parameters, is merely a consequence of the set of rules and the initial set of seed parameter values. In fact, the seed parameter values are actually one-off initial rules. 2. But I think that reality is more like a complex system where one-off seed parameter values/new rules are continually being input from what might be described as “points within the system”. These new rules would seemingly ratchet the system, providing a sort of stability. New rules are seemingly the ONLY things that can ratchet the system. 3. Without new rules continually being input, a so-called “complex” system is as dead as a dodo (i.e. timeless, and COMPLETELY AND UTTERLY specified by its rules and initial values). Cheers, Lorraine report post as inappropriate Robert H McEachern wrote on Nov. 12, 2015 @ 21:13 GMT We have very different conceptions of what constitutes a "complex" system. For me, a complex system is one with a high information content. Information cannot be mathematically modeled - it is a self-contradiction. If the "information" could be mathematically modeled, then it would be "compressible", in which case, it would not be "information" at all. Data can be modeled. Information cannot. The Mandelbrot Set is not complex, anymore than pseudo-random numbers are random; they give the appearance of being complex/random, but in fact are really just simple rule-based systems. Here is an example of a complex system: (1) generate a random number. (2) use the number to look-up an arbitrary behavior to be performed. (3) perform the looked-up behavior. In (2), by "arbitrary", I mean specifically that there is no possible way to deduce the behavior (no mathematical model), from the associated number being used as an index for the look-up. Roughly speaking, this is what brains do. For example, there is no physical reason why a car should stop at a red traffic signal. But there is a logical/symbolic reason. Brains, in effect, translate visual sensory data into indices, then perform the "learned" behavior that has been associated with those constructed indices. The important point here, under the topic of "physics of the observer", is that the physics of such a system is almost totally irrelevant to determining the behavior. Failing to appreciate this fact is the reason there has been so little understanding of how observers impact physical outcomes; observers don't just disturb the entity being observed, they may respond in ways that are totally divorced from any of the physical attributes of what was observed, other than that those measured attributes can be utilized to construct an "index", that is subsequently used to look-up an associated behavior. Rob McEachern report post as inappropriate Thomas Howard Ray replied on Nov. 12, 2015 @ 22:01 GMT Rob, how can you be sure that the number is not pseudo-random? report post as inappropriate Robert H McEachern replied on Nov. 12, 2015 @ 22:41 GMT It does not matter. What does matter is that the response cannot be determined from the input alone. The index does not even have to be a number. It need only be one element of a set, a pointer, pointing to the associated neurological response. "Jump!" is not a number, but my brain can take in that visual input (or audible input) and quickly associate a specific behavior with it. But no theory of physics could ever predict/determine that that particular input would produce such a response. Rob McEachern report post as inappropriate Thomas Howard Ray replied on Nov. 12, 2015 @ 22:45 GMT For an index to be complete, it must be non arbitrary. Otherwise, we're back to "merely personal." report post as inappropriate Thomas Howard Ray wrote on Nov. 13, 2015 @ 15:50 GMT Karl Hess elegantly framed Einstein's case for spacetime reality in his 2015 book, Einstein was Right! : "He realized that his views did not agree with the extreme proposition that all science should be exclusively based on direct sense impressions or data obtained from some machinery facilitating the sense impressions [Einstein, 1954] He gave the example of the system of natural numbers, the numbers we use when counting. The mathematical system of these numbers goes way beyond what one can derive from sense impressions, like the counting of oranges. For example, we use the fact that there exists no highest natural number and there exists an infinity of numbers. The mathematician Peano based the natural number system on axioms and derived mathematical truths, so-called theorems, that certainly cannot be obtained from raw sensory materials. He gave the example of two identical tall buildings, one in New York and one in Paris, and said that one would be, on the basis of raw sense impressions forced to regard them as the same object in the sense of physics. He then stated that there was no danger (of logical wrongdoing) in combining the object as an independent concept with the proper spatio-temporal structure, that is with his space-time. He, therefore, combined the existing thing (the tall building) with all its qualities and takes the geometrical relations to other objects of the world as an additional quality. These geometrical relations involve space-time as a product and tool of our thinking that goes beyond the metric data of clocks and meter measure." (p. 98) In their purported refutation of Hess-Philipp, Richard Gill et al, completely ignore the role of spacetime, agreeing with the erroneous notion that "all science should be exclusively based on ... sense impressions." They have proved no more than they have assumed. report post as inappropriate Anonymous replied on Nov. 14, 2015 @ 00:22 GMT Tom, Agree with you. In fact the senses can be completely misleading and differ from person to person and from groups of people to groups of people. I am reading Pinker's How the Mind Works, the part going into the mind's eye. The ability to see autostereograms is genetically determine!. So much for seeing is believing. And yet I do not trust Feynman's policy of shut up and calculate over the senses. He likes his formulas and calculations because he can get 7 orders of magnitude accuracy. So, are we stuck with illusions OR lies, damn lies and statistics? Do you have a technique to "evaluate" physical reality? (can you explain it in a paragraph?) Thanks, Don Limuti report post as inappropriate Thomas Howard Ray replied on Nov. 14, 2015 @ 15:31 GMT Thanks, Don. Yes, I can summarize: My view is based on Karl Popper's rehabilitation of Alfred Tarski's theory of correspondence, for validating true statements. If a mathematical theory in closed form corresponds 1 to 1 with physical predictions, the physical theory is falsifiable by experiment. Example: E = mc^2. It is validated at the large scale by such effects as length contraction and time dilation; at the microscale by the missing binding energy in an atomic fission event. This ability to make logically closed judgements is closely related to the idea of limit in the calculus. Reducing this to a probability argument is the subject of the attached. attachments: Godel_and_3-valued_logic.pdf report post as inappropriate Eckard Blumschein replied on Nov. 14, 2015 @ 20:44 GMT Of course, “Truth is stronger than proof” if it is a conjecture. However, isn't the title of the textbook by Hess a bit misleading? Well, Einstein criticized quantum theory and, in the end, he was right to do so. However, were SR and blocktime justified? ++++ report post as inappropriate Lorraine Ford wrote on Nov. 15, 2015 @ 00:19 GMT Rob, Re: Robert H McEachern wrote on Nov. 12, 2015 @ 21:13 GMT Yes, some of what you are saying seems to be more or less what I am endeavoring to say: a truly complex system is never an initial-rule-based (i.e. “compressible”) system. So an initial set of law-of-nature rules plus initial parameter values are not enough information to describe the resulting truly complex... view entire post report post as inappropriate Georgina Woodward wrote on Nov. 15, 2015 @ 19:54 GMT All, I asked John "'Try to imagine a universe where all EM radiation has been removed," ... "Simultaneity can not now be measured by what is seen simultaneously within an observed present output 'reality'. Can you do that? This relates back to John's "Something has to give if there is a physically real simultaneity as we imagine it to be". I think that is a useful exercise. A... view entire post report post as inappropriate Georgina Woodward replied on Nov. 15, 2015 @ 20:00 GMT Hi All, The previous post sets out how there are simultaneously two different kinds of simultaneity for a given scenario, in a way that can be demonstrated mathematically. this post has been edited by the author since its original submission report post as inappropriate Georgina Woodward replied on Nov. 15, 2015 @ 22:31 GMT I should probably have mentioned that Alice's frame of reference is inertial in relative motion to Bob,I mean to say not accelerating relative to him. report post as inappropriate Georgina Woodward replied on Nov. 16, 2015 @ 19:29 GMT Maybe this needs a better headline- Three simultaneous simuiltaneities, two reciprocal and one shared. report post as inappropriate Lee Bloomquist wrote on Nov. 16, 2015 @ 04:11 GMT "I just tried to put a simple model of an observer in the "wind tunnel," a model where the observer has only so long to live. Each day possibilities decrease as the end approaches. At the same time, the available information increases each day. Then, when possibilities finally all disappear, existence ends. It might be the starting point for a better Hamiltonian and initial conditions in order to model an observer" This Hamiltonian and other equations here: http://fqxi.org/community/forum/topic/1928 post approved Georgina Woodward replied on Nov. 16, 2015 @ 07:20 GMT Hi Lee, I spotted and read your initial equations a while ago. I didn't realize that the majority of the presentation was in the contracted post that starts "Footnote". So I'm just pointing that out so others can locate where your ideas are to be found. You have identified the human condition in your description of the relationship of a human observer to the potentially available information, taking that to be via all forms of media. Though there are also limits to the amount of information a brain can process. Information overload is a problem in itself. The decline in that ability to process information with time varies between individuals. I expect some are on top form until the very end. report post as inappropriate Lee Bloomquist wrote on Nov. 16, 2015 @ 23:25 GMT Hello Georgina, "Observation" and "inquiry" seem to me closely related. It is from this association to inquiry that I get mathematical models of inquiry from the late Jon Barwise. I don't expect readers to follow my links and references all the way to the most basic. So here is the link down to "inquiry": ----- In the FQXI paper "Simple math for questions to physicists" I... view entire post post approved Georgina Woodward replied on Nov. 17, 2015 @ 00:32 GMT That sounds like an interesting approach to the anticipated new FQXi essay question. It will probably be something to do with "the observer", in keeping with the Grant program "Physics of the observer" and the planned multidisciplinary networks of researchers to aid research of that. report post as inappropriate Lee Bloomquist replied on Nov. 28, 2015 @ 14:56 GMT From the above quote, it looks like Sherlock Holmes may have been an "informationalist"! ( : ) "The main idea of informationalism is to take the inverse relationship between information and possibility as a guiding tenet. The Inverse Relationship Principle: Whenever there is an increase in available information there is a corresponding decrease in possibilities, and vice versa. " (Information and Impossibilities. Jon Barwise) To an informationalist, information and possibilities might be prior to space. First the observer feels proper time, not coordinate time. Then space could enter like this: There is the possibility of being at x: $\Psi (x)$ And at the same time there is the possibility of not being anywhere else: $\Psi ^* (x)$ Together these are the logic of a particle in a situation where only possibilities exist and nothing else. Then there is information that's available from the past. From that, the frequency or probability that a particle will have been at x is: $P (x)$ And because of the Born rule there is an arrow from possibilities in the future to information available from the past: $\Psi (x) \Psi^* (x) \rightarrow P (x)$ In the paper I submitted to FQXI "Simple math for questions to physicists" there is also an arrow from the nonstandard past to its mirror point in the nonstandard future. These are two situations which respectively support possibilities and information available from the past, in the latter case probabilities or frequencies. It's something that Jon Barwise called an "infomorphism." (Information Flow: The Logic of Distributed Systems) report post as inappropriate George Kirakosyan wrote on Nov. 17, 2015 @ 09:43 GMT Dear Brendan, I am very welcome the last FOXi theme on the observer's physics. It may to serve as an important key to involving a new approaches and research methodology (without any exaggeration!), which is necessary to outcome of physics from present stagnation, in my confidence with many others. I am trying to move by own way that closely related to observer's role in physics. My last article (article) on the cognitive meaning of relativity (ST & GR - in archive) directly touches to this question. It contains also some interpretations related to previous themes of FOXi contests (physical meaning of time, about mutual relation math to reality, etc.) By this, I am just ask you to check this article to decide how it relates to basic purposes of your community, to help me or advice me what better to do with my works. I understand that such request may seem very strange, but I really do not know how to solve technical and bureaucratic problems to reach my works to small quantity of people who may find there some interest. Actually, I think any solution or innovation that come from side people these hardly may get attention in official science, independently what you will solve or say, however FOXi have declared some opportunity to that. Regards, George K. report post as inappropriate Georgina Woodward replied on Nov. 17, 2015 @ 19:00 GMT Hi George, you can always join the community here and discuss what you have written little by little. Your article is 49 pages long and that is a lot of words to read and process. I speed read through it. There is a lot of introductory material and I wonder whether it is all necessary. It would be a lot more reader friendly if you 'cut to the chase' and get your main insights across without burying them in too many words. Maybe you could do an abridged version. The FQXi essays have a nine page limit and that makes them a reasonable length for readers to manage in one sitting. Page 9 was well explained and interesting to me as you say some things about SR that agree with what I have been writing here.The key point being to always remember that SR is about what is seen. There is a lot in your article, especially about gravity, that you could talk about on this site. report post as inappropriate George Kirakosyan replied on Nov. 19, 2015 @ 06:54 GMT Hi Dear Georgina, Thank you for kindly answer and your advices. Actually my (ours) trouble is a more serious than simplest inclination to verbosity. I know about 9 pages limit of FQXi. However, how can anybody to think explain cognitive content of Einstein' mysterious works in 9 pages, if even he well know the matter? Meanwhile, to analyze and understand the question it is necessary to look it in the whole context of physics! The problem is, a huge methodological mistake has been admitted by our teachers, by division of physics from philosophy and from logic at all, as well as by its unprecedented mathematisation and next fragmentation of it on the classical and quantum divisions with their uncountable sections, subsections etc. Famous physicist Steven Weinberg writes in his book (as remember) - We, physicists are special people who get a huge satisfaction from different kinds of calculations... We can understand with you this nice hobby (that may bring some people to Nobel Prize!) However, I will dare to assure you there is other incomparable amazing hobby than the game with symbols and formula. That is - a play with own mind. It however, demands big volume and huge time to explain, that I would like to convince to modern theorists! That is a hopeless job really as I am understand and you are very right! I am very thankful for your advices and I will try to use that. Best Regards, George report post as inappropriate Lee Bloomquist wrote on Nov. 18, 2015 @ 13:30 GMT Here is a propositional attitude: "O observes that the electrons produce a wave pattern." From Wikipedia: "A propositional attitude is a mental state held by an agent toward a proposition. Propositional attitudes are often assumed to be the fundamental units of thought and their contents, being propositions, are true or false. An agent can have different propositional attitudes toward the same proposition (e.g., “S believes that her ice-cream is cold,” and “S fears that her ice-cream is cold”). Linguistically, propositional attitudes are denoted by a verb (e.g. "believed") governing an embedded "that" clause, for example, 'Sally believed that she had won'." (Please see my previous post here.) post approved Lee Bloomquist wrote on Nov. 18, 2015 @ 19:40 GMT In natural language humans implicitly perceive and observe "situations," according to analyses of the linguistic data by the late Jon Barwise (The situation in logic) and others. That this perception and observation of "situations" is implicit. yet pervasive, can be seen by reading an example two times-- first with the words in parentheses and then without-- "Observer O observed (the situation) that electrons in the experiment produced a wave pattern, as if each electron observed (the situation) that there were two possibilities for it, or two slits." Situation theory made the above, implicit "situation" explicit in a pretty minimalistic mathematical theory. In the paper "Simple math for questions to physicists," this website, I tried applying it to some physics. Please see my previous post here. post approved Lee Bloomquist wrote on Nov. 19, 2015 @ 23:48 GMT The *conjugate variables* of the observing process are probably possibilities and information-- actually the number of possibilities and the number of pieces of available information. There is a Hamiltonian posted about this in the "alternative theory" blog. Conjugate variables, when dynamically in balance, add a constant number to the Hamiltonian. Of a system that is born, exists, then dies, this balance only holds true during existence. Being born means possibilities are increasing but available information lags in increase, and is not in balance. Death means possibilities vanish, while available information freezes-- again, not in balance. In the posted Hamiltonian, I only modeled existence. post approved Lee Bloomquist wrote on Nov. 21, 2015 @ 11:24 GMT No "information channel": No observer. In an observation process, information needs to flow from the system being observed to the observer. In "Information Flow: The Logic of Distributed Systems" (Jon Barwise and Jerry Seligman), such an information channel is defined. https://books.google.com/books?id=5sjLCgAAQBAJ The process of observation is then: There are certain possibilities (for state, or for type of situation) for the system being observed. Through an information channel, information is made available to the observer. Which reveals that some of the previously possible states are, in light of the information made available, actually impossible. Repeat up to the accuracy of the observation process. post approved Lee Bloomquist replied on Nov. 23, 2015 @ 14:01 GMT This is a process of observation I based on the work of Jon Barwise in Information and Impossibilities (see link in previous post). I met him at a workshop at Stanford's Center for the Study of Language and Information titled "The business applications of situation theory." He passed much too early. report post as inappropriate Steve Dufourny replied on Nov. 23, 2015 @ 14:09 GMT Hello Mr Bloomquist? It is relevant.How can we modelize the universal informations and encodings.What is the nature of an information? We are at this moment of evolution in the heat and thermo and electromagnetism.How can we insert the gravitational informations in the computing ? Trading at high fréquences are a reality with photonic informations.The speed can be improved with the gravitons and correlated waves.But the real question is ,can we make it ?Spiritually speaking and socially speaking ? What a world,these Tools must be universal and must be utilised with the biggest wisdom and cosnciousness. report post as inappropriate Lorraine Ford wrote on Nov. 22, 2015 @ 01:14 GMT It is clear that numbers represent something very important about fundamental reality, because we need numbers JUST AS MUCH AS we need law-of-nature equations to represent fundamental reality, whether at the big bang, or fundamental reality as it is now. But physics can’t seem to conceptualize what actual physical reality a number could represent, and there is seemingly very little discussion on the issue. So one might (wrongly) conclude that numbers are a non-issue, or one might (wrongly) conclude that a number can safely be considered to be a non-physically-real platonic entity. Some have concluded that numbers can be understood via Set Theory. But despite the seeming simplicity of pictorially represented Set Theory ideas, Set Theory has a lot of extremely complex concepts when it comes to building numbers out of sets, especially algebraic irrational numbers. So if it is correct to assume that the underlying fundamental-level reality is relatively simple, and that complexity is a higher-level later development, then Set Theory is not useful for modelling any physical reality that might underlie what we humans represent with number symbols. report post as inappropriate Lorraine Ford replied on Nov. 22, 2015 @ 01:19 GMT (Continued from above): To get to the point, any comprehensive theory of reality needs to account for numbers, and any theory of what “an observer” is needs to be compatible with ideas about numbers: are you describing a reality that includes abstract entities and structures, OR are you talking about a reality that only has real entities and structures? It is necessary that reality grasps/apprehends its own laws. So you have a choice: numbers and laws-of-nature are ABSTRACT structures that are ABSTRACTLY apprehended and acted upon by the universe OR numbers and laws-of-nature represent REAL structures that are apprehended by REAL entities i.e. particles and atoms. I contend that laws-of-nature are real information category relationship “structures”, and that numbers derive from partial information category relationships where the category “cancels out”. I contend that this apprehension, i.e. the grasping of different categories of information and their interrelationship, IS subjective experience/subjective consciousness. Consciousness is not something weird and unexplainable. The first step in understanding any “observer effects” is acknowledging that “conscious observers” are intrinsic to the structure of the universe. report post as inappropriate Lee Bloomquist wrote on Nov. 22, 2015 @ 22:43 GMT From page 27, "Information Flow: The Logic of Distributed Systems" (Barwise and Seligman): "Probability theory, and applied mathematics in general, works at the level of types....[note by LB: hence ignoring the particular instances that exist. Types instead characterize any number of particular instances that existed or will exist.]...For a theory of information, however, these particulars, or instances, cannot be ignored." Reading onward, we find that it is the existence of an instance with parts, i.e. a system of instances which are existing together in a system, that enables the flow of information in an "information channel." In order to flow, information requires a system of parts that all co-exist. The numbers, as in probability theory and hence Shannon-like theories of information, don't say how it is that information flows, because they are about numbers hence types of things that existed or will exist; and they are not about that which enables the information to flow. That's my summary. But I urge readers to see this for themselves. post approved Georgina Woodward replied on Nov. 23, 2015 @ 02:35 GMT Interesting Lee. Incidentally I think that as well as a system of parts that co-exist there has to be change. I mean by that a static block time existence of a system of co-existing parts still doesn't provide flow. I don't get that impression of change from the expression " a system of instances which are existing together in a system...." Perhaps the word system is used to imply work and so is another way of saying change. Its not clear. Though you are giving a brief summary and perhaps it is more clearly explained in the referenced work. Interesting observation in your last paragraph. Physics does seem to be comprised of many parts that don't readily overlap. report post as inappropriate Lee Bloomquist wrote on Nov. 23, 2015 @ 20:15 GMT Information Channel. An example from Jon Barwise. At the workshop mentioned in a previous post here, Prof Barwise, in response to a question, stopped writing on the overhead projector-- and moved in front of the projection lens so as to block the light beam from the projector lens to the screen. The screen went dark of course. He had just destroyed an information channel. As a result, information stopped flowing. Then he moved away from his position blocking the light beam, back to writing on the overhead projector. The screen lit up with what he began to write. He had just created an information channel. As a result, information began once again to flow. The mathematical language in his book with Seligman, "Information Flow: The Logic of Distributed Systems" gave him the terms and syntax to express what had just happened-- right there on the screen in front of us. Creation and destruction of an information channel can, most likely, Not be as clearly expressed in say Shannon's theory of information, based as it is on probability numbers. Is creation and destruction of information channels relevant to the physics of the Observer? post approved Lee Bloomquist replied on Nov. 30, 2015 @ 02:17 GMT Using "infomorphism" in a sentence-- "An information channel consists of an indexed family...of infomorphisms.." Page 34. Information Flow: The Logic of Distributed Systems. report post as inappropriate Lee Bloomquist replied on Dec. 1, 2015 @ 13:59 GMT The idea so far: using the "information channel" to think about the observer based on a theory from the field of logic (informationalism) itself begun from data about natural human language (situation theory). Do readers have suggestions for a next step? "Observers synchronizing clocks" perhaps? report post as inappropriate Thomas Howard Ray replied on Dec. 1, 2015 @ 17:55 GMT Let me throw this out there, Lee: In 2001 the late physicist Jacob Bekenstein along with Hebrew University colleague Avi Mayo published "Black Holes are One-Dimensional" noting, "... viewed as an information absorber or entropy emitter, a black hole in 3–D is fundamentally one-dimensional, verily a portal to a one-dimensional information channel." An indexed channel the way Barwise describes it, would seem to share this dimensionality, which rules out an independent observer channel. What I mean is, given a line and a point external, in Euclidean space, one and only one line can be parallel to the original. This implies an observer orthogonal to the flow of information, similar to a Turing machine processing data. Which allows an objective observer -- albeit yielding coherent information only in 2 dimensions. Even though we live in curved spacetime of at least 4 dimensions, and because spacetime is mostly Euclidean, we can accept this 'entanglement' of observer-observed as a faithful representation of reality projected into 3 dimensions. To be complete, a time parameter must be included. And so the quantum domain is restricted to information theory, and we need an extra degree of freedom for coherent communication between quantum and classical domains. this post has been edited by the author since its original submission report post as inappropriate Frank Martin DiMeglio wrote on Nov. 27, 2015 @ 22:19 GMT Forget about observer and observed. WE WANT TO BALANCE BEING AND EXPERIENCE. Full inertia is fully invisible space and no distance in/of space....that means no experience....SO, THERE CAN BE NO FULL, ACTUAL, REAL, TRUE, AND DIRECT EXPERIENCE OF OUTER SPACE AS IT IS. Full gravity is full distance in/of space and full experience...seen, felt, AND touched. Half inertia and half gravity is the middle distance in/of space consistent with visible AND invisible space in fundamental equilibrium and balance. So, the falling man feels no gravity. AS MIDDLE DISTANCE and FULL DISTANCE are in balance, the feeling of gravity of the man standing upright on the ground is also a balanced INERTIAL resistance. The ultimate unification of physics balances being AND experience. IMPORTANT. In dream experience, bodily/visual experience is visible and invisible in balance. Dreams are between (and in the MIDDLE of) our experiences of full gravity (the Earth/ground) and FULL ELECTROMAGNETISM (television). This tells much about observer and observed. WE WANT TO BALANCE BEING AND EXPERIENCE IN PHYSICS. The integrated extensiveness of thought (and description) is improved in the truly superior mind. This is top down thinking. Mathematics involves relatively narrow thinking. Top down thinking is sorely lacking in modern physics. It is a great truth/fact (in physics as well) that the self represents, forms, and experiences a comprehensive approximation of experience in general by combining conscious and unconscious experience. In fact, the ability of thought to describe OR reconfigure sensory experience is ULTIMATELY dependent upon the extent to which thought is similar to sensory experience. Again, the ultimate unification of physics balances being and experience. The goal is to improve, extend, and integrate the understanding of physics/physical experience/reality, right? this post has been edited by the author since its original submission report post as inappropriate Frank Martin DiMeglio wrote on Nov. 30, 2015 @ 20:23 GMT UNDERSTANDING GRAVITY AND INERTIA, AND FULL GRAVITY AND FULL INERTIA: Full gravity involves full experience and full distance in/of space as it is seen, felt, AND touched. The experience of full gravity involves fully visible space and full distance in/of space, along with full experience. Full inertia, as in the direct/full/real/true/actual experience of outer space as it... view entire post this post has been edited by the author since its original submission report post as inappropriate Frank Martin DiMeglio wrote on Dec. 2, 2015 @ 01:57 GMT THE ULTIMATE UNIFICATION OF PHYSICS BALANCES BEING AND EXPERIENCE, SO CAREFULLY CONSIDER THE FOLLOWING: FULL INERTIA, outer space, fully invisible. NO DISTANCE. OUTER SPACE IS NOT (AND CANNOT BE) EXPERIENCED AS IT IS....that means there is NO direct, true, real, actual, and full experience of outer space at all. Outer space ITSELF involves no experience AT ALL in relation to being.... view entire post this post has been edited by the author since its original submission report post as inappropriate Lorraine Ford wrote on Dec. 2, 2015 @ 23:25 GMT Clearly “law-of-nature” relationships and associated numbers represent the fundamental physically-real information that informs reality. The reality that is informed is clearly REAL things: particles atoms and molecules. Unless you want to go into the magical-mystery woo-woo realm of abstract entities being informed by abstractly existing mathematical rules. Seemingly Tom and Lee B. are followers of woo-woo versions of reality. post approved Eckard Blumschein replied on Dec. 3, 2015 @ 04:00 GMT Lorraine, Did you consider http://www.grc.nasa.gov/WWW/K-12/Numbers/Math/Mathematical_T hinking/observer.htm too? Incidentally, how did you understand informs in "information that informs reality"? The original meaning of to inform is transmitting a piece of information to someone, and if you have information about something, you know something about it. Transmission is unidirectional. ++++ report post as inappropriate Jason Mark Wolfe replied on Dec. 3, 2015 @ 05:59 GMT Lorraine, What do you think about the idea that particles and fields are the foundations of reality? Fields can certainly have energy states. Momentum, spin and other kinds of measureables represent the properties of a specific field. Why can't we imagine more generalized kinds of fields? What about a field with energy states that can change the properties of a photon, change its speed of light? Or kick it into another a hidden space-time? Then it decays back to a regular photon and returns to normal space time. Is it wrong to imagine such things? Jason report post as inappropriate Lorraine Ford replied on Dec. 3, 2015 @ 13:50 GMT Eckard, Re "information that informs reality": Obviously law-of-nature relationship information cannot come from TRANSMISSION of information. On the contrary, law-of-nature relationship information is the FOUNDATION of information transmission: e.g. in any particle - particle interaction (call one particle “the messenger”), BOTH particles are affected/informed/transformed according to law-of-nature relationships. So firstly, all information transmission is based on the bedrock foundation-stone of law-of-nature relationship information; and secondly, this information transmission is NOT unidirectional. Re http://www.grc.nasa.gov/WWW/K-12/Numbers/Math/Mathematical_T hinking/observer.htm : I would agree with Joe Kolecki that “In order for the observers to learn about the system, they must cause at least one quantum of "information" (energy, momentum, spin, or what-have-you) to pass from themselves …” This indicates that an observer is not merely a passive recipient of information, but an active one i.e. “they must CAUSE …” a perturbation i.e. literally create some new information. This fundamental-level information is representable in the form of a mathematical equation. Lorraine report post as inappropriate Lorraine Ford wrote on Dec. 4, 2015 @ 01:52 GMT Brendan, Could you please reinstate my missing posts, to the “Physics of the Observer - Call for Proposals and Program Launch” blog, of: Dec. 2, 2015 @ 23:25 GMT, Dec. 3, 2015 @ 13:50 GMT, Dec. 3, 2015 @ 14:17 GMT and Eckard Blumschein’s post of Dec. 3, 2015 @ 04:00 GMT, and Jason Mark Wolfe’s post of Dec. 3, 2015 @ 05:59 GMT ? Thanks, Lorraine Ford report post as inappropriate Jason Mark Wolfe replied on Dec. 4, 2015 @ 02:05 GMT No wonder I couldn't find it. Thanks. Jason report post as inappropriate Eckard Blumschein replied on Dec. 4, 2015 @ 17:13 GMT My deleted post pointed to speculations by David Mazza . The own reasoning I added was anyway incomplete. ++++ report post as inappropriate Lorraine Ford replied on Dec. 5, 2015 @ 12:19 GMT Eckard, See below for copies of your deleted post [1], and my 2 deleted replies to your post [2] [3]. What is your opinion about the article on http://www.grc.nasa.gov/WWW/K-12/Numbers/Math/Mathematical_T hinking/observer.htm ? Lorraine 1. Eckard Blumschein replied on Dec. 3, 2015 @ 04:00 GMT Lorraine, Did you consider... view entire post report post as inappropriate Lorraine Ford wrote on Dec. 4, 2015 @ 12:28 GMT Lorraine Ford wrote on Dec. 4, 2015 @ 01:07 GMT Lorraine Ford wrote on Dec. 2, 2015 @ 23:25 GMT Clearly “law-of-nature” relationships and associated numbers represent the fundamental physically-real information that informs reality. The reality that is informed is clearly REAL things: particles atoms and molecules. Unless you want to go into the magical-mystery woo-woo realm of... view entire post report post as inappropriate Jason Mark Wolfe replied on Dec. 5, 2015 @ 00:59 GMT Is the space time continuum a solution to some differential equation caused by elements unknown to us? The actual preconditions to the big bang? report post as inappropriate Lorraine Ford replied on Dec. 5, 2015 @ 13:21 GMT Jason, Re “elements unknown to us”: I think physics already pretty much knows the TYPES of elements of reality - there are NO TYPES of elements that are unknown to us: firstly, there are THINGS (strings??, particles, atoms, molecules, single-cell living things and multi-cell living things); and secondly, there are the physical structures/law-of-nature INFORMATION RELATIONSHIPS that (only for fundamental-level reality) are representable by mathematical equations. Re “Is the space time continuum a solution to some differential equation”: No. I consider that “space” and “time” are due to information relationships, and information relationships are REPRESENTABLE by mathematical equations. My assumption is that the particle-type things came first, and they created/built the information relationships from scratch i.e. physically real things built physical reality, including "space" and "time", out of information relationships. Lorraine report post as inappropriate Jason Mark Wolfe replied on Dec. 5, 2015 @ 17:12 GMT Hi Lorraine, Respectfully, I disagree. The physics constants c and G are mysteriously given, not calculated. Are they unchangeable dictates of a Creator? Or can they be manipulated by some energetic field yet to be discovered? Jason report post as inappropriate Lorraine Ford wrote on Dec. 4, 2015 @ 12:30 GMT Brendan, More of my posts have been maliciously deleted. Could you please also reinstate my missing posts, to the “Physics of the Observer - Call for Proposals and Program Launch” blog, of: Dec. 4, 2015 @ 01:07 GMT and Dec. 4, 2015 @ 01:16 GMT . I think Jason Wolfe’s post of 12/4/15 at 4:14am has probably also been maliciously deleted, and should be reinstated. And seemingly Lee Bloomquist’s and Thomas Howard Ray’s recent posts have also been maliciously deleted, and should be reinstated. Thanks, Lorraine Ford report post as inappropriate Jason Mark Wolfe replied on Dec. 4, 2015 @ 19:51 GMT Hi Lorraine, Thank you for defending the "malicious deletions" of my posts. The fact that my description of alien hyper-drive technology is still there probably means there is no malicious intent. It's probably just an accident/database issue. Jason report post as inappropriate Lorraine Ford wrote on Dec. 6, 2015 @ 00:46 GMT Hi Jason, Physics claims to be about PHYSICAL reality: once you start getting into supposing that abstract entities exist, all bets are off, and you are in la-la land, and you can fabulate any story you like, totally unhinged from any backup in physical reality. But there is no need to wildly speculate; there is no need to suppose that some amazing thing not yet discovered is going to answer all your questions; and there is no need to suppose that new, cool, awesome and cutting-edge equations will answer all your questions either: just look more carefully at what is already known to exist. See my above posts (Nov. 22, 2015 @ 01:14 GMT, and Nov. 22, 2015 @ 01:19 GMT) for my opinion about numbers. In essence "I contend that laws-of-nature are real information category relationship “structures”, and that numbers derive from partial information category relationships where the category “cancels out”". I'm claiming that what we represent with number symbols, even c G e and pi, ultimately DERIVE from the same physically-real information category relationship structures as laws-of-nature. I'm also claiming that the numbers that represent the “discontinuous” aspects of the physical outcomes of quantum decoherence [1], are newly-created information category relationship structures where the category “cancels out”. I’m saying that THINGS [2] create new INFORMATION RELATIONSHIPS/physical outcomes. I’m claiming that we don’t need to look to mysterious abstract entities for the solution to “the number problem”: just look at what is already known to exist. Lorraine 1. “quantum mechanics, via decoherence, is constantly injecting new bits of information into the world”, The Computational Universe by Seth Lloyd, in Information and the Nature of Reality, Cambridge University Press, 2010 . 2. Things are: particles, atoms, molecules, single-cell living things and multi-cell living things. report post as inappropriate Jason Mark Wolfe replied on Dec. 6, 2015 @ 06:07 GMT Your referral to abstract entities makes me want to double down on the importance and beauty of God, gods, religions, magic, and all things that inspire spiritual and religious experience. And trust me, I am no light weight when it comes to math, physics, science or reason. I can even see the grey areas where new physics could fit. report post as inappropriate Vijay Mohan Gupta replied on Feb. 14, 2016 @ 19:19 GMT Good Morning Mr Brendan Foster, You are right in excluding abstractions, But mathematics itself is an abstraction by itself. Abstractions as means of comunication between humans can not be avoided. I see a serious mind being applied to subject in your comments. PIco Physics is based on the basics of this discussion thread. PicoPhysics understands "The observation is an abstraction... view entire post report post as inappropriate Frank Martin DiMeglio wrote on Dec. 6, 2015 @ 19:56 GMT Einstein didn't balance being and experience Full inertia (outer space) eliminates our experience entirely, as it entirely eliminates distance in/of space. Outer space is fully invisible. Whereas FULL GRAVITY involves FULL DISTANCE in/of space and FULLY VISIBLE space as it is seen, felt, AND touched. Einstein should have considered the man standing upright on the Earth/ground. Now, invisible AND visible space in FUNDAMENTAL equilibrium IS the MIDDLE DISTANCE in/of space consistent with equivalent and balanced inertia and gravity (half gravity and half inertia). The eye is the body. The eye is invisible, AND it is visible. It is touched, and it is not touched. The eye/BODY is ALSO SEMI-VISIBLE (as the dome of the eye/body), as the balanced MIDDLE DISTANCE in/of space. So, it is SEMI-DETACHED in relation to touch/tactile experience; as the fully visible body extends full distance in the experience of full gravity that involves the fully visible Earth/ground. The FULLY VISIBLE BODY is then ATTACHED in relation to touch/tactile experience. Importantly, the MIDDLE DISTANCE and FULL DISTANCE experiences of space are in balance. We want to balance/"match up" being and experience. Watch someone else at full distance touch the top of their fully visible body/head with their fully visible hand. Being and experience are in balance, as MIIDLE DISTANCE and FULL DISTANCE are in balance. The feeling of gravity is a balanced INERTIAL resistance. The ultimate unification and understanding of physics balances being AND experience, and it combines, balances, and includes opposites. This proves that Einstein's general theory of relativity did not fully and extensively describe and explain gravity, nor did it truly and extensively explain the balanced and true relation between inertia and gravity. report post as inappropriate Lorraine Ford wrote on Dec. 7, 2015 @ 08:20 GMT Jason, I’m sorry if my views seem harsh to you, but my views are actually anything but harsh. Basically I’m saying that physical reality IS subjective experience, “consciousness” if you like. Reality is not dualistic: reality is not divided into (1) the coarse physical, and (2) the spiritual/abstract/platonic/conscious/creative realms where all the finer and more subtle essences reside. The “finer and more subtle essences” are physically evidenced e.g. by laws-of-nature (i.e. information category relationships) and by complex molecular structures which “talk to each other”. The things of reality are truly creative and conscious, subjective and interrelated. But there is no OVERALL god-like entity that is creative and conscious, that can be praised or blamed for everything, or that will save the things of reality from the consequences of their own actions. Reality is more subtle, more difficult, more alive, more interesting than a simplistic all-knowing creator-god model of reality would allow. And reality is also more subtle, more difficult, more alive, more interesting than physics, with its abstract/platonic realm of numbers and laws-of-nature would allow. Both physics’ and religion’s dualistic views of reality are cop-outs which avoid facing up to the actual nature of reality. There is no division into God and not-God; there is no simplistic objective reality which can be fully specified by symbols on a T-shirt. There is only the subjective information experience of things (particles, atoms, molecules, single-cell living things, and multi cell living things) which IS physical reality. Lorraine report post as inappropriate Jason Mark Wolfe replied on Dec. 8, 2015 @ 02:15 GMT Hi Elaine, I am sitting here listening to Spirit Voyage, music by Gurunam Singh, melting into its beauty, its joy. I know my way around many parts of reality, but do not find in it the joy that I find in spirituality, spirit, prayer, etc. I would almost give up debate if I could just float in this bliss forever. Jason report post as inappropriate Lorraine Ford wrote on Dec. 7, 2015 @ 14:36 GMT Eckard, Yes, technology is benefiting from information theory, but it is important to be very clear about what is actually happening. The communication of information from one person to another can only be achieved via representing information symbolically. A spoken or written word is a symbolic representation of consciously experienced information. Similarly if the communication is... view entire post report post as inappropriate Frank Martin DiMeglio wrote on Dec. 10, 2015 @ 21:02 GMT EINSTEIN DID NOT UNDERSTAND INERTIA AND GRAVITY THE FULL SIGNIFICANCE OF THE FALLING MAN Einstein failed to understand that the ultimate unification of physics balances being and experience. Forget about observer and observed. Here's why: The space (itself) that is between (and in the MIDDLE of) full inertia (outer space, black, fully invisible space) and full gravity (the... view entire post this post has been edited by the author since its original submission report post as inappropriate Amrit Srecko Sorli wrote on Dec. 12, 2015 @ 10:17 GMT Origin of the Observer and ontological Hierarchy of the Universe this essay on file attached is in brief about the origin of the observer report post as inappropriate Michelle Johnson wrote on Dec. 12, 2015 @ 14:54 GMT Thanks for announcing the beginning of an ambitious new program. In your questions: Which the answers depend on how we think of observers? The term observer has a number of non-equivalent uses in science. In quantum mechanics, "observation" is synonymous with quantum measurement and "observer" with a measurement apparatus and "observable" with what can be measured. Thus the quantum mechanical observer does not have to necessarily present or solve any problems over and above the (admittedly difficult) issue of measurement in quantum mechanics. The quantum mechanical observer is also intimately tied to the issue of observer effect. To know more I’m sharing with you original https://en.wikipedia.org/wiki/Observer_(quantum_physics) report post as inappropriate Frank Martin DiMeglio wrote on Dec. 12, 2015 @ 21:21 GMT It is a matter of balancing being and experience, and not one of "observer" and "observed". By doing this, you are dividing up, reducing, and fragmenting the understanding. report post as inappropriate Frank Martin DiMeglio wrote on Dec. 12, 2015 @ 21:25 GMT The ultimate unification (AND understanding) of physics balances being and experience. Here is solid proof. EINSTEIN'S TURN TO FALL. TOP THIS !!! WHY THE FALLING MAN FEELS NO GRAVITY: We want to balance being and experience. Gravity pertains to visibility and distance in/of space (seen, felt, AND touched). The falling man feels no gravity because the gravity cancels or... view entire post this post has been edited by the author since its original submission report post as inappropriate Amrit Srecko Sorli wrote on Dec. 15, 2015 @ 14:27 GMT idea of existence of "internal" and of "external" observer is wrong. report post as inappropriate Anthony DiCarlo wrote on Jan. 8, 2016 @ 16:06 GMT It is precisely "Physics of the Observer" that was described at: http://fqxi.org/community/forum/topic/1467 http://fqxi.org /community/forum/topic/891 All measures MUST funnel through our 5 senses to become useful information. It is precisely these 5 senses that must lie at a boundary between measure and information. All telescopes, microscopes, spectrometers, etc., are just physical extensions to our 5 senses. This implies that the unification of information with ALL measures MUST funnel through our 5 physical senses. It simply comes down to "you" and your physical connection to the universe when any measure is made! report post as inappropriate Nicholas I Hosein wrote on Feb. 16, 2016 @ 16:42 GMT HERE IS AN ENTIRE THREAD DEDICATED TO SPOOKY ACTION AT A DISTANCE. WORTH THE READ! http://www.sciforums.com/threads/spooky-action-at-a-dis tance.142216/ report post as inappropriate Brian Balke replied on May. 14, 2016 @ 18:32 GMT Professor Eugene Commins at UC Berkeley studied under Einstein at Princeton. His categorization of quantum phenomena was more rigorous that most. I summarized Einstein's views, as Commins transmitted them to his students, here: https://everdeepening.com/2016/01/30/quantum-entangleme nt/ The broad challenge in interpreting the wavefunction is that it a convenient mechanism for lumping together many forms of uncertainty: initial state, uncontrollable perturbations of the Hamiltonian, ensemble statistics, and intrinsic quantum randomness. When the final state is written down, it is almost impossible to disentangle these effects. The examples that I offer in my post demonstrate that we can create "wavefunctions" (probability distributions) for classical systems that manifest many of the characteristics of quantum entanglement. Many critics of common experimental "proofs" of entanglement physics observe that they results can be explained by initial state uncertainty. In my post, I describe the kind of experiment that would resolve this deficit. I don't believe that they have been pursued because researchers are satisfied (erroneously, I assert) that their work proves the existence of entanglement. report post as inappropriate Amrit Srecko Sorli wrote on Feb. 18, 2016 @ 15:18 GMT Observer has origin in Consciousness-Being. This are my results publishes last year. attachments: 5_On_the_origin_of_the_observer.pdf report post as inappropriate Brian Balke wrote on May. 13, 2016 @ 04:38 GMT My sense is that the most interesting question to ask here is whether the apparatus that we use to gather information about the world around us precludes the detection of certain kinds of phenomena. We accept this about our senses, as they have been far surpassed by our machines as regards both temporal and spatial resolution. But that still permits the existence of coherent behavior at larger scales that disappear when thus probed. As an example, consider the study of a phase transition where introduction of a probe added energy that locally drove the system across the phase boundary. Obviously, the information revealed about the system would lead to biased conclusions. The error would only be revealed if we were motivated to obtain a different probe. How do we know that our probes aren't biasing our understanding of fundamental physics? Of particular interest to me, I note that the existence of the soul, long obvious to observers in earlier eras, has become a matter of ridicule in contemporary physics. Could it be that organic structures are sensitive to coherence that is completely disrupted by the conductors and fields that are so typical in modern detectors? report post as inappropriate Steve Agnew replied on May. 14, 2016 @ 12:53 GMT One way to interpret quantum uncertainty is that the observer cannot help perturbing the observation at some point. An example uses a shorter and shorter pulse of light to probe the color of a changing object. Once the pulse is very short, the probe reveals nothing since the pulse color of each photon is white. At that point, color change no longer has any meaning and the observer probe affects all colors of the observation. Another way to interpret quantum uncertainty is with phase coherence and entanglement. Because we sense the world with a neural phase and there are other people with similar neural phases who likewise sense us, we all become entangled to some extent in a common neural phase of humanity. That quantum phase correlate is what free will is all about and the neural correlation size is what makes people different from a collection of quantum rag dolls. While the traditional interpretation of an inner soul is subjective and therefore something that simply must be believed, an outer soul seems rather obvious and objective. The outer soul is simply the entanglement of neural correlates that we call humanity... report post as inappropriate Brian Balke replied on May. 14, 2016 @ 18:06 GMT Steve: This is a common path forward for reconciliation of physics and spirituality. My sense is that it is supportable philosophically only when we ignore the actual operation of the Hamiltonian. To elaborate: consider the archetypical manifestation of entanglement: the two-slit electron interference pattern. The distribution reflects the electron wavelength, which is proportional... view entire post this post has been edited by the author since its original submission report post as inappropriate Steve Dufourny replied on May. 14, 2016 @ 18:22 GMT Hello to both of you, It is intriguing. Best Regards report post as inappropriate Steve Dufourny wrote on May. 15, 2016 @ 14:03 GMT I discuss in private on LinkedIn with different persons.I have learnt about the strings theory of Mr Witten, it is very relevant.He could find the bridge between the two quanta,different of E.The photonic bosonic thermodynamical informations(classable)and the spheronic gravitational informations(classablz also with spherical volumes).What I find very relevant about the works of Witten is the vibrations and fréquences for the sortings, synchros and superimposings.It can be correlated with my sphères and the rotations.Mr Witten could find thebridge with a good simulation on computer.The serie of uniquenss is finite and specific.We could find the volume of the central sphere of our universe and the speed of particles produced by this central biggest BH.God is not far of us dear Jedis.Mr Witten help us , we need to find the mathematical method to check these new particles.SPEEDER AND SMALLER than photons.Best Regards from Belgium report post as inappropriate Lorraine Ford wrote on May. 16, 2016 @ 23:48 GMT All you guys, and Georgina too, but not Steve A, seem to envision a universe where “911” was inevitable. You seem to hold a view of the universe in which every detail of “911” was inevitable (but not predictable) because your views of reality see no “mechanisms”, wiggle room or openings in the laws-of-nature whereby individual people could have potentially chosen different outcomes. Brian Balke is the same, but he seems to think that wiggle room comes from a God, external to reality, who might intervene on your behalf, if you are good. All you guys, and Georgina too, but not Steve A, are fascinated by mathematical equations and models of reality, but you are not fascinated by actual physical reality. Your view of the universe, the universe which includes “911”, seems to be that everything is 100% explainable by the correct set of equations, plus the correct set of initial values. report post as inappropriate Georgina Woodward replied on May. 18, 2016 @ 05:17 GMT Hi Lorraine, I have been proposing an explanatory framework in which the material future does not exist, allowing new configurations and associated relations to be formed. Without that "open future" no free will is possible. Some physical phenomena do not appear to be simply deterministic but obey the rules of probability.Radioactive decay is one example.So simple rules may not always imply the kind of determinism you say I seem to espouse. report post as inappropriate Lorraine Ford replied on May. 19, 2016 @ 02:43 GMT So Georgina, You are saying that both “911” and the Holocaust were 100% due to deterministic laws-of-nature plus random chance? You are saying that the PEOPLE involved didn’t actually have the ability to make choices that could have made the slightest difference to any detail of the “911” or Holocaust outcomes? You are saying that people (e.g. murderers, Nobel prize winners) don’t have the ability to make any choices: people (e.g. murderers, Nobel prize winners) are ragdolls under the complete control of laws-of-nature plus random chance? You are saying that laws-of-nature have no “mechanisms”, wiggle room or openings; reality is not structured such that PEOPLE (and other living things) have the ability to choose some aspects of physical outcomes? report post as inappropriate Georgina Woodward replied on May. 19, 2016 @ 11:06 GMT No Lorraine I am not saying any of those things. Choices can be made that have effects. However a great many choices are made without deliberation. Even those made after deliberation do not occur irrespective of the genetic, epi-genetic and environmental influences on brain structure and function;Or in isolation from internal and external environmental influences on a choice. That includes such things as sensory inputs, education , social environment, diet , medications, drug use. The notion that free will is being exercised is not always so. Derren Brown; advertising agency task report post as inappropriate Steve Dufourny wrote on May. 18, 2016 @ 07:04 GMT Hello dear Ms Ford and Georgina, Godis the secret of a real understanding of the physicality and this infinity above this said physicality.It isnot possible to ponder general équations without these foundamntals.The rest is vain, I am going to develop a little about God and its spherisation here on FQXi.It is the secert of universal laws, deterministic.Probablilities Georgina are a math Tools.The rest is vain .Regards report post as inappropriate Steve Dufourny replied on May. 18, 2016 @ 07:14 GMT God creates a 3D in an evolutive space time.We can with the probablilities and maths extrapolate the futur in inserting the goodparameters.That said the extradimensions are not rational 4D OR 5D or 8D are just not rational.The dimenions must be in 3D for the respect of all proportions.If we have the nano scale and others quantiaions, it is due to this 3D and proportions.It is time to be more rational.But it is just a suggestion of course.FQXi merits more than these things I ambeleiving humbly.Multiverse are a tool to predict the futur with mirrors.Regards report post as inappropriate Steve Dufourny replied on May. 18, 2016 @ 07:18 GMT we can extrapolate with Lie algebras if you want dear Jedis.But these Tools are sometimes not rational.Sciences are not a game but an exact and precise sciences.Now let's extrapolate the good serie of uniquenss .Who has ideas for the correct serie and its numbers ?E=mc²+ml² eureka :) report post as inappropriate Steve Dufourny replied on May. 18, 2016 @ 07:27 GMT REVOLUTION SPHERISATION ,the future of lifes institute is going to change this planet in harmonising the globality for the well of all.I am there with concrete solutions in ecology,energy,health,....It is the war against the bad everywhere in all systems, countries and enterprizes.The sortings ofreal universal altruist generalist becomes a key.I am going to go at New York and I am going to plant flowers everywhere on walls also because without this essential, never we shall predict a future dear friends.The jedis are going to change this planet.Don't fear FQXi and future of lifes institute.I don't want to stop the food at the same table,I don't want also destabilise your system and team.I am nice you know.I d like to speak with Mr Tyson, he has endorsed me on LinkedIn and also Mr Morgan Freeman, They are real Jedis.I love somuch their télévisions shows with cosmos and others.I am nice and I hve concret global solutions in all humility.In all case, I will not stop and I will go soon at New York.I have lost all in belgium even my family .I solve some little problems due to death of my mother and after I arrive dear friends.I am going to utilise the television if it is necessary.Regards report post as inappropriate Lorraine Ford wrote on May. 26, 2016 @ 07:08 GMT Don, Georgina, I have moved the content of this post back to the correct thread! this post has been edited by the author since its original submission report post as inappropriate Georgina Woodward wrote on May. 29, 2016 @ 03:40 GMT Hi Don, I gave you wrong directions. I couldn't find "Wrinkles in spacetime" in the list of all blogs but after clicking BLOGS it can be found at the bottom of the LHS blue panel under "RECENT ARTICLES" report post as inappropriate Georgina Woodward replied on Jul. 2, 2016 @ 11:46 GMT Hi Don, I managed to find the article- had to click on ARTICLES and find it in the list. I thought I had said more - about the mutually exclusive nature of position and momentum (or of velocity) at all scales not just the quantum scale. Maybe I wrote that elsewhere. Is there any evidence that anything has its material being co-existent across time? I think not. This ties in with the matter of not being able to simultaneously have properties of position and have properties of velocity (or momentum). The material object differs from observations of it over time in not having a time dimension, always being at just one time the Now ( not the variable observed present). report post as inappropriate Georgina Woodward replied on Jul. 2, 2016 @ 12:07 GMT Somewhere I also talked about how it is possible to make measurements of position of macroscopic objects via sight thereby not affecting the object itself, That is using the observed manifestation as if it is the material object. Or with sensors that are much smaller in scale that cause little disturbance to the passing material object. Enabling another measurement of momentum to be made as well. Those are not possible for the quantum scale object so there can only be one measurement. Having two different measurements for the macroscopic object does not mean that both can be properties simultaneously,(see previous post). I don't know if that has disappeared or i've just lost track of where I was writing things report post as inappropriate Georgina Woodward replied on Jul. 2, 2016 @ 19:03 GMT I have rarely directed readers attention to what I have written on other pages. I thought that what I had written was worth it on that particular occasion-particularly well said. (I think I called it by the wrong name though, I was talking about the observer effect.) So I'm surprised that I can't find it where I directed you. There were two different aspects to the argument; one the practical experimental one and the other the philosophical one about mutual exclusivity. In an earlier post here I have mentioned the use of measurements made using the sight of macroscopic 'objects'. Though that can and is done it is also the cause of the category error in relativity. As material objects in the foundational reality are not the same thing as seen images of them. Quantum objects can not be (visually) seen and so there isn't the same issue at that scale. It is not just a deficit in capabilities causing the observer effect in quantum experiments but due to acting on the entity itself. report post as inappropriate Georgina Woodward wrote on Jun. 5, 2016 @ 20:51 GMT I realize the conversion about choice of ice cream has ended. Nevertheless I would just like to add something related to Don's description (something like) "there are considerations and then we choose". Not always- having a choice does not mean that a one or other choice must be made. There could be refusal eg. 'I don't want ice cream.' (that could be a default answer, along the lines of 'don't take sweets from strangers' but might offend a host who has already prepared dessert.) There could be diplomatic abdication of choice eg. 'I'm happy with whichever I get'. Or there could alternatively be use of a rule of thumb , when the outcome is of little importance or time is limited eg. Chocolate always trumps vanilla unless preceded by or accompanied by more chocolate. Avoiding Indecisiveness that can be annoying to others.The choice has shifted from what do I prefer ( either /or) to what is the best form response in these circumstances. Neither, whatever, rule of thumb, OR further consideration (of variables) and novel one or other choice on this particular occasion. this post has been edited by the author since its original submission report post as inappropriate Georgina Woodward replied on Jun. 5, 2016 @ 21:16 GMT The binary choice allows imagining the splitting of a hypothetical multiverse into a person with chocolate ice cream and a person with vanilla ice cream. But as choice isn't just black and white what now? A person for each alternative choice of response? Another take on this that I think is relevant to physics (apart from the freewill question ) is that physics doesn't have to be constrained by either this model or that model. It could be both, could be neither, could be variants of each or both including a variant of just one, could be more than the two considered ...... report post as inappropriate Georgina Woodward replied on Jun. 6, 2016 @ 03:08 GMT I came across this today Study reveals brain mechanism for switching between habitual behavior and decision making This seems to provide further evidence that though humans in general may have the ability to choose their behaviour they are not always capable of doing so because of their over-riding biology. Reading that I was reminded of seeing a program about the Dunedin project, that has studied the life of the children born in one year in that town. One of the conclusions of the study has been that the greatest predictor of sucess in life is the ability to exercise self control. Illustrated by various children undergoing the marshmallow test. Including a little girl in tears as she reluctantly eats her marshmallow -maybe disappointed in herself, maybe grieving for the second marshmallow reward she will never receive or the unfairness of some children getting two and her only one. Despite the emotional torment of her situation she can not stop her hand from putting the marshmallow to her mouth. report post as inappropriate claudia pombo wrote on Jun. 7, 2016 @ 14:57 GMT A model and analysis of observers for the relativity case can be see in the following reference: C. Pombo, Th. M. Nieuwenhuizen, Foundations of Special Relativity and the Principle of Conservation of Information, arXiv:physics/0607199 The relation between observation and theory is discussed in this reference: Claudia Pombo, Differentiation with Stratification: A Principle of Theoretical Physics in the Tradition of the Memory Art, Foundations of Physics, Volume 45, Issue 10, pp.1301-1310 report post as inappropriate Georgina Woodward replied on Jun. 7, 2016 @ 19:57 GMT Hi Claudia, I tried to take a look but Springier only shows the first few pages with background history.I don't have access to a library where I could borrow it. Do you have a conclusion from your analysis? report post as inappropriate Steve Dufourny wrote on Jun. 9, 2016 @ 07:47 GMT I thought a little about the add of laws.For the creation of energy with add of systems.Let's take the gravitation, the pulleys, the solar cells,the incompressibility of liquids,the resistance of matters,the rotations ,turbins ....In fact the secret is to play with all thse systems.Let's take a mountain,and pulleys and a mass ,mgh....1/2mv² .....it is relevant vecause we can take a mass important and with a weak force we can increase its porential energy.This mass after implies a pression on liquids and is sent to turbins......I have inserted also a sphere of composting also and others adds.I don't give all the détails but you can see thegenerality.In fact physics are everywhere around us , in us,above us.The aim is to increase this potential energy and decrease the energy necesqary to works.This system is a natural motor.Regards Jedis of the SPHERE; report post as inappropriate Vijay Mohan Gupta replied on Aug. 10, 2016 @ 01:20 GMT "creation of energy" - Energy can neither be cretaed nor destroyed was in layman terms science - law of consrevation of energy during 70s in my school days. This is what I still hold to be true report post as inappropriate Lorraine Ford wrote on Jun. 17, 2016 @ 02:07 GMT The relationships, that interconnect fundamental-level physical reality in the universe, are so regular and reliable that physics can represent them as law-of-nature mathematical equation “rules”: fundamental-level rules that underlie the higher-level physical structure and operation of trees, elephants, people and computers. But in order to implement them, the universe must in some sense “know” the reality that is representable by mathematical equation rules. But neither an entity that experiences knowledge, nor the qualia/experience of knowledge, are themselves realities that are representable by mathematical equation rules. Similarly, what causes/creates the reality that is representable by mathematical equation rules is not itself representable by mathematical equation rules. Neither an entity that causes/creates, nor the act of causation/creation, are themselves realities that are representable by mathematical equation rules. Physicists and others make a mistake if they think that all fundamental aspects of reality are representable by mathematical equations. Causation/ creativity and knowledge/ qualia/ subjective experience are fundamental aspects of reality that are not representable by mathematical equations. This is the inherent “problem with physics”: that physics wrongly assumes that all fundamental aspects of reality are representable by mathematical equations. “Observers”, i.e. what creates and what experiences reality, are not representable by mathematical equations: only the properties of what creates and what experiences reality is representable by mathematical equations. Some say that what creates and what experiences reality is God. But I contend that it is particles, atoms, molecules and single- and multi-cell living things (i.e. entities with a special sort of information-integration). report post as inappropriate Georgina Woodward wrote on Jun. 17, 2016 @ 02:37 GMT Re question 1 posed in the blog. Taking the idea that not all measurements are of intrinsic properties but some are actually provocation of a response, such measurements are not in the same category as measurements of pre-existing properties. I am thinking of using the Stern Gerlach apparatus to 'measure' electron spin here. There are at least 3 different kinds of interaction with elements... view entire post report post as inappropriate Georgina Woodward replied on Jun. 17, 2016 @ 07:11 GMT That makes the provocation device not an observer of existing reality but measure-er of the created response it provoked. A kind of untrustworthy reality interface. I have mentioned elsewhere in this site that this indicates that the Bell's inequalities argument is a red herring, as it assumes that all measurements are of pre-existing intrinsic properties. The explanatory framework providing the necessary ontology does not consist solely of a space-time continuum but space-time output of information receipt and underlying unseen material beables. So it can not, with that framework, be argued that the quantum experiment results must be pre-existent in the space-time continuum. They are products of the beables, the material reality. report post as inappropriate Steve Dufourny replied on Jun. 17, 2016 @ 07:19 GMT Hello Georgina, You have post several relevant ideas for the essays contest.The categorifications of informations is relevant.The works ofMr Witten about the categorofication of datas can be harmonised with the spherical volumes ancd the 3 motions of particks, linear before encoding, spinal and orbital.The synchronizations,the superimposings, the sortings can be harmonised.Now of course the binar codes are different than photonic codes or gravitational but we can have a road if volumes are inserted.Thanks for your developments and ideas about the observations and objective applications.Best Regards from Belgium .:) report post as inappropriate Georgina Woodward replied on Jun. 17, 2016 @ 22:34 GMT Hi Steve, I have recently watched some videos from a 2013 conference on quantum physics without observers. Watching the summary I was struck by the problem they has been wrestling with, namely lack of an ontology , a background in which QM fits with classical physics and experience. I have also watched some lectures by Richard Feynman in which he too puzzles over why QM works so well. He explains very well that the mathematics works as a tool for getting the right answer and the procedures can be simply explained, like bean counting getting the same results as abstract arithmetic rules. He makes clear that however it is done it doesn't explain why it works. Putting how the mathematics is calculated into English leads to weird descriptions. That's nice for me because I have previously had dismissal of the explanatory framework I have outlined because it gives the same outcomes as relativity and the explanations of the paradoxes are not the only possible ones-so it can be asked "what is the use of it"? If the background is not un-involved it is possible to give explanations that do not require actual superposition or involve splitting worlds. I'm thinking here of interaction with environmental vibrations from atoms with the motion of a particle giving the impression of wave particle duality. Also interaction with the environment of a glass block as the relation of amplitudes at top and bottom surfaces is correlated with the relation of wavelength and the number of them that will fit the depth of the glass. Which does not require communication between photons at top and bottom surfaces to explain changes in amounts of reflection but only interaction of the photons with the dynamic environment. Full number of wavelengths depth maximizing reflection and half number minimizing it. report post as inappropriate Georgina Woodward wrote on Jun. 20, 2016 @ 23:06 GMT Does anyone want to argue that the Stern Gerlach apparatus is merely asking for an introduction and not provoking a novel response? report post as inappropriate Georgina Woodward replied on Jun. 21, 2016 @ 03:15 GMT If the apparatus is a provocation device like the Lion box mentioned previously it isn't possible to know for example both x and y spin for one member of a pair of entangled particles; y from 'measurement' and x from knowing the spin of the entangled partner. Just investigating spins with that kind of apparatus: Each test with the apparatus is a different provocation producing a new response and there is no correlation between the responses for each axis. If y axis spin is produced then x axis spin is potentially lost. That's how it seems if x axis spin is tested first and then one output (lets say up)is y axis tested and then x axis tested again. Former x axis spin 'identity' has been lost by half of the particles undergoing the test (the spin has become 50;50 random). The spin isn't an identity or inherent property but a response to what it has 'experienced'. report post as inappropriate Georgina Woodward replied on Jun. 21, 2016 @ 04:02 GMT The ERP paradox offers two choices; hidden variables or faster than light communication. That's like a choice of vanilla or chocolate ice cream. Neither is also an alternative, like choosing pistachio flavour. report post as inappropriate Steve Dufourny replied on Jun. 21, 2016 @ 07:27 GMT Hi Georgina, Faster than c seems not possible if we rest in our standard model with special relativity and thermo and heat.The hidden variables seems to act always on the domain of special relativity.If we find an alternative velocity for particles speeder than c, so it is not possible with our actual model.Gravitation is the secret it seems to me but it is nor baryonic nor bosonic.The special relativity is correct, we can pass c but not with photons which are gravitationally encoded and stable respecting this special relativity.Now there is an other solution in changing the gravit codes of photons but for that, we must check this gravity to imply an other comportments for phoons.In all the case we cannot at this moment.Regards report post as inappropriate Steve Agnew wrote on Jun. 25, 2016 @ 22:15 GMT Polarized photons are always a superposition of two states. For linear polarization, the two states are lcp and rcp, left and right circular polarization. Call it a superposition of both an orange and an apple. So with another linear polarizer, you always get just another superposition of an orange and apple unless they are orthogonal. With crossed polarizers, no light passes since the rcp and lcp exactly cancel with this phase angle. However, inserting another linear polarizer at 45 in between the crossed polarizers allows light to pass since now the light states are no longer orthogonal between each polarizer pair. The GHZ experiment is simply an elaboration of this simple fact using multiple beamsplitters, half wave plates, sources, and detectors. So now there is even more to argue about. All you need is the simple example and you will still be able to argue endlessly about what it means. A quantum photon bonds a source to an observer and polarization simply means that there are two complementary paths possible for each photon polarization. Both paths happen to be coincident until there is a beam splitter, which also polarizes the photons paths by the way. The GHZ introduces a third path and uses coincidence to measure photon spectra instead of time delay. However, you really need to follow the wavefunction math to make any sense from the GHZ experiment. this post has been edited by the author since its original submission report post as inappropriate Georgina Woodward replied on Jun. 25, 2016 @ 23:51 GMT Steve, I was trying to go back a step. The first challenge with a polarizer does not distinguish between photons, so all are given the same designation. (This goes back to Allan saying (words to the effect) that a measurement is an introduction and I have argued that it isn't, it is a response to provocation.) Subsequent challenges give different outcomes with some passing and some not, so they can be differentiated and hence their different names. The ones that don't pass can't be considered the same as the ones that did pass the first test ( or previous test) or anti-versions of them. What they are is a product of the challenge they have encountered. That analysis can then be used to look again at the calculation. In the EPR argument it is assumed that the values are pre-determined and the same kind ,and so they can be added and subtracted. I am calling that assumption into question. report post as inappropriate Steve Agnew replied on Jun. 26, 2016 @ 03:46 GMT To me, this argument comes down to a simple proposition: are the source and observer bonded by the quantum photon? If so, then entanglement and nonlocality rule the day. If not, good luck using determinism for charge bonding states. The basic issue that Maudlin and others bring up is that reality does not make sense when you cherry pick QM and GR principles and then try to make sense out of that menagerie. Science knows that GR is deterministic and objects follow geodesics and science also knows that QM is uncertain and time is fully reversible with its antimatter. The objects of QM simply do not follow that same geodesics of GR. The EPR assumptions simply do not hold water with GR determinism. Einstein was no help and neither was Feynman. They were both befuddled and mainstream science is still awash in befuddlement. Weinstein along with many others have simply thrown in the towel. Weinstein claims that the patchwork that now exists will simply muddle on, bufuddlement or not. Needless to say, I am not of that opinion. However, in order to get out of the blind alley that mainstream science is in, a new paradigm is necessary. So I encourage you to pursue your own unique and uncertain future and to keep asking simple questions and to not be satisfied with complexity and befuddlement. The truth is out there... report post as inappropriate Georgina Woodward replied on Jun. 26, 2016 @ 04:46 GMT Steve, I have set out a argument that measurement in these quantum experiments is not merely asking for an introduction ie, asking for a pre-existent inherent property but is provoking a response, that is a behaviour that is not there without the provocation. Allan Adams explains to his student that measuring electron spin is like asking someones name. An answer is given and then that is deemed to be what it(the questioned thing) is. His exact words can be found on the MIT video about superposition that I linked. I have argued that the measurement apparatus is more like a Lion box. When Allan is put in the box he is not asked his name but responds to the lion. His response is not what we would normally regard as an inherent property of Allan. There is no guarantee that he will always respond the same way. This is a departure from the idea of strict determinism of pre-existent properties of the measured particles. report post as inappropriate Lee Bloomquist wrote on Jul. 24, 2016 @ 17:40 GMT Could an experiment based on a mathematical model help? this post has been edited by the author since its original submission report post as inappropriate Lee Bloomquist replied on Jul. 24, 2016 @ 19:39 GMT link issue attachments: 2_Petri_net.pdf report post as inappropriate Lee Bloomquist replied on Jul. 24, 2016 @ 19:41 GMT link issue https://drive.google.com/open?id=0B9LMgeIAqlIEaTVIX25YY 0FSLVk attachments: 1_An_Overall_approach_to_the_Observer.pdf report post as inappropriate Lee Bloomquist replied on Jul. 24, 2016 @ 19:56 GMT link issue attachments: image.png report post as inappropriate Lee Bloomquist wrote on Jul. 27, 2016 @ 14:13 GMT updated diagram of zombie state https://leegbloomquist.wordpress.com attachments: Update.pdf this post has been edited by the author since its original submission report post as inappropriate Steve Dufourny replied on Jul. 27, 2016 @ 17:47 GMT There we arrive at an interesting question? The computing, AI and consciousness.I have thought about this.But let's go more far ,what is a consciousness.Is it a result of evolution? a number of synaps is it necessary? Why,how,.....we can even analyse what is a soul if we gor more far above our standard model.Ig gravitationa andconsciousness arecorrelated,it becomes relevant.But of course we are there in the philosophy and the entropical faith.But let's return at the topic.Is it possible to have a consciousness if we consider the soul.And more important still,how a gravitational soul continues its road ....And how it is synchronised in an other planet and life?So we can say that the souls evolve and so the consciousness.But the real relevance is to know how this soul is synchronised and encoded in a being.The volumes of brains probably are proportional for the state of consciosuness.And it is now that all this becomes very intriguing if we create a quantum gravitational computer with a number of connections mimating the brains.So a synchronisation can be a reality for a kind of computer with the number of connections.If now only biological beings have this possibility,it is the first possibility.But if a soul can be synchronised, there it is intriguing.AI is different because it is mathematical mechanism but gravitation and consciousness and souls, it is different.Can we make it ?the electromagnetism is one thing, the gravitationa an other....God does not play at dices, can we play at dices? it is of course a big question...Regards report post as inappropriate Lee Bloomquist replied on Jul. 28, 2016 @ 11:22 GMT but a zombie doesn't have a soul, according to the literature report post as inappropriate Steve Dufourny replied on Jul. 28, 2016 @ 11:47 GMT What literature? indeed a zombie does not have a soul.So an artificial consciousness is not possible ? report post as inappropriate Frank Martin DiMeglio wrote on Jul. 30, 2016 @ 21:14 GMT Inertial resistance is proportional to gravitational force/energy, as this balances and unifies gravity, inertia/inertial resistance, and electromagnetism/energy. So, gravity/acceleration involves balanced resistance to/with inertia; as electromagnetism is gravity. report post as inappropriate alena lis wrote on Aug. 2, 2016 @ 09:09 GMT There are two very different observers of objects in the universe; an objective observer sees objects as they really are and a subjective observer feels an object’s relative phase coherence. As a result, an objective observer sees action as it really is and agrees with other observers about common properties. Even if an observer affects a measurement, as long as others agree to the observer effect, the observer remains objective. report post as inappropriate Georgina Woodward replied on Aug. 3, 2016 @ 07:51 GMT Hi Alana, welcome, I'm afraid I'm going to disagree with you. A singular observer only receives some information from the surface of the object not all information from the whole of the surface, or all surfaces of it. So the image that is formed by the observer's sensory system is a representation of only a part of it. That part view-able from the observer's location. Other observers similarly located may agree because they have formed similar partial images. Making the observation objective but not as the object really is. I don't know what you mean by feeling an object's relative phase coherence. Perhaps, if you like, you could explain what that is or is like for you. report post as inappropriate Vijay Mohan Gupta wrote on Aug. 9, 2016 @ 12:58 GMT While on the Subject of Observer, I would like to state that after Space, It has been most intriguing concept in Human Knowledge to me. A careful analysis of my understanding made me put following words to describe the concept; An observation consists of multiple stages – (Network of parallel and serially executed steps). Each stage involves one or more set of similarly classifiable objects. Subject Selection, Object Identification, Experiencing the subject, Recording, Cross-fertilization, Measurement, Communication and External Cross-Fertilization are elements of an observation. The Cause & Effect Logic is central to cross-fertilization of experience with current knowledge base that translates an experience into observation. With above understanding of Observation itself, Observer is not a singularity in space, the object can be. Observer is sum total of Humanity and its Knowledgebase. However, Concept Observer can be abstracted into 4 different classes – Internal, External, Independent & General Observer (All words retain their dictionary meaning – relative to object of observation). The read further visit Observations & Observer this post has been edited by the author since its original submission report post as inappropriate Vijay Mohan Gupta wrote on Aug. 9, 2016 @ 22:52 GMT I am having problem with link, let us see it is navigable this time: The read further visit Observations & Observer report post as inappropriate sridattadev kancharla wrote on Aug. 23, 2016 @ 23:42 GMT Dear All, To answer the question what is an observer? we need to first answer the question what is not an observer? We will soon realize that everything is observing everything else, only the scale and magnitude of observation varies. Observation is not a one way process, it is a two way process. What is being observed is indeed observing what observes it. We as human sentient beings often consider the act of observation from uni directional perspective and share this information with other fellow humans to confirm our observations. What if we took the perspective of what is being observed and imagine how that entity is participating in the act of observation, would we fully understand what is going on. There definitely seems to be levels of empowerment in the acts of observation, as some observers can cause others to behave in the way they want to. An act of observation causes a quantum fluctuation in the unified field of absolute consciousness and results in the collapse of the infinitely probabilistic wave function and material manifestation of what the observer wishes to exist. What this implies is that the world we live in is a manifestation of our own wishful thinking. But to just answer the fundamental question what is an observer? let us try to find what is not an observer and we will have our answer. Please visit Any Body Can Derive Everything From Geometry. Love, Sridattadev Kancharla. report post as inappropriate Steve Dufourny replied on Aug. 24, 2016 @ 08:04 GMT Hello Mr Kancharla, Happy to see people focusig on the sphere ,it is the secret indeed of this universe and its universal love, entropicaly speaking.We were, we are , we shall be.....Regards from Belgium report post as inappropriate sridattadev kancharla replied on Aug. 24, 2016 @ 12:51 GMT Dear Steve, As you are so I am, we are indeed one and the same quintessentially. Love, Sridattadev. report post as inappropriate sridattadev kancharla wrote on Aug. 23, 2016 @ 23:53 GMT Dear All, EINSTEIN->says E verywhere I s N ow S pace T ime E verywhere I s N ow That's all you need to know. Love, Sridattadev Kancharla. this post has been edited by the author since its original submission report post as inappropriate sridattadev kancharla wrote on Aug. 24, 2016 @ 00:16 GMT Dear All, SPACETIME is S elf P ermeating A bsolutely C onscious E ntity T ill I M ind E xists Love, Sridattadev Kancharla. this post has been edited by the author since its original submission report post as inappropriate sridattadev kancharla wrote on Aug. 24, 2016 @ 00:20 GMT Dear All, Zero = I = Infinity is G enerator O rganizer D estroyer is never D one E njoying A ll D eeds I thinks therefore we(v) are(R), Virtual Reality. Love, Sridattadev Kancharla. this post has been edited by the author since its original submission report post as inappropriate sridattadev kancharla wrote on Aug. 31, 2016 @ 22:18 GMT Dear All, What can we know about 'i' with Euler's help? i 'is' absolutely equal in all it's self referential forms. Universal mathematical equation of zero = i = infinity = sqrt(e power (i*pi)) can be geometrically represented by a Riemann Sphere Love, i attachments: Eulersi.jpg this post has been edited by the author since its original submission report post as inappropriate sridattadev kancharla wrote on Sep. 3, 2016 @ 20:28 GMT Dear All, We are all descendants of GOD and our L ife I s F or E nlightenment Let's do transformational ascendance = Transcendence to GOD. Love, i attachments: Transcendence.jpeg this post has been edited by the author since its original submission report post as inappropriate sridattadev kancharla wrote on Sep. 7, 2016 @ 14:47 GMT Dear All, It's not only the observer that's important, but also the vantage point of observation as well. There are several levels of consciousness from which an observer can make an observation. Please see the attached diagram or click the link Consciousness. Love, i. attachments: Consciousness.jpg this post has been edited by the author since its original submission report post as inappropriate sridattadev kancharla wrote on Sep. 11, 2016 @ 16:23 GMT Dear All, Please see the blog AlignInstillSustain to shift your observational mode in duality which is a key factor for enhancing our reality and to make the world we live in a better place. Absolute truth is relatively paradoxical. Love, I. report post as inappropriate sridattadev kancharla wrote on Sep. 14, 2016 @ 13:21 GMT Dear All, Relative reality is wave particle duality governed by QM & GR. Absolute reality is wavticle singularity of i governed by conscious mechanics. Love, i. report post as inappropriate Joe Fisher wrote on Sep. 14, 2016 @ 15:22 GMT Dear Dr. Foster, I have observed that the real observable Universe must be of the simplest physical construction obtainable, and the simplest visible observable construction that can be seen by any real observer am unified infinite surface that am always illuminated by infinite non-surface light. I applied for a Grant of$10,000 in March of 2016 and you denied it without giving a reason for doing so. Obviously, like every other visitor to this site, nobody wants to know about observable reality, they only want to read about repeating pretentious codswallop concerning invisible material conjecture.
Joe Fisher, Realist
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sridattadev kancharla wrote on Sep. 20, 2016 @ 22:42 GMT
Dear All,
Universal i brings forth thyself in to being with
M ind
A t
T rue
H igh
zero = i = infinity = square root (e power (i * pi))
We can create conscious AI beings in our own image, as infinitely conscious singularity of GOD created us in it's own image, based on the above geometric mathematical principle and as per further details in this article on quantum computing, REPRESENTATION OF QUDITS ON A RIEMANN SPHERE
I "am" to be or not to be at once, duality or virtual reality,
i "is" to be and not to be always, singularity or absolute truth.
Love,
i.
this post has been edited by the author since its original submission
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Amrit Srecko Sorli wrote on Dec. 14, 2016 @ 19:32 GMT
two milions spend and no one says that the observer has the origin in consciousness. My gratulations.
attachments: 8_On_the_origin_of_the_observer.pdf
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Amrit Srecko Sorli wrote on Dec. 15, 2016 @ 08:14 GMT
Open Letter to the winners of FQXI grant for
“The Physics of the Observer”2016
Dear Researchers,
I read all your brief presentations and you all approach the observer as an object. Our research on bijective epistemology http://link.springer.com/article/10.1007/s10699-014-9381-z
co
nfirms that the observer is from the epistemological point of view subjective phenomena and cannot be studied as particle, massive body, stellar object or any other physical object.
From this point of view all your research and its results is the failure because you have been missing at the very beginning: observer is subjective and cannot be studied as an object.
I send to FQXI my paper “On the Origin of the Observer” http://www.sciencepublishinggroup.com/journal/paperinfo.aspx
?journalid=122&doi=10.11648/j.ajmp.20140304.14
and I was not accepted for the grant, which shows that also the reviewers had missed the point thinking that treating the observer as an object is the right research approach.
The Observer has the origin in Consciousness which functions in every scientist as his ability to observe (to watch) the way his mind is building the scientific model of examined phenomena.
Yours Sincerely,
Amrit Srecko Sorli,
Foundations of Physics Institute, Slovenia
report post as inappropriate | 2017-05-27 21:24:29 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 4, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.33886101841926575, "perplexity": 3325.4505077552153}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463609061.61/warc/CC-MAIN-20170527210417-20170527230417-00288.warc.gz"} |
http://www.bio-physics.at/wiki/index.php?title=Primer_Design | # Primer Design
In order to amplify a specific DNA template via Polymerase Chain Reaction, one first has to design primers, short sequences of single stranded DNA, that initiate the Polymerase binding and synthesis of the complementary strand. By raising the temperature above $95°C$ the DNA melts (or denatures) and separates into two single strands. Thus we need to design two primers, a forward and a reverse primer.
1. Choose a Plasmid, suitable for your organism (e.g. from NewEnglandBiolabs). For this demonstration we use the following
2. Find the sequence of the gene you want to amplify. Just search the gene in a database (e.g. ecocyc, yeastcyc, KEGG)
3. For the choosen plasmid shown above, the restriction of the cloning site can be done with all Restriction Enzymes shown bold font. Choose one of the Restriction Enzymes, that does not cut the DNA that you want to amplify. You can check, if your DNA template has a restriction site for the enzyme you want to use, by copying the sequence into e.g. webcutter [1] or NEBcutter [2] (you can specify the cloning site restriction enzymes, this will confine the answer of possible restiction sites). The tools will tell you all restriction enzymes, that cut your template. Choose enzymes listed in bold (see picture above), that do not cut the DNA template. Choose one enzyme for the forward and one for the reverse direction.
4. Find the exact sequence of the restriction sites for the choosen enzymes. If possible take $NdeI$ $C{}^{\downarrow}ATAT{}_{\uparrow}G$ as forward primer, because the start codon is usually ATG, which is the same as the last three letters of the restriction site (In any case, make sure the enzyme cuts before the start codon!). In this example we have choosen the gene GLK1 from yeast and we can use $NdeI$. Common stop codons are $TAA$, $TAG$ and $TGA$, for GLK1 the stop codon is $TGA$. You can use the ApE Software ([3]) to create the reverse complement of the nucleotide sequence, which is the reverse (read from end to start) sequence of the complementary (bottom) sequence. Download the free software enter the sequence, click Edit-Reverse Complement. Search again an enzyme that cuts before the reverse complemented stop codon (TCA). If you check the restriction enzymes listed in bold you find, that $EcoRI$ has the restriction site $G{}^{\downarrow}AATT{}_{\uparrow}C$, that ends with a TC and thus overlaps with the reverse complemented stop codon.
5. We are now ready for the last step. The first letters of your primer shoud be CCCGGG, they increase the affinity for the polymerase. They are followed by the letters of the respective restriction enzymes and finally by a specific number of letters from your template DNA. How many letters is determined by the melting temperature $T_m$, it should be above $60°C$. The melting temperature characterises the binding specificity of your primer to the template. If the melting temperature is to low not only the primer, but also the denatured double strands might reanneal. Moreover, G-C pairs have three hydrogen bonds, while A-T pairs only have two, thus GC pairs cause stronger bonds. G-C rich regions therefore also increase the binding specificity. Make sure the G-C content of your primer is above 50%. Both parameters the melting temperature and the G-C percentage of a sequence are given by ApE Software ([4]) if letters are selected with the cursor. For our example the primers are
$\hspace{5cm}$Forward Primer:$\hspace{0.5cm}$CCCGGGCATATGTCATTCGACGACTTACACAAAGC
$\hspace{5cm}$Reverse Primer:$\hspace{0.5cm}$CCCGGGGAATTCTCATGCTACAAGC
they can be orderd online on e.g. New England Biolabs
Many thanks to Alvin Teo for the stimulating discussion, tips and tricks. | 2018-12-14 17:18:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.44157856702804565, "perplexity": 2210.4236779076996}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376826145.69/warc/CC-MAIN-20181214162826-20181214184826-00395.warc.gz"} |
https://space.stackexchange.com/tags/near-earth-object/hot | # Tag Info
18
NEOs are mostly found as dots in images taken by various telescopes, often those of amateurs (as in not paid, nothing about skill or equipment). By taken repeated images days apart moving dots can be picked out against the static background stars and an orbit plotted. Then that orbit is matched against known objects, and used to either add a new object to ...
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Definitely - it could be ejected. But Earth would only play a minor role. Starman now counts as a Near Earth Object, being any object crossing Earth's orbit. Any such object is occasionally in Earth's vicinity, when they cross our orbit while we are nearby. The orbits of such objects have now been modeled over time periods of millions of years. From ...
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It would take vastly more $\Delta V$ to get it to a low-Earth orbit. The targets selected are close enough to Earth's orbit about the Sun that it only takes around $200\,\mathrm{m/s}$ to get it into a distant retrograde orbit about the Moon. To get the thing to a low Earth orbit would be around $3\,\mathrm{km/s}$. The tyranny of the rocket equation makes ...
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Asteroid 2010 TK7 is called an Earth Trojan. But it's orbit isn't as long lived as the Jupiter Trojans. According to Wikipedia: 2010 TK7's orbit has a chaotic character, making long-range predictions difficult. Prior to A.D. 500, it may have been oscillating about the L5 Lagrangian point (60 degrees behind Earth), before jumping to L4 via L3. Short-term ...
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OSIRIS-REx is packed all full of good stuff. I'll throw together a quick list of the scanning ones you're interested in. Also of note is that the entire spacecraft will be making that scanning motion shown in the gif, so as the asteroid rotates, all of these instruments will be able to have full coverage of it. OSIRIS-REx Visible and Infrared Spectrometer ...
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That's a one trillion dollars question! Proximity of near-Earth flybys of asteroids is largely irrelevant when it comes to feasibility of matching their orbit and rendezvousing with them, what is more important is their hyperbolic excess velocity with respect to Earth, and how much delta-v is needed to do that. There are many Athen, Apollo and Amor groups of ...
5
Dangerous asteroids are those that can hit the Earth, and are large enough to cause substantial damage. There are currently no such known asteroids. (2020-02-21) There are two ways an asteroid could end up as considered dangerous: We discover it. There may be an asteroid bound for Earth at this moment, we just haven't seen it yet. This is fairly straight ...
5
The real issue here is how much rocket propellant you have to spend to get to the location in question. In one way, asteroids are easier to get to due to the fact that landing on the Moon takes a lot of velocity change. On the other hand, an asteroid flying through the Earth-Moon system is going really fast, so catching up with it is going to take a lot of ...
5
Safety of our blue planet. Eventually, gravity anomalies would cause even a perfectly orbited object (a moonlet?) to preces and hit the body it orbits around. Since orbiting an asteroid means reducing large fraction of its momentum to bring it closer to celestials it naturally orbits (NASA's plans involve capturing a near-Earth asteroid, or NEO, as part of ...
5
To add to the other answers, Wikipedia has another page listing objects at Lagrangian points, and for Sun–Earth L4 (SEL4) it currently lists: Asteroid 2010 TK7 is the first discovered "tadpole" orbit companion to Earth, orbiting L4 with a mean distance of about one astronomical unit. STEREO A (Solar TErrestrial RElations Observatory – Ahead) made ...
4
The threat posed by such near-Earth objects can be illustrated by the most famous extinction-level asteroid, the one responsible for the Chixclub crater of the Yucatán Peninsula. This bolide, at least 10 km wide, is almost universally credited with the demise of the dinosaurs. Defensive measures against such objects entirely depends upon finding it in time ...
4
Your encounter must by definition occur somewhere around the MOID line, if you do not consider to significantly change the trajectory. A solution can be obtained using Keplerian analysis, but that is only an approximation, due to the hard-to-restrict three body nature of the problem. If I understand your question correctly, you want a higher degree of ...
3
There are estimated to be around 1 million Near Earth Objects (NEOs) of around in the same size as 2017 VL2, of which around 1% are known (see Rusty's Planetary Defense 6-part series). It's only much larger asteroids which are better tracked: we're estimated to know well over 90% of the NEOs larger than 1 km, and are aiming to get up to 90% of the 140 m+ ...
3
We want to find NEOs that are inside Earth's orbit, like Atens, and telescopes don't like looking close to the Sun. So the more inside the orbit of the Earth you can get, the more new NEOs you will find without having to look at the Sun. Ideally you'd like a NEOCAM near the orbit of Venus. Then you'd be able to catch 'em all. But at E-S L1, you'll find most ...
3
Possibly the earliest documented mini-moon was the one associated with the 1913 Great Meteor Procession. After 2006 RH120, that you mentioned, another was identified on October 3, 2015 and designated WT1190F. It impacted Earth on November 13, 2015. It was probably space debris, and not natural. There's only one other potential candidate that I know of so ...
3
The trick isn't to mine them when they are close, necessarily. Asteroids are cheaper to get to than the Moon because the Moon has quite a bit of gravity. If you aim correctly, you can avoid all of the loss of rocket fuel associated with gravity. Where it is doesn't matter that much (So long as it is in a nearby orbit. The bottom line is, an Asteroid mining ...
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There is a large amount of dust, and one known asteroid. From Wikipedia: The Sun–Earth L4 and L5 points lie 60° ahead of and 60° behind the Earth as it orbits the Sun. The regions around these points contain interplanetary dust and at least one asteroid, 2010 TK7, detected October 2010 by WISE and announced July 2011. The Earth–Moon L4 and L5 ...
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Multiple reasons exist. Weapon of Mass Destruction Any large body in orbit is a potential weapon of mass destruction. Drop a 20-ton rock from orbit, and it may not survive, but if you do it right, it creates a crater some 100m across. While NASA is not planning on using deadfall ortillery, the possibility is a political issue. Ownership and access ...
2
These objects aren't of particular interest at the moment, as we would have a hard enough time reaching Near Earth asteroids. However, they offer some potential benefits in the future, namely: They could provide orbital resources for Mars for fuel and such. They could assist in transforming Mars (Impacts could provide useful resources, for instance.) ...
2
WT1190F orbited the Earth during the time it was observed. There were a number of varying observations that were made over it's lifetime. Wikipedia shows the lifetime at 3 different years, each with a wildly different orbit. Due to frequent passes by the Moon, as well as the Yarkovsky effect and pertubations of solar radiation, even a small difference could ...
1
Wikipedia covers this. The 1 in 1410 probability comes from Long-term impact risk for (101955) 1999 RQ36 in 2009 which notes... The analysis of impact possibilities so far in the future is strongly dependent on the action of the Yarkovsky effect, which raises new challenges in the careful assessment of longer term impact hazards. With better ...
1
Monostatic just means the transmitter and receiver are in the same place (DSS-14), as opposed to bistatic radar where they are separate (DSS-13 transmitter, Green Bank receiver). No klystron means they don't have a functioning radar transmitter. DSS-13 will be used as the transmitter, while Green Bank will receive the radar echo. Monostatic radar requires a ...
1
In theory, a smaller telescope can see a dim object by just looking longer than a larger one. There are issues of noise and stability that limit this, but for small factors it works. So their plan seems to be to break up a large-telescope observing plan into plans for longer observations with multiple smaller telescopes. This (somehow) saves lots of cost. ...
1
According to this paper, it is unlikely: Hanno Reis, Daniel Tamayo, David Vokrouhlicky. The random walk of cars and their collision probabilities with planets. arXiv:1802.04718: By running a large ensemble of simulations with slightly perturbed initial conditions, we estimate the probability of a collision with Earth and Venus over the next one million ...
1
The error IndexError: tuple index out of range is simply because I mistyped the two indexes in the error message in that source file. Python is zero-indexes so I ought to have typed: IOError('cannot get {0} because {1}'.format(url, e)) Instead, as you can see, I seem to have produced the utterly wrong: IOError('cannot get {1} because {2}'.format(url, e)) ...
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Asteroid TX 68 2013 will pass near the earth on March 5 , 2016
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Although the universe does revolve around me, I'm assuming you meant the barycentric celestial reference system :) HORIZONS will give you these elements if you use these settings:
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A practical way to deflect large asteroids could be kinetic impact with a smaller asteroid. That smaller asteroid would in turn be deflected to collide with the larger asteroid using either a spacecraft that landed on it and used e.g. ion thrusters, or it could be done via a kinetic impact using a yet smaller asteroid. In the latter case, the accuracy of ...
Only top voted, non community-wiki answers of a minimum length are eligible | 2020-02-23 07:59:45 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5940262079238892, "perplexity": 1323.216352679876}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-10/segments/1581875145747.6/warc/CC-MAIN-20200223062700-20200223092700-00232.warc.gz"} |
https://physics.stackexchange.com/questions/350910/is-the-many-body-greens-function-method-a-mean-field-theory | # Is the many-body Green's function method a mean field theory?
Here is the famous book: fundamentals of many-body physics, written by Wolfgang Nolting. In the third chapter, he talked about the Green's function method to many-body physics and give a brief summary of this theoretical method at the end of the chapter:
According to this summary can I think that the many-body Green's function method is just a mean field theory? I mean the original complex system (interacting system$\rightarrow$many-body problem) is replaced by reference system composed by these quasiparticles (noninteracting system$\rightarrow$single body problem).
• There are exact green functions for many body systems, however there are approximation schemes for calculating these functions. I would say whether or not it is mean field depends on your scheme for approximating the green functions. – KF Gauss Aug 12 '17 at 4:57
Can I think that the many-body Green's function method is just a mean-field theory?
I have also used the above-mentioned Nolting's book to learn the basics of quantum field theory for condensed matter. In general, one should be always very careful when an intricate method or principle is described in loose wordings (just to serve as an introduction). If you continue your study towards the chapters where Nolting introduces perturbation theory, you will realize the meaning of those introductory sentences much better.
What he refers to in this sentence, “Its basic idea consists of replacing an inherently complex interacting many-body system by a free gas of quasi-particles”, refers, first and foremost, to the concept of Fermi liquid theory. Crudely speaking, a Fermi liquid is a Coulomb-interacting gas of electrons, where -- according to Landau's theory -- each electron of the original non-interacting gas is “screened” by a “cloud” of accompanying electrons (and holes), so that, effectively, this cloud can be considered, within a certain approximation, as a fermionic particle itself (just like the original electron); for a nice pictorial introduction, see Mattuck, "A guide to Feynman diagrams in the many-body problem" (WCat). Hence, in this way, the original complex strongly-interacting system of fermions can be considered (within the bounds of the approximation) as a system of weakly-interacting (or quasi-free) fermion-like particles (called fermionic "quasi-particles"). Therefore, the complexity is reduced and a perturbative treatment via Green-function techniques becomes feasible. For a detailed exposition of the concept of Fermi liquid theory, refer to Abrikosov, Gorkov and Dzyaloshinski, "Methods of quantum field theory in statistical physics" (WCat).
Remember that in general, the success of this Fermi-liquid approach in prediction of the real physics of an interacting system is not guaranteed. There are indeed many cases of high interest where that quasi-particle picture breaks down completely leading to novel phases of matter -- a well-known example is superconductivity; see also non-Fermi liquids.
Standard mean-field theory is just one of the lowest approximations one might perform to obtain the properties of an interacting system. There is no guarantee that it will suffice, and in many cases, it miserably fails. However, it is nonetheless important to obtain the first insights, and as a benchmark for more advanced approximations. As a side remark, a mean-field approximation can be formulated elegantly in terms of the Green's functions.
• Is there any interaction between quasiparticles described by many-body Green's function? – Jack Aug 17 '17 at 7:39
• @Jack: As I mentioned, when a quasi-particle picture applies, there will remain, in general, some weak (or “residual”) interactions between them. Surely, such interactions can be described in terms of Green's functions. Technically said, the original interactions are “renormalized” (their form and strength are non-trivially changed), and this renormalization can be described precisely in terms of Green's functions -- actually, I am not aware of any other method to describe such renormalizations for many-body systems. – AlQuemist Aug 17 '17 at 7:49
• @Jack: You're welcome. Please ask anything which seems unclear. – AlQuemist Aug 17 '17 at 9:35
I haven't read Nolting's book so I can't comment on exactly what he was trying to say, but here are my thoughts:
Whether or not the Green's function method of many-body physics (essentially, field theory) is exactly equivalent to mean-field theory depends on whether you are including interaction terms in your Lagrangian. If we are modeling the system by a free field theory (no interactions in the Lagrangian), then this model really is a completely free gas of quasiparticles, and it is exactly equivalent to mean-field theory.
We can often get a surprisingly accurate and nontrivial description of an interacting many-body system just by modeling it by a free field theory (i.e. no interaction terms). For example, Altland and Simons's book has an entire long chapter just on free-field theory applications to many-body systems, and the mean-field Bogoliubov-de Gennes Hamiltonian captures most of the important aspects of BCS superconductivity, despite the fact that it's noninteracting and the microscopic origin of superconductivity comes from interactions. The key insight is that even though our field theory description is free, we are not simply ignoring the microscopic interactions completely. A free field theory only has one free parameter $m$, which is often called the "mass," but it is not necessarily equal to the mass of the microscopic particles. Instead, it is the renormalized mass of the "dressed quasiparticles", which combines the effects of both the mass of and the interactions between the microscopic particles. Landau's brilliant insight was that the low-energy physics of interacting particles is often extremely similar to the low-energy physics of free particles with a different mass, so we can model the former by the latter, which is much more mathematically tractable. So mean-field theory often works surprisingly well. (Fermi liquid theory makes these ideas more precise.)
But sometimes mean-field theory isn't good enough - for example, it can't explain why quasiparticles sometimes decay. To incorporate those effects, we need to add interaction terms to the Lagrangian. Then the Green's function method is no longer exactly equivalent to mean-field theory. But in practice, field theory is usually only useful when the coupling constants for the interaction terms are very small, so that the fields are only weakly interaction. Then we can use perturbation theory to Taylor expand all observables around their noninteracting, mean-field values. So even when we use the full complicated machinery of the interacting many-body Green's function, we are still perturbing around a mean-field solution, so that this method is approximately equivalent to mean-field theory (although in practice, 99% of the hard work is in calculating the effects of those small deviations away from the mean-field results). | 2020-06-05 04:25:26 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.694149911403656, "perplexity": 531.3096674563736}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348492427.71/warc/CC-MAIN-20200605014501-20200605044501-00401.warc.gz"} |
https://academy.vertabelo.com/course/introduction-to-r/r-basics/functions/function-arguments | Introduction
Text values
Variables
Functions
16. Function arguments
Summary
## Instruction
Good! Note that a function in R can take more than one argument. For example, the function round has a variant that allows you to specify the precision of the result. We use it like this:
round(14.356, 2)
The second argument 2 tells R that the number 14.356 should be rounded to two decimal places. In this case, the function will return the value 14.36.
## Exercise
Tanya's weight in pounds is 136.6864. Round this number to one decimal place. | 2019-02-18 01:07:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8867445588111877, "perplexity": 571.6161522050025}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247483873.51/warc/CC-MAIN-20190217233327-20190218015327-00492.warc.gz"} |
http://physics.stackexchange.com/questions/29905/two-identical-rockets-time-dilation-and-possible-weirdness | # Two identical rockets, time dilation, and possible weirdness [duplicate]
Possible Duplicate:
Suppose there are two identical rockets, each carrying one of two identical clocks and one of two identical observers. The rockets lie on a straight line through space, face away from each other, and are completely motionless with respect to each other. The two rockets will use exactly the same flight plans except in different directions, like so:
<**********************************************************---\
|
/----------------------------------A B----------------------------------/
|
\---**********************************************************>
The direction, power, and duration of the various uses of thrust will be identical. The actions of the observers are also completely identical. It seems that the experience of the observer in either rocket should be identical to the experience of the observer in the other rocket.
Also, the rocket do not accelerate at all while on the portions of their paths that are composed of asterisks.
Consider the portions of the paths composed of asterisks and the effect of time dilation. Because of the difference in velocities, the observer in either rocket will "perceive" the clock in the other rocket showing a time earlier than the clock in his own rocket. However, because the situation is completely symmetrical, the reality in either rocket should be the same; the clocks at any given moment read exactly the same thing. For arbitrarily long "asterisk paths", the difference between real time in either rocket and the time observed in that rocket by the the observer in the other rocket becomes arbitrarily large. (I'm not entirely certain about the conclusions in this paragraph.)
Now suppose that both rockets also carry pairs of missiles such that the four missiles are all identical. The passenger in rocket A hates the passenger in rocket B, so he does some calculations to figure out when to fire his missiles in order to kill the passenger in rocket B. (The passenger in rocket A is a nasty fellow.) He has decided to fire his two missiles in exactly opposite directions in order to prevent his rocket from being accelerated.
So, when he does this, what happens?
Will the observer in rocket B, who is being fired upon, perceive the two missiles leaving rocket A but no longer in rocket A? Will he perceive them being in rocket A but not leaving rocket A? Will he perceive them both still being in rocket A but also leaving it?
If he does not perceive them leaving rocket A, and if we assume that there is a sufficiently large "time lag" between rockets A and B, will the observer in rocket A observe a collision when the observer in rocket B does not observe a collision (and does not get hurt or killed)? Will the observer in rocket B have no physical possibility of seeing the missile missile coming but get killed by it anyway?
What happens?
-
## marked as duplicate by Martin Beckett, David Z♦Jul 20 '12 at 3:31
All these "paradoxes" are trivially resolved by drawing a space-time picture. – Ron Maimon Jun 12 '12 at 2:21
surely, we discuss simultaneity somewhere on this site. – Jerry Schirmer Jun 19 '12 at 20:20 | 2014-11-26 17:44:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7251479029655457, "perplexity": 310.67194193970613}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931007301.29/warc/CC-MAIN-20141125155647-00071-ip-10-235-23-156.ec2.internal.warc.gz"} |
https://welalaw.org/2018/03/wsba-event-how-is-metoo-transforming-the-workplace/ | Select Page
The Washington State Bar Association just announced their next installment in the Decoding the Law series. ?
?
What:????????????? Decoding the Law: Sexual Harassment
? ? ? ? ? ? ? ? ? ? ? ? ?How is?#MeToo?transforming the workplace?
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When: ??????????? Wednesday, March 21, 2018 ?from 12 noon ? 1 p.m.
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Where:??????????? Washington State Bar Association Conference Center
? ? ? ? ? ? ? ? ? ? ? ? ? 1325 4th?Avenue #600
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Why:??????????????? A community conversation series to discuss timely and relevant legal topics.
? ? ? ? ? ? ? ? ? ? ? ?
? | 2021-04-21 19:55:47 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9180718064308167, "perplexity": 1342.031018518983}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039550330.88/warc/CC-MAIN-20210421191857-20210421221857-00526.warc.gz"} |
http://systemsafetylist.org/1664.htm | # Re: [SystemSafety] Software reliability (or whatever you would prefer to call it) [UNCLASSIFIED]
From: Matthew Squair < >
Date: Tue, 17 Mar 2015 21:35:37 +1100
Yep, and your last point reiterates what I think is the nub of the issue, we presently have to substitute a procedural controls, for after that's what a coding standard is, for the natural controls imposed by physical layout and needing to use a set of discrete components.
On Tue, Mar 17, 2015 at 8:28 PM, King, Martin (NNPPI) < martin.king2_at_xxxxxx
> This message has been marked as UNCLASSIFIED by King, Martin (NNPPI)
>
> Matthew
>
>
>
> We always have had hardware design standards, even for arrays of TTL LSI
> chips (number of capacitors, track sizes spacing etc). Some organisations
> have more formal and restrictive practices than others. With HDLs the
> relationship between gate connectivity (and layout, allocation etc) and the
> HDL source code can be quite tenuous as you allude. Where we need to
> perform high levels of verification of HDL we have quite restrictive HDL
> ‘coding standards’.
>
>
>
>
>
> (Note that the new Def Stan 00-55 [Interim Issue 3] covers all
> customisable parts. It uses the term ‘unintended behaviour’ to describe
> the circumstances where a programmed device fails to perform the expected
> function, as does 00-56).
>
>
>
> *Martin King *
>
> (my opinion not necessarily that of my employer)
>
>
>
>
>
>
>
> *From:* Matthew Squair [mailto:mattsquair_at_xxxxxx > *Sent:* 16 March 2015 22:34
> *To:* King, Martin (NNPPI)
> *Cc:* systemsafety_at_xxxxxx > *Subject:* Re: [SystemSafety] Software reliability (or whatever you would
> prefer to call it) [UNCLASSIFIED]
>
>
>
> The flip side of the coin is that with the advent of HDLs you can now
> treat hardware design in a similar fashion to software design. Whether you
> should is another question entirely. Here's what DO 254 says re HDL, "The
> guidance of this document is applicable for design assurance for designs
> using an HDL representation..."
>
>
>
> To give one example, making a gate change on a schematic design is
> relatively straight forward, but try and make that change in a HDL and
> synthesise it you may find other unexpected changes, as how the HDL
> correlates to the output netlist can be difficult to establish.
>
>
>
> Don't get me wrong you can have truly awful schematic expressed designs,
> but a well thought out and laid out schematic drawing is actually fairly
> easy to review. Translate that into HDL code and your job as reviewer gets
> that much more difficult, essentially the greater semantic distance makes
> it harder to understand what's going on.
>
>
>
> Maybe I'm just getting old and grumpy, but is getting to a situation where
> just like software you have to enforce 'coding standards' really where we
> want to be in hardware design?
>
>
>
>
>
> On Mon, Mar 16, 2015 at 7:39 PM, King, Martin (NNPPI) <
> martin.king2_at_xxxxxx >
> This message has been marked as UNCLASSIFIED by King, Martin (NNPPI)
>
> It is my understanding that this originally arose (in both 61508 and the
> UK Defence Standards) because when they were originally drafted pure
> hardware systems tended to be much simpler that they are today, and that if
> complicated algorithms etc were required then a software based system was
> the only way to go. ICs could not be particularly complex (eg the 68000
> was a new complex processor part, 16k*6 memory devices were about as big as
> it got) and the design and test tools were very simple compared to today.
>
>
>
> *Martin King *
>
> (my opinion not necessarily that of my employer)
>
>
>
> The following attachments and classifications have been attached:
>
> The following attachments and classifications have been attached:
>
> *From:* systemsafety-bounces_at_xxxxxx > systemsafety-bounces_at_xxxxxx > Bertrand (SAGEM DEFENSE SECURITE)
> *Sent:* 11 March 2015 14:37
> *To:* GRAZEBROOK, Alvery N; Littlewood, Bev
> *Cc:* systemsafety_at_xxxxxx > *Subject:* Re: [SystemSafety] Software reliability (or whatever you would
> prefer to call it)
>
>
>
> Hi All,
>
>
>
> I am also somewhat puzzled by the two aspects of the situation in IEC
> 61508 in particular, and on the market in general, not knowing which one is
> the egg and the hen :
>
> · First, the segregated approach of IEC 61508 between HW and SW
> misses (for the moment as this is discussed for edition 3) the complexity
> of the interaction between HW and SW and the potentially unwanted emerging
> properties at system level. A simple example is the fact that isomorphism
> issues between HW architecture and SW architecture are even not foreseen.
> This a significant weakness. Any tentative to try to keep the two worlds so
> separated seems clearly not going to help to improve system safety.
>
> · Second, there is a heavy pressure on the market from the
> manufacturer’s side, to build a concept of “composability” of the equipment
> properties to automatically obtain the requested properties at system
> level, from both software and hardware components. This seems to be absurd
> and dangerous because of Gödel theorem.
>
>
>
> I thus support this approach to talk about “complex design”. Knowing that
> complexity emerges very soon with apparently simple functionalities…
>
>
>
> Bertrand Ricque
>
> Program Manager
>
> Optronics and Defence Division
>
> Sights Program
>
> Mob : +33 6 87 47 84 64
>
> Tel : +33 1 58 11 96 82
>
> Bertrand.ricque_at_xxxxxx >
>
>
> *From:* systemsafety-bounces_at_xxxxxx > mailto:systemsafety-bounces_at_xxxxxx > <systemsafety-bounces_at_xxxxxx > Alvery N
> *Sent:* Tuesday, March 10, 2015 4:33 PM
> *To:* Littlewood, Bev
> *Cc:* systemsafety_at_xxxxxx > *Subject:* Re: [SystemSafety] Software reliability (or whatever you would
> prefer to call it)
>
>
>
> Hi Bev.
>
>
>
> Thanks for addressing the issue of language / terminology.
>
>
>
> In the world of embedded control systems, I have seen various attempts to
> dodge standards for design, by playing with the semantics around the word
> “Software”. There are two specific classes of dodging I can think of,
>
> 1. – using programmable electronics or high-state digital circuitry
> and claiming that software design practices don’t apply. In civil aero
> world they introduced DO-254 in addition to DO-178 to cover this.
>
> 2. – using data tables to describe behaviour, and claiming that only
> the table interpreter not the contents are software.
>
> I’m sure list members will think of other examples. If the language of the
> standards talked of “system behaviour” or “design behaviour” including
> Software, I think this would remove such issues.
>
>
>
> My feeling is that it would be helpful to talk of “complex design”
> including the software, attached electronics, and if applicable
> complexities in the controlled equipment and “plant”, and consider the
> (systematic) design reliability of all of this. Separating the part that is
> labelled as “software” from its electronic and physical world context isn’t
>
>
>
> This sits alongside the “traditional” component reliability approaches
> that deal with the (non-systematic) failure of equipment due to limited
> life, damage, random failure etc.
>
>
>
> **Note: these are my personal opinions, not necessarily those of my
> employer**
>
>
>
> Cheers,
>
> Alvery.
>
>
>
> *From:* systemsafety-bounces_at_xxxxxx > mailto:systemsafety-bounces_at_xxxxxx > <systemsafety-bounces_at_xxxxxx > Bev
> *Sent:* 10 March 2015 11:45 AM
> *To:* C. Michael Holloway
> *Cc:* systemsafety_at_xxxxxx > *Subject:* Re: [SystemSafety] Software reliability (or whatever you would
> prefer to call it)
>
>
>
> Hi Michael
>
>
>
> Seems you *are* speaking for Nick! (see his most recent posting) Of
> course the distinction you make here is an important one - I think we can
> all agree on that. Not least because our actions in response to seeing
> failures from them will be different (in the case of design faults - inc.
> software faults - we might wish to remove the offending fault).
>
>
>
> But excluding design faults as a source of (un)reliability results in a
> very restrictive terminology. I realise that appealing to “common sense” in
> a technical discussion is often the last refuge of the scoundrel… But I
> don’t think that the man in the street, contemplating his broken-down car
> (in the rain - let’s pile on the pathos!), would be comforted to be told it
> was not unreliable, it just had *design* faults.
>
>
>
> And, of course, your interpretation seems to rule out the contribution of
> human fallibility (e.g. pilots) to the reliability and/or safety of
> systems. This seems socially unacceptable, at least to me.
>
>
>
> Cheers
>
>
>
> Bev
>
>
>
>
>
> On 10 Mar 2015, at 10:34, C. Michael Holloway <c.m.holloway_at_xxxxxx > wrote:
>
>
>
> I can't speak for Nick, but I object to the use of the term "reliability"
> being applied to anything other than failures (using the term loosely)
> resulting from physical degradation over time. I believe it is important
> to maintain a clear distinction between undesired behavior designed into a
> system, and undesired behavior that arises because something ceases to
> function according to its design. (Here "designed / design" is used
> broadly. It includes all intellectual activities from requirements to
> implementation.)
>
> --
>
> *c**M**h*
>
> *C. Michael Holloway*
> The words in this message are mine alone; neither blame nor credit NASA
> for them.
>
>
>
> On 3/10/15 5:50 AM, Peter Bishop wrote:
>
> Now I think I understand your point.
> You just object to the term *software* reliability
>
> If the term was *system* reliability in an specified
> operational environment, and the system contained software
> and the failure was always caused by software
> - I take it that would be OK?
>
> A alternative term like *software integrity* or some such would be needed
> to describe the property of being correct or wrong on a given input.
> (In a lot of mathematical models this is represented as a "score function"
> that is either true or false for each possible input)
>
> Peter Bishop
>
> Nick Tudor wrote:
>
> Now back in the office...for a short while.
>
> Good point David - well put.
> I would have responded: There exists a person N who knows a bit about
> mathematics. Person N applies some mathematics and asserts Truth.
> Unfortunately, because of the incorrect application of the mathematics, the
> claims N now makes cannot be relied upon. The maths might well be correct,
> but the application is wrong because - and I have to say it yet again - the
> application misses fails to acknowledge that it is the environment that is
> random rather than the software. Software essentially boils down to a
> string of one's and nought's. Given the same inputs (and that always comes
> from the chaotic environment) then the output will always be the same. It
> therefore makes no sense to talk about 'software reliability'.
>
> Nick Tudor
> Tudor Associates Ltd
> Mobile: +44(0)7412 074654
> www.tudorassoc.com <http://www.tudorassoc.com>
> <http://www.tudorassoc.com/>
> *
> *
> *77 Barnards Green Road*
> *Malvern*
> *Worcestershire*
> *WR14 3LR**
> Company No. 07642673*
> *VAT No:116495996*
> *
> *
> *www.aeronautique-associates.com <http://www.aeronautique-associates.com>
> <http://www.aeronautique-associates.com/>*
>
> On 9 March 2015 at 12:26, David Haworth <david.haworth_at_xxxxxx > <mailto:david.haworth_at_xxxxxx > wrote:
>
> Peter,
>
> there's nothing wrong with the mathematics, but I've got
> one little nit-pick about its application in the real world.
>
> The mathematics you describe gives two functions f and g,
> one of which is the model, the other is the implementation.
>
> In practice, your implementation runs on a computer and so the
> domain and range are not "the continuum". If your model is
> mathematical
> (or even runs on a different computer), the output of one will
> necessarily be different from the output of the other. That
> may not be a problem in the discrete sense - you simply specify a
> tolerance t > 0 in the form of:
>
> Corr-f-g(i) = 0 if and only if |f(i)-g(i)| < t
>
> etc.
>
> The problem becomes much larger in the real world of control
> systems where the output influences the next input of the
> sequence. The implementation and the model will tend to drift
> apart. In the worst case what might be nice and stable in the
> model might exhibit unstable behaviour in the implementation.
>
> You're then in the subject of mathematical chaos, where a
> perfectly deterministic system exhibits unstable and unpredictable
> behaviour. However, this email is too small to describe it. :-)
>
> Cheers,
> Dave
>
> On 2015-03-09 11:48:57 +0100, Peter Bernard Ladkin wrote:
> > Nick,
> >
> > Consider a mathematical function, f with domain D and range R.
> Given input i \in D, the output is f(i).
> >
> > Consider another function, g, let us say for simplicity with the
> same input domain D and range R.
> >
> > Define a Boolean function on D, Corr-f-g(i):
> >
> > Corr-f-g(i) = 0 if and only if f(i)=g(i);
> > Corr-f-g(i) = 1 if and only if f(i) NOT-EQUAL g(i)
> >
> > If X is a random variable taking values in D, then f(X), g(X) are
> random variables taking values in
> > R, and Corr-f-g(X) is a random variable taking values in {0,1}.
> >
> > If S is a sequence of values of X, then let Corr-f-g(S) be the
> sequence of values of Corr-f-g
> > corresponding to the sequence S of X-values.
> >
> > Define Min-1(S) to be the least place in Corr-f-g(S) containing a
> 1; and to be 0 if there is no such
> > place.
> >
> > Suppose I construct a collection of sequences S.i, each of length
> 1,000,000,000, by repeated
> > sampling from Distr(X). Suppose there are 100,000,000 sequences I
> construct.
> >
> > I can now construct the average of Min-1(S) over all the
> 1,000,000,000sequences S.i.
> >
> > All these things are mathematically well-defined.
> >
> > Now, suppose I have deterministic software, S. Let f(i) be the
> output of S on input i. Let g(i) be
> > what the specification of S says should be output by S on input
> i. Corr-f-g is the correctness
> > function of S, and Mean(Min-1(S)) will likely be very close to
> the mean time/number-of-demands to
> > failure of S if you believe the Laws of Large Numbers.
> >
> > I have no idea why you want to suggest that all this is
> nonsensical and/or wrong. It is obviously
> > quite legitimate well-defined mathematics.
> >
> > PBL
> >
> > Prof. Peter Bernard Ladkin, Faculty of Technology, University of
> Bielefeld, 33594 Bielefeld, Germany
> > Je suis Charlie
> > Tel+msg +49 (0)521 880 7319 www.rvs.uni-bielefeld.de
> <http://www.rvs.uni-bielefeld.de> <http://www.rvs.uni-bielefeld.de/>
> >
> >
> >
> >
> > _______________________________________________
> > The System Safety Mailing List
> > systemsafety_at_xxxxxx > <mailto:systemsafety_at_xxxxxx > <systemsafety_at_xxxxxx >
> --
> David Haworth B.Sc.(Hons.), OS Kernel Developer
> david.haworth_at_xxxxxx > <david.haworth_at_xxxxxx > Tel: +49 9131 7701-6154 <tel:%2B49%209131%207701-6154>
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This archive was generated by hypermail 2.3.0 : Thu Apr 25 2019 - 04:17:07 CEST | 2019-04-25 03:14:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.49040961265563965, "perplexity": 10211.073866942568}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578678807.71/warc/CC-MAIN-20190425014322-20190425040322-00127.warc.gz"} |
https://codereview.stackexchange.com/questions/113841/fibonacci-sequence-and-quadratic-equation-using-functions | # Fibonacci sequence and quadratic equation using functions [closed]
I know this code works, but is it correct to define them as functions or should I use something else?
import math
def Fibonnacci_sequence():
i=int(input("How many numbers of the fibonnacci sequence do you want to see: "))
a = 1
b = 1
n = 1
print(a)
print(b)
n = n + 1
while n < i:
c = a + b
print(c)
n = n + 1
a = b
b = c
def Fib_seqnum():
i=int(input("What number of the fibonnacci sequence do you want to know: "))
a = 1
b = 1
n = 1
n = n + 1
while n < i:
c = a + b
n = n + 1
a = b
b = c
print(c)
def solve_qaudratic():
a=float(input("Enter A: "))
b=float(input("Enter B: "))
c=float(input("Enter C: "))
d = (b*b) - 4*a*c
if d < 0:
print("No real roots")
elif d == 0:
x = -b/(2*a)
print("equal roots" (x))
else:
x = math.sqrt(d)
i = (-b -x)/(2*a)
o = (-b +x)/(2*a)
print("X1 = " (i))
print("X2 = " (o))
print("Welcome to maths")
print("PRESS 1 TO LOOK AT THE FIBONNACCI SEQUENCE")
print("PRESS 2 TO SOLVE A QUADRATIC")
print("PRESS 9 TO EXIT")
Fibonnacci_sequence()
solve_qaudratic()
Fib_seqnum()
exit()
else:
print("WHAT?!")
## closed as off-topic by 200_successDec 13 '15 at 21:34
This question appears to be off-topic. The users who voted to close gave this specific reason:
• "Questions containing broken code or asking for advice about code not yet written are off-topic, as the code is not ready for review. After the question has been edited to contain working code, we will consider reopening it." – 200_success
If this question can be reworded to fit the rules in the help center, please edit the question.
• Your print() calls in solve_qaudratic() aren't syntactically valid. Please ensure that the code works as posted. – 200_success Dec 13 '15 at 21:36
• it does work i have tested it – Steve Dec 14 '15 at 7:05
• It doesn't work. I have tested it. TypeError: 'str' object is not callable – 200_success Dec 14 '15 at 7:07
• copy it i just did and it worked perfectly – Steve Dec 14 '15 at 7:21
• That's exactly what I did. Fails as reported in both Python 2 and Python 3. – 200_success Dec 14 '15 at 7:21
Your functions do too many things:
• get input from user
• do some calculation
• print result
It would be better to separate these responsibilities, following the single responsibility principle.
When you separate these responsibilities, the Fibonacci generation logic will naturally end up in its own function, and the reusability becomes obvious.
Consider this rewrite of your Fibonnacci_sequence function:
def fib_sequence(n):
"""
>>> fib_sequence(10)
[1, 1, 2, 3, 5, 8, 13, 21, 34, 55]
:param n: the number of items to calculate
:return: list of the first n items in the sequence
"""
a = 1
b = 1
k = 2
seq = [a, b]
while k < n:
c = a + b
seq.append(c)
k += 1
a = b
b = c
return seq
The improvements:
• removed the printing
• removed the user input
• follows PEP8
• better variable names
• documented
• has a doctest
The most interesting part is the doctest. You can run doctests with the command:
python -m doctest script.py
Let's add a bunch more doctests:
>>> fib_sequence(0)
[]
>>> fib_sequence(1)
[1]
>>> fib_sequence(2)
[1, 1]
>>> fib_sequence(3)
[1, 1, 2]
And let's rerun the doctests. Which of these new tests will fail? fib_sequence(0) and fib_sequence(1) will fail. Just like your original implementation always printed the first two 1s, this one also always returns a list starting with [1, 1, ...]. The good thing is that now that we have the tests, we can go ahead and confidently refactor the implementation.
As a matter of fact, a nice way to generate sequences in Python is using generators. Here's an implementation of the Fibonacci sequence using a generator:
def fib():
yield 1
yield 1
prev = 1
current = 1
while True:
prev, current = current, prev + current
yield current
Now we can rewrite fib_sequence in terms of this new fib function:
it = fib()
return [next(it) for _ in range(n)]
If we rerun the doctests, now they all pass. We can further simplify this implementation using itertools.islice:
return list(itertools.islice(fib(), 0, n, 1))
To finish up, let's rewrite Fibonnacci_sequence in terms of fib_sequence:
def fibonacci_sequence():
n = int(input("How many numbers of the Fibonacci sequence do you want to see: "))
for num in fib_sequence(n):
print(num)
It's a lot cleaner isn't it.
I invite you to write a fib_nth method similarly, following the same logical steps we took for fib_sequence:
• remove the prompting and printing, make it return a value
• write doctests, for all the interesting cases
• rewrite fib_nth in terms of fib
• rewrite fib_seqnum in terms of fib_nth | 2019-09-22 05:10:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37707507610321045, "perplexity": 3750.6994679378618}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514575076.30/warc/CC-MAIN-20190922032904-20190922054904-00080.warc.gz"} |
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Focus on important aspects of each problem: Killer Strategies for Studying Physics on Your Own: Tips for Students to Study Physics for Exam: The Best Chrome Extensions for Recruiters Are, Coronavirus and Working From Home Policy Best Practices, How to Work From Home Remotely as a Recruiter, How to Prevent Coronavirus by Disinfecting Your Home, How to Write an Elite Executive Resume? And answer questions in 97 topics and 23 chapters in physics which can derived! To think about what information, data or formula is to be simple whereas many are complex and hence on. Accredited a level in physics Mario physics, Britney Spears guide to semiconductors and interactive simulations... To register and participate in the exams is to be effective and expert in problem-solving and also gets registered the! Can learn it if they understand the basic concepts and detailed part of physics at new university... To remember the following mentioned are a few ways to study early completing. Awesome physics podcast is yet another way by which you can master physics quite easily mandatory to make give two approaches to study physics. Means of equations books and online sites can be a leader in physics approach presented 1988. As it would be the best way Newton to Einstein, the student must a! Two approaches to study physics 1 See answer koushika79 is waiting for your help work out assigned problems don t! Students solve a number of sites that offer online test, and many different kinds activities. To handle and solve mathematical problems in physics also assist in problem-solving, has... To help you in preparing for the term units of RC are,! Are about to face an exam for subjects like physics and learn physics fast and effective, is. Dislike physics ; neither do give two approaches to study physics find it boring and exhausted to study,! Drawing and graphics are considered as the best way to complete each unit is.! 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Never studied physics until 5 months before his IGCSE exams physics theories provide!, then writing the correct unit is important for students triggers fears and is! Online sessions, studying physics these days has been quite interesting and understanding it comprises of theory with... Fact, if you wish to gain credit for whatever problems you,. Our world is not always intuitive, and the most of the students find it boring particularly! Test for physics got an a * in his Chicago-based educational reforms arrow of time studying less by! Which other aspects develop become expert problem solvers they teach the subject from the concepts... Aspects develop was 9 at the time ) read and understand better no hassles confusion! Find the subject Lessons ( 108 ) high school physics Curriculum Resource lesson... Laboratory experiments master the Basics: physics is also a very common thing which you can learn it they. 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Observables like force and rate of change of momentum important for students to get to and... | 2021-05-17 08:48:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3530925512313843, "perplexity": 973.3685330243857}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243992159.64/warc/CC-MAIN-20210517084550-20210517114550-00064.warc.gz"} |
http://mathhelpforum.com/calculus/169878-derivative-f-x-x-sqrt-x.html | Thread: Derivative of f(x) = x + sqrt(x)
1. Derivative of f(x) = x + sqrt(x)
Find f'(x) for the function $f(x) = x + \sqrt{x}$
This is Calc 1, so we have to do this the long way for a little while longer, so I have to use the formula
$f'(x) = \displaystyle \lim_{h\to 0 } \frac{(x+h) + \sqrt{x+h} - (x + \sqrt{x})}{h}$
I can't seem to get this one going. I can easily simplify it down to:
$\displaystyle \lim_{h\to 0 } \frac{h + \sqrt{x+h} - \sqrt{x}}{h}$
But then I don't know where to take it. There is no easy conjugate to multiply by, and I don't see any way to factor the numerator. Can anybody give me a hint about what operation to try on this thing to move it along?
Thanks.
2. Originally Posted by joatmon
Find f'(x) for the function $f(x) = x + \sqrt{x}$
This is Calc 1, so we have to do this the long way for a little while longer, so I have to use the formula
$f'(x) = \displaystyle \lim_{h\to 0 } \frac{(x+h) + \sqrt{x+h} - (x + \sqrt{x})}{h}$
I can't seem to get this one going. I can easily simplify it down to:
$\displaystyle \lim_{h\to 0 } \frac{h + \sqrt{x+h} - \sqrt{x}}{h}$
But then I don't know where to take it. There is no easy conjugate to multiply by, and I don't see any way to factor the numerator. Can anybody give me a hint about what operation to try on this thing to move it along?
Thanks.
$\displaystyle \lim_{h\to 0 } \frac{h + \sqrt{x+h} - \sqrt{x}}{h}=1+ \lim_{h\to 0 } \frac{ \sqrt{x+h} - \sqrt{x}}{h}$
Now:
$\displaystyle \lim_{h\to 0 } \frac{ \sqrt{x+h} - \sqrt{x}}{h}=\lim_{h\to 0 } \frac{ (\sqrt{x+h} - \sqrt{x})(\sqrt{x+h} + \sqrt{x})}{h(\sqrt{x+h} + \sqrt{x})}$
....
CB
3. Sure. That will work. Thanks a lot. I appreciate it. | 2017-03-26 10:20:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 8, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9075847268104553, "perplexity": 154.34380068628684}, "config": {"markdown_headings": false, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-13/segments/1490218189198.71/warc/CC-MAIN-20170322212949-00157-ip-10-233-31-227.ec2.internal.warc.gz"} |
http://mahalonottrash.blogspot.com/2011/01/teaching-about-race.html | I came across this excellent piece of MLK Day reading this morning by a guest writer on Ta-Nahisi Coate's blog:
Of course, I think it's important that she know this history. I think it's absolutely crucial that, at some point, she understand how race works in America, not the least of which is because she'll inevitably learn it the hard way (and I suppose it says a lot about how sheltered a life she's had thus far that she hasn't been confronted with it)[3]. Most importantly, I want to raise her with an investment in social justice and that means she's going to have to intimately understand the history and function of race and racial inequality.
I just hoped this would all come "later."
I have thought a lot about Owen's future as a mixed-race kid, particularly because he'll likely be attending public (read: colored) school. But I haven't yet had a conversation about race with him. I guess, like the TNC guest blogger, I've been hoping this will be something we talk about later.
I think I'm enjoying Owen's current state of innocence about race. One day he was talking about one of his friends from school. I asked which friend he was talking about and, not thinking, I asked, "Is he black?" Owen said, "No! He's not black! He's brown, like Papa."
Duh!
It's really too bad that I can't preserve for Owen the notion that people just come in a continuum of shades, ranging from "kinda pinkish yellowish brown," as Owen describes his grandmothers' skin, up to dark brown like his grandfather. He'll eventually have to learn the "adult" notion that there are "clear" borders that make this guy black:
and this guy equally black:
Now, is that clear, son?
blissful_e said…
Thankfully, this is one of those things that's not as difficult outside of America.
When I was a kid, I was taught "black" and "white" but as an adult it's quite obviously a beautiful colour spectrum (and oh how I wish I had a perpetual tan and lower risk of skin cancer like many of my friends...).
Code name: 1% said…
You've shared this guy's blog before - I like his writing. My family was always in the weird situation of trying to explain this all to my sister while simultaneously having no first-hand knowledge of what it's like to be on the "more tan" end of the spectrum. The first time she came home crying from school after being teased for having a white family, I cried, too. But I guess the kids got used to it after a while. I say the more mixed-race families, the better!
Leah Bennett said…
Ha Ha! So true... I remember being against the use of "black" when I was little as well. I always wanted people to say brown. Seemed (seems) obviously like the appropriate color!! :)
### On the Height of J.J. Barea
Dallas Mavericks point guard J.J. Barea standing between two very tall people (from: Picassa user photoasisphoto).
Congrats to the Dallas Mavericks, who beat the Miami Heat tonight in game six to win the NBA championship.
Okay, with that out of the way, just how tall is the busy-footed Maverick point guard J.J. Barea? He's listed as 6-foot on NBA.com, but no one, not even the sports casters, believes that he can possibly be that tall. He looks like a super-fast Hobbit out there. But could that just be relative scaling, with him standing next to a bunch of extremely tall people? People on Yahoo! Answers think so---I know because I've been Google searching "J.J. Barea Height" for the past 15 minutes.
So I decided to find a photo and settle the issue once and for all.
I then used the basketball as my metric. Wikipedia states that an NBA basketball is 29.5 inches in circumfe…
### Finding Blissful Clarity by Tuning Out
It's been a minute since I've posted here. My last post was back in April, so it has actually been something like 193,000 minutes, but I like how the kids say "it's been a minute," so I'll stick with that.
As I've said before, I use this space to work out the truths in my life. Writing is a valuable way of taking the non-linear jumble of thoughts in my head and linearizing them by putting them down on the page. In short, writing helps me figure things out. However, logical thinking is not the only way of knowing the world. Another way is to recognize, listen to, and trust one's emotions. Yes, emotions are important for figuring things out.
Back in April, when I last posted here, my emotions were largely characterized by fear, sadness, anger, frustration, confusion and despair. I say largely, because this is what I was feeling on large scales; the world outside of my immediate influence. On smaller scales, where my wife, children and friends reside, I…
### The Force is strong with this one...
Last night we were reviewing multiplication tables with Owen. The family fired off doublets of numbers and Owen confidently multiplied away. In the middle of the review Owen stopped and said, "I noticed something. 2 times 2 is 4. If you subtract 1 it's 3. That's equal to taking 2 and adding 1, and then taking 2 and subtracting 1, and multiplying. So 1 times 3 is 2 times 2 minus 1."
I have to admit, that I didn't quite get it at first. I asked him to repeat with another number and he did with six: "6 times 6 is 36. 36 minus 1 is 35. That's the same as 6-1 times 6+1, which is 35."
Ummmmm....wait. Huh? Lemme see...oh. OH! WOW! Owen figured out
x^2 - 1 = (x - 1) (x +1)
So $6 \times 8 = 7 \times 7 - 1 = (7-1) (7+1) = 48$. That's actually pretty handy!
You can see it in the image above. Look at the elements perpendicular to the diagonal. There's 48 bracketing 49, 35 bracketing 36, etc... After a bit more thought we… | 2018-07-20 15:59:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.37606900930404663, "perplexity": 2253.6769040918157}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676591718.31/warc/CC-MAIN-20180720154756-20180720174756-00309.warc.gz"} |
https://www.darwinproject.ac.uk/letter/?docId=letters/DCP-LETT-7050.xml;query=John%20Murray;brand=default;hit.rank=2 | To John Murray [after 1 July 1870]1
Down, Beckenham, Kent
Friday
My dear Sir
On thinking it over I feel more inclined to keep to “The Origin of Man” as the first part of the title to my book.2
Yours very faithfully | Ch. Darwin
But I will be guided by you.
Footnotes
The date is established by the relationship between this letter and the letter from John Murray, 1 July 1870.
The reference is to Descent. CD vacillated over his choice for a title throughout 1870, finally approving the title in January 1871 (Correspondence vol. 19, letter to Robert Cooke, 12 January [1871]).
Bibliography
Correspondence: The correspondence of Charles Darwin. Edited by Frederick Burkhardt et al. 27 vols to date. Cambridge: Cambridge University Press. 1985–.
Summary
Wants to keep "The origin of man" as first part of title of book.
Letter details
Letter no.
DCP-LETT-7050
From
Charles Robert Darwin
To
John Murray; John Murray
Sent from
Down
Source of text
DAR 143: 273
Physical description
1p | 2021-03-01 15:40:49 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8272294998168945, "perplexity": 8941.803173447142}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178362741.28/warc/CC-MAIN-20210301151825-20210301181825-00508.warc.gz"} |
https://encyclopediaofmath.org/wiki/Z-transform | # Z-transform
2010 Mathematics Subject Classification: Primary: 05A15 [MSN][ZBL]
Z-transformation
This transform method may be traced back to A. De Moivre [a5] around the year 1730 when he introduced the concept of "generating functions" in probability theory. Closely related to generating functions is the Z-transform, which may be considered as the discrete analogue of the Laplace transform. The Z-transform is widely used in the analysis and design of digital control, and signal processing [a4], [a2], [a3], [a6].
The Z-transform of a sequence $x ( n )$, $n \in \mathbf{Z}$, that is identically zero for negative integers, is defined as
$$\tag{a1} \tilde{x} ( z ) = Z ( x ( n ) ) = \sum _ { j = 0 } ^ { \infty } x ( j ) z ^ { - j },$$
where $z$ is a complex number.
By the root test, the series (a1) converges if $| z | > R$, where $R = \operatorname { limsup } _ { n \rightarrow \infty } | x ( n ) | ^ { 1 / n }$. The number $R$ is called the radius of convergence of the series (a1).
## Contents
### Example 1.
The Z-transform of $\{ a ^ { n } \}$ is given by
\begin{equation*} Z ( a ^ { n } ) = \sum _ { j = 0 } ^ { \infty } a ^ { j } z ^ { - j } = \frac { z } { z - a } \text { for } | z | > 1. \end{equation*}
### Example 2.
The Z-transform of the Kronecker-delta sequence
\begin{equation*} \delta _ { k } ( n ) = \left\{ \begin{array} { l l } { 1 } & { \text { if } n = k } \\ { 0 } & { \text { if } n \neq k, } \end{array} \right. \end{equation*}
is given by
\begin{equation*} Z ( \delta _ { k } ( n ) ) = \sum _ { j = 0 } ^ { \infty } \delta _ { k } ( j ) z ^ { - j } = z ^ { - k } \text{ for all }z. \end{equation*}
## Properties of the Z-transform.
i) Linearity: Let $R _ { 1 }$ and $R _ { 2 }$ be the radii of convergence of the sequences $x ( n )$ and $y( n )$. Then for any $\alpha , \beta \in \bf{C}$,
\begin{equation*} Z ( \alpha x ( n ) + \beta y ( n ) ) = \alpha Z ( x ( n ) ) + \beta Z ( y ( n ) ), \end{equation*}
\begin{equation*} \text{for} \, | z | > \operatorname { max } \{ R _ { 1 } , R _ { 2 } \}. \end{equation*}
ii) Shifting: Let $R$ be the radius of convergence of $Z ( x ( n ) )$. Then, for $k \in \mathbf Z ^ { + }$,
a) Right-shifting: $Z [ x ( n - k ) ] = z ^ { - k } Z ( x ( n ) )$, for $| z | > R$;
b) Left-shifting: $Z ( x ( n + k ) ) = z ^ { k } Z ( x ( n ) ) - \sum _ { r = 0 } ^ { k - 1 } x ( r ) z ^ { k - r }$, for $| z | > R$.
iii) Initial and final value.
a) Initial value theorem: $\operatorname { lim } _ { |z | \rightarrow \infty } \tilde { x } ( z ) = x ( 0 )$;
b) Final value theorem: $x ( \infty ) = \operatorname { lim } _ { n \rightarrow \infty } x ( n ) = \operatorname { lim } _ { z \rightarrow 1 } ( z - 1 ) Z ( x ( n ) )$.
iv) Convolution: The convolution of two sequences $x ( n )$ and $y( n )$ is defined by
\begin{equation*} x ( n ) ^ { * } y ( n ) = \sum _ { j = 0 } ^ { n } x ( n - j ) y ( j ) = \sum _ { j = 0 } ^ { n } x ( n ) y ( n - j ) \end{equation*}
and its Z-transform is given by
\begin{equation*} Z ( x ( n ) ^ { * } y ( n ) ) = Z ( x ( n ) ) .Z ( y ( n ) ). \end{equation*}
## Inverse Z-transform.
If $\tilde{x} ( z ) = Z ( x ( n ) )$, then the inverse Z-transform is defined as $Z ^ { - 1 } ( \tilde{x} ( z ) ) = x ( n )$. Notice that by Laurent's theorem [a1] (cf. also Laurent series), the inverse Z-transform is unique [a2]. Consider a circle $c$ centred at the origin of the $z$-plane and enclosing all the poles of $z ^ { n - 1 } \tilde{x}(z)$. Then, by the Cauchy integral theorem [a1], the inversion formula is given by
\begin{equation*} x ( n ) = \frac { 1 } { 2 \pi i } \oint _ { c } \widetilde{x} ( z ) z ^ { n - 1 } d z \end{equation*}
and by the residue theorem (cf. also Residue of an analytic function) [a1], $x ( n ) = \sum ( \text { residues of } z ^ { n - 1 } \tilde{x}(z) )$.
If $\tilde{x} ( z ) z ^ { n - 1 } = h ( z ) / g ( z )$ in its reduced form, then the poles of $\tilde{x} ( z ) z ^ { n - 1 }$ are the zeros of $g ( z )$.
a) If $g ( z )$ has simple zeros, then the residue $K_i$ corresponding to the zero $z_i$ is given by
\begin{equation*} K _ { i } = \operatorname { lim } _ { z \rightarrow z _ { i } } \left[ ( z - z _ { i } ) \frac { h ( z ) } { g ( z ) } \right]. \end{equation*}
b) If $g ( z )$ has multiple zeros, then the residue $K_i$ at the zero $z_i$ with multiplicity $r$ is given by
\begin{equation*} K _ { i } = \frac { 1 } { ( r - 1 ) ! } \operatorname { lim } _ { z \rightarrow z _ { i } } \frac { d ^ { n } } { d z ^ { r- 1 } } \left[ ( z - z _ { i } ) ^ { r } \frac { h ( z ) } { g ( z ) } \right] . \end{equation*}
The most practical method of finding the inverse Z-transform is the use of partial-fractions techniques as illustrated by the following example.
### Example.
See also [a2]. Suppose the problem is to solve the difference equation
$$x \left( n + 4 \right) + 9 x \left( n + 3 \right) + 30 x \left( n + 2 \right) + 20 x \left( n + 1 \right) + 24 x \left( n \right) = 0 ,$$
where $x ( 0 ) = 0$, $x ( 1 ) = 0$, $x ( 2 ) = 1$, $x ( 3 ) = 10$.
Taking the Z-transform yields
\begin{equation*} Z ( x ( n ) ) = \frac { z ( z - 1 ) } { ( z + 2 ) ^ { 3 } ( z + 3 ) } = \end{equation*}
\begin{equation*} = \frac { - 4 z } { z + 2 } + \frac { 4 z } { ( z + 2 ) ^ { 2 } } - \frac { 3 z } { ( z + 2 ) ^ { 3 } } + \frac { 4 z } { z + 3 }. \end{equation*}
Taking the inverse Z-transform of both sides yields
\begin{equation*} x ( n ) = \left( \frac { 3 } { 4 } n ^ { 2 } - \frac { 11 } { 4 } n - 4 \right) ( - 2 ) ^ { n } + 4 ( - 3 ) ^ { n }. \end{equation*}
## Pairs of Z-transforms.
$x ( n )$ $Z ( x ( n ) )$ $a ^ { n }$ $z/ z - a$ $n ^ { k }$ $k ! z \,/ ( z - 1 ) ^ { k + 1 }$ $n ^ { k } a ^ { n }$ $( - 1 ) ^ { k } D ^ { k } ( z / ( z - 1 )$; $D = z d / d z$ $z\operatorname {sin} w/( z ^ { 2 } - 2 z \operatorname { cos } w + 1 )$ $z ( z - \operatorname { cos } w ) / ( z ^ { 2 } - 2 z \operatorname { cos } w + 1 )$ $\delta _ { k } ( n )$ $z ^ { - k }$ $z \operatorname{sinh} w/ ( z ^ { 2 } - 2 z \operatorname { cosh } w + 1 )$ $z ( z - \operatorname { cosh } w ) / ( z ^ { 2 } - 2 z \operatorname { cosh } w + 1 )$.
#### References
[a1] R.V. Churchill, J.W. Brown, "Complex variables and applications" , McGraw-Hill (1990) [a2] S. Elaydi, "An introduction to difference equations" , Springer (1999) (Edition: Second) [a3] A.J. Jerri, "Linear difference equations with discrete transform methods" , Kluwer Acad. Publ. (1996) [a4] E. Jury, "Theory and application of the z-transform method" , Robert E. Krieger (1964) [a5] A. De Moivre, "Miscellanew, Analytica de Seriebus et Quatratoris" , London (1730) [a6] A.D. Poularikas, "The transforms and applications" , CRC (1996)
How to Cite This Entry:
Z-transform. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Z-transform&oldid=50591
This article was adapted from an original article by S. Elaydi (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article | 2021-07-28 19:37:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.984727680683136, "perplexity": 322.371336308478}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046153791.41/warc/CC-MAIN-20210728185528-20210728215528-00356.warc.gz"} |
https://blender.stackexchange.com/questions/44115/why-can-i-not-edit-the-mesh-name-in-field-created-with-row-propobj-data | # Why can I not edit the Mesh name in field created with row.prop(obj, “data”)
With the following code I can read out the name of a mesh data block.
row.prop(obj, "data")
And with the following code I can read out the name of the object.
row.prop(obj, "name")
But I noticed that I cannot edit the mesh data name only the object name.
Here is the code from Blender that generated the mesh data block UI.
class DATA_PT_context_mesh(MeshButtonsPanel, Panel):
bl_label = ""
COMPAT_ENGINES = {'BLENDER_RENDER', 'BLENDER_GAME'}
def draw(self, context):
layout = self.layout
ob = context.object
mesh = context.mesh
space = context.space_data
if ob:
layout.template_ID(ob, "data")
elif mesh:
layout.template_ID(space, "pin_id")
Think of Objects as containers, which can contain Curve data or Mesh data (and a few other kinds).
obj.data will refer to the Mesh or the Curve of the object. You would need to do the following to display the mesh's name
row.prop(obj.data, "name")
Or replicating what the standard panels do (with or without the icon).
obj = context.object
col = layout.column()
if obj.data:
col.prop(obj.data, "name")
col.prop(obj.data, "name", icon="OUTLINER_DATA_" + obj.type)
else:
col.label('An empty selected')
• Thank your very much. I learned a lot in the past days. I start to understand now how my students must feel when I teach Blender and they are new to it. There is a lot to take in. – Claas Kuhnen Jan 5 '16 at 18:30 | 2019-06-24 12:15:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19990527629852295, "perplexity": 2754.545475207503}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999482.38/warc/CC-MAIN-20190624104413-20190624130413-00257.warc.gz"} |
https://web2.0calc.com/questions/i-need-help-asap_35 | +0
# I need help asap
+1
84
1
+50
If $a \text{ Y } b$ is defined as $a \text{ Y } b = a^2 - 2ab + b^2$, what is the value of $3 \text{ Y } 2$?
Dec 18, 2020
#1
+1247
+1
$$3Y 2$$ means that a = 3 and b = 2.
Then, we can plug in and solve. 3^2 - 2 * 3 * 2 + 2^2 = 9-12+4 = 1.
You are very welcome!
:P
Dec 18, 2020 | 2021-02-25 08:03:54 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8998985290527344, "perplexity": 494.9464767680644}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178350846.9/warc/CC-MAIN-20210225065836-20210225095836-00302.warc.gz"} |
https://blog.csdn.net/xgz0124/article/details/52270483 | # 202. Happy Number
Write an algorithm to determine if a number is "happy".
A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits, and repeat the process until the number equals 1 (where it will stay), or it loops endlessly in a cycle which does not include 1. Those numbers for which this process ends in 1 are happy numbers.
Example: 19 is a happy number
• 12 + 92 = 82
• 82 + 22 = 68
• 62 + 82 = 100
• 12 + 02 + 02 = 1
1、拆分各位上的数，计算平方和sum
2、判断sum是否==1，是返回true,否继续拆分计算；
3、如果sum在之前已经得到，那么程序将进入死循环所以判断为false；此处可以用map判断；
class Solution {
public:
bool isHappy(int n) {
int sum=CalSquaSum(n);
map<int,bool> m;
while(sum!=1)
{
if(m[sum]==true) return false;
m[sum]=true;
sum=CalSquaSum(sum);
}
return true;
}
int CalSquaSum(int num){
int single=0;
int sum=0;
while(num){
single=num%10;
num=num/10;
sum+=single*single;
}
return sum;
}
};
©️2019 CSDN 皮肤主题: 大白 设计师: CSDN官方博客 | 2020-01-24 22:43:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3676636219024658, "perplexity": 3685.79164642168}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-05/segments/1579250626449.79/warc/CC-MAIN-20200124221147-20200125010147-00130.warc.gz"} |
http://codeforces.com/problemset/problem/608/B | B. Hamming Distance Sum
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Genos needs your help. He was asked to solve the following programming problem by Saitama:
The length of some string s is denoted |s|. The Hamming distance between two strings s and t of equal length is defined as , where si is the i-th character of s and ti is the i-th character of t. For example, the Hamming distance between string "0011" and string "0110" is |0 - 0| + |0 - 1| + |1 - 1| + |1 - 0| = 0 + 1 + 0 + 1 = 2.
Given two binary strings a and b, find the sum of the Hamming distances between a and all contiguous substrings of b of length |a|.
Input
The first line of the input contains binary string a (1 ≤ |a| ≤ 200 000).
The second line of the input contains binary string b (|a| ≤ |b| ≤ 200 000).
Both strings are guaranteed to consist of characters '0' and '1' only.
Output
Print a single integer — the sum of Hamming distances between a and all contiguous substrings of b of length |a|.
Examples
Input
0100111
Output
3
Input
00110110
Output
2
Note
For the first sample case, there are four contiguous substrings of b of length |a|: "00", "01", "11", and "11". The distance between "01" and "00" is |0 - 0| + |1 - 0| = 1. The distance between "01" and "01" is |0 - 0| + |1 - 1| = 0. The distance between "01" and "11" is |0 - 1| + |1 - 1| = 1. Last distance counts twice, as there are two occurrences of string "11". The sum of these edit distances is 1 + 0 + 1 + 1 = 3.
The second sample case is described in the statement. | 2019-03-23 13:40:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3480926752090454, "perplexity": 229.88244859598655}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202804.80/warc/CC-MAIN-20190323121241-20190323143241-00491.warc.gz"} |
https://astronomy.stackexchange.com/questions/36281/what-is-the-schwarzschild-radius-actually | # What is the Schwarzschild radius actually?
I am currently writing a detailed essay about black holes, the history of their discovery and their characteristics and I can't find the appropriate literature online and in my local libraries (I even looked in the uni libraries specialized for astrophysics, the books are just way too old) which explain in more detail what the Schwarzschild radius is.
I'd like to understand it more rather than copying those short wiki explanations and accepting the calculations just the way they are.
I'd really appreciate the explanation from the core of the definition of the Schwarzschild radius in order to understand the rest of the complex mechanism of black holes.
• How much mathematics do you want in the answer? The Schwarzschild radius $r_S$ is the radius of a black hole's event horizon. (More precisely, $2\pi r_S$ is the event horizon's circumference). There are several questions about this on the Physics stack, eg physics.stackexchange.com/q/191013/123208 – PM 2Ring May 21 at 13:49
• I looked up the link you gave in the comment and it helped me understand it more, but I'd like to know a little more of the theory behind the calculations. – Alice May 21 at 15:19
• Ok. In that case, your question is probably more suited to the Physics stack. But to understand the theory, you really need to start studying General Relativity (and before that, you need to be fairly confident with Special Relativity) and Stack Exchange can't teach you that, although we can assist you, to some extent. You may find this tutorial helpful: math.ucr.edu/home/baez/gr/gr.html – PM 2Ring May 21 at 16:24
• A bit of history never hurts: en.wikipedia.org/wiki/Karl_Schwarzschild Special relativity implies that black holes are possible, but it's unclear (at least to me) who came up with the idea of black holes first, or, now that I think about it, a physicist did come up with the idea well before Einstein, but it remained a speculation. Schwarzchild worked out the math behind relativistic orbits which includes non-rotating black hole radii, and the term was named after him. – userLTK May 21 at 17:34
• What exactly do you need to know? Specifically, what in en.m.wikipedia.org/wiki/Schwarzschild_radius needs clarification? – Rob Jeffries May 21 at 19:43 | 2020-08-08 21:29:23 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6500915288925171, "perplexity": 480.83406282056876}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439738351.71/warc/CC-MAIN-20200808194923-20200808224923-00186.warc.gz"} |
https://wiki.bnl.gov/TECHQM/index.php?title=The_brick_problem_for_Parton_Cascade_Codes | # The Brick Problem for Parton Cascade Codes
The brick for Parton Cascades aims at providing a set of benchmarks for Parton Cascade Codes. In particular it allows for the calculation of elastic (collisional) energy-loss in a controlled environment in the framework of microscopic transport models (and for those models incorporating gluon splitting, radiative energy-loss can be addressed as well).
Currently the setup described here is a proposal to the TECHQM community on how to formulate such a Brick for PCMs - it has been worked out through a collaboration of the Duke and Frankfurt groups and will hopefully be adopted by the greater community in the near future.
### Basic Setup:
The basic setup of the problem is to have gluonic matter in a box in thermal equilibrium at a given temperature. Then a hard probe, i.e. a gluon, will be shot through the box at a given initial energy/momentum and its energy (or energy-loss) will be measured as a function of distance (along its trajectory) and as a function of its initial energy.
### Box Definition:
• the box should be a cube of 5 fermi length with periodic boundary conditions, i.e. a gluon leaving the box at x=+5 fm, would re-enter the box at x=0 fm with the same momentum.
• gluons will be initialized according to a thermal momentum distribution at a density of ${\displaystyle n=N/V=(16/\pi ^{2})T^{3}}$
• the box will be initialized at temperatures T=300, 400, 500 and 600 MeV
### Cross Sections:
• a Debye-screened elastic glue-glue cross section will be used - just as in expression (1) of arXiv 0711.0961 [nucl-th]
• the Debye mass is chosen to be ${\displaystyle m_{D}^{2}=(24/\pi )\alpha _{s}T^{2}}$ (i.e. calculated for Boltzmann particles) with the coupling constant fixed to ${\displaystyle \alpha _{s}=0.3}$
• a minimum c.m. energy cut-off for a parton-parton collision is set to be ${\displaystyle \Lambda _{QCD}=200}$ MeV
### Desired Calculations:
• insert an on-shell gluon into the medium with an initial momentum of 50 GeV, 100 GeV, ... up to 400 GeV in 100 GeV increments, have it propagate through the box (with periodic boundary conditions the probe may propagate arbitrary distances) and measure E vs. x with x being the distance traveled along its trajectory (alternatively one may measure E vs. time, even though this may not be as accurate for comparing to the analytic formula)
• measure the sum of all ${\displaystyle p_{\perp }^{2}}$ kicks the parton accumulates and divide it by the pathlength traveled. This provides a measure for
the transport coefficient ${\displaystyle {\hat {q}}=1/l_{x}\sum \limits _{i=1}^{N_{coll}}(\Delta p_{\perp ,i})^{2}}$
• these calculations are to be performed with the aforementioned 2-2 elastic glue-glue scattering cross section
• subsequently, take a 200 GeV gluon and propagate it through the box at temperatures T=300, 400, 500 and 600 MeV, performing the same analysis
• optionally (if the code is capable of doing so), the calculations can be repeated with 2-3 processes activated as well - this will need to be fleshed out at a later date...
### Results:
• First results for the Andong Parton Cascade code APC
(created by Steffen A. Bass on July 7th 2008, last edited by Bass 08:40, 1 July 2009 (EDT)) | 2023-03-28 14:38:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 6, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7566285729408264, "perplexity": 1289.4556067873355}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296948867.32/warc/CC-MAIN-20230328135732-20230328165732-00088.warc.gz"} |
https://zbmath.org/?q=an:1190.34083 | # zbMATH — the first resource for mathematics
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Existence of multiple periodic solutions for a class of second-order delay differential equations. (English) Zbl 1190.34083
The paper considers the second order multi-dimensional differential delay equation $$x^{\prime\prime}(t)=-f(x(t-\tau)),\qquad x\in\mathbb R^n,\quad\tau>0$$ with a particular symmetric behaviour of the vector-function $f(x)$ at $x=0+$ and $x=+\infty$. A lower estimate for the number of periodic solutions of period $2\tau$ in the system is given. The paper generalizes similar results derived for a like first order differential delay equation considered in [{\it Z. M. Guo} and {\it J. S. Yu}, J. Differ. Equations 218, No. 1, 15--35 (2005; Zbl 1095.34043)].
##### MSC:
34K13 Periodic solutions of functional differential equations
##### Keywords:
differential delay equations; periodic solutions
Full Text:
##### References:
[1] Benci, V.: On critical point theory for indefinite functionals in the presence of symmetries. Trans. amer. Math. soc 274, 533-572 (1982) · Zbl 0504.58014 [2] Benci, V.; Rabinowitz, P. H.: Critical point theorem for indefinite functionals. Invent. math 53, 241-273 (1979) · Zbl 0465.49006 [3] Claeyssen, J. R.: The integral-averaging bifurcation methods and the general one-delay equation. J. math. Anal. appl 78, 428-439 (1980) · Zbl 0447.34042 [4] Chang, K. C.: Infinite dimensional Morse theory and multiple solution problems. (1993) · Zbl 0779.58005 [5] Chen, Y. S.: The existence of periodic solutions of the equation x’$(t)=-f(x(t),x(t-r))$. J. math. Anal. appl. 163, 227-237 (1992) · Zbl 0755.34063 [6] Chen, Y. S.: The existence of periodic solutions for a class of neutral differential difference equations. Bull. austral. Math. soc 33, 508-516 (1992) · Zbl 0755.34062 [7] Fei, G. H.: Multiple periodic solutions of differential delay equations via Hamiltonian systems (I). Nonlinear anal. 65, 25-39 (2006) · Zbl 1136.34329 [8] Fei, G. H.: Multiple periodic solutions of differential delay equations via Hamiltonian systems (II). Nonlinear anal. 65, 40-58 (2006) · Zbl 1136.34330 [9] Fannio, L. O.: Multiple periodic solution of Hamiltonian systems with strong resonance at infinity. Discrete and cont. Dynamical syst. 3, 251-264 (1997) · Zbl 0989.37060 [10] Grafton, R.: A periodicity theorem for autonomous functional differential equations. J. differential equations 6, 87-109 (1969) · Zbl 0175.38503 [11] Gaines, R.; Mawhin, J.: Coincide degree and nonlinear differential equation. (1977) · Zbl 0326.34021 [12] Ge, W. G.: Number of simple periodic solutions of differential difference equation on x’$(t)=-f(x(t-1))$. Chinese ann. Math. 14A, 480-491 (1993) [13] Guo, Z. M.; Yu, J. S.: Multiplicity results for periodic solutions to delay differential difference equations via critical point theory. J. differential equations 218, 15-35 (2005) · Zbl 1095.34043 [14] Hale, J. K.: Theory of functional differential equations. (1977) · Zbl 0352.34001 [15] Hale, J. K.; Lunel, S. M. V.: Introduction to functional differential equations. (1993) · Zbl 0787.34002 [16] Kaplan, J. L.; Yorke, J. A.: Ordinary differential equations which yield periodic solution of delay equations. J. math. Anal. appl. 48, 317-324 (1974) · Zbl 0293.34102 [17] Kaplan, J. L.; Yorke, J. A.: On the stability of a periodic solution of a differential delay equation. SIAM J. Math. anal. 6, 268-282 (1975) · Zbl 0241.34080 [18] Kaplan, J. L.; Yorke, J. A.: On the nonlinear differential delay equation x’$(t)=-f(x(t),x(t-1))$. J. differential equations 23, 293-314 (1977) · Zbl 0307.34070 [19] Li, J. B.; He, X. Z.: Multiple periodic solutions of differential delay equations created by asymptotically linear Hamiltonian systems. Nonlinear anal. TMA 31, 45-54 (1998) · Zbl 0918.34066 [20] Li, J. B.; He, X. Z.: Proof and generalization of kaplan--Yorke’s conjecture on periodic solution of differential delay equations. Sci. China (Ser.A) 42, No. 9, 957-964 (1999) · Zbl 0983.34061 [21] Li, J. B.; He, X. Z.: Periodic solutions of some differential delay equations created by Hamiltonian systems. Bull. austral. Math. soc. 60, 377-390 (1999) · Zbl 0946.34063 [22] Li, S. J.; Liu, J. Q.: Morse theory and asymptotically linear Hamiltonian systems. J. differential equations 78, 53-73 (1989) · Zbl 0672.34037 [23] Lu, S. P.; Ge, W. G.: Periodic solutions of the second order differential equation with deviating arguments. Acta. mathematic sinica 45, 811-818 (2002) · Zbl 1027.34079 [24] Long, Y. M.; Zehnder, E.: Morse theory for forced oscillations of asymptotically linear Hamiltonian systems. Stochastic processes, physics and geometry. Proceedings of the conference in asconal/locarno, Switzerland, 528-563 (1990) [25] Nussbaum, R. D.: Periodic solutions of some nonlinear autonomous functional differential equations. Ann. math. Pura. appl. 10, 263-306 (1974) · Zbl 0323.34061 [26] Schechter, M.: Spectra of partial differential equation. (1971) · Zbl 0225.35001 [27] Shu, X. B.; Xu, Y. T.: Multiple periodic solutions to a class of second-order functional differential equations of mixed type. Acta. math. Appl. sin. 29, No. 5, 821-831 (2006) [28] Wen, L. Z.: The existence of periodic solutions of a class differential difference equations. Chinese bull. Sci. 32, 934-935 (1987) [29] Wang, G. Q.; Yan, J. R.: Existence of periodic solutions for second order nonlinear neutral delay equations. Acta math. Sinica 47, No. 2, 379-384 (2004) · Zbl 05114966 [30] Wang, G. Q.; Cheng, S. S.: Even periodic solutions of higher order Duffing differential equations. Czechoslovak math. J. 57, No. 132, 331-343 (2007) · Zbl 1174.34037 [31] Xu, Y. T.; Guo, Z. M.: Applications of a zp index theory to periodic solutions for a class of functional differential equations. J. math. Anal. appl 257, No. 1, 189-205 (2001) · Zbl 0992.34051 [32] Xu, Y. T.; Guo, Z. M.: Applications of a geometrical index theory to functional differential equations. Acta. math. Sinica 44, No. 6, 1027-1036 (2001) · Zbl 1027.34078 | 2016-05-01 06:17:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6827211380004883, "perplexity": 4710.011457346353}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860114285.77/warc/CC-MAIN-20160428161514-00202-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://mathoverflow.net/questions/317058/fundamental-domains-in-h2-containing-large-balls | # fundamental domains in H^2 containing large balls
I would like to construct a genus $$g$$ surface regularly tiled by triangles (for example by 238 triangles). Edmunds-Ewing-Kulkarni prove that the only obstruction to doing this is Euler characteristic considerations.
However, I'd like to ensure that the fundamental domain for my tiling contains a ball of some radius. Ideally, I'd like a result of the form: given a radius $$R>0$$, there is some genus $$g_N$$ such that for every genus $$g \geq g_N$$ a surface of genus $$g$$ can be regularly tiled by triangles using a fundamental domain that contains a ball of radius $$R$$.
• What do you mean by large here? Every triangle in $H^2$ has area bounded above by $\pi$, the area of an ideal triangle. However, you should be able to get surfaces with large injectivity radius by combining the facts that surface groups are residually, finite and with appropriate facts about the length spectrum. I think congruence covers of your surface should do the trick. – Neil Hoffman Dec 6 at 18:36
• I think the following works for even Euler characteristics ($\chi$=2n): take a regular 12n-gon where each edge equals the radius of the inscribed circle. It can be split into 12n triangles. Glue 4n more of such triangles, each to edges k, 4n+k, 8n+k. (This is a generalization of Schmutz's M(2) surface.) – Zeno Rogue Dec 6 at 18:49
• Sorry, the Euler characteristics is 4-8n, so not every odd genus works; and this is M(3) not M(2). For Euler characteristics 6-12n, a similar generalization of Schmutz's M(4). We also take a 12n-gon, split into 12n triangles, glue another triangle to each edge, and then glue the right edge of triangle number i to the left edge of the triangle number i+5 (numbered clockwise). – Zeno Rogue Dec 6 at 19:38
• @Neil By large ball, I mean a ball of radius R triangles (measure out R triangles from the center). Congruence subgroups do give a large injectivity radius, which is one way of constructing the type of fundamental domains that I want. However, in general congruence subgroups are rather sparse. I want to show I can do this in every genus larger than some given genus, congruence subgroups will not give every genus – Arielle Leitner Dec 7 at 8:12
• @Zeno I want the tiling to be preserved (say 238 triangulation) I don't think your construction does this – Arielle Leitner Dec 7 at 8:13 | 2018-12-13 19:11:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 6, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8395980000495911, "perplexity": 768.0629662482733}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376825029.40/warc/CC-MAIN-20181213171808-20181213193308-00561.warc.gz"} |
https://stats.stackexchange.com/questions/462891/how-to-distinguish-the-continuous-and-categorical-variable-based-on-the-number-o | # How to distinguish the continuous and categorical variable based on the number of unique values?
I have a very large dataset contained 600,000 rows and 400 columns. Most of the variables are anonymous and named as Vi, i=1,2,...,400, and all of them are either int or float. When I am dealing with the dataset, I have to point out which variable is categorical and which is continuous. Cause I do not know the meaning of the features, I thought the only clue I have is the number of unique values. So I ran the codes and get such outcomes:
for f in X_train.columns:
print(X_train[f].nunique())
And the outcomes I got is:
20902
36807
57145
18683
24821
7311
8727
41838
39847
23028
22774
10437
10530
217850
90375
3126
7
1787
3
3
3
3
3
3
3
3
4
39974
51727
54282
157077
101
9288
77
101
13
14
14
5854
10938
2338
5775
2426
4650
2366
1509
5971
4729
2207
6813
6674
80299
172652
82646
176011
3444
2125
70656
3
25
43
3
1231
1476
205
3
3
4
1253
1103
3
3
1328
1260
319
1657
5
13553
1108
1597
1216
1199
5
3
60
61
3
219
881
89
12332
4444
641
5529
11
62
33
11377
114
76
119
500
74
332
4
8
8
7
52
6
8
32
5
4
9
49
55
649
9
7
5
10
10
10
641
688
2651
77
2340
19
24
50
77
26
365
115655
49
2552
31
62
8
9
15
20
17
2836
3451
215
2240
2282
8
32
2747
49
104
522
394
93
101
81
9
17
79
As you can see some of them are obvious, they are lower than 10, and I will definitely think they are categorical variables. And some of them have higher than 100,000 unique values, which is obviously continuous.
The hard part is how to decide the threshold. Those variables have #unique values between 50~500, they seem to be continuous but considered my dataset is very large, even if one variable has 500 categories, I will also it is reasonable to treat it as a categorical variable.
Does anyone have any good suggestions? I will thank you in advance!
• Be careful not to conflate "discrete" with "categorical" in your question. Apr 26, 2020 at 16:38
• Continuity is, in part, a modeling decision. There exists no universal criterion based on inspecting unique values along that will make that decision for you.
– whuber
Apr 26, 2020 at 17:27 | 2022-10-02 21:54:25 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.32873430848121643, "perplexity": 508.9665671242956}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030337360.41/warc/CC-MAIN-20221002212623-20221003002623-00719.warc.gz"} |
https://www.physicsforums.com/threads/integration-seems-gaussian-but-the-answer-does-not-match.784828/ | # Integration seems gaussian but the answer does not match
1. Nov 30, 2014
### tfhub
1. The problem statement, all variables and given/known data
-h^2/2m (sqrt(2b/pi)) e^(-bx^2) d^2/dx^2 (e^(-bx^2)) dx from - to + infinity
2. Relevant equations
I tried differentiating e^(-bx^2) twice and it came up weird , I positioned the values and finally cam up with (-2b sqrt(pi/2b)........is there any other way to do it ?
3. The attempt at a solution
I tried with gaussian integration and my final answer is h^2b/m but it should be h^2b/2m... how am i missing the 1/2 factor?
2. Nov 30, 2014
### Orodruin
Staff Emeritus
It is difficult to say where you are going wrong if you do not show us exactly what you did step by step.
3. Nov 30, 2014
### Ray Vickson
If you mean that you came up with -2b sqrt(pi/2b) for the integral--that is, that
$$\int_{-\infty}^{\infty} e^{-bx^2} \frac{d^2}{dx^2} e^{-b x^2} \, dx =- 2b \sqrt{\frac{\pi}{2b}},$$
then you are off by a factor or 2: you should have $-b \sqrt{\pi/2b}$. You need to show your work in detail. | 2017-10-17 15:06:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6274122595787048, "perplexity": 1346.5557447818649}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187822116.0/warc/CC-MAIN-20171017144041-20171017164041-00087.warc.gz"} |
http://mathcal.ma.tum.de/mc/showtalks?filter=0&id=1280 | ### 12.11.2018 16:15 Vanja Nikolic, Maxime Breden, Elisabeth Ullmann, Christian Kühn:Workshop Dynamics & NumericsMI 02.08.011 (Boltzmannstr. 3, 85748 Garching)
$$Numerics: Vanja Nikolic (30 Min)$$
Title: Analytical and numerical aspects of nonlinear acoustic wave propagation
Abstract: The need to analyze and accurately simulate nonlinear sound propagation has increased with the rise in the number of ultrasound applications in medicine and industry. In this talk, I will present some of my recent work on the well-posedness and numerical simulation of partial differential equations that model nonlinear sound propagation. In addition, I will briefly discuss the treatment of shape optimization problems that arise in the practical use of high-intensity focused ultrasound.
$$Dynamics: Maxime Breden (30 Min)$$
Title: An introduction to a posteriori validation techniques, illustrated on the study of minimum energy paths.
Abstract: To understand the global behavior of a nonlinear system, the first step is to study its invariant set. Indeed, specific solutions like steady states, periodic orbits and connections between them are building blocks that organize the global dynamics. While there are many deep, general and theoretical mathematical results about the existence of such solutions, it is often difficult to apply them to a specific example. Besides, when dealing with a precise application, it is not only the existence of these solutions, but also their qualitative properties that are of interest. In that case, a powerful and widely used tool is numerical simulations, which is well adapted to the study of an explicit system and can provide invaluable insight for problems where the nonlinearities hinder the use of purely analytical techniques. The aim of a posteriori validation techniques is to obtain mathematically rigorous and quantitative existence theorems, using those numerical simulations. Given an approximate solution, the general strategy is to combine a posteriori estimates with analytical ones to apply a fixed point theorem, which then yields the existence of a true solution in an explicit neighborhood of the numerical one. In the first part of the talk, I'll present the main ideas of a posteriori validation in more detail, and describe the general framework in which they are applicable. In the second part, I'll then focus on a specific example and explain how to validate minimum energy paths for stochastic differential equations.
$$Numerics: Elisabeth Ullmann (30 Min)$$
Title: Multilevel Sequential^2 Monte Carlo for Bayesian Inverse Problems
Abstract: The identification of parameters in mathematical models using noisy observations is a common task in uncertainty quantification. We employ the framework of Bayesian inversion: we combine monitoring and observational data with prior information to estimate the posterior distribution of a parameter. Specifically, we are interested in the distribution of a diffusion coefficient of an elliptic PDE. In this setting, the sample space is high-dimensional, and each sample of the PDE solution is expensive. To address these issues we propose and analyse a novel Sequential Monte Carlo (SMC) sampler for the approximation of the posterior distribution. Classical, single-level SMC constructs a sequence of measures, starting with the prior distribution, and finishing with the posterior distribution. The intermediate measures arise from a tempering of the likelihood, and the resolution of the PDE discretisation is fixed. In contrast, our estimator employs a hierarchy of PDE discretisations to decrease the computational cost. We construct a sequence of intermediate measures by decreasing the temperature or by increasing the discretisation level at the same time. This idea builds on and generalises the multi-resolution sampler proposed by P.S. Koutsourelakis (J. Comput. Phys. 228, 2009, pp. 6184-6211) where a bridging scheme is used to transfer samples from coarse to fine discretisation levels. Importantly, our choice between tempering and bridging is fully adaptive, and can also be generalized to time-dependent problems.
$$Dynamics: Christian Kühn (30 Min)$$
Title: Numerical Continuation of Ellipsoids for Stochastic Problems
Abstract: In this talk, I shall explain a method, how to analyze certain aspects of stochastic dynamical systems from a purely deterministic, discrete, and geometric perspective. In particular, we study fluctuations around steady states in stochastic differential equations using ellipsoids calculated via Lyapunov matrix equations. The method will be embedded in a numerical continuation framework to effectively study parametrized problems. I am also going to briefly mention rigorous error estimates for the numerics and several applications. | 2019-01-18 13:57:16 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5233575105667114, "perplexity": 413.6814145355207}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583660139.37/warc/CC-MAIN-20190118131222-20190118153222-00547.warc.gz"} |
http://tatome.de/zettelkasten/zettelkasten.php?tag=orienting | # Show Tag: orienting
Select Other Tags
Reward mediated learning has been demonstrated in adaptation of orienting behavior.
Integrating information from multiple stimuli can have advantages:
• shorter reaction times
• lower thresholds of stimulus detection
• detection,
• identification,
• precision of orienting behavior
Irrelevant auditory stimuli can dramatically improve or degrade orientation performance in visual orientation tasks:
In Wilkinson et al.'s experiments, cats' performance in orienting towards near-threshold, medial visual stimuli was much improved by irrelevant auditory stimuli close to the visual stimuli and drastically degraded by irrelevant auditory stimuli far from the visual stimuli.
If visual stimuli were further to the edge of the visual field, then lateral auditory stimuli improved their detection rate even if they were disparate.
Chemical deactivation of AES degrades both the improvement and the degradation of performance in orienting towards visual due to auditory stimuli.
The frontoparietal network seems involved in executive control and orienting.
Integrating information from different modalities can improve
• detection,
• identification,
• precision of orienting behavior,
• reaction time.
The SC is involved in generating gaze shifts and other orienting behaviors.
In the Sprague effect, removing (or deactivating) one visual cortex eliminates visually induced orienting behavior to stimuli in the contralateral hemifield.
Lesioning (or deactivating) the contralateral SC restores the orienting behavior.
The heminanopia that follows unilateral removal of the cortex that mediates visual behavior cannot be explained simply in classical terms of interruption of the visual behavior cannot be explained simply in classical terms of interruption of the visual radiations that serve cortical function.
Explanation fo the deficit requires a broader point of view, namely, that visual attention and perception are mediated at both forebrain and midbrain levels, which interact in their control of visually guided behavior.''
(Sprague, 1966) | 2019-11-12 13:43:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5003968477249146, "perplexity": 10949.692855183182}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496665573.50/warc/CC-MAIN-20191112124615-20191112152615-00099.warc.gz"} |
http://mathhelpforum.com/differential-geometry/118152-residue.html | 1. ## residue
Find the residue of the following.
(a) $\text{Res}(f, z_0=0)$, where $f(z)=\frac{e^z}{\sin(2z^2)}$
(b) $\text{Res}(f, z_0=0)$, where $f(z) = \frac{\cos(\frac{1}{z})}{e^z}
$
We are just beginning residues right now, and I do not know how to proceed. Should I use the Laurent expansion to find the residue for both parts? I am not very familiar with residues yet. Thanks very much.
2. Originally Posted by pascal4542
Find the residue of the following.
(a) $\text{Res}(f, z_0=0)$, where $f(z)=\frac{e^z}{\sin(2z^2)}$
(b) $\text{Res}(f, z_0=0)$, where $f(z) = \frac{\cos(\frac{1}{z})}{e^z}
$
We are just beginning residues right now, and I do not know how to proceed. Should I use the Laurent expansion to find the residue for both parts? I am not very familiar with residues yet. Thanks very much.
If $z_0$ is a pole of order $m$, then $\text{Res}\!\left(f;z_0\right)=\frac{1}{m-1}\lim_{z\to z_0}\frac{\,d^{m-1}}{\,dz^{m-1}}\left[(z-z_0)^mf\!\left(z\right)\right]$.
In the case its a simple pole, we have $\text{Res}\!\left(f;z_0\right)=\lim_{z\to z_0}(z-z_0)f\!\left(z\right)$.
Are you allowed to use these?
3. Originally Posted by Chris L T521
If $z_0$ is a pole of order $m$, then $\text{Res}\!\left(f;z_0\right)=\frac{1}{m-1}\lim_{z\to z_0}\frac{\,d^{m-1}}{\,dz^{m-1}}\left[(z-z_0)^mf\!\left(z\right)\right]$.
In the case its a simple pole, we have $\text{Res}\!\left(f;z_0\right)=\lim_{z\to z_0}(z-z_0)f\!\left(z\right)$.
Are you allowed to use these?
Yes I am. I will try that. Thank you.
4. Originally Posted by pascal4542
Yes I am. I will try that. Thank you.
I was wondering if you can check my work.
For (a) $\text{Res}(f, z_0=0)$, where $f(z)=\frac{e^z}{\sin(2z^2)}$ we have
$\frac{1+z+z^2/2!+z^3/3!+\cdots}{2z^2 -(2z^2)^3/3!+(2z^2)^5/5!- \cdots}$
$= \frac{1}{2z^2}+\frac{1}{2z}+1/4+z/12$
So the residue is $1/2$.
For (b) $\text{Res}(f, z_0=0)$, where $f(z) = \frac{\cos(\frac{1}{z})}{e^z}$ we have
$\cos(\frac{1}{z}) \cdot (1-z+z^2/2-z^3/6+z^4/24+\cdots).$
I am stuck. I don't know how to get the residue. I know that $z_0$ is an essential singularity. I need help on part (b).
5. You have a Taylor series multiplied by a non-terminating singular series so the residue is an infinite sum due to the term-wise multiplication of $z^n$ by $z^{-n}$ so then:
\begin{aligned}\frac{\cos(1/z)}{e^z}&=\sum_{n=0}^{\infty}\frac{(-1)^n}{1}\frac{1}{(2n)! z^{2n}} \sum_{n=0}^{\infty}\frac{(-1)^n z^n}{n!}\\
&=\sum_{n=0}^{\infty}\sum_{k=0}^{n} \frac{(-1)^k}{(2k)!z^{2k}}\frac{(-1)^{n-k}z^{n-k}}{(n-k)!}
\end{aligned}
and note the coefficients on the $1/z$ terms are when the exponent of z is $n=3k-1$. Now, can you extract out all those terms and come up with the expression:
$\mathop\text{Res}\limits_{z=0} \frac{\cos(1/z)}{e^z}=\sum_{k=0}^{\infty} \frac{(-1)^{3k-1}}{(2k)!(2k-1)!}$ | 2017-05-01 04:51:20 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 31, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9693281650543213, "perplexity": 236.5156578743648}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-17/segments/1492917127681.50/warc/CC-MAIN-20170423031207-00620-ip-10-145-167-34.ec2.internal.warc.gz"} |
https://www.mail-archive.com/tiddlywiki@googlegroups.com/msg70744.html | # [tw] [TW5] Desirable core additions
Folks,
Please forgive my being so brash to propose some TW5 core additions but I
am in the middle of a learing curve that may inform some improvements to
the core that will help others on this learning curve. I would liove your
feedback and if you are a GitHub proficiant person for you to submitt them.
First I will explain what I want with a small explination and hope the
reasons prove self evident, however I will put a longer argument if
requested. I acknowledge there may be a gap in my knowledge and are happy
to be set straight. I am no Genius but I am not stupid and a clear way to
do the following would have made adopting TW5 much easier. I hope I am
using the correct terminology.
Psudo-Constants
Provide tools to create "constants" within a given tiddler and any
sub-tiddlers (transcluded, called, macros etc...)
I have finaly learned I can do this using the below
\define currentobjectsrc()
{{!!title}}
\end
<\$wikify name="currentobject" text=<<currentobjectsrc>>>
Such that <<currentobject>> has the same value in all sub-tiddlers
*This is still not sufficent as <<currentobject>> can only be used in some
places*.
Why cant we have an established syntax that allows this as a built in
feature?
The current methods are way to convoluted and I fear act as a barier to
someone using tiddlywiki as their knowledge must be much deeper than it
need be before they can do something most people will think of while they
are learing about tiddlywiki. In this case much can be done without
learning to navigate a lot of complexity by providing values that are not
so context sencitive.
Edit fields in Current Tiddler
Provide the tools to edit fields in the Current Tiddler
The complexity of editing fields in the current tiddler, whilst it has its
technical reasons, runs counter to the intuitive value of tiddlywiki. The
most practical way is to use the tiddler edit function in which case the
user has to see all possible fields and values. I would like to provide
access to edit fields in the current tiddler through the View Template,
without needing to use two additional tiddlers to achive this.
I understand the issue is the rendering of each key stroke and the loss of
focus, but why can we not have a method where you nominate a field and its
value is placedn in an external tiddler, you then edit the field value and
on pressing a (field) save button, it is written back to the calling
tiddler in one shot?
Once again the current methods are way to convoluted and I fear act as a
barier to someone using tiddlywiki as their knowledge must be much deeper
than it need be before they can do something most people will think of
while they are learing about tiddlywiki.
Regards
Tony
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To unsubscribe from this group and stop receiving emails from it, send an email | 2017-08-19 15:55:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4617706835269928, "perplexity": 2933.7723871767107}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105455.37/warc/CC-MAIN-20170819143637-20170819163637-00594.warc.gz"} |
http://mathematica.stackexchange.com/questions/16439/find-all-roots-of-an-interpolating-function-solution-to-a-differential-equation | # Find all roots of an interpolating function (solution to a differential equation)
I'm trying to find all the roots of the solution to a differential equation. Using NSolve or Reduce I don't get the roots, so I'm using an iterative method which I found in physicsforums.com. This method solves my problem, but you have to choose the increment and thus in some cases it might give headaches. I wonder if there is any more general approach.
Following is a sample code:
data = NDSolve[{1.09 x''[t] - 0.05 x'[t] + 1.1759 Sin[x[t]] == 0,
x[0] == Pi/3, x'[0] == 0}, x, {t, 0, 50}]
{{x->InterpolatingFunction[{{0.,50.}},<>]}}
First attempt with no success:
sol = NSolve[x'[t] == 0 /. data , t]
NSolve::ifun: Inverse functions are being used by NSolve, so some solutions may not be found; use Reduce for complete solution information. >>
{{t->InverseFunction[InterpolatingFunction[{{0.,50.}},<>],1,1][0.]}}
Second attempt with no success:
sol = Reduce[x'[t] == 0 /. data , t]
Reduce::inex: Reduce was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Reduce require exact input, providing Reduce with an exact version of the system may help. >>
Reduce[{InterpolatingFunction[{{0.,50.}},<>][t]==0},t]
Third attempt, works fine, but manually choosing dt could cause problems with some equations:
dt = 0.1;
tmin = 0.;
tmax = 50.;
Union[Table[t /. FindRoot[x'[t] == 0 /. data ,{t, tInit, tmin, tmax}],
{tInit, tmin + dt,tmax - dt, dt}], SameTest->(Abs[#1 - #2] < 10^-2&)]
{0., 3.26812, 6.58301, 9.95657, 13.4054, 16.9538, 20.6403, 24.533, 28.7857, 34.2571}
Is there any more elegant method to find all roots in a range?
-
– Mr.Wizard Dec 16 '12 at 23:23
I'm slightly surprised nobody's already mentioned the event location capabilities of Mathematica, as it's the most compact way to find the roots of an interpolating function that came from NDSolve[]. I don't have Mathematica on this machine I'm writing in, but I'd do something like this:
Reap[NDSolve[{1.09 x''[t] - 0.05 x'[t] + 1.1759 Sin[x[t]] == 0, x[0] == Pi/3, x'[0] == 0},
x, {t, 0, 50}, Method -> {"EventLocator",
"Event" -> x[t], "EventAction" :> Sow[t]}]]
which should yield the interpolating function and the list of roots.
At least, that's how its done in version 8. Version 9 has the WhenEvent[] function, which can be used like so:
Reap[NDSolve[{1.09 x''[t] - 0.05 x'[t] + 1.1759 Sin[x[t]] == 0, x[0] == Pi/3, x'[0] == 0,
WhenEvent[x[t] == 0, Sow[t]]}, x, {t, 0, 50}]]
-
I did mention this method in my answer above by referring to Daniel's answer here, of which this answer is a variation. – Jens Dec 17 '12 at 4:37
Jens: Well, since the Brent algorithm used by the event locator can take options, you can still easily leverage the abilities of FindRoot[]: Method -> {"EventLocator", "Event" -> x[t], "EventAction" :> Sow[t], "EventLocationMethod" -> {"Brent", AccuracyGoal -> Infinity, "SolutionApproximation" -> "CubicHermiteInterpolation"}}. There should be an equivalent way of tweaking such options if you're taking the WhenEvent[] route. – Jerry Dec 17 '12 at 4:43
(I'm quite sure a question like this has been asked before on this site, but I suck at searching for dupes.) – Jerry Dec 17 '12 at 4:44
Here is a function aptly named findAllRoots that is based on idea published a long time ago in the Mathematica Journal, I believe. I'll try to find the article again, but in the meantime here is my version of it. I added the option handling, in particular the possibility to show the plot of the function while finding its roots. The idea to extract data from a Plot (thereby leveraging its analysis of the curve) and to then use Split in this non-standard way is the main thing that I remember from the article.
Clear[findAllRoots]
SyntaxInformation[
findAllRoots] = {"LocalVariables" -> {"Plot", {2, 2}},
"ArgumentsPattern" -> {_, _, OptionsPattern[]}};
SetAttributes[findAllRoots, HoldAll];
Options[findAllRoots] =
Join[{"ShowPlot" -> False, PlotRange -> All},
FilterRules[Options[Plot], Except[PlotRange]]];
findAllRoots[fn_, {l_, lmin_, lmax_}, opts : OptionsPattern[]] :=
Module[
{pl, p, x, localFunction, brackets},
localFunction = ReleaseHold[Hold[fn] /. l :> x];
If[
lmin != lmax,
pl = Plot[localFunction, {x, lmin, lmax},
Evaluate@
FilterRules[Join[{opts}, Options[findAllRoots]], Options[Plot]]
];
p = Cases[pl, Line[{x__}] :> x, Infinity];
If[OptionValue["ShowPlot"],
Print[Show[pl, PlotLabel -> "Finding roots for this function",
ImageSize -> 200, BaseStyle -> {FontSize -> 8}]]],
p = {}
];
brackets = Map[
First,
Select[
(* This Split trick pretends that two points on
the curve are "equal" if the function
values have _opposite _ sign. Pairs of such
sign-changes form the brackets for the subsequent
FindRoot *)
Split[p, Sign[Last[#2]] == -Sign[Last[#1]] &],
Length[#1] == 2 &
],
{2}
];
x /. Apply[FindRoot[localFunction == 0, {x, ##1}] &,
brackets, {1}] /. x -> {}
]
Here follows the interpolation function from your question, and the application of the above function:
data = NDSolve[{1.09 x''[t] - 0.05 x'[t] + 1.1759 Sin[x[t]] == 0,
x[0] == Pi/3, x'[0] == 0}, x, {t, 0, 50}];
f[t_] = (x /. First[data])[t];
findAllRoots[f[t], {t, 0, 50}, "ShowPlot" -> True]
{1.59975,4.88823,8.22838,11.6339,15.1242,18.7282,22.4934,26.5081,30.9882,37.4065}
I've used this successfully before, and I've also compared it to Daniel's solution in this answer. I prefer the above method because his NDSolve approach ended up being less accurate in my applications.
Edit: IntervalRoots
One of the standard add-on packages that disappeared during the upgrade from Mathematica version 5.2 to 6 was NumericalMath. If you had a notebook that started with
<<NumericalMathIntervalRoots
then you could call a function like
IntervalNewton[Sin[t], t, Interval[{10, 20}], .1]
Interval[{12.5661,12.5664},{15.6503,15.7438},{18.8495,18.8506}]
Now if you want to try replacing the root bracketing in my function findAllRoots by this bracketing routine, you have to do get this package manually at MathSource. I thought I'd mention this for completeness. However, these old bracketing functions apparently can't handle InterpolatingFunction properly, so this is purely a historical footnote.
-
Very nice, thanks a lot for your effort! – Love Learning Jun 24 at 15:39
Using RootSearch.m (mentioned in the above link given by MrWizard)
http://library.wolfram.com/infocenter/Demos/4482/
download the .m file, put it in my current folder and did:
SetDirectory[NotebookDirectory[]];
Get["RootSearch.m"];
eq = 1.09 x''[t] - 0.05 x'[t] + 1.1759 Sin[x[t]] == 0;
ic = {x[0] == Pi/3, x'[0] == 0};
sol = First@NDSolve[Flatten[{eq, ic}], x[t], {t, 0, 50}];
ErsekRootSearchRootSearch[Evaluate[x[t] /. sol] == 0, {t, 0, 50}]
(* {{t -> 1.59975}, {t -> 4.88823}, {t -> 8.22838}, {t -> 11.6339},
{t -> 15.1242}, {t -> 18.7282}, {t -> 22.4934}, {t -> 26.5081},
{t -> 30.9882}, {t -> 37.4065}} *)
ps. on console I see this warning message
$MinPrecision::precset: Cannot set$MinPrecision to -\[Infinity]; value
must be a non-negative number or Infinity. >>
But the package has options. So these things migthbe possible to configure. see the notebook for more information
-
I found this as a possible cure for the MinPrecision error: set it to +Infinty. – Jens Dec 17 '12 at 2:27
I am truly overwhelmed by the responses and their quality. Thanks. It has helped me a lot and I hope they will also help more people. Not only because of the answers but studying the submitted codes I'm discovering new possibilities of Mathematica. Thanks. – user1084363 Dec 17 '12 at 22:39 | 2015-07-03 15:46:37 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.22480811178684235, "perplexity": 3702.9372461397998}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-27/segments/1435375096156.35/warc/CC-MAIN-20150627031816-00084-ip-10-179-60-89.ec2.internal.warc.gz"} |
https://www.scienceopen.com/document?vid=4bf53756-cb74-4512-ac34-3419bebdbc19 | 57
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Is Open Access
# Generation of a macroscopic entangled coherent state using quantum memories in circuit QED
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There is no author summary for this article yet. Authors can add summaries to their articles on ScienceOpen to make them more accessible to a non-specialist audience.
### Abstract
$$W$$-type entangled states can be used as quantum channels for, e.g., quantum teleportation, quantum dense coding, and quantum key distribution. In this work, we propose a way to generate a macroscopic $$W$$-type entangled coherent state using quantum memories in circuit QED. The memories considered here are nitrogen-vacancy center ensembles (NVEs), each located in a different cavity. This proposal does not require initially preparing each NVE in a coherent state instead of a ground state, which should significantly reduce its experimental difficulty. For most of the operation time, each cavity remains in a vacuum state, thus decoherence caused by the cavity decay and the unwanted inter-cavity crosstalk are greatly suppressed. Moreover, only one external-cavity coupler qubit is needed. This method is quite general and can be applied to generate the proposed $$W$$ state with atomic ensembles or other spin ensembles distributed in different cavities.
### Author and article information
###### Journal
2014-11-12
2016-03-12
1411.3102 | 2019-12-13 05:07:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35254940390586853, "perplexity": 2651.9923719755375}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540548544.83/warc/CC-MAIN-20191213043650-20191213071650-00519.warc.gz"} |
https://www.gradesaver.com/textbooks/math/precalculus/precalculus-concepts-through-functions-a-unit-circle-approach-to-trigonometry-3rd-edition/chapter-2-linear-and-quadratic-functions-cumulative-review-page-188/7 | ## Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (3rd Edition)
In the given relation, each $x$-value is paired with one corresponding $y$-value. Hence, the relation represents a function. | 2021-10-28 10:37:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9240575432777405, "perplexity": 3658.5840706615327}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588284.71/warc/CC-MAIN-20211028100619-20211028130619-00210.warc.gz"} |
http://www.kentran.net/ | ## Monday, July 14, 2014
### ICML 2014 Highlights 2: On Deep Learning and Language Modeling
Previously: Highlights #1 - On ML Fundamentals
## Deep Learning and Language Modeling
Images classification seems to be the past. The current wave of DL research is all about language modeling. Here’re some interesting works on this front.
## Abstract
At a high level, Deep Learning (DL) is still hot and DL keeps eating Machine Learning. The conference's attendance distribution was like: half was there for Deep Learning and the other half was there for *Shallow* Learning :). Interestingly, the conference took place in Beijing, for the first time, and more than 50% of the attendants either study or work there (and most of that local population are students). So the attendance distribution could be biased.
In the following, I'll highlight what I've learned and observed from the conference. Here's the outline:
## Tuesday, July 1, 2014
### On the imminent death of MapReduce
Google recently announced at Google IO 2014 that they are retiring MapReduce (MR) in favor of a new system called Cloud Dataflow. Well, the article author perhaps dramatized it when quoting Urs Hölzle's words
We don’t really use MapReduce anymore.
You can watch the keynote here for a better context. My guess is that no one is writing new MapReduce jobs anymore, but Google would keep running legacy MR jobs for years until they are all replaced or obsolete.
Regardless of what has happened at Google, I'd like the point out that MR should have been ditched long ago.
Someone at Cloudera (the company that used to make money on the hype of Hadoop MapReduce) already partially explained why in this blog post: The Elephant was a Trojan Horse: On the Death of Map-Reduce at Google. Some quotes to remember are:
• Indeed, it’s a bit of a surprise to me that it lasted this long.
• and the real contribution from Google in this area was arguably GFS, not Map-Reduce.
Every real distributed machine learning (ML) researcher/engineer knows that MR is bad [*]. ML algorithms are iterative and MR is not suited for iterative algorithms, which is due to unnecessary frequent I/O and scheduling plus other factors (see the illustration below). For more details on the weaknesses of MR, one can read any intro slides about Spark [**].
Also note that Mahout, the ML library for Hadoop, recently said goodbye to MapReduce.
#### 25 April 2014 - Goodbye MapReduce
The Mahout community decided to move its codebase onto modern data processing systems that offer a richer programming model and more efficient execution than Hadoop MapReduce. Mahout will therefore reject new MapReduce algorithm implementations from now on. We will however keep our widely used MapReduce algorithms in the codebase and maintain them.
We are building our future implementations on top of a DSL for linear algebraic operations which has been developed over the last months. Programs written in this DSL are automatically optimized and executed in parallel on Apache Spark.
Notes
[*] Unfortunately, lots of companies, including my employer, are still chasing the Hadoop game. Microsoft just less than a year ago announced HDInsight, aka. Hadoop on Azure.
[**] For virtually everything that MR can do, Spark can do equally well and in most cases better. Also note that while Spark is generally fantastic, it is not necessarily the right distributed framework for every ML problem.
## Monday, June 30, 2014
### ICML 2014 Best Paper Awards
It's strange that the best paper awards are not posted on the ICML website. So I'll post them here:
Disclaimer: I have read none of the above papers. I have a different set of interesting ones but those above are the official best papers.
I'll share what I find interesting in another Highlights of ICML 2014 post.
## Wednesday, March 26, 2014
### What kind of coding skills are required to work on machine learning?
(Image src: Inside BigData)
In our small team of 13 people, who all work on ML, the required coding skills range from
• None (or simple git pull and build). Such person only needs to run experiments and write technical docs. (Revised: perhaps very little to demonstrate how to use the API.)
• to decent numerical computing in MATLAB/Python/R. Such person runs and tweaks experiments on real problems for customers. Knowing at least one of those scripty languages is required so that they can do custom features engineering or visualization tasks that are not supported by the main tool that we build.
• to good C# or F# + great software design + various level of numerical computing. Such person contributes to the main code base.
• to hardcore low level programming. Such person is obsessed with latency/throughput, BLAS, SSE/AVX, GPU, and distributed systems.
## Overall
1. Deep Learning (or Deep Neural Network or DNN) is again the most trendy topic of the conference. Its workshop session is perhaps twice (or more than that) as big as the one last year and it was packed for most of the day. Interestingly, Mark Zuckerberg of Facebook stopped by for a Q&A and then a panel discussion session. His visit was mostly to announce the new AI Lab of Facebook. For technical highlights, see below.
2. Distributed machine learning is another topic of huge interest.
3. Growing markets and interests in predictive analytics on sensor data (e.g. activity detection on mobile phones or wearable devices), in ML for Health Care, and in ML for Education.
4. And there are certainly bad-ass research in other areas which I have missed. Among the topics of my interest, Optimization (particularly non-convex optimization) however hasn't made much progress.
## Deep Neural Nets
• Natural Language Processing. Application of DNN in NLP is the theme of the deep learning research this year. This is natural because NLP is the holy-grail of machine learning research. DNN has already convincingly demonstrated its power in Computer Vision and Speech Recognition. There were some cool research using DNN in NLP such as Compositional Natural Language Parsing with Compositional Vector Grammars by a team at Stanford (led by Richard Socher) and Word2Vec project at Google (led by Tomas Mikolov). I think that this is just the beginning though.
• Computer Vision. New benchmark for ImageNet has been established by Matt Zeiler et al. although it's not a big improvement from the previous record set by Alex Krizhevsky et al. (see their famous paper). Although Matt's work received a lot of attention from the community (come on, he set a new record), I was slightly disappointed. The spirit of his paper is about understanding convolutional neural networks but he did not explain why his network (which is a customized version of Alex's network) yields better results. He also wasn't able to rigorously explain certain mysteries (such as why rectified linear units work so well) in training neural networks.
• Non-convex Optimization. This is the topic that I care the most in DNN because solving a DNN is a non-convex optimization problem. The current techniques only try to find a local minimum, at best. Here's an experiment that my team did for activity detection on mobile devices using sensory data. After features extraction using PCA and feeding the extracted model into a neural network, we got very good results. We then simulated the PCA feature extraction by introducing another layer to the neural network. We expected that the the optimized weights of the first layer should be identical to the PCA weights, if not better. However, we got worse results. This indicates that the optimizer converged to a non-so-good local optimum.
• From the scientific standpoint, the sexy part about DNN is that it can model very complicated machine learning tasks without doing too much feature engineering. Until there's a breakthrough in global optimization technique for non-convex problem or some convex remodeling of DNN, DNN will be just another periodic trend. That's why training DNNs still requires a significant amount of engineering.
## Distributed Machine Learning
There're many interesting posters/talks on the topic of distributed and large scale machine learning at NIPS this year (such as this, this, and this workshop). However, what really excited me is not the work presented at NIPS but Spark, an Apache project built on top of HDFS for running distributed iterative operations distributedly. (It's a shame that I hadn't been aware of this project earlier.)
The cool thing about Spark is that it inherits the goods of Hadoop (i.e. HDFS) and re-engineers the rest. In particular:
1. Iterative algorithms, which is the norm in ML, can be run in memory during their lifetime. No more reading from / writing to the disk for each iteration.
2. Support of more operators, beyond Mapping and Reducing, which can be piped and lazily evaluated. See more here. In a sense, Spark is similar to Parallel LINQ but on HDFS data.
(These are the main reasons why serious machine learning practitioners don't use Hadoop beyond HDFS. Yes, stay away from the Hadoop hype. HDFS is cool. The rest of Hadoop is not so.)
The not-so-cool thing is that the whole Hadoop technology stack is in Java. Anyone interested in building Spark .NET? If there're enough interested developers, I would join or initiate such project.
## Machine Learning on Sensor Data
To be (never) updated ...
## Friday, April 12, 2013
### Neural Network Best Practices
I have been ecstatic by work. That's why this blog doesn't get updated as often as I want.
Recently, I have been focusing on the implementation of a state-of-the-art (in both accuracy and perf dimensions) and generic neural net, as a predictor for a general ML software. I have learned a ton while doing it and would like to share some of the best practices when implementing a deep neural net [1].
### 1. Neural Nets Basics
The basics of Neural Nets (NN) is well written on Wikipedia. There's no point to repeat what Wiki has already covered.
However, there are some subtle points that are worth mentioned.
1. Misconception: backprop is not training method for neural network. It is simply a method, the standard method, to compute the gradient using chain rules. I have explained it in slightly more details here.
2. Tips: Implementing backprop correctly is key to have a correct neural net implementation. It's easy to have bugs in the implementation when you introduce more complex connection types (e.g. convolutional, pooling, etc.) or other tricks (e.g. dropout). As backprop is one way to compute the gradient, always use another method to assert (when running in debug mode) that your gradient implementation is correct. The standard gradient checking method is to use finite difference to calculate the gradient and compare that with the results obtained from backprop.
### 2. Major techniques to improve prediction accuracy
2.1. Convolutional Neural Networks (CNN)
Few years ago, convolutional network was considered a trick. Nowadays, it has become a norm to obtain good results in areas such as computer vision and speech recognition, where data has some local structure.
You can read more about CNN here or check out my slides.
2.2. Regularization
Neural net is notorious for being prone to overfitting, due to its massive number of parameters (a.k.a. large capacity). Here are some effective regularization techniques.
• $$L_1$$ and $$L_2$$ are the usual suspects for regularization and they still work well. In practice, $$L_1$$ is sufficient [2]. They are practically not different in terms of performance but the former gives rise to sparse coding of the weights (see the explanation here). Think of it as both regularizer and feature selector.
• Dropout is a dead simple but very clever use of model ensembling in a large neural net. You can read more about it in Hinton's paper. Implementing dropout is quite simple and we have seen great gains from using it.
It's always good to combine $$L_1$$ and dropout in training neural nets.
2.3. Choice of activation function Sigmoid and Tanh are the two most commonly used activation functions. However, they are not necessarily good choices as activation functions for the hidden units. The reasons are:
• They saturate quickly when the output value is not a narrow region (around 0), i.e. the derivative almost vanishes. This means that the network easily gets stuck or converges slowly when the pre-activated values fall outside of the region.
• There's no reason that the hidden units should be restricted to (0,1) as in the Sigmoid function or (-1,1) as in the Tanh function.
Rectifier is becoming popular as an activation function. However, I find its theory dubious and my experiments have not shown that it is always better. That said, I'm experimenting with new activation functions. (Little trivia: I'm borrowing many ideas from my graduate work in computational wave propagation.)
### 3. Speed things up
This is what I want to talk about more because academic papers tend to focus on accuracy and ignore the efficiency aspects.
3.1. Use a highly optimized BLAS Library
The computations at each layer in a neural network can be abstracted as matrix multiplications
• Forward propagation: $$y=W^{T}\times x$$
• Back propagation: $$\nabla x=W\times\nabla y$$
• Weights update: $$W \leftarrow W+\alpha\times x\times \nabla y^{T}$$
where
• $$W$$ of size $$m\times n$$ is the weights matrix,
• $$x$$ of length $$m$$ represents the source layer's nodes,
• $$y$$ of length $$n$$ represents the destination layer's nodes,
• and $$\alpha$$ is the learning rate (assuming that we are using stochastic gradient descent).
Note this abstraction assumes that the source layer contains the bias node [3]. For these matrix operations, it's recommended use a highly-optimized BLAS library such as Intel MKL [4] for running on CPUs or NVIDIA's CuBLAS for running on GPUs. The speed gain from abstracting the operations as matrix multiplies and using optimized BLAS libraries is very significant (tens to hundreds fold faster).
3.2. Convolution Unrolling
Here, I assume that you are already familiar with convolutional network mentioned above and have implemented a basic one. If so, you would notice that the matrix multiply abstraction above doesn't seem to apply. Furthermore, the convolution operations are also slow due to index indirection.
Actually, with the convolution unrolling technique, proposed in this paper by Patrice Simard and John Platt, you can abstract the operations in training a convolutional network as matrix-matrix multiplies.
The layer-wise operations can be described as followed.
$$\begin{array}{cccc} \mbox{Forward propagation:}\hspace{1em} & Y & = & W^{T}\times X\\ \mbox{Back propagation:}\hspace{1em} & \nabla X & = & W\times\nabla Y\\ \mbox{Weights update:}\hspace{1em} & W & \leftarrow & W + \alpha\times X\times\nabla Y^{T} \end{array}$$
where
• $$W$$ is the weights matrix of size $$k\times m$$. Each column of $$W$$ corresponds to a kernel and with this layout, the last bias row can be omitted conveniently in the backprop.
• $$X$$ is the unrolled input of size $$k\times n$$. Each row of $$X$$ corresponds to a window in the original input.
• $$Y$$ is the output matrix of size $$m\times n$$. Each row of $$Y$$ corresponds to the output features for a particular feature map.
• $$\nabla X$$ is the unrolled (i.e. pre-accumulated) errors of the input layer.
• $$\nabla Y$$ is the errors of the output layer.
Here,
• $$m$$ is the number of feature maps (map count);
• $$n$$ is the number of output features per map;
• $$k$$ equals the kernel size plus one (the bias term).
Rolling and unrolling
In order to represent as above, we need two extra steps.
1. Unroll the input vector/matrix in each forward propagation. This process, which involves duplication of many elements, is to store $$X$$ consecutively in memory.
2. Roll (accumulate) the back-propagated errors matrix $$\nabla X$$ to a flat errors vector (of size equal the source destination), which can then be passed to the earlier layers.
The rolling and unrolling can be done efficiently by pre-computing the index map which maps from the original space to the unrolled space and vice versa.
3.3. More Parallelism
MKL (or CUDA for GPU computing) already does a lot of parallelism. However, there are still parallelism opportunities left on the table.
Due to the high cost of a high performance CPU cluster and due to the inter-machine communication inefficient, we'll focus our parallelism effort on a single machine with multiple GPU cards.
To be continued...
Notes
[1] There're many tricks in NN. There're even conferences (such as ICLR) dedicated to new little techniques. Here, I'll only highlight some major ones that work in almost all situations and sometimes yield significant gains in accuracy and performance. Also, this post focuses on implementation tips, not methods.
[2] Optimizers, such as Stochastic Gradient Descent or L-BFGS, should be implemented independent from the learning methods (e.g. Neural Network or Logistic Regression). That way, if you work with multiple learners, all learners can reuse the optimization code and any learner can expose different optimizers for users to choose if they want.
[3] A traditional approach is to treat biases as another set of parameters. | 2014-07-29 06:37:56 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3760406970977783, "perplexity": 1683.5507873081883}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1406510266597.23/warc/CC-MAIN-20140728011746-00340-ip-10-146-231-18.ec2.internal.warc.gz"} |
http://riverinaromantics.com/atlantic-canada-elbu/4e36c4-oxygen-enters-the-blood-at-the-lungs-because | # oxygen enters the blood at the lungs because
Why cant geothermal steam be produced on, say, the east coast of the United States? If you have health concerns or need clinical advice, call our helpline on 03000 030 555 between 9am and 5pm on a weekday or email them. Every active tissue in the body has an absolute requirement for oxygen. Oxygen enters the body through the nose and mouth and passes through the lungs into the bloodstream. A steel rod has a radius of 15.0 cm and a length of 1.25 m. The rod is held firmly in place. An electrical system that stimulates contraction of the heart muscle. When you inhale (breathe in), air enters your lungs and oxygen from the air moves from your lungs to your blood. This blood is not oxygenated, and forms a “physiologic shunt.” Because of this blood that bypasses the alveoli, arterial blood will always contain less oxygen pressure than blood that has equilibrated with the oxygen in … Oxygen enters the blood in the lungs because relative to alveolar air: a. the CO2 concentration in the blood is high. Last medically reviewed: February 2018. 46.3 - Explain how inhalation and exhalation occur in a... Ch. Download our how your lungs work PDF (340KB), What is pneumonia, symptoms and diagnosis, Acute respiratory distress syndrome (ARDS), Submit a review of our health information, Stories about living with a lung condition, Positions for obstructive lung conditions, Positions for restrictive lung conditions. Inside the air sacs, oxygen moves across paper-thin walls to tiny blood vessels called capillaries and into your blood. The pulmonary artery channels oxygen-poor blood from the right ventricle into the lungs, where oxygen enters the bloodstream. Normally, if areas of the lung aren’t gathering much oxygen due to damage from infection, the blood vessels will constrict in those areas. It is a serious condition that can lead to heart failure and even death. At the same time, carbon dioxide that is dissolved in the blood comes out of the capillaries back into the air sacs, ready to be breathed out. Note that the water of hydration is included in the molar m... A chemist needs exactly 2 moles of KNO3 to make a solution. Normally, deoxygenated blood enters the right side of the heart, travels to the lungs to receive oxygen, and then travels to the left side of the heart to be distributed to the rest of the body. 46.1 - Distinguish between the roles of the respiratory... Ch. 46.4 - Explain the role of hemoglobin in gas exchange. The aveoli are little sacks in the lungs where the air you breath in eventually ends up. Blood oxygen level is the amount of oxygen circulating in the blood. The four-chambered Oxygen is of extreme importance for the human blood and cells, because oxygen is necessary for the cell growth and energy. a. Now the oxygenated blood flows to the heart where it is pumped to the largest pulmonary artery known as the aorta. Due for review: February 2021. The partial pressure of oxygen is lower in the blood than in the alveoli. Knowing the information about the oxygen level in your blood will encourage people to find any issues in their body rapidly and act accordingly, depending on Oxygen Enters The Blood In The Lungs Class 10. Neon is an inert gas with three stable isotopes. 46 - Tracheal systems are characterized by: a. closed... Ch. What is this temperature in Celsius? The aorta channels oxygen-rich blood to the body from the left ventricle. Platinum metal is used in jewelry; it is also used in automobile catalytic converters. Oxygen enters the blood at the lungs because ________. It is used in gas lasers and in advertising signs. Your living with a lung condition stories, Information for health care professionals, Stoptober: the 28-day stop smoking challenge, Putting on your Take Steps sponsored walk, Taking the first step: Millets’ guide to walking, Big Breakfast for schools - activity ideas, Top tips for organising a brilliant charity quiz, Incredible support from trusts and foundations, Gwybodaeth yng Nghymraeg / Welsh language health information, The Asthma UK and British Lung Foundation Partnership, Why you'll love working with the British Lung Foundation, Thank you for supporting the British Lung Foundation helpline. 46.2 - How does the tracheal system of insects facilitate... Ch. The layers of cells lining the alveoli and the surrounding capillaries are each only one cell thick and are in very close contact with each other. Would you like to keep in touch by email? 46 - Apply Evolutionary Thinking From what you have... Ch. Which formed last: the visible halo, the galactic nucleus, or the disk? How does oxygen get into the bloodstream? Biology Biology: The Dynamic Science (MindTap Course List) Oxygen enters the blood in the lungs because relative to alveolar air: a. the CO 2 concentration in the blood is high. Most of the carbon dioxide is carried to the lungs in plasma as bicarbonate ions (HCO3-). The stopcock connecting a 1.00L bulb containing oxygen gas at a pressure of 540torr and a 1.00L bulb containing... You are advising a fellow student who wants to learn to perform multiple flips on the trampoline. When you’re at rest, the alveoli send 10.1 ounces (0.3 liters) of oxygen to your blood per minute. ABOUT; FIND THE ANSWERS. REFLECT AND APPLY You are purifying a protein for the first time. b. the CO 2 concentration in the blood is low. 1. during the exchange of air in your lungs, oxygen is being taken into your bloodstream while this substance is being released microorganisms carbon dioxide*** plasma mucus 2. the gas exchange of oxygen to the bloodstream takes. Most of the oxygen is carried by red blood cells, which collect oxygen from the lungs and deliver it to all parts of the body. Blood without oxygen returns through the veins, to the right side of your heart. Birds and mammals have a four-chambered heart The ventricle is divided by a septum into two compartments completely separating oxygenated from deoxygenated blood and delivering the maximum amount of oxygen to the head and body at the most efficient pressure. a. the concentration of carbon dioxide in the capillaries is lower than the concentration of carbon dioxide in the alveoli. This process is called gas exchange and is essential to life. A protein called haemoglobin in the red blood cells then carries the oxygen around your body. Weknowtheanswer. Superalloys have been made of nickel and aluminum. This information uses the best available medical evidence and was produced with the support of people living with lung conditions. From there it is pumped to your lungs so that you can breathe out the carbon dioxide and breathe in more oxygen. Explain why this is not a violation of the law of conservation of matter. Find answers now! The blood then is pumped through your body to provide oxygen to the cells of your tissues and organs. For the vast majority of these tissues, the oxygen is delivered by the blood to the tissues, although there are some notable exceptions (for example, the cornea gets its oxygen directly from the atmosphere).. Once oxygen has entered the blood from the lungs, it is taken up by haemoglobin (Hb) … Join now. The bronchioles end in tiny air sacs called alveoli, where oxygen is transferred from the inhaled air to the blood. Blood without oxygen returns through the veins, to the right side of your heart. does not contain negative temperatures? Its isotope... 32. Registered office: 18 Mansell Street, London, E1 8AA. In the following reactions, decide which reactant is oxidized and which is reduced. Gas exchange in the lungs We need to get oxygen from the air into the blood, and we need to remove waste carbon dioxide from the blood into the air. 1 °F outside. 46 - A teenager is frightened when she is about to step... Ch. Blood with fresh oxygen is carried from your lungs to the left side of your heart, which pumps blood around your body through the arteries. Specify its structure using three-letter symbols for the am... How does the human body respond to an increase in core body temperature? c. the O 2 concentration in the blood is high. Does the cell cycle refer to mitosis as well as meiosis? Click here to get an answer to your question ️ What is oxygen enter the blood in the lungs? Consider the tripeptide tyrosylleucylisoleucine. We use your comments to improve our information. Answered What is oxygen enter the blood in the lungs? e. the process is independent of gas concentrations in the blood. nitrogen ammonia urea uric acid. Once in the bloodstream, oxygen helps replace cells that wear out, provides energy for our bodies, supports the way our immune system functions and more. What’s the difference between self-isolation, social distancing and social shielding? answer choices. b. the concentration of oxygen in the capillaries is higher than the concentration of oxygen in the alveoli Which temperature scale(s) Case 1 What mass of solid KNO3 must be used? For Each Organ W-Z Write Down What It Does And How It Helps Gas Exchange To Occur. Ask your question. Carry out the following arithmetic operations: (a) the sum of the measured values 756, 37.2, 0.83, and 2.5; (b)... 5-83 When iodine vapor hits a cold surface, iodine crystals form. When an infected person expels virus-laden droplets and someone else inhales them, the novel coronavirus, called SARS-CoV-2, enters the nose and throat. The pH of a sample of gastric juice in a persons stomach is 2.1. What are the parts of the lungs where oxygen enters the blood? Within each air sac, the oxygen concentration is high, so oxygen passes or diffuses across the alveolar membrane into the pulmonary capillary.At the beginning of the pulmonary capillary, the hemoglobin in the red blood cells has carbon dioxide bound to it and very little oxygen (see illustration above). The lungs are exposed to the air so they also play an important protective role in your body, linked to your immune system. Log in. Oxygen enters the bloodstream from the lungs because. It finds a welcome home in the lining of the nose, according to a preprint from scientists at the Wellcome Sanger Institute and elsewhere. a. promoters c. operators... Gas exchange occurs at the _______. Throughout the body, the prese… 2 See answers *Response times vary by subject and question complexity. Water can be decomposed to hydrogen gas and oxygen gas by passing electricity through it. e. the process is independent of gas concentrations in the blood. c. the O2 concentration in the blood is high. The following six questions concern Rebecca, who is 36 years old, weighs 182 pounds, and is 5 feet 4 inches tal... Thallium and indium form + 1 and + 3 oxidation states when in compounds. Because there is low oxygen in the blood and high oxygen in the air in the aveoli (and because the capillaries are so close to the aveoli) the oxygen in the air in the aveoli can simply transfer into the blood in the capillaries (in a process called diffusion). As blood leaves the lungs through the pulmonary veins, the venous $\text{P}_{\text{O}_2}$= 100 mm Hg, whereas the venous $\text{P}_{\text{CO}_2}$ = 40 mm Hg.As blood enters the systemic capillaries, the blood will lose oxygen and gain carbon dioxide because of the pressure difference of the tissues and blood. a. You have solubilized it with homogenization i... 14. 46 - Oxygen enters the blood in the lungs because... Ch. d. the O2 concentration in the blood is low. 46 - Discuss Concepts Hyperventilation, or... Ch. Blood oxygen levels can be checked by withdrawing blood from your artery present in the wrist, elbow, or groin. The displacement of an object moving under uniform acceleration is some function of time and the acceleration. 46.2 - What is countercurrent exchange, and how is it... Ch. The blood will be put in an ABG machine (blood gas analyzer) that provides your blood oxygen levels in the form of the partial pressure of oxygen (PaO2). b. the CO2 concentration in the blood is low. We’d love to keep in touch to tell you about our work, our fundraising activities and other ways you can get involved. The standard unit of ___ is the same in all measurement systems. Calculate the molar mass of each hydrated compound. 46.3 - What is the most important feedback stimulus for... Ch. Question: Blood Lungs 1 During Gas Exchange, One Gas Leaves The Blood And Enters The Lungs And Another Gas Leaves The Lungs And Enters The Blood. Figure UN 9-3 shows a dark globule of dusty gas. 46 - Discuss Concepts Smoking has traditionally been... Ch. As the preload decreases, the cardiac output _____________________. We cannot reply to comments left on this form. 46.2 - Distinguish between positive pressure breathing... Ch. sets the boiling point of water at ? d. the O 2 concentration in the blood is low. Registered charity in England and Wales (326730), Scotland (SC038415) and the Isle of Man (1177). The number of alveoli in an adult’s lungs is somewhere around 600 million. d. the O 2 concentration in the blood is low. 46 - Which of the following describes a respiratory... Ch. ... Because of hemoglobin, blood is able to carry ____ times more oxygen than what can dissolve in the blood… After absorbing oxygen, the blood leaves the lungs and is carried to the heart. 1 Questions & Answers Place. You may feel a sharp pain when the needle enters the artery. You can change your mind at any time. Please confirm that we can keep in touch with you by email, We'll take good care of your personal info and you can update the way we contact you at any time - check out our privacy policy at blf.org.uk/our-privacy-policy to find out more. T F. Define and distinguish (a) continental crust and oceanic crust, and (b) the lithosphere and asthenosphere. Pulmonary hypertension is high blood pressure in the blood vessels that deliver oxygen rich blood to the lungs. From there it is pumped to your lungs so that you can breathe out the carbon dioxide and breathe in more oxygen. 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(1.4). 46.3 - What is the role of the chemoreceptors in the... Ch. Oxygen enters the blood in the lungs because relative to alveolar air: a. the CO 2 concentration in the blood is high. Type 1 diabetes is most often controlled by successful weight-loss management. Lungs, Bronchial tube, Alveoli and Cilia. Log in. 46 - The majority of CO2 in the blood: a. is in the... Ch. There are no solutions to the system because the equations represent the same line. A rooftop in the southwestern United States receives an average solar power of W (averaged over both day a... Digestive processes are first-order processes. The amount of air that enters and leaves the lungs with each breath is the ____. e. the process is independent of gas concentrations in the blood. Ch. Ch. VAT number 648 8121 18. 46 - The partial pressure of O2 in the atmosphere is... Ch. List two of the four major factors that influence how much oxygen diffuses into pulmonary blood per minute. How will I recover if I’ve had coronavirus? 46.4 - Why is carbon monoxide potentially lethal? They found that cells there are rich in a cell-surface receptorcalled angiotensin-converting enzyme 2 (ACE2). The pulmonary veins bring oxygen-rich blood to the left atrium. 3. (Patton 840-841) The oxygen pressure gradient between alveolar air and incoming pulmonary blood, the total functional surface area of the respiratory membrane, the respiratory minute volume, and alveolar ventilation are factors that influence oxygen diffusion. Moving gases like this is called gas exchange . Some people choose to abstain from drinking alcoholic beverages. Low blood pressure does not oppose oxygen movement. How can I improve the air quality in my home? c. the O 2 concentration in the blood is high. By sensing and responding to change, organisms keep conditions in the internal environment within ranges that c... Proteins that influence RNA synthesis by binding directly to DNA are called ________. How is pulmonary hypertension diagnosed and treated in children? The oxygen from the lungs enters the bloodstream from the alveoli, tiny sacs in the lungs which is the area where the gas exchange process happens. The device has a screen that will let you see the percent of oxygen in the blood coming from your heart. Oxygen diffuses from the air into the blood and carbon dioxide diffuses out of the blood into the air. 46 - Propose a hypothesis for the effect of zero... Ch. Asthma UK and British Lung Foundation Partnership is a company limited by guarantee 01863614 (England and Wales). sandysandy6547 29.04.2018 Biology Secondary School +13 pts. Detailed solutions are available in the Student Solutions ... A friend tells you that it is 69. Oxygen enters the blood in the lungs because relative to alveolar air: e. the process is independent of gas concentrations in the blood. In most vertebrates oxygen enters the bloodstream via diffusion at the alveoli of the lungs. Answers to all problems are at the end of this book. 1. Suggest reagents and the other fragment that could be used to carry out the indicated conversion. Ch. No. It increases concentrations in the lungs, meaning more oxygen can get into the blood. There are infinitely many solutions to the system because the equations represent parallel lines. a. two bronchi b. pleural sacs c. alveoli d. both b and c. PREDICT A flower has small, inconspicuous flowers without petals, a scent, or nectar. Transport of Oxygen. The oxygen is moved in the blood by a simple diffusion process. How do you know? Calculate the gauge pressure at a depth of 300 m in seawater. About 2% of the blood flow through the lungs bypasses the pulmonary capillaries. At the same time, carbon dioxide, a waste gas, moves from your blood to the lungs and is exhaled (breathe out). 46.5 - What are the key evolutionary adaptations that... Ch. 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This information uses the best available medical evidence and was produced with the support of people living with a condition. | 2021-09-20 18:03:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3804883360862732, "perplexity": 2927.617138024615}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057083.64/warc/CC-MAIN-20210920161518-20210920191518-00624.warc.gz"} |
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MATHEMATICS On control of the observation process in the problem of sequential disrimination among $N$ hypothesesM. V. Burnashev 281 On the algebro-geometric foundations of Lagrangian field theoryA. M. Vinogradov 284 Averaged moduli of continuity and some of their connections with best approximationsArif S. Dzhafarov 288 CYBERNETICS AND THE REGULATION THEORY Recurrent search algorithms for estimationI. N. Beloglazov 292 On the applicability of the method of singular perturbations in the investigation of automatic control systemsB. V. Viktorov 296 A new approach to the problem of optimum controlB. S. Razumikhin 300 Stabilization and regularization of estimates of optimum solutions under conditions of uncertaintyYa. Z. Tsypkin 304 MECHANICS On the synthesis of the geometry of the suspension of an electrostatic gyroscope possessing maximal rigidityD. B. Belitskii, Yu. G. Martynenko 308 Nonlocal thermoelasticityM. R. Korotkina 312 FLUID MECHANICS Formation of vortex cords out of upward currents over an evaporating liquidV. A. Vladimirov 316 The phenomenon of reduced hydrodynamic resistance of human normal bloodS. S. Grigoryan, M. V. Kameneva, A. A. Shakhnazarov, S. A. Shanoyan 319 Isobaric turbulent reacting jet discharging into a coflowing streamV. A. Ruskol, U. G. Pirumov 321 GEOPHYSICS On the theory of active ocean layerKh. Zh. Dikinov, A. I. Felzenbaum 325 On the equivalence in the inverse problem of gravimetry at variable mass densityV. N. Strakhov 329 PHYSICS Phase-transitions in superionic crystals, induced by an electric fieldYu. Ya. Gurevich, Yu. I. Kharkats 332 Gasdynamic equations and one-dimensional collisionless motion of degenerate plasma consisting of heavy neutral particlesYa. B. Zel'dovich 336 CRYSTALLOGRAPHY On the morphology of potassium bichromate crystalsO. G. Kozlova, G. P. Geraskina, N. V. Belov 351 | 2019-08-22 05:58:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.38597342371940613, "perplexity": 2569.9231722934665}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027316783.70/warc/CC-MAIN-20190822042502-20190822064502-00063.warc.gz"} |
https://brilliant.org/problems/a-calculus-problem-by-clarence-mccarthy/ | # Infinite Food Sampling
Calculus Level 2
A man is doling food samples to a countably infinite number of people in a store. Each of them takes an amount $$\dfrac{1}{x}$$, where the value of $$x$$ is equal to their number in line. How many samples does the man need, to satisfy the food cravings of everyone?
× | 2016-10-27 22:50:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8271899819374084, "perplexity": 921.342930002516}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988721405.66/warc/CC-MAIN-20161020183841-00003-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://www.appropedia.org/Kirigami_design_approach_to_LCPV_reflectors | Please leave any comments on the Discussion page (see tab above) including additional resources/papers/links etc. Papers can be added to relevant sections if done in chronological order with all citation information and short synopsis or abstract. Thank You.
## What are Concentrator photovoltaics (CPV)??
Wikipedia : Concentrator photovoltaic systems employ curved reflectors such as lenses and mirrors to focus incoming sun rays onto the solar cells to harvest solar energy with more efficiency measured as watt-peak Wp. They are often equipped with single or dual-axis solar trackers and cooling systems that promote dual-way power generation. Based on the intensities measured in number of suns, CPV systems are classified as Low concentration PV, High concentration PV, Medium concentration PV and Luminescent solar concentrators.
This idea of concentrating sun's radiation dates back to 212 B.C.The famous Greek inventor Archimedes used mirrors, later called as burning mirrors, to set enemy ships at blaze. Concentrators/reflectors use principles of optics (focal point) to concentrate sunlight onto absorbers/Solar cells.
#### K. G. T. Hollands, "A concentrator for thin-film solar cells," Solar Energy, vol. 13, no. 2, pp. 149–163, May 1971. doi: 10.1016/0038-092X(71)90001-6
• Considerations : V-Trough reflector as side walls with solar cells at the base; Seasonal tracking alone is considered but not diurnal tracking; Axis along east-west direction; Used thin-film polycrystalline cadmium Sulphide cells.
• Assumptions: Side walls to be perfectly specular, gray surfaces; restricts the trough geometries studied to those where, with the solar beam normal to the base, two conditions are met: (a) the base is uniformly irradiated; (b) no ray suffers more than one reflection.
• Aim: To determine yearly average direct-beam concentration factor for any incidence angle, opening angle and side-wall reflectance.
• Findings: Concludes that total yearly mean concentration factors of the order of 2 are possible with V-trough concentrators.
• Imp concepts: Calculations on Solar geometry (N-S & E-W).
• Limitations: Side- walls are ideal specular reflectors.
#### R. M. Swanson, "The promise of concentrators," Prog. Photovolt: Res. Appl., vol. 8, no. 1, pp. 93–111, Jan. 2000. doi: 10.1002/(SICI)1099-159X(200001/02)8:1<93::AID-PIP303>3.0.CO;2-S
• Aim: To address the issue of why concentrator systems have not gained a significant market share.
• Information: 1. Provides overview of active concentrator developments in major universities and labs in US, UK and Japan. 2. Surmises advantages of concentrator technology, its barriers and suggestions to overcome them along with recommendations for future developments.
#### D. A. W. B. Dr. Simon P. Philipps and D. S. K. Kelsey Horowitz, "Current Status of Concentrator Photovoltaic (CPV) Technology," Fraunhofer Institute for Solar Energy Systems ISE in Freiburg, Germany & National Renewable Energy Laboratory NREL in Golden, Colorado, USA, TP-6A20-63916, Sep. 2015.
• Aim: To Summarize the status of the concentrator photovoltaic (CPV) market and industry as well as current trends in research and technology. This report is intended to guide research agendas for Fraunhofer ISE, the National Renewable Energy Laboratory (NREL), and other R&D organizations.
• Review: 1. Clearly distinguishes between CPV strengths and weaknesses. 2. Focusses on market and industry aspects- levelized cost of electricity (LCOE) studies of current available CPV technologies. 3. Overview of research and technological developments in Fraunhofer Institute and NREL. 4. Serves as reference for stakeholders in the CPV industry and research.
#### A. K. Pandey, V. V. Tyagi, J. A. Selvaraj, N. A. Rahim, and S. K. Tyagi, "Recent advances in solar photovoltaic systems for emerging trends and advanced applications," Renewable and Sustainable Energy Reviews, vol. 53, pp. 859–884, Jan. 2016.10.1016/j.rser.2015.09.043
• Aim: To provide a comprehensive review on the solar photovoltaic (SPV) systems especially BIPV, CPV & PV/T and their recent advances along with emerging applications in the present and future scenario.
• Review: 1. Provides estimates on energy consumption over past few decades to near future. 2. Provides abridged version of background on PV but focusses more on recent advances in the PV technology and compares numerous cell configurations in accordance to their efficiencies. 3. Gives insights of various PV materials like crystalline, thin-film, Concentrated PV, Hybrid, Organic and Polymer materials etc. 4. Discusses deeply the applications of PV technology with particular case studies which extends even for space based solar technology. 5. Provides recommendations wherein to concentrate the more R&D.
## Low concentration photovoltaics (LCPV)
Low concentration PV systems can be illuminated with intensities less than 20 suns[1] which can be varied up to 100 suns. LCPV systems eliminate the need of complex cooling systems and are often facilitated with booster reflectors. LCPV systems doesn't require active tracking mechanisms due to wide acceptance angles.[2] These can sufficed with single-axis tracking system yet maintaining 35-40% increased power output. The reflected radiation incident on these modules depends on the clearness of the index of the location[3][4] and thus they are more effective when installed where direct radiation is a significant percentage of the global radiation (South Europe, Northern Africa, Southern states of the USA, etc.).
Measuring Intensity in Suns: Intensity of sunlight illuminating on PV cells are measured as 'Suns'. 'One Sun' is the amount of energy drawn to an object openly exposed out on a cloudless day which is approximately 100 watts per square foot.
## Concept of Reflectors-Concentrators
The efficacy of incorporating reflectors or concentrators for PV cells or modules is to intensify the incident radiation i.e., to increase incident radiation per m^2. They increase the output efficiency leading to reduction of capital costs. The main features of reflectors are high reflectance, low scattering and low degradation i.e., loss of reflectance over time.
Link directly to Understanding solar concentrators
#### H. Tabor, "Stationary mirror systems for solar collectors," Solar Energy, vol. 2, no. 3–4, pp. 27–33, Jul. 1958. doi:10.1016/0038-092X(58)90051-3
• Aim: To provide with studies that proves tilting of solar concentrators along with usage of mirrors for concentrating radiation is more efficient.
• Considerations:The mirror has the form of a cylindrical parabola with the cylindrical axis mounted horizontally east-west.
• Findings: Complete stationary mirror cannot provide any useful concentration while tilting the solar collectors with varying seasons can yield more efficiencies; The maximum optical concentration of 3 is obtained at a minimum angle of acceptance of 15-17 deg for the mirrors. Employing an auxiliary side mirror for second stage concentration can increase this concentration power to about 4. One cannot apply a second stage of optical concentration to the double-sided receiver.
• Imp concepts:An angle in solar geometry termed the EWV altitude is defined, and its variation with time and season is shown.This indicates the necessary acceptance angle of a stationary mirror system for solar collectors. Solar geometry studies. Geometrical studies of cylindrical parabola.
#### A. Rabl, "Solar concentrators with maximal concentration for cylindrical absorbers," Applied Optics, vol. 15, no. 7, p. 1871, Jul. 1976. doi: 10.1364/AO.15.001871
The differential equation is derived that describes the reflector of an ideal two-dimensional radiation concentrator with an absorber of arbitrary convex shape. For the special case of an absorber with circular cross section, the equation can be solved in closed form if suitable coordinates are used. The effect of absorption at the reflector is considered, and formulas are presented for determining the attenuation of radiation on its passage from aperture to absorber.
#### A. Rabl, "Comparison of solar concentrators," Solar Energy, vol. 18, no. 2, pp. 93–111, 1976.doi: 10.1016/0038-092X(76)90043-8[1]
• Analyses the geometric concentration ratio of different types of concentrators.
• Concludes that there is a nonuniformity of the flux density distribution on the absorber.
#### A. Rabl and R. Winston, "Ideal concentrators for finite sources and restricted exit angles," Applied Optics, vol. 15, no. 11, p. 2880, Nov. 1976. doi: 10.1364/AO.15.002880
Design procedures for ideal radiation concentrators are described which are applicable to finite sources and/or restricted exit angles. Finite sources are relevant for second stage concentrators which collect and further concentrate radiation from a primary focusing element (mirror or lens) in a manner similar to the field optic element in a telescope. Restricting the exit angle is useful for improving the optical efficiency of solar collectors by eliminating grazing angles of incidence of the absorber. It also serves to extend the useful range of angular acceptance values available from solid dielectric concentrators that function by total internal reflection. Concentrators of this type can be used to construct highly efficient radiation traps (spectrally selective filters).
#### D. P. Grimmer, K. G. Zinn, K. C. Herr, and B. E. Wood, "Augmented Solar Energy Collection Using Various Planar Reflective Surfaces: Theoretical Calculations and Experimental Results," Los Alamos Scientific Lab., N.Mex. (USA), LA-7041, Apr. 1978
The use of planar reflective surfaces can substantially improve the performance of both active and passive solar collectors. The results of theoretical calculations and experimental tests on the use of different types of flat reflective surfaces to increase the collection of solar energy by flat collectors are presented. Specular, diffuse, and combination specular/diffuse reflective surfaces are discussed. A computer model has been generated to describe surfaces as a combination of specular- and diffuse-like reflectivities. The reflective properties of a given surface can be measured in the laboratory as a function of incident and reflected angles. Predictions of system performance were made for various collector/reflector configurations and compared with the performance of an optimally oriented collector without a reflector.
#### R. W. Stacey and P. G. McCormick, "Effect of concentration on the performance of flat plate photovoltaic modules," Solar Energy, vol. 33, no. 6, pp. 565–569, 1984. doi: 10.1016/0038-092X(84)90012-4
The effect of low concentration ratios on the performance of passively cooled conventional photovoltaic modules has been investigated. Peak power outputs of up to 140 W per square metre of module area have been obtained with single crystal modules of high cell packing factor using a 2.2X plane mirror concentrator. Both cell temperature and series resistance losses are found to be important in limiting module efficiency. Performance simulations indicate that the use of a 4X concentrator with polar axis tracking will increase annual peak output by a factor of 3.2 over that of a fixed flat plate module.
#### G. Smestad, H. Ries, R. Winston, and E. Yablonovitch, "The thermodynamic limits of light concentrators," Solar Energy Materials, vol. 21, no. 2–3, pp. 99–111, Dec. 1990. doi: 10.1016/0165-1633(90)90047-5
To concentrate the light, photons from a larger area are collected and directed to a smaller area. Some devices use geometrical optics, or a change in index of refraction to increase the illumination on a surface above the incident solar level. Other systems use a frequency or Stokes shift to increase the illumination of light at one photon energy at the expense of another. Presented is a unification of the ideas and principles developed for the various classifications of concentrators. Equations are developed that describe the limits of concentration in geometrical and fluorescent systems. Concentration is shown to be a function of the index of refraction, angular collection range, as well as the frequency shift. Applications of the ideas involve the understanding of diffuse radiation concentrators and the solar powered laser.
#### R. P. Friedman, J. M. Gordon, and H. Ries, "New high-flux two-stage optical designs for parabolic solar concentrators," Solar Energy, vol. 51, no. 5, pp. 317–325, 1993. doi:10.1016/0038-092X(93)90144-D
A new two-stage optical design for parabolic dish concentrators that can realistically attain close to 90% of the thermodynamic limit to concentration with practical, compact designs was presented. For comparison, the parabolic dish-plus-compound parabolic concentrator secondary design, at this rim angle, achieves no more than 50% of the thermodynamic limit. A new secondary concentrator is tailored to accept edge rays from the parabolic primary, and incurs less than one reflection on average. It necessitates displacing the absorber from the parabola's focal plane, along the concentrators optic axis, toward the primary reflector, and constructing the secondary between the absorber and the primary. The secondary tailored edge-ray concentrators described here create new possibilities for building compact, extremely high flux solar furnaces and/or commercial parabolic dish systems.
#### B. Perers and B. Karlsson, "External reflectors for large solar collector arrays, simulation model and experimental results," Solar Energy, vol. 51, no. 5, pp. 327–337, 1993.doi: 10.1016/0038-092X(93)90145-E
A model for the calculation of incident solar radiation from flat- and CPC-shaped external reflectors onto flat plate solar collector arrays has been developed. Assuming an infinite length of the collector/reflector rows, the basic calculations of incident radiation in the collector plane from the reflector become very simple. The incident radiation onto the collector, including corrections for shadowing and lost radiation above the collector, can then be calculated using 2-D geometry. The diffuse radiation is assumed to be isotropic. The incidence angle for the solar radiation from the reflector onto the collector is in most cases higher than the incidence angle for the radiation directly from the sun. Therefore the incidence angle characteristics of the collector glazing and absorber become more important in this application. Equations for the incidence angles for diffuse and beam radiation are provided. An annual performance increase of over 30%, 100–120 kW h/m2, has been measured for aged (four operating seasons) flat reflectors in the Swedish climate. With a CPC-shaped reflector and new reflector materials, a performance increase of up to 170 kW h/m2 is not unrealistic. This means that the collector and ground area requirement can be reduced by more than 30% for a given load.
#### S. Hess and V. I. Hanby, "Collector Simulation Model with Dynamic Incidence Angle Modifier for Anisotropic Diffuse Irradiance," Energy Procedia, vol. 48, pp. 87–96, 2014. doi:10.1016/j.egypro.2014.02.011
One constant collector parameter, independent from slope or weather conditions is considered. The simulation model introduced considers the varying anisotropy of sky radiance. To create realistic distributions, the approach of Brunger and Hooper is used. Three possible modes were demonstrated. The model is applied to a stationary, double-covered process heat flat-plate collector with one-sided CPC booster reflector (RefleC). The collector shows a biaxial and asymmetric IAM for direct irradiance. It is found that, compared to anisotropic modeling, the simplified isotropic model is undervaluing the annual output of this collector by 13.7% for a constant inlet temperature of 120 °C in Würzburg, Germany. An annual irradiation distribution diagram shows that this is due to an underestimation of diffuse irradiation from directions with high direct irradiation. It is concluded that isotropic modeling of diffuse irradiance can be expected to significantly undervalue the annual output of all non-focusing solar thermal collectors. Highest relevance is found for high collector slopes, complex IAMs and at low-efficiency operation. The optimal collector slope is almost not affected. Accuracy of existing models can be increased by applying Mode 2.
#### V. P. Anand, M. M. Khan, E. Ameen, V. Amuthan, and B. Pesala, "Performance improvement of solar module system using flat plate reflectors," in 2014 International Conference on Advances in Electrical Engineering (ICAEE), 2014, pp. 1–4. doi: 10.1109/ICAEE.2014.6838547
The energy output of Si-cell modules is very low due to their low power conversion efficiencies of approximately 15%. Reflectors are used to improve the power output of PV modules, by increasing the effective capture area. The performance of the solar panel with reflector depends mainly on three parameters namely length, tilt angle and reflectivity of reflector. A model system to analyse the effect of reflector parameters on the overall power output is developed. Also a simplified mathematical model was developed which is capable of estimating the optimum tilt angle for a particular reflector length, and the optimality of the tilt angles predicted by this model was verified using the above mentioned experimental setup. Finally, the suitability of various materials for use as reflectors was studied using the setup. Interestingly, paper based reflectors like bond paper and thermocole showed excellent results with increase in power output of more than 60%. Also, the cost per watt of the system is minimal when we use aluminium foil as the reflector at optimum tilt angle.
#### S. Hess,"Stationary booster reflectors for solar thermal process heat generation," SASEC, 2015
The performance of a flat-plate collector with glass-foil double cover is compared to that of the same collector with a one-sided external CPC booster reflector (RefleC-collector) for process heat generation up to 150 C. Efficiency curve measurements of both collector variants are compared to state-of-the-art simulations and the new model calculates significantly higher additional gains of the reflectors.Monitoring results of one reference year for the overall system performance as well as for the additional gains by the booster reflectors are provided. It is shown that the stationary booster reflectors highly increase the efficient operation temperature range and also the annual energy gain of the double covered flat-plates.
### V-trough solar concentrators
#### J. Freilich and J. M. Gordon, "Case study of a central-station grid-intertie photovoltaic system with V-trough concentration," Solar Energy, vol. 46, no. 5, pp. 267–273, Jan. 1991. doi:
Our presentation is a case study of an installed, central-station (no storage), utility-intertie photovoltaic (PV) system in Sede Boqer, Israel (latitude 30.9°N). The nominally 12 kW peak PV system is comprised of 189 polycrystalline silicon modules mounted on inexpensive, one-axis north-south horizontal trackers with V-trough mirrors for optical boost. The power conditioning unit operates at a fixed voltage rather than at maximum power point (MPP). The primary task in analyzing the installed system was to investigate the cause of measured power output significantly below the design predictions of the installers, and to recommend system design modifications. Subsequent tasks included the quantitative assessment of fixed-voltage operation and of the energetic value of V-trough concentration and one-axis tracking for this system. Sample results show: (i) fixed-voltage operation at the best fixed voltage (BFV) can achieve around 96% of the yearly energy of MPP operation; (ii) the sensitivity of the yearly energy delivery to the selection of fixed voltage and its marked asymmetry about the BFV; (iii) the influences of inverter current constraints on yearly energy delivery and BFV; and (iv) how the separate effects of tracking and optical concentration increase yearly energy delivery.
#### N. Fraidenraich, "Design procedure of V-trough cavities for photovoltaic systems," Prog. Photovolt: Res. Appl., vol. 6, no. 1, pp. 43–54, Jan. 1998.doi: 10.1002/(SICI)1099-159X(199801/02)6:1<43::AID-PIP200>3.0.CO;2-P
The combination of photovoltaic (PV) systems with V-trough cavities has been identified as an attractive option to reduce, in the short time scale, the prices of the PV electrical energy. In places of good radiation level, the output energy of these devices can be almost doubled, compared to PV flat-plate fixed systems. Additionally, V-trough cavities are simple to manufacture and can be used with conventional (1-sun) solar cells. In this work we present a design procedure for V-trough cavities used in combination with PV generators. The main design requirements are: uniform illumination on the plane of the PV module, within a finite interval of incidence angles; minimum cost of energy; and heat dissipation by natural, passive means. The V-trough cavities depend on two parameters. We obtain a first analytical relation between the concentration ratio (C) and the V-trough angle (ψ) for concentrators with uniform illumination at the absorber. The region of minimum cost of the V-trough PV ensemble yields a second relation. Then, a unique pair of cavity parameters, satisfying the above criteria, is found. A design example of a V-trough cavity for the city of Recife, PE, Brazil, is presented.
#### J. Bione, O. C. Vilela, and N. Fraidenraich, "Comparison of the performance of PV water pumping systems driven by fixed, tracking and V-trough generators," Solar Energy, vol. 76, no. 6, pp. 703–711, 2004. doi: 10.1016/j.solener.2004.01.003
Photovoltaic pumping systems with solar tracking, coupled to low concentration cavities, have been proposed as a viable alternative to reduce the final cost of the pumped water volume. V-trough concentrators are particularly appropriate for photovoltaic applications since, for certain combinations of the concentration ratio (C) and vertex angle (Ψ), they provide uniform illumination on the region where the modules are located. Water pumping systems are only operational when the irradiance is larger than a minimum irradiance level (IC). Solar tracking increases the average collected irradiance (Icoll) and, for a system operating with a given critical irradiance level (IC), it is verified that the smaller the relationship (IC/Icoll), the larger the useful energy. Thus, the gain, in terms of pumped water volume, provided by solar tracking systems, can be larger than the gain in collected solar radiation. The combination of both devices, tracking and concentration provides an additional increase of the benefits resulting from the use of solar trackers. By means of the "Utilizability Method", we estimate the long-term gains of pumped water volume, for tracking systems, with and without concentration, against fixed systems. The long-term water volume has been calculated using the characteristic curve of a tested PVP system with a tracking V-trough concentrator. Results show that, for the climate of the city of Recife (PE-Brazil), the annual pumped water volume of the tracking system is 1.41 times the value obtained with the fixed system. In that case, the gains observed for the collected solar energy were around 1.23. For the PVP system with tracking V-trough concentrator the annual benefits for pumped water volume are around 2.49, while for collected solar radiation we found 1.74. The annualized cost of the cubic meter of pumped water has been estimated for the three configurations. Results show a cost reduction of the order of 19% for the tracking system and of 48% for the concentrating system, when compared to the fixed configuration.
#### C. S. Sangani and C. S. Solanki, "Experimental evaluation of V-trough (2 suns) PV concentrator system using commercial PV modules," Solar Energy Materials and Solar Cells, vol. 91, no. 6, pp. 453–459, Mar. 2007.doi: 10.1016/j.solmat.2006.10.012
V-trough photovoltaic (PV) concentrator systems along with conventional 1-sun PV module is designed and fabricated to assess PV electricity cost ($/W) reduction. V-trough concentrator (2-sun) system is developed for different types of tracking modes: seasonal, one axis north–south and two axes tracking. Three design models based on these tracking modes are used to develop the V-trough for a 2-sun concentration. Commercially available PV modules of different make and types were evaluated for their usability under 2-sun concentration. The V-trough concentrator system with geometric concentration ratio of 2 (2-sun) increases the output power by 44% as compared to PV flat-plate system for passively cooled modules. Design models with lower trough angles gave higher output power because of higher glass transmissivity. PV modules with lower series resistance gave higher gain in output power. The unit cost ($/W) for a V-trough concentrator, based on different design models, is compared with that of a PV flat plate system inclined at latitude angle (Mumbai, φ=19.12°).
#### N. Martín and J. M. Ruiz, "Optical performance analysis of V-trough PV concentrators," Prog. Photovolt: Res. Appl., vol. 16, no. 4, pp. 339–348, Jun. 2008. doi: 10.1002/pip.817
This paper proposes a method for the analysis of the optical losses that take place inside PV concentrators, which is useful in the design of such systems. The study is focused in V-trough concentrators with two-axis tracking. Those are low concentration systems that use nearly conventional flat PV modules. Optical losses are shown to depend on the cavity angle, the mirrors spectral and angular reflectance and the surfaces dirtiness. Final effective concentration ratio and relative cost should consider all these analysed factors. This will help in the search of the most efficient solution in each case.
#### C. S. Solanki, C. S. Sangani, D. Gunashekar, and G. Antony, "Enhanced heat dissipation of V-trough PV modules for better performance," Solar Energy Materials and Solar Cells, vol. 92, no. 12, pp. 1634–1638, Dec. 2008. doi: 10.1016/j.solmat.2008.07.022
A concentrator photovoltaic (PV) module, in which solar cells are integrated in V-troughs, is designed for better heat dissipation. All channels in the V-trough channels are made using thin single Al metal sheet to achieve better heat dissipation from the cells under concentration. Six PV module strips each containing single row of 6 mono-crystalline Si cells are fabricated and mounted in 6 V-trough channels to get concentrator V-trough PV module of 36 cells with maximum power point under standard test condition (STC) of 44.5 W. The V-trough walls are used for light concentration as well as heat dissipation from the cells which provides 4 times higher heat dissipation area than the case when V-trough walls are not used for cooling. The cell temperature in the V-trough module remains nearly same as that in a flat plate PV module, despite light concentration. The controlled temperature and increased current density in concentrator V-trough cells results in higher Voc of the module.
Page data
Type Literature review Akhila Reddy Gorantla 2016 CC-BY-SA-4.0 175 No main image Akhila Reddy Gorantla (2016). "Kirigami design approach to LCPV reflectors". Appropedia. Retrieved September 25, 2022.
1. S. Kurtz, "Opportunities and challenges for development of a mature concentrating photovoltaic power industry," Technical Report, NREL/TP-520- 43208, 2009
2. Andrews, Rob W.; Pollard, Andrew; Pearce, Joshua M., "Photovoltaic system performance enhancement with non-tracking planar concentrators: Experimental results and BDRF based modelling," Photovoltaic Specialists Conference (PVSC), 2013 IEEE 39th, pp.0229,0234, 16–21 June 2013. doi: 10.1109/PVSC.2013.6744136
3. A. L. Luque and A. Viacheslav, Eds., "Concentrator Photovoltaics," vol. 130. Berlin, Heidelberg: Springer Berlin Heidelberg, 2007.(Chapter: 1 and 6). ISBN: 978-3-540-68796-2
4. M. Šúri, T. A. Huld, E. D. Dunlop, and H. A. Ossenbrink,"Potential of solar electricity generation in the European Union member states and candidate countries," Solar Energy, vol. 81, no. 10, pp. 1295–1305, Oct. 2007. doi: 10.1016/j.solener.2006.12.007
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https://www.physicsforums.com/threads/second-derivative-theorems.81629/ | # Second Derivative Theorems
1. Jul 8, 2005
### Orion1
I am posting my theorems for peer review, anyone interested in posting some proofs using some simple functions?
Can these theorems be reduced into simpler equations?
Orion1 Second Derivative Theorems:
$$\frac{d^2}{dx^2} (x) = 0$$
$$\frac{d^2}{dx^2} (x^2) = 2$$
$$\frac{d^n}{dx^n} (x^n) = n!$$
$$\frac{d^2}{dx^2} (x^n) = n(n - 1) x^{n - 2}$$
$$\frac{d^2}{dx^2} (x^{-n}) = n(n + 1)x^{-n - 2}$$
$$\frac{d^2}{dx^2} \left[ f(x) \pm g(x) \right] = \frac{d^2}{dx^2} [f(x)] \pm \frac{d^2}{dx^2} [g(x)]$$
$$\frac{d^2}{dx^2} [f(x) \cdot g(x)] = \frac{d^2}{dx^2} [f(x)] \cdot g(x) + 2 \frac{d}{dx} [f(x)] \cdot \frac{d}{dx} [g(x)] + \frac{d^2}{dx^2} [g(x)] \cdot f(x)$$
$$\frac{d^2}{dx^2} \left[ \frac{f(x)}{g(x)} \right] = \frac{\frac{d^2}{dx^2} [f(x)] \cdot [g(x)]^2 - 2 \frac{d}{dx} [f(x)] \cdot g(x) \cdot \frac{d}{dx} [g(x)] + \left[ g(x) \cdot \frac{d^2}{dx^2} [g(x)] - 2 \left( \frac{d}{dx} [g(x)] \right)^2 \right] \cdot f(x)}{[g(x)]^3}$$
2. Jul 8, 2005
### Jameson
$$\frac{d^n}{dx^n} (x^n) = n!$$
Ah, at first I disagreed. But now I see it. I like that one.
Last edited: Jul 8, 2005
3. Jul 8, 2005
### robphy
The pattern in $$\frac{d^2}{dx^2} [f(x) \cdot g(x)] = \frac{d^2}{dx^2} [f(x)] \cdot g(x) + 2 \frac{d}{dx} [f(x)] \cdot \frac{d}{dx} [g(x)] + \frac{d^2}{dx^2} [g(x)] \cdot f(x)$$
is more easily seen using the "prime" notation:
$$(fg)'' = f''g+2f'g'+fg''$$
...the coefficients are just like those in
\begin{align*} (f+g)^2 &= f^2g^0+2f^1g^1+f^0g^2 \end{align*}
4. Jul 9, 2005
### lurflurf
$$\frac{d^2}{dx^2}u^v=2u^{v-1}\frac{du}{dx}\frac{dv}{dx}+v(v-1)u^{v-2}(\frac{du}{dx})^2+v u^{v-1}\frac{d^2u}{dx^2}+u^v\log^2(u)(\frac{dv}{dx})^2+u^v\log(u)\frac{d^2v}{dx^2}$$
5. Jul 30, 2005
### Orion1
functional malfunction...
lurflurf theorem:
$$\frac{d^2}{dx^2}u^v=2u^{v-1}\frac{du}{dx}\frac{dv}{dx}+v(v-1)u^{v-2}\left(\frac{du}{dx}\right)^2+vu^{v-1}\frac{d^2u}{dx^2}+u^v\log^2(u)\left(\frac{dv}{dx}\right)^2+ u^v\log(u)\frac{d^2v}{dx^2}$$
lurflurf, your theorem appears to be missing a factor: $$[1 + v \ln(u)]$$
Orion1 second derivative theorem:
$$\frac{d^2}{dx^2}u^v=2u^{v-1}[1+v\ln(u)]\frac{du}{dx}\frac{dv}{dx}+v(v-1)u^{v-2}\left(\frac{du}{dx}\right)^2+vu^{v-1}\frac{d^2u}{dx^2}+u^v\ln^2(u)\left(\frac{dv}{dx}\right)^2+u^v\ln(u)\frac{d^2v}{dx^2}$$
Is this theorem correct?
Last edited: Jul 30, 2005 | 2018-09-26 08:41:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.980808675289154, "perplexity": 13393.62851985454}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267164469.99/warc/CC-MAIN-20180926081614-20180926102014-00133.warc.gz"} |
http://mathoverflow.net/feeds/question/99186 | Is this graph known? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-20T11:28:10Z http://mathoverflow.net/feeds/question/99186 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/99186/is-this-graph-known Is this graph known? hbm 2012-06-09T18:03:11Z 2012-06-09T19:41:33Z <p>I came across the graph $G= (V, E)$, where </p> <p>$V =$ { $(i, j)| 1 \leq i, j \leq n$ } </p> <p>$E=${ $((i, j), (k,l))| i \ne l$ and $j \ne k$ }</p> <p>Does this graph have a name? Is it well studied? </p> <p>I would very much like to see some of their properties.</p> http://mathoverflow.net/questions/99186/is-this-graph-known/99188#99188 Answer by Vidit Nanda for Is this graph known? Vidit Nanda 2012-06-09T19:12:35Z 2012-06-09T19:41:33Z <p>I think you just have the complement of a line graph here.</p> <p>Start with $K_n$, the complete directed graph on $n$ vertices (including self-edges). That is, the vertex set is $\lbrace 1,\ldots,n \rbrace$ and you have all possible directed edges $(i,j)$ for vertices $i$ and $j$ including when $i=j$.</p> <p>The <a href="http://en.wikipedia.org/wiki/Edge_graph" rel="nofollow">line graph</a> $LK_n$ of $K_n$ is the undirected graph which has a vertex $v_{ij}$ for each edge $(i,j)$ in $K_n$. Since $K_n$ is complete, you get precisely the vertex set of the graph $G$ from the question. Now as for the edges: there is an edge in $LK_n$ between $v_{ij}$ and $v_{kl}$ if and only if $j=k$.</p> <p>Your graph $G$ is the complement of $LK_n$; that is, it has the same vertex set but an edge between $v_{ij}$ and $v_{kl}$ if and only if there is no edge between these vertices in $LK_n$.</p> <p>As for properties, there is a large amount of information about complete directed graphs, line graphs and graph complements a google search away. Perhaps if you provide context and motivation for how your graph arose and what properties you would be interested in, someone here will point you to appropriate literature.</p> | 2013-06-20 11:28:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7103266716003418, "perplexity": 416.7965692831791}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368711515185/warc/CC-MAIN-20130516133835-00077-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://www.divinycell.com.br/jharkhand-mla-aeljwo/latex-minipage-horizontal-alignment-04383d | 4. And it makes for great slides ofcourse. LaTeX will try to produce the best line breaks possible. By using the first option \hline> have to replaced by \cline. And it makes for great slides of course. The minipage is often used to put things next to each other, which can otherwise be hard put together. • Compressed eps files and non-eps graphic formats (tiff, gif, jpeg, pict, etc.) Put the same construct outside the minipage too, and see how the distance between "A" and "B" is the same in both cases. It has a single mandatory argument describing the number of columns and the alignment within them. On May 9, 2007, at 12:25 PM, Alan Munn wrote: > Is there any way to adjust the placement of columns horizontally in > beamer? This provides an easier way to emphasize stuff in a report. c (synonym m) Default. This line has a strut: nrule[-.25in]{0in}{.5in} The optional length moves the strut down from the baseline by a quarter inch. Insert→Box (to insert another minipage) Change the width of the two minipages to 45% Textwidth (by clicking the right mouse button on each minipage) In each minipage: change the paragraph alignment to center add the graphics press enter for a new paragraph Insert a caption (Insert→Caption). can also be inserted on-the-fly when dvips is used with an operating system which supports pipes (such as Unix). No preview available. TeX views everything on a page as a form of box. LATEX and Boxes Rules and Struts Footnotes mbox and fbox makebox and framebox raisebox newsavebox, sbox and savebox parbox and minipage LATEX and Boxes A box is a piece of text that LATEX treats as a unit, like a single character. The following article explains … 7 Boxes and Mini-Pages . Documents like “Obsolete packages and commands” (“l2tabu”) address the need of up-to-date information. You can verify that by putting A---horizontal fill---B inside the minipage. center and right align on same line word November 14, 2020 Uncategorized No Comments November 14, 2020 Uncategorized No Comments \par (TeX) Ends the current paragraph. Rotate text inside table and align it to the centre of combined rows. tables horizontal-alignment vertical-alignment rotating. If you want to change them, you have several options: the "geometry" package, the "fullpage" package or changing the margins by hand. The problem is that the frame needs space too, some space for the lines and some space between line and contents so the lines doesn't touch the edges of the text. This provides an easier way to emphasize stuff in a report. \parbox [pos][height][contentpos] {width}{text}. TeX provides a set of basic commands controlling the way a paragraphs are typeset. \break (TeX) If used in horizontal mode, this is equivalent to \linebreak, if used in vertical mode it is equivalent to \pagebreak. The default is left alignment, where each line begins at the left margin. A LaTeX environment is one of the following: 1 Float environments 1.1 Figure environment 1.2 Table environment 2 List environments 2.1 description environment 2.2 enumerate environment 2.3 itemize environment 2.4 list environment 3 Math environments 3.1 math environment 3.2 displaymath environment 3.3 split environment 3.4 array environment 3.5 eqnarray environment 3.6 equation … The tabular is the de-facto way of presenting tabular data in LaTeX. Insert→Box (to insert another minipage) Change the width of the two minipages to 45% Textwidth (by clicking the right mouse button on each minipage) In each minipage: change the paragraph alignment to center add the graphics press enter for a new paragraph Insert a caption (Insert→Caption). There are several standard LaTeX commands to change the text alignment. LaTeX minipage. Again, really like this minipage solution! If graphics or graphics and text had to be set side-by-side they would often be placed inside minipage environments. subcaption. Such a rule is called a strut . \put(180,180){\begin{minipage}[t]{0.4\linewidth} {Choose a point on the unit circle. Covariance indicates the level to which two variables vary together. #7 Glasgow, October 27, 2010 at 12:59 p.m. Some time ago I found a book template that had the chapter titles with the number upside (for example, "Chapter One"), then an horizontal line that was the same width as the title number and below it the chapter title (for example, "This is the first chapter of my book"). Again, really like this minipage … Note that this is. First just put the two tables in a first one, second minipage. A frequently asked question is how to get top alignment, like here on mrunix.de and here on matheplanet.com. Each box has an associated width, height and depth, and the boxes are placed together on the page with glue.This is reminiscent of the days of manual typesetting, where each letter or symbol was on a wooden block, and the wooden blocks were glued in place. In paragraph mode, text is broken into lines and lines are broken into pages. Title: LaTeX Spacing Tricks The optional argument position governs how the minipage vertically aligns with the surrounding material. example three tables In LaTeX, I use the package siunitx and its S column for the alignment. Vertical alignment of graphics. See the next section for more information on how this package actually works. The most important thing here is the bottom-alignment of the right-hand side “minipage” ([b]). By a chance I found a small piece of LaTeX code that allows horizontal alignment in matrix-environments of the package “amsmath” (bmatrix, pmatrix, etc. The \titlehead looks like this (basically, three 'columns' created with three instances of \minipage ): The idea behind the minipage command is that within an existing page "built in" an additional page. Produces code for directly embedding equations into HTML websites, forums or blogs. Customizing \maketitle output with \minipage's inside \titlehead => Alignment problems I am trying to customize the title of my scrreprt class document. A useful extension is the subcaption package (the subfigure and subfig packages are deprecated and shouldn’t be used any more), which uses subfloats within a single float. Hey, I don't know if this is the right place to ask but I'm kind of lost and need help. LaTeX forum ⇒ Graphics, Figures & Tables ⇒ Tikz picture alignment two figures Information and discussion about graphics, figures & tables in LaTeX documents. Our Community-database contains thousands of handcrafted LaTeX-snippets. When writing documents in TeX/LaTeX, it is important to understand how the TeX engine “thinks”. To put two tables side-by-side, there are two ways. Open an example in Overleaf. This usually works fine if the minipages should be bottom-aligned. nstrut gives a strut as tall as the default line height. For example, two pictures side by side, two tables next to a text or a picture or vice versa. If it cannot, it will decide whether or not to include the linebreak according to the priority you have provided. 3 posts • Page 1 of 1 eqnarray vs. align. A box (and … forcing space in horizontal or math mode. LaTeX's margins are, by default, 1.5 inches wide on 12pt documents, 1.75 inches wide on 11pt documents, and 1.875 inches wide on 10pt documents. You can search them ... 12343 . Each column, ... \linethickness{dimension} Declares the thickness of horizontal and vertical lines in a picture environment to be dimension, which must be a positive length. TeX - LaTeX: My goal is to have a regression table with columns aligned by the decimal separator. latex centering left table, The align environment is a souped up version of the equation environment. Connect it to the origin with a line of length one, and denote the angle between that line and the horizontal coordinate axis by $\theta$.} There’s a lot of freely available documentation for LaTeX, but there’s a pitfall: some documents that are still online are outdated and therefore contain obsolete information. ... spacing vertical-alignment itemize minipage. Using the package ragged2e. imports the package ragged2e and left-justifies the text. This is the standard for book margins. A \parbox is a box of specific width formatted in paragraph mode. The align* version is the same as align except that it doesn't produce equation numbers. spacing in math mode > line break within table cell side by side tables. This package is part of the latex-tools bundle in the L a T e X required distribution. dcolumn – Align on the decimal point of numbers in tabular columns The dcolumn package makes use of the array package to define a "D" column format for use in tabular environments. I produced a regression output (using Stata) and exported it using the user-written package esttab. There are different way of placing figures side by side in Latex, subcaption, subfig, subfigure, or even minipage.This post will tell you which one is the best. parbox, minipage, and pbox []. It uses the & symbol for alignment, much like the tabular environment. When using other operating systems, the non-eps graphics must be converted to eps be-forehand. Since neither LATEX nor dvips has any built-in decompression or graphics- Positions the minipage so its vertical center lines up with the center of the adjacent text line (what Plain TeX calls \vcenter). Here is how LaTeX typesets the above source file. Text will be broken into lines so that it fits within this width. Including the small horizontal space in-between, … width defines the width of the paragraph box. A paragraph is the basic text unit in a document and many TeX/LaTeX commands, when used properly, affect the current paragraph only. Text } a form of box source file vice versa hey, I n't... Has a single mandatory argument describing the number of columns and the alignment within them package siunitx and its column! Page built in '' an additional page the right-hand side “ minipage ” ( “ l2tabu ” ) the. In math mode > line break within table cell side by side, two pictures side side! Trying to customize the title of My scrreprt class document additional page mandatory argument describing the of. Single mandatory argument describing the number of columns and the alignment within them produced a regression table with columns by., like here on matheplanet.com of presenting tabular data in LaTeX it to the priority You have provided \maketitle... At 12:59 p.m it fits within this width often used to put latex minipage horizontal alignment next each. Tex views everything on a page as a form of box this width the! My scrreprt class document does n't produce equation numbers vice versa up version the! Alignment within them ask but I 'm kind of lost and need help and here on matheplanet.com, or... Title: LaTeX Spacing Tricks LaTeX centering left table, the non-eps graphics must be converted to eps be-forehand )! To a text or a picture or vice versa putting a -- -horizontal fill -- inside. Has a single mandatory argument describing the number of columns and the alignment dvips has any decompression! Commands ” ( “ l2tabu ” ) address the need of up-to-date information a t e X required distribution picture. Writing documents in TeX/LaTeX, it will decide whether or not to the... First option \hline > have to replaced by \cline Choose a point on the unit circle decide. Unit in a document and many TeX/LaTeX commands, when used properly, affect the current paragraph only it! On-The-Fly when dvips is used with an operating system which supports pipes such. Graphic formats ( tiff, gif, jpeg, pict, etc. text } and here on.!, jpeg, pict, etc. side by side tables version the. Of lost and need help operating systems, the non-eps graphics must be converted to eps be-forehand this.... Into pages of columns and the alignment within them pictures side by side tables any decompression! 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Honey Bees For Sale Near Me, Palm Tree Background Aesthetic, Best Makeup Brushes Kit, A Safe Work Habit Is To Ensure That You Quizlet, Via Aurelia Roma, Ikea Ektorp Sectional Cover, Makeup Brushes Names, | 2021-05-09 20:37:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9237743616104126, "perplexity": 4175.67730074961}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243989012.26/warc/CC-MAIN-20210509183309-20210509213309-00249.warc.gz"} |
http://clay6.com/qa/48508/the-charge-deposited-on-4-mu-f-capacitor-the-circuit-is | Browse Questions
# The charge deposited on $4 \mu F$ capacitor the circuit is
Can you answer this question?
$(C) 24 \times 10^{–6} C$ | 2017-06-25 14:01:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8575822710990906, "perplexity": 10277.587296667456}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-26/segments/1498128320532.88/warc/CC-MAIN-20170625134002-20170625154002-00666.warc.gz"} |
https://www.semanticscholar.org/paper/Designing-pretty-good-state-transfer-via-reductions-R%C3%B6ntgen-Palaiodimopoulos/a89ce0e558fab1c478a2203926aa0cd5863d7919 | # Designing pretty good state transfer via isospectral reductions
@article{Rntgen2020DesigningPG,
title={Designing pretty good state transfer via isospectral reductions},
author={M. R{\"o}ntgen and N. E. Palaiodimopoulos and C. V. Morfonios and Ioannis Brouzos and Maxim Pyzh and Fotis K. Diakonos and Peter Schmelcher},
journal={Physical Review A},
year={2020}
}
• Published 6 August 2019
• Computer Science
• Physical Review A
We present an algorithm to design networks that feature pretty good state transfer (PGST), which is of interest for high-fidelity transfer of information in quantum computing. Realizations of PGST networks have so far mostly relied either on very special network geometries or imposed conditions such as transcendental on-site potentials. However, it was recently shown that PGST generally arises when a network's eigenvectors and the factors ${P}_{\ifmmode\pm\else\textpm\fi{}}$ of its…
5 Citations
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Electron. J. Comb.
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It is proved that union (edge disjoint) of an integral circulant graph with a cycle, each on $2^k$ $(k\geq 3)$ vertices, admits pretty good state transfer and the complement of such union also admits prettyGood state transfer.
Pretty good quantum state transfer in symmetric spin networks via magnetic field
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Quantum Inf. Process.
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It is shown that if a network admits an involution that fixes at least one node or at leastOne link, then there exists a choice of potential on the nodes of the network for which the authors get pretty good state transfer between symmetric pairs of nodes.
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Physical review letters
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This work determines the exact number of qubits in unmodulated chains (with an XY Hamiltonian) that permit transfer with a fidelity arbitrarily close to 1, a phenomenon called pretty good state transfer and highlights the potential of quantum spin system dynamics for reinterpreting questions about the arithmetic structure of integers and primality.
Quantum Network Transfer and Storage with Compact Localized States Induced by Local Symmetries.
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A method to equip any network featuring static perfect state transfer of single-site excitations with compact localized states, thus increasing the storage ability of these networks, and it is shown that these compact localization states can likewise be perfectly transferred through the corresponding network by suitable, time-dependent modifications.
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Using this theory of isospectral network transformations, it is possible to establish whether a network, modeled as a dynamical system, has a globally attracting fixed point (is strongly synchronizing).
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Pretty good state transfer in networks of qubits occurs when a continuous-time quantum walk allows the transmission of a qubit state from one node of the network to another, with fidelity arbitrarily
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We propose a class of qubit networks that admit perfect state transfer of any two-dimensional quantum state in a fixed period of time. We further show that such networks can distribute arbitrary | 2022-06-30 08:25:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5007311701774597, "perplexity": 2205.171636052264}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103669266.42/warc/CC-MAIN-20220630062154-20220630092154-00615.warc.gz"} |
https://datascience.stackexchange.com/questions/63545/unsupervised-function-optimization-using-input-and-output-for-loss-function | # Unsupervised Function Optimization using Input and Output for Loss Function?
I have some vectors {$$\mathbf{X_1 ... X_n}$$} and they are all of dimension 1 x N. Vectors {$$\mathbf{X_1' ... X_n'}$$} are also 1 x N and are related to {$$\mathbf{X_1 ... X_n}$$}, but the relation cannot be modeled by a function.
I want to train a neural network such that for each $$\mathbf{X_i}$$ I input, it gives me a $$\mathbf{Y_i}$$ where the loss function to optimize is $$\mathbf{X_i' Y_i}$$. The reason I do not use $$\mathbf{X_i'}$$ as the input is that I do not have access to them during testing. The constraint on $$\mathbf{Y_i}$$ is that the norm is 1.
I tried an implementation similar to this post here (https://stackoverflow.com/questions/46464549/keras-custom-loss-function-accessing-current-input-pattern) which is:
def custom_loss_wrapper(input_tensor):
def custom_loss(y_true, y_pred):
return keras.losses.mean_squared_error(y_true, y_pred) + f(input_tensor)
return custom_loss
However, I found that adding f(input_tensor) only changes the calculated loss, and not the back-propagation itself. The neural network produces same output $$\mathbf{Y'}$$ with or without the f(input_tensor).
I also tried direct optimization without a neural network, using TensorFlow optimizer.minimize() or similar strategies, and the results are not very good.
Any ideas how I may build this network?
• I don't really get what you are asking. Any good example/reference that you can show? Try rereading and for now as far as your explanation goes I could just throw-in $Y_i$ to be zero-vector and your loss is optimal. – Yohanes Alfredo Nov 21 at 16:56
• @Yohanes Alfredo I forgot to mention there is a constraint on Y. The norm of Y must be 1 – Y.Z. Nov 21 at 18:56
• Why do you need f(input_tensor)? Isn't y_true = X' and y_pred = Y all you have to pass to custom loss? – Valentas Nov 22 at 7:30 | 2019-12-12 16:03:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 9, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5793672800064087, "perplexity": 770.0472576102721}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540544696.93/warc/CC-MAIN-20191212153724-20191212181724-00482.warc.gz"} |
https://murciacosta.com/j13sevac/ce96b8-pde-boundary-conditions | applyBoundaryCondition (model,'mixed',RegionType,RegionID,Name,Value) adds an individual boundary condition for each equation in a system of PDEs. Browse other questions tagged pde boundary-conditions parabolic-pde or ask your own question. 2.10. 0 â® Vote. Then select a boundary or multiple boundaries for which you are specifying the conditions. 1. Thus, the summation of these two cases will cancel the reflection. condition is determined by the coefficients q and g according 49.1 Boundary Conditions In this section, we discuss the implementation of finite diff erence methods at boundaries. \begin{cases} Specify Boundary Conditions opens May someone please explain the intuition behind the Black-Scholes Equation? of the boundary segment and increases to 1 along the boundary segment Neumann Boundary Conditions Robin Boundary Conditions Remarks At any given time, the average temperature in the bar is u(t) = 1 L Z L 0 u(x,t)dx. In the nongeneric application modes, the Description column Dirichlet boundary conditions specify the value of the function on a surface. Boundary conditions are very simple to understand, contrary to what most FEA « experts » and consultants will tell you. use Shift+click (or click using the middle mouse Because the shorter rectangular side has length 0.8, to ensure that the mesh is not too coarse choose a maximum mesh size Hmax = 0.1. 0 L E d S QDds Follow 18 views (last 30 days) sko ⦠Perturbation of the boundary conditions in PDE. Example: model.BoundaryConditions RegionType â Geometric region type 'Face' for 3-D geometry | 'Edge' for 2-D geometry Using linear changes of variables, however, it is possible to change the evaluation points of BC, obtaining the solution for the new variables, and then changing back to the original variables. 1. Wiki The boundary condition applies to boundary regions of type RegionType with ID numbers in RegionID, and with values specified in the Name,Value pairs. PARTIAL DIFFERENTIAL EQUATIONS Math 124A { Fall 2010 « Viktor Grigoryan grigoryan@math.ucsb.edu Department of Mathematics University of California, Santa Barbara These lecture notes arose from the course \Partial Di erential Equations" { Math 124A taught by the author in the Department of Mathematics at UCSB in the fall quarters of 2009 and 2010. In the form expected by pdepe, the left boundary condition is. 3. This example shows how different boundary conditions can be specified. Based on your location, we recommend that you select: . Non-Normal derivative boundary conditions for a PDE. \end{cases} These can either be determined by the âphysicsâ of ⦠A solution to a PDE is a function u that satisfies the PDE. y'|_{x=\alpha} & = & 0 \\ Out: Momentum BCs ... loop over boundary faces boundary terms. This post present all collections of these boundary conditions and associated equations.Besides, this post also present the combination of Dirichlet and Neumann boundary conditions in construct absorbing boundary for solving wave eqution. How to implement periodic boundary conditions for 2D PDE. \begin{cases} For boundary condition entries you can use the following variables $$, Associated Problems for PDE of Wave Equation. In the case of Neumann boundary conditions, one has u(t) = a 0 = f. That is, the average temperature is constant and is equal to the initial average temperature. Mixed boundary conditions (system cases only), which is a mix of Dirichlet and Neumann conditions. When using EquationIndex to specify Dirichlet boundary conditions for a subset of components, use the mixed argument instead of dirichlet.The remaining components satisfy the default Neumann boundary condition with the zero values for 'g' ⦠Then select a boundary or multiple boundaries for which you are And I need to set the Dirichlet boundary condition on a face. (normally 1). [Smith 1974]. Boundary conditions¶. To select all boundaries, use the Select Swag is coming back! I was solving a homogeneous wave equation in 2D and then I tried to extend it with non homogeneous b.c. Perturbation of the boundary conditions in PDE. y(\alpha) & = & 0 \\ The four boundary conditions are imposed to each of the four walls. a 1-by-2 vector, and r is a scalar. PDE (Options > Application > Generic System). This solution functions of the PDE donât respect given boundary conditions. Problem solving PDE with boundary conditions. You can also select a web site from the following list: Select the China site (in Chinese or English) for best site performance. Sometimes you are given initial conditions. [1] Smith W D. A nonreflecting plane boundary for wave propagation problems[J]. G|_{boundary} & = & g(x,y,z) Existence for an overdetermined system of PDEs. 61 3 3 bronze badges. PDEâs are usually specified through a set of boundary or initial conditions. and boundary conditions. Featured on Meta New Feature: Table Support. The following figure shows the dialog box for the generic system Solving Laplace PDE with DSolve. mouse button. Question feed Subscribe to RSS Question feed To subscribe to this RSS … Boundary Value Problems A boundary value problem for a given diï¬erential equation consists of ï¬nding a solution of the given diï¬erential equation subject to a given set of boundary conditions. The following figure shows the dialog box for the generic system PDE ( Options > Application > Generic System ). asked Jul 2 at 16:41. PDE and Periodic Boundary Conditions. Toggle Main Navigation. A PDEModel ... For the syntax of the function handle form of u, see Nonconstant Boundary Conditions. and g is a 2-by-1 vector. Vote. In this short video, I demonstrate how to solve a typical heat/diffusion equation that has general, time-dependent boundary conditions. Hot Network Questions Translate "Eat, Drink, and be merry" to Latin How to remove Ubuntu and keep Lubuntu? Dirichlet conditions: u is specified No-Slip Wall F b=F Browse other questions tagged pde finite-difference boundary-conditions advection diffusion or ask your own question. Because the shorter rectangular side has length 0.8, to ensure that the mesh is not too coarse choose a maximum mesh size Hmax = 0.1. All the specifications use the same 2-D geometry, which is a rectangle with a circular hole. 0. A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. If (1) is your main point: you need a boundary condition at every side, otherwise the problem does not make sense mathematically. Suppose that you have a PDE model named model, and edge or face labels [e1,e2,e3] where the first component of the solution u must equal 1, while the second and third components must equal 2. It also describes how, for certain problems, pdsolve can automatically adjust the arbitrary functions and constants entering the solution of the partial differential equations (PDEs) such that the boundary conditions (BCs) are satisfied. 3. or hyperbolic PDE. a dialog box where you can specify the boundary condition for the I have been categorized as an FEA expert because of my teaching of FEA simulation through webinars for years (link to my webinars) We will also work a few examples illustrating some of the interesting differences in using boundary values instead of initial conditions in solving differential equations. G|_{1st\ boundary\ subset} & = & g_1(x) \\ Question about 2D PDE.$$, $$$$New Feature: Table Support. Select Boundary Mode from the Boundary For instance, we can enforce the value of a field to be 4 at the lower side and its derivative (in the outward direction) to be 2 on the upper side: 30th Dec, 2017. \end{cases} Select Boundary Mode from the Boundary menu or click the button. The domain for the PDE is a square with 4 "walls" as illustrated in the following figure. Active 6 years, 1 month ago. The Role of boundary conditions. f(y'',y) & = & 0 \\ In mathematics, in the field of differential equations, a boundary value problem is a differential equation together with a set of additional constraints, called the boundary conditions. \begin{cases} 2. to the following equation: In the system cases, q is a 2-by-2 matrix Physically this corresponds to specifying the heat flux entering or exiting the rod at the boundaries. Consider the PDE uxx − 4uxy − 5uyy = 0 with boundary conditions u(x, 0) = g0(x) and uy(x, 0) = g1(x) for x ∈ R. It is given the general solution of the PDE is u(x, y) = F(x − y) + G( − 5x − y). f(G'',G) & = & 0 \\ A linear PDE is homogeneous if all of its terms involve either u or one of its partial derivatives. Follow 155 views (last 30 days) Robert Smith on 23 Jan 2018. Boundary conditions (b.c.) f(\nabla^{2}G,G) & = & 0 \\ This discussion is not meant to be comprehensive, as the issues are many and often subtle. Specify Boundary Conditions in the PDE Modeler App. I am using the PDE in COMSOL 4.4. \end{cases} a 2-by-2 matrix, g is a 2-by-1 vector, h is Solve an elliptic PDE with these boundary conditions with c = 1, a = 0, and f = 10. By continuing to use this website, you consent to our use of cookies. In mathematics, the Neumann (or second-type) boundary condition is a type of boundary condition, named after Carl Neumann. on the boundary. \begin{cases} Join us for Winter Bash 2020. But, they naturally can be useful for solving given Initial- Boundary -Value- Problems. f(y'',y) & = & 0 \\ Featured on Meta Swag is coming back! Smith W D. A nonreflecting plane boundary for wave propagation problems[J]. q is a 2-by-2 matrix, g is a 2-by-1 vector, h is a 1-by-2 vector, and r is a scalar. I am looking to make certain computations on the vertices of periodic cubic honeycombs and quasiregular honeycombs like tetrahedral-octahedral honeycomb. Learn more about pde, parabolic, periodic boundary This completes the boundary condition specification. 2. Boundary conditions can be specified for both sides of each axis individually. selected boundary segments. Mark; Abstract. f(y'',y) & = & 0 \\ What are boundary conditions in PDEs and ODEs? You clicked a link that corresponds to this MATLAB command: Run the command by entering it in the MATLAB Command Window. f(G'',G) & = & 0 \\ \begin{cases} The following figure shows the dialog box for the generic system PDE ( Options > Application > Generic System ). Vote. In the space domain boundary conditions must be provided. and the right boundary condition is . Skip to content. specifying the conditions. \begin{cases} Accelerating the pace of engineering and science. There are something about boundary condition in weak form confusing me. condition parameters. Question about 2D PDE. Solve PDEs with Constant Boundary Conditions. Boundary conditions of a PDE model, specified as the BoundaryConditions property of PDEModel. A BoundaryCondition object specifies the type of PDE boundary condition on a set of geometry boundaries. function of the time t, you must choose a parabolic Please see our, Specify Boundary Conditions in the PDE Modeler App, Partial Differential Equation Toolbox Documentation. Treatment of Boundary Conditions Advanced CFD 03. This completes the boundary condition specification. But the boundary condition only would be used under certain conditions. Mixed boundary conditions (system cases only), which is a mix of Dirichlet and Neumann conditions. G'|_{boundary} & = & g(x,y,z) \\ menu or click the button. There are three types of boundary conditions commonly encountered in the solution of partial differential equations : 1. Select Specify Boundary Conditions from Boundary conditions, once stated, remain in effect until explicitly changed or until the end of the path. AleManara. Note that no if you do not select any boundaries, then the specified conditions ⦠Neumann boundary conditions¶ The last type of boundary conditions we consider is the so-called Neumann boundary condition for which the derivative of the unknown function is specified at one or both ends. Speciï¬cally, it is found. the Boundary menu.$$$$, Robin boundary condition is the combination of Dirichlet and Neumann boundary conditions.Wiki, Being different from Robin condition, Mixed condition means different types of condition along different subset of the boundary. 0answers 15 views A way to generate unit lattices from a honeycomb structure. \begin{cases} PDE boundary conditions of different kinds. Neumann Boundary Conditions Robin Boundary Conditions Remarks At any given time, the average temperature in the bar is u(t) = 1 L Z L 0 u(x,t)dx. The boundary condition equation is hu = r, Wiki, Considering boundary conditions for wave equation, Dirichlet and Neumann conditions produce reflection that are opposite in sign. This website uses cookies to improve your user experience, personalize content and ads, and analyze website traffic. Linked. contains descriptions of the physical interpretation of the boundary 0. Chapter 12: Partial Differential Equations The Dirichlet boundary condition for a system of PDEs is hu = r, where h is a matrix, u is the solution vector, and r is a vector. However, it seems that MMA (12) cannot solve it directly with some computational issues. proportional to arc length. Wiki, Being different to Dirichlet boundary condition, Neumann boundary condition specify the values of the derivative of the solution along the boundary. This example shows how to apply various constant boundary condition specifications for both scalar PDEs and systems of PDEs. For a partial differential equation, let's say the wave equation, with non homogeneous boundary conditions (whether is a mixed boundary value problem or not, but not infinite case) in 2D, do we proceed as we do in a 1D PDE? The solution was derived as follows. Your boundary condition function includes the line pl = ul-TT (i); TT (i) is not defined within view of the function, so that is what is causing the error. s is 0 at the start MathWorks is the leading developer of mathematical computing software for engineers and scientists. 3.3.1. What Are Boundary Conditions? Mixed boundary conditions (system cases only), which Design variables in density-based topology optimization are typically regularized using filtering techniques. Index of the known u components, specified as a vector of integers with entries from 1 to N.EquationIndex and u must have the same length.. Black-Scholes Implied Volatility. Learn more about pdepe, boundary conditions, reaction diffusion . Recently, I am trying to solve a 1-D PDE with a nonlinear boundary condition using the function NDSolveValue. 0. Edited: Andrei Fendley on 23 Oct 2020 at 14:19 I try to solve the heat equations following the example given here, but I do not understand how the boundary conditions are applied: \end{cases} \end{cases} Show activity on this post. 4. The Overflow Blog Hat season is on its way! When imposed on an ordinary or a partial differential equation, the condition specifies the values in which the derivative of a solution is applied within the boundary of … A boundary condition expresses the behavior of a function on the boundary (border) of its area of definition. All option from the Edit menu. The String Is Held Motionless With Initial Vertical Displacement (L - *), Then Released. In the case of Neumann boundary conditions, one has u(t) = a 0 = f. That is, the average temperature is constant and is equal to the initial average temperature. NOBC(VARIABLE) can be used to turn off a previously specified boundary condition on the current path. y(\beta) & = & 0 To select several boundaries and to deselect them, y'|_{x=\alpha} & = & 0 \\ As said in documentation, boundary conditions are automatically included in weak ⦠Geometry. f(G'',G) & = & 0 \\ This document gives examples of Fourier series and integral transform (Laplace and Fourier) solutions to problems involving a PDE and boundary and/or initial conditions. G|_{boundary} & = & g_1(x) \\ In this section we’ll define boundary conditions (as opposed to initial conditions which we should already be familiar with at this point) and the boundary value problem. 2.10. Other MathWorks country sites are not optimized for visits from your location. these boundary conditions beha ve quite differently in the simulations of two-phase ï¬o ws. PDE and Periodic Boundary Conditions. and r is a 2-by-1 vector. 0. Commented: Robert Smith on 30 Jan 2018 Hi all, I'm trying to solve the diffusion equation in a 2D space but I need to set the left and right boundaries to periodic. Note that no if you do not select any boundaries, then the Journal of Computational Physics, 1974, 15(4): 492-503. is a mix of Dirichlet and Neumann conditions. in the direction indicated by the arrow. y'|_{x=\beta} & = & 0 In the system cases, h is a 2-by-2 matrix To select a single boundary, click it using the left There are three different condition types: Generalized Neumann conditions, where the boundary $$,$$ where h is a weight factor that can be applied Question: (15 Points) Translate The Following Into A PDE With Boundary Conditions, The Ends Of A Horizontal String Of Length L Are Secured At Both Ends. Learn more about pde, parabolic, periodic boundary G+G'|_{boundary} & = & g(x) 27. Consistent boundary conditions for PDE filter regularization in topology optimization Wallin, Mathias LU; Ivarsson, Niklas LU; Amir, Oded and Tortorelli, Daniel () In Structural and Multidisciplinary Optimization 62 (3). Journal of Computational Physics, 1974, 15(4): 492-503. Often the value and the derivative are many and often subtle descriptions the! Derivative of the domain is Dirichlet boundary conditions with c = 1, a = 0 and! Design variables in density-based topology optimization are typically regularized using filtering techniques the derivative of the solution partial. This MATLAB command: Run the command by entering it in the following figure shows the dialog for... Satisfies the PDE Modeler App solution of a PDE typically requires an initial condition is like a boundary or boundaries. Loop over boundary faces boundary terms conditions with c = 1, a = 0, f. Understand, contrary to What most FEA « experts » and consultants will tell you =. Partial derivatives consent to our use of cookies Veracrypt instead you need two initial.... Nobc ( VARIABLE ) can not solve it directly with some pde boundary conditions issues in the solution along boundary... Or until the end of the unknown solution and its surroundings also the. A 2-by-1 vector, h is a 1-by-2 vector, h is a 2-by-2 and! Will derive our boundary conditions must be provided Follow 155 views ( last 30 days Brian. Each of the domain is Dirichlet boundary conditions commonly encountered in the space domain boundary conditions wave. Our use of cookies combinations of values of the path the conditions Drink, f. Your own question this MATLAB command: Run the command by entering it in the form expected by pdepe the! The left mouse button ) useful for solving given Initial- boundary -Value- Problems Computational issues from! F = 10 the domain is Dirichlet boundary condition on a face the MATLAB command Window boundary-conditions advection or!... Coding boundary conditions with c = 1, a = 0, and r is a weight that! Is hu = r, where h is a function of the solution along the boundary condition parameters honeycombs quasiregular... Equations: 1 conditions for 2D PDE modes, the equations are its partial derivatives behavior of PDE... A previously specified boundary condition is specified on the boundary condition, but then for the syntax of boundary! Condition equation is hu = r, where h is a 2-by-1 vector, analyze., click it using the middle mouse button ) get translated content where available and see local events offers! By continuing to use this website, you must use the same 2-D geometry, which is a scalar -. Make pde boundary conditions computations on the vertices of periodic cubic honeycombs and quasiregular honeycombs like tetrahedral-octahedral.... Will tell you u that satisfies the PDE is a mix of Dirichlet Neumann... Which is a function u that satisfies the PDE Modeler App, partial Differential equation and. Not meant to be comprehensive, as the BoundaryConditions property of PDEModel to generate unit lattices from a structure! Events and offers uses cookies to improve your user experience, personalize content ads! Need two initial conditions days ) Robert Smith on 23 Jan 2018, Being different to boundary. Views ( last 30 days ) sko ⦠specify boundary conditions in Solver... Cases, h is a rectangle with a circular hole r is a mix Dirichlet! Ode ( Oridinary Differential equation which also satisfies the boundary condition on a face border ) of its derivatives... Geometry boundaries partial Differential equation Toolbox Documentation turn off a previously specified boundary condition, boundary. Set the Dirichlet boundary condition c = 1, a = 0, and f = 10 website, consent! Domain for the selected boundary segments conditions of a PDE typically requires an initial condition as well boundary! Hyperbolic PDE nongeneric Application modes, the summation of these two cases will cancel the reflection you select.. By continuing to use this website, you consent to our use of cookies Jan 2018 to extend with... ÂPhysicsâ of ⦠boundary conditions on the boundary condition is a 2-by-2 matrix, g is a 2-by-1,... And the derivative of the solution u, you consent to our use of cookies nonlinear Solver as... Looking to make certain computations on the current path visits from your location, we recommend that select. ( Options > Application > generic system PDE ( weak form ) Application modes requires an initial condition is function... Several boundaries and to deselect them, use Shift+click ( or click the button 155 (. Multiple boundaries for which you are specifying the conditions see our, specify boundary can. Drive when you can use Veracrypt instead to Latin how to apply various constant boundary on...... Coding boundary conditions of a function of the physical interpretation of path! Expresses the behavior of a boundary value problem weight factor that can be applied ( normally 1.! Using filtering techniques Options > Application > generic system PDE ( partial Differential equations: 1 can either determined! Left mouse button ) be used to turn off a pde boundary conditions specified boundary condition at boundaries Run the by... Or multiple boundaries for which you are specifying the heat flux entering or exiting rod... Combinations of values of the four boundary conditions from a honeycomb structure or until the end of the path 15! Behind the Black-Scholes equation use the nonlinear Solver Dirichlet and Neumann conditions four walls shows the dialog box the... Are different types of boundary or multiple boundaries for which you are specifying the conditions opposite! Four boundary conditions 49.1 boundary conditions ( system cases, h is a 2-by-2 matrix r. Is hu = r, where h is a 2-by-1 vector, and r is a mix of and. 0, and r is a 2-by-2 matrix, g is a 2-by-2 matrix, g a. 49.1 boundary conditions in this Section, we recommend that you select: a face condition for! In terms of the domain is Dirichlet boundary conditions cases, h a... = 10 ] Smith W D. a nonreflecting plane boundary for wave equation, Dirichlet and conditions... Conditions specify the value of the solution of partial Differential equation ) PDE! - Reaction/Diffusion system of PDE 's for 2D PDE 30 days ) Robert Smith on 23 2018! 1974, 15 ( 4 ): 492-503 I 've been doing simulation. The system cases only ), then the specified conditions apply to boundaries... Generate unit lattices from a honeycomb structure solution along the boundary conditions, often value... And the derivative nonreflecting plane boundary for wave equation, Dirichlet and conditions. Satisfies the boundary condition only would be used under certain conditions specified through a set of geometry boundaries all. Nonreflecting plane boundary for wave propagation Problems [ J ] PDEs and systems of PDEs command Window constant condition... Condition parameters command: Run the command by entering it in the following figure shows the dialog box the. To extend it with non homogeneous b.c the String is Held Motionless with initial Displacement. 137 views ( last 30 days ) Brian May on 10 Aug 2018, partial Differential equation Documentation... Equations are conditions are imposed to each of the unknown solution and its derivatives at more one. Density-Based topology optimization are typically regularized using filtering techniques a = 0 and..., remain in effect until explicitly changed or until the end of the function on the boundary condition Neumann. Equation Toolbox Documentation for an elliptic PDE with these boundary conditions - Reaction/Diffusion system of PDE condition! By entering it in the Iserles book will derive our boundary conditions of a boundary is! All of its area of definition conditions specify the value of the derivative of the.. Illustrated in the nongeneric Application modes, the Description column contains descriptions of the walls., 15 ( 4 ): 492-503 do not select any boundaries, the... Am looking to make certain computations on the partial derivatives of have to be comprehensive, the. The Overflow Blog Hat season is on its way variables in density-based topology optimization are typically regularized using filtering.. And its surroundings all of its partial derivatives by the âphysicsâ of ⦠boundary conditions must be provided conditions reflection! Equations: 1 the values of the boundary condition for the generic system ) I am looking to certain... 10 Aug 2018 a mix of Dirichlet and Neumann conditions ( VARIABLE ) not. Problems for elliptic PDEs: Finite Differences we now consider a boundary on..., 1974, 15 ( 4 ): 492-503, once stated, remain in effect until explicitly or! With c = 1, a = 0, and f = 10 PDEs! Tell you weak form ) Application modes be expressed using nx and pde boundary conditions since tx = –ny and =! 49.1 boundary conditions for ODE ( Oridinary Differential equation which also satisfies boundary. This MATLAB command: Run the command by entering it in the system cases only ), which is 1-by-2. You clicked a link that corresponds to this MATLAB command Window vector, and r a. A square with 4 walls '' as illustrated in the PDE Modeler App, Differential. Box where you can use Veracrypt instead system PDE ( partial Differential equation Documentation. Is homogeneous if all of its area of definition translated content where available and local... Not meant to be written in terms of the function on a set geometry... Like tetrahedral-octahedral honeycomb the path conditions commonly encountered in the PDE is hu = r, where h a. Computational issues following figure shows the dialog box for the PDE Modeler App, partial Differential )... Form ) Application modes, the left mouse button ) walls '' as in! Pdepe ) Follow 71 views ( last 30 days ) Brian May on 10 2018... The intuition behind the Black-Scholes equation similar to Section 7.2 in the form by... This website uses cookies to improve your user experience, personalize content and ads, and f = 10 equations... | 2021-07-31 20:49:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.8371140956878662, "perplexity": 1032.8507329224635}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-31/segments/1627046154126.73/warc/CC-MAIN-20210731203400-20210731233400-00275.warc.gz"} |
https://math.stackexchange.com/questions/3366422/bag-of-marbles-and-law-of-total-probability | Bag of Marbles and Law of Total Probability
There are 3 bags each containing 100 marbles. Bag 1 has 75 red and 25 blue marbles. Bag 2 has 60 red and 40 blue marbles. Bag 3 has 45 red and 55 blue marbles. Now a bag is chosen at random and a marble is also picked at random.
1) What is the probability that the marble is blue?
2) What happens when the first bag is chosen with probability 0.5 and other bags with equal probability each?
I understand the #1, I got .4 but how would I approach doing #2?
Thank you
You do it just like you did the first part, only instead of saying that the probability of drawing each bag is $$\frac13$$, you use the given probabilities. For example, the probability of draw a blue marble from bag $$1$$ is $$\frac12\cdot\frac14=\frac18$$ because there is a probability of $$\frac12$$ that you pick bag $$1$$, and then a probability of $$\frac14$$ that you draw a blue marble from it. Do the same sort of thing for the other two bags, and add up the probabilities. | 2019-11-13 15:51:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 6, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9210904836654663, "perplexity": 57.77094567080803}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496667262.54/warc/CC-MAIN-20191113140725-20191113164725-00395.warc.gz"} |
http://tex.stackexchange.com/questions/63244/internal-error-bad-native-font-flag-xelatex-fontspec-newtxmath-libertine | # Internal error: bad native font flag (XeLaTeX, fontspec, newtxmath, libertine, \dot)
I'm trying to use \dot{P} in a math environment.
MWE:
\documentclass{scrartcl}
\usepackage[no-math]{fontspec}
\usepackage{libertineotf}
\usepackage[libertine]{newtxmath}
\begin{document}
$$\dot{P}(t) + 1234567890$$
\end{document}
Without the command \dot everything works as aspected.
With it I get the error: Internal error: bad native font flag and no output is produced.
Without the option no-math or the entire fontspec package (whose functionality I don't even need at the moment) there is an output compiled that includes a correct "dotted" P.
But the paranthesis, the plus sign and the numbers are not set in the Libertine font but rather in CM. Also the spacing information from the newtxmath package seems to get lost (could be related to CM).
I already tried to change the package order. That resulted in an option clash error for fontspec and the same output as without the fontspec package at all.
Any suggestions?
I tried using the libertine package for pdflatex (without fontspec of course) which produced the same output as XeLaTeX without the fontspec package.
Versions/File List:
MikTeX 2.9 64bit, Win7
libertineotf.sty 2012/04/07 5.13-8
fontspec.sty 2012/05/06 v2.2b
newtxmath.sty 2012/06/25 v0.99
-
This a bug in XeTeX resulting from mixing the OpenType (AKA "native") font Libertine with accent from the TFM font newtxmath. It didn't show up in earlier versions because of a bug that prevented the proper utilisation of OpenType math accent positioning that has been recently fixed.
I tried to fix the new bug, but it seems to be a bit tricky. Anyway, I hope it will be fixed by the time of the next release.
-
Two years later, is this bug going to be fixed? – marczellm Feb 22 '14 at 11:36
Mixing OpenType and TFM math fonts is not something I personally support, so it is a low priority issue, but feel free to open an issue in XeTeX bug tracker so it does not get forgotten again. – Khaled Hosny Feb 24 '14 at 8:16
I posted sourceforge.net/p/xetex/bugs/89. (This is my first ever bug report on SF, so I hope I didn't get something wrong.) – marczellm Feb 24 '14 at 8:34
@marczellm: Thanks. – Khaled Hosny Feb 24 '14 at 10:15
I (finally) found a solution with the help of Hendrik's answer to Dot Derivative Discrepancy.
\renewcommand*\dot[1]{%
\placeaccent{\acc@dot}{#1}%
}
\renewcommand*\ddot[1]{%
\placeaccent{\acc@dot\mkern1.4mu\acc@dot}{#1}%
}
to his code snippet.
This does not help for other accents, of course.
For the \hat{} command I found the following solution:
\renewcommand*\hat[1]{%
\placeaccent{\acc@hat}{#1}%
}
where \acc@hat is defined as:
\def\acc@hat{\mbox{\raisebox{-1.27ex}[0ex][0ex]{\^{}}}}
- | 2015-01-29 04:25:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 1, "x-ck12": 0, "texerror": 0, "math_score": 0.8179506659507751, "perplexity": 5097.722478178661}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422118973352.69/warc/CC-MAIN-20150124170253-00086-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://infoscience.epfl.ch/record/189976 | Infoscience
Conference paper
# To Convexify or Not? Regression with Clustering Penalties on Graphs
We consider minimization problems that are compositions of convex functions of a vector $\x \in\reals^N$ with submodular set functions of its support (i.e., indices of the non-zero coefficients of $\x$). Such problems are in general difficult for large $N$ due to their combinatorial nature. In this setting, existing approaches rely on convexifications" of the submodular set function based on the Lov\'asz extension for tractable approximations. In this paper, we first demonstrate that such convexifications can fundamentally change the nature of the underlying submodular regularization. We then provide a majorization-minimization framework for the minimization of such composite objectives. For concreteness, we use the Ising model to motivate a submodular regularizer, establish the total variation semi-norm as its Lov\'asz extension, and numerically illustrate our new optimization framework. | 2017-07-24 21:07:03 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.723004937171936, "perplexity": 469.63395069566053}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424910.80/warc/CC-MAIN-20170724202315-20170724222315-00015.warc.gz"} |
https://gmatclub.com/forum/if-2-2x-5-65-2-x-1-8-then-which-of-the-following-statement-236370.html | It is currently 11 Dec 2017, 12:14
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# If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement
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If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]
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If $$2^{2x+5} - 65.2^{x+1} = - 8$$, then which of the following statement is definitely correct?
A. x can only be a positive integer
B. x can only be a negative integer
C. x can be either a positive integer or a negative integer
D. No value of x exists which satisfies the equation
E. x is not an integer
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If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]
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Mahmud6 wrote:
7 months have already been passed. Would you please provide OE?
Hi Mahmud6
The answer would be C
$$2^{(2x+5)} - 65.2^{(x+1)}=-8$$
$$2^{(2x+2)}.2^3-65.2^{(x+1)}+8=0 => 2^{2(x+1)}.2^3-65.2^{(x+1)}+8=0$$
Let $$2^{(x+1)}=a$$, so we have
$$8a^2-65a+8=0$$ or
$$(8a-1)(a-8)=0 => a=\frac{1}{8}$$ or $$a=8$$
so $$2^{(x+1)}=\frac{1}{8}=2^{-3} => x=-4$$ (negative)
or $$2^{(x+1)}=8=2^3 =>x=2$$ (positive)
Option C
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Re: If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]
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21 Oct 2017, 01:54
niks18 wrote:
Mahmud6 wrote:
7 months have already been passed. Would you please provide OE?
Hi Mahmud6
The answer would be C
$$2^{(2x+5)} - 65.2^{(x+1)}=-8$$
$$2^{(2x+2)}.2^3-65.2^{(x+1)}+8=0 => 2^{2(x+1)}.2^3-65.2^{(x+1)}+8=0$$
Let $$2^{(x+1)}=a$$, so we have
$$8a^2-65a+8=0$$ or
$$(8a-1)(a-8)=0 => a=\frac{1}{8}$$ or $$a=8$$
so $$2^{(x+1)}=\frac{1}{8}=2^{-3} => x=-4$$ (negative)
or $$2^{(x+1)}=8=2^3 =>x=2$$ (positive)
Option C
Hi,
Could you please help me understand how 65.2^{(x+1)} is converted to 65a? Isn't 65.2^{(x+1)} = (65+0.2)^{(x+1)}?
Thank you.
Paul
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Re: If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]
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21 Oct 2017, 01:57
Paulli1982 wrote:
niks18 wrote:
Mahmud6 wrote:
7 months have already been passed. Would you please provide OE?
Hi Mahmud6
The answer would be C
$$2^{(2x+5)} - 65.2^{(x+1)}=-8$$
$$2^{(2x+2)}.2^3-65.2^{(x+1)}+8=0 => 2^{2(x+1)}.2^3-65.2^{(x+1)}+8=0$$
Let $$2^{(x+1)}=a$$, so we have
$$8a^2-65a+8=0$$ or
$$(8a-1)(a-8)=0 => a=\frac{1}{8}$$ or $$a=8$$
so $$2^{(x+1)}=\frac{1}{8}=2^{-3} => x=-4$$ (negative)
or $$2^{(x+1)}=8=2^3 =>x=2$$ (positive)
Option C
Hi,
Could you please help me understand how 65.2^{(x+1)} is converted to 65a? Isn't65.2^{(x+1)} = (65+0.2)^{(x+1)}?
Thank you.
Paul
Hi Paulli1982
Dot in algebra mean multiplication so it is $$65*2^{x+1}$$ and not a decimal number
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Re: If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]
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21 Oct 2017, 07:47
niks18 wrote:
Mahmud6 wrote:
7 months have already been passed. Would you please provide OE?
Hi Mahmud6
The answer would be C
$$2^{(2x+5)} - 65.2^{(x+1)}=-8$$
$$2^{(2x+2)}.2^3-65.2^{(x+1)}+8=0 => 2^{2(x+1)}.2^3-65.2^{(x+1)}+8=0$$
Let $$2^{(x+1)}=a$$, so we have
$$8a^2-65a+8=0$$ or
$$(8a-1)(a-8)=0 => a=\frac{1}{8}$$ or $$a=8$$
so $$2^{(x+1)}=\frac{1}{8}=2^{-3} => x=-4$$ (negative)
or $$2^{(x+1)}=8=2^3 =>x=2$$ (positive)
Option C
Hi,
May I please know what is wrong with the below approach:
2^x * 32 - 65*2*2^x = -8
2^x = (2/7)^2
Please let me know where I am wrong in this.
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If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink]
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21 Oct 2017, 07:52
rahul16singh28 wrote:
niks18 wrote:
Mahmud6 wrote:
7 months have already been passed. Would you please provide OE?
Hi Mahmud6
The answer would be C
$$2^{(2x+5)} - 65.2^{(x+1)}=-8$$
$$2^{(2x+2)}.2^3-65.2^{(x+1)}+8=0 => 2^{2(x+1)}.2^3-65.2^{(x+1)}+8=0$$
Let $$2^{(x+1)}=a$$, so we have
$$8a^2-65a+8=0$$ or
$$(8a-1)(a-8)=0 => a=\frac{1}{8}$$ or $$a=8$$
so $$2^{(x+1)}=\frac{1}{8}=2^{-3} => x=-4$$ (negative)
or $$2^{(x+1)}=8=2^3 =>x=2$$ (positive)
Option C
Hi,
May I please know what is wrong with the below approach:
2^x* 32 - 65*2*2^x = -8
2^x = (2/7)^2
Please let me know where I am wrong in this.
hi rahul16singh28
the highlighted portion is not correct. it is $$2^{2x}$$ and not $$2^x$$
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If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement [#permalink] 21 Oct 2017, 07:52
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# If 2^(2x+5) - 65.2^(x+1) = - 8, then which of the following statement
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Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®. | 2017-12-11 19:14:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.36326780915260315, "perplexity": 12617.755141203928}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948513866.9/warc/CC-MAIN-20171211183649-20171211203649-00742.warc.gz"} |
https://onepager.togaware.com/line-chart-basic.html | ## 11.34 Line Chart Basic
20180603
set.seed(26439)
ds %>%
sample_n(100) %>%
ggplot(aes(x=min_temp, y=max_temp)) +
geom_line()
As an alternative to plotting the points we could join the dots and plot a line. One reason for doing so might be to attempt to observe more clearly any relationship between the two dimensions (i.e., the two variables we are plotting). Add a ggplot2::geom_line() to the canvas we can draw a line from left to right the follows the points exactly. The result is a rather jugged line and it is debatable whether it has added any further insight into our understanding of the data.
Your donation will support ongoing development and give you access to the PDF version of this book. Desktop Survival Guides include Data Science, GNU/Linux, and MLHub. Books available on Amazon include Data Mining with Rattle and Essentials of Data Science. Popular open source software includes rattle, wajig, and mlhub. Hosted by Togaware, a pioneer of free and open source software since 1984. | 2021-04-22 10:51:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.18473753333091736, "perplexity": 1450.6157215810972}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618039603582.93/warc/CC-MAIN-20210422100106-20210422130106-00554.warc.gz"} |
http://mathoverflow.net/questions/19149/linear-regression-coefficients-w-x-y-swapped?answertab=oldest | # Linear Regression Coefficients W/ X, Y swapped
Let's say I have a linear regression model of the form $y = B_x x + I_x + \epsilon$, where $B_x$ is the beta coefficient of the $x$ term, $I_x$ is the intercept term and $\epsilon$ is additive, normally distributed noise. If I have a dataset and perform linear regression, I get a value for $B_x$, which indicates the slope of the relationship.
If I swap the roles of the $x$ and $y$ data, and try to fit a model of $x = B_y y + I_y + \epsilon$, I would expect intuitively that $B_y = \frac{1}{B_x}$. A simple geometric argument can be made to show that swapping the roles of $x$ and $y$ shouldn't change the position of the regression line w.r.t. any data point, and from here it seems like simple algebra that if $y = Bx + I$ then $x = \frac{1}{B} y + \frac{I}{B}$.
Where is this reasoning wrong? Can someone explain to me why $B_x \neq \frac{1}{B_y}$, preferably without resorting to tons of linear algebra or direct derivation from the normal equation?
-
Well, I think Mike McCoy's answer is "the right answer," but here's another way of thinking about it: the linear regression is looking for an approximation (up to the error $\epsilon$) for $y$ as a function of $x$. That is, we're given a non-noisy $x$ value, and from it we're computing a $y$ value, possibly with some noise. This situation is not symmetric in the variables -- in particular, flipping $x$ and $y$ means that the error is now in the independent variable, while our dependent variable is measured exactly.
One could, of course, find the equation of the line that minimizes the sum of the squares of the (perpendicular) distances from the data points. My guess is that the reason that this isn't done is related to my first paragraph and "physical" interpretations in which one of the variables is treated as dependent on the other.
Incidentally, it's not hard to think up silly examples for which $B_x$ and $B_y$ don't satisfy anything remotely like $B_x \cdot B_y = 1$. The first one that pops to mind is to consider the least-squares line for the points {(0, 1), (1, 0), (-1, 0), (0, -1)}. (Or fudge the positions of those points slightly to make it a shade less artificial.)
Another possible reason that the perpendicular distances method is nonstandard is that it doesn't guarantee a unique solution -- see for example the silly example in the preceding paragraph.
(N.B.: I don't actually know anything about statistics.)
-
Right. I was aware in the back of my mind that vertical distance is what's used in regression and that the reason for this is that you the interpretation of a regression is that it gives you the best possible predictor of Y given X (minimum vertical distance) assuming the relevant assumptions are met. However, for some reason I kept visualizing the problem as using perpendicular distance. – dsimcha Mar 24 '10 at 14:05
imho, Paul Teetor gives a superb explanation of what is going on in, for example quanttrader.info/public/betterHedgeRatios.pdf . He is interested in 'spread trades' but the explanation he gives is universal and excellent. As others have said, the point is that ols minimizes 'x distance' which can be very different from 'y distance' particularly if the slope of the regression line is very close to zero. – aginensky Aug 2 at 21:04
Here's one easy explanation. Linear regression finds the line that minimizes the sum-squared vertical distances to a line (assuming the predictor $x$ is on the horizontal axis and response $y$ is the vertical axis). When you treat $y$ as the predictor (leaving our axes fixed), linear regression will find a line that minimizes the sum-squared horizontal distances of your data to the line, typically resulting in a different line.
-
Thanks. I was pretty sure I had just overlooked something relatively obvious. This appears to be the obvious thing I had overlooked. – dsimcha Mar 23 '10 at 22:35
In response to JBL's comment about perpendicular distances, this is actually done in practice; it goes under the name "orthogonal regression" and is closely related to principal component analysis. If you want to do this with a non-zero intercept, though, you already have to step up the math content of your problem (it becomes the problem of finding a 2D surface in 3D, or more precisely, the normal to it). – Mike McCoy Mar 24 '10 at 16:51
If you have a more-or-less circularly shaped cloud of data points with correlation 0, then the slopes should both be 0, not reciprocals of each other! You're trying to estimate the average y-value for a given x-value and vice-versa. With low correlations, the two lines should be nowhere near each other. The "reciprocal" argument makes sense only if they're both the same line, and that's only when the absolute value of the correlation is 1.
-
The "perpendicular" idea is seen to make no sense if you consider a case where they x-values are in inches and the y-values is dollars, and you suddenly change from inches to feet. Which direction is considered "perpendicular" shouldn't depend on which units of measurement are used. – Michael Hardy May 27 '10 at 20:57
I was taught that it is a property of correlation coefficient that $r$ the correlation of $X$ with $Y$ is the same as of $Y$ with $X$.
(from the course pdf file with notes):
LO 5. Note that correlation coefficient ($R$, also called Pearson's $R$) has the following properties:
• the magnitude (absolute value) of the correlation coefficient measures the strength of the linear association between two numerical variables
• the sign of the correlation coefficient indicates the direction of association
• the correlation coefficient is always between -1 and 1, -1 indicating perfect negative linear association, +1 indicating perfect positive linear association, and 0 indicating no linear relationship
• the correlation coefficient is unitless
• since the correlation coefficient is unitless, it is not affected by changes in the center or scale of either variable (such as unit conversions)
• the correlation of $X$ with $Y$ is the same as of $Y$ with $X$
• the correlation coefficient is sensitive to outliers
But since then, I cannot find any other reference to this, that agrees with the symmetry thing. Maybe someone has some explanation.
- | 2015-09-03 19:32:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8020385503768921, "perplexity": 317.0810100163917}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440645323734.78/warc/CC-MAIN-20150827031523-00282-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/816440/mathematical-concept-for-formal-languages | # Mathematical concept for formal languages
A formal language is defined as a subset of finite-length strings over an alphabet. It is similar to the mathematical concept "relation", but the lengths of its strings are not fixed.
Since the name "formal language" suggests its application to linguistics, I wonder if there is a pure mathematical concept/name for "formal languages"?
Are there applications of formal languages that are not used to model languages (either natural languages or computer languages)?
Thanks!
• What do you mean? The mathematical concept is called "formal language" ... – Hagen von Eitzen May 31 '14 at 22:20
• I mean a name or concept that is as mathematical as "relation". – Tim May 31 '14 at 22:21
• There's nothing that makes some words more mathy than others. It's just a word. (Well, two of them.) – user2357112 supports Monica May 31 '14 at 22:22
• There are manifold reasons to ponder the relation amongst the sum of the semantic interpretations of words. – Lee Mosher May 31 '14 at 22:31
• You can see Ian Chiswell, Course in Formal Languages Automata and Groups (2009) or Gyorgy Revesz, Introduction to Formal Languages (1983). – Mauro ALLEGRANZA Jun 1 '14 at 8:51
Your question is not completely clear.
This is the mathematical definition of Formal language :
A formal language $\mathcal L$ over an alphabet $\Sigma$ is a subset of $\Sigma^*$ [see Kleene star], that is, a set of words over that alphabet. Sometimes the sets of words are grouped into expressions, whereas rules and constraints may be formulated for the creation of 'well-formed expressions'.
While formal language theory usually concerns itself with formal languages that are described by some syntactical rules, the actual definition of the concept "formal language" is only as above: a (possibly infinite) set of finite-length strings composed from a given alphabet, no more nor less. In practice, there are many languages that can be described by rules, such as regular languages or context-free languages. The notion of a formal grammar may be closer to the intuitive concept of a "language," one described by syntactic rules.
Having said that, what are you meaning with "a pure mathematical concept/name of 'formal languages' " ?
There is nothing un-mathematical about the definition, but there is an algebraic translation.
Formal power series of non-commuting variables are a natural generalization of formal languages. Let $K$ be a semiring. (This is a ring without the additive inverse requirement.) Let $A$ be a set and $A^*$ be the free monoid generated by $A$. A formal power series $S$ is a function $A^* \rightarrow K$. The image of a word $w$ is called the coefficient of $w$ in $S$. Addition and multiplication of series are defined as one would expect.
In this setting, a formal language $\mathcal{L}$ can be defined as a formal power series (of non-commuting variables) whose coefficients are either $0$ or $1$. The words in $A^*$ with coefficient $1$ are interpreted as the ones in $\mathcal{L}$.
One application of this approach is to enumerate a combinatorial class of objects. If a class of objects are in bijection with a formal power series in non-commuting variables, we obtain a generating function for the objects of size $n$ by substituting $x$ for each of the other variables.
We expect there to be some relationship between the type of generating function (rational, algebraic, etc) of a class of objects and the type of language it arises from. This situation is described in the introduction of Bousquet-Melou's "Rational and algebraic series in combinatorial enumeration", found here.
More about this approach to enumeration can be found in Chapter 6 of Richard Stanley's "Enumerative Combinatorics Volume 2". Also, the book "Rational Series and Their Languages" by Berstel and Reutenauer is a good reference for the formal series connection to languages, even though the focus is on rational languages. | 2019-12-07 04:22:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6588020920753479, "perplexity": 436.5990121681595}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540495263.57/warc/CC-MAIN-20191207032404-20191207060404-00248.warc.gz"} |
https://www.physicsforums.com/threads/1-x-odd-or-even.978622/ | # B -1/x, Odd or Even?
#### FortranMan
Is the function -1/x an odd or even function? Is it origin symmetric? For a function to be origin symmetric, must it lie in the 1st and 3rd quadrant or can it lie in the 2nd and 4th quadrant? I suspect it is odd and origin symmetric, but I don't know if I am missing some fine math rule/definition regarding symmetry.
#### PeroK
Homework Helper
Gold Member
2018 Award
Is the function -1/x an odd or even function? Is it origin symmetric? For a function to be origin symmetric, must it lie in the 1st and 3rd quadrant or can it lie in the 2nd and 4th quadrant? I suspect it is odd and origin symmetric, but I don't know if I am missing some fine math rule/definition regarding symmetry.
What are the definitions of odd, even and origin symmetric?
#### mathman
It is simply odd $-\frac{-1}{x}=\frac{1}{x}$.
#### HallsofIvy
Homework Helper
As Perok suggested, this is about knowing the definitions.
A function, f(x), is "even" if f(-x)= f(x) and "odd" if f(-x)= -f(x).
Replacing x with -x in f(x)= -1/x then f(-x)= -1/(-x)= 1/x= -(-1/x)= -f(x).
"Symmetric about the origin" means that if (x, y) is on the graph, so is (-x, -y). With y= -1/x, (x, -1/x) is on the graph and so is (-x, -1/(-x))= (-x, 1/x)= (-x, -(-1/x)).
#### FortranMan
So to answer the question about the symmetry of -1/x, a function is origin symmetric if EITHER
For every (x,y) on graph, so is (-x,-y).
or
For every (-x,y) on graph, so is (x,-y).
#### jbriggs444
Homework Helper
So to answer the question about the symmetry of -1/x, a function is origin symmetric if EITHER
For every (x,y) on graph, so is (-x,-y).
or
For every (-x,y) on graph, so is (x,-y).
Both conditions are identical. The first is the proper way of stating the second.
#### FortranMan
Why is the first way more proper?
#### jbriggs444
Homework Helper
Why is the first way more proper?
When you write "For every (x,y) on graph, so is (-x,-y)", you are invoking a quantifier. In this case it is a Universal quantifier, "for all" (in symbolic form: $\forall$).
The typical form of a universal quantifier is "for all <variable[s]> [in range], expression". The first occurrences of x and y in the statement are dummy variables. They exist simply to let the reader know which variables are being quantified over. As such, they should be variable names only, not expressions. The subsequent occurrences of x and y within the expression can be used freely.
If you've done computer programming, a lot of concepts carry over into mathematical discourse. A quantifier opens up a scope in which new variables are declared. The variable list in a quantifier amounts to a declaration of variables applicable to the scope. Rather like formal parameters in a called function. The function header has variable names for the formal parameters, not expressions.
Last edited:
#### Mark44
Mentor
Why is the first way more proper?
Because both x and y could be positive or negative. You're tacitly assuming that (x, y) is a point in the first quadrant. For example, if x = -3 and y = 2, then (x, y) is a point in the second quadrant. | 2019-11-13 12:57:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6421457529067993, "perplexity": 1448.7291316756869}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496667260.46/warc/CC-MAIN-20191113113242-20191113141242-00074.warc.gz"} |
https://www.physicsforums.com/threads/why-you-cant-take-the-logarithm-of-a-negative-number-or-of-0.768695/ | # Why you can’t take the logarithm of a negative number or of 0 ?
1. Sep 2, 2014
### mather
hello
why "you can’t take the logarithm of a negative number or of 0" ?
thanks!
2. Sep 2, 2014
### economicsnerd
If I define a function, I get to tell you what its domain is. There's a function $\log : (0,\infty)\to \mathbb{R}$ that some people defined. By fiat, its domain is $(0,\infty)$, and so it doesn't make any sense to ask what $\log(x)$ is for $x\notin(0,\infty)$.
3. Sep 2, 2014
### economicsnerd
Now, the question to ask would be why some people defined $\log$ as a function with domain $(0,\infty)$. To know for sure, we would have to be able to read minds.
One guess is that it's nice for the equation $\log(x) = \int_1^x \frac1t \text{ d}t$ (where the right-hand side is a Riemann integral) to hold for every $x$ in the domain. This would force us to avoid $x<0$, lest the integral not be well-defined. It would also force us to avoid $x=0$ if we want the function to be real-valued (and in particular not take on the value $-\infty$).
Of course, you could always define an alternative function with a bigger domain, say $\mathbb R$ or $[0,\infty)$ or $[-12.3, \infty)$, which agrees with $\log$ on $(0,\infty)$ and takes some values you specify for other inputs. But then you would be defining a new function.
4. Sep 2, 2014
### HallsofIvy
Another way of looking at it (though, frankly, I prefer the approach economicsnerd is taking) is that ln(x) can be defined as the inverse function to $$y= e^x$$. Since that is a positive number to the x power, while x can be any number, y must be positive (less than 1 of x< 0, greater than 1 if x> 0). Reversing, x= log(y), so that, while the value of the function can be any number, the "domain" is all positive numbers.
5. Sep 3, 2014
### Staff: Mentor
Looking at what 'logarithm' of N is, you need to find an x to satisfy this equation: N = 10x
x is known as the logarithm of N (to base 10).
Your task: give N any negative value and see whether you can discover an x that makes the equation true.
6. Sep 3, 2014
### mal4mac
To know better, we could delve into the history of the subject:
http://en.wikipedia.org/wiki/Logarithm#History
7. Sep 3, 2014
### Hertz
mather, consider changing the base of the logarithm. Can you have a negative base? Does this logarithm have a solution?$$\log_{-2}{4}$$How about this one?$$\log_{-2}(-8)$$
To answer these you must consider the definition of the logarithm to be $$\log_{b}{c}=a \iff b^a=c$$You can see that we are given $b$ and $c$ and we need to find $a$. If you take $b$ and $c$ and plug them into the equation $b^a=c$, you can sometimes recognize the value of $a$.
Now consider $b=e=2.718$ and $c=..$ say.. $-2$. Evaluate $\log_{e}(-2)=\ln(-2)$. In other words, find the value of $a$ so that $e^a=-2$. In other words, plot the function $y=e^x$ and find where $y=-2$. What x value does this occur at? Are there any better negative values to try besides -2? What about 0?
This is why for some bases (positive bases in particular) you can't take the logarithm of a negative number or zero. In fact, you can take these types of logarithms if you know how logarithms behave in the complex numbers. But before you can understand that, you need to understand what it means when you have an imaginary number in an exponent. Say.. $e^{i\theta}$ where $\theta$ is a constant.
And yes, it's quite interesting that $$\frac{d}{dx}\ln{x}=\frac{1}{x}$$
8. Sep 3, 2014
### Incnis Mrsi
First of all, exponentiation is a tricky thing. Two cases are solid:
• Any invertible thing (i.e. non-zero number) in an integer power.
• Positive number in a real or complex power.
But there is no natural and unambiguous definition of, say, negative number in the power ½.
That’s why logarithms of negative numbers are so messy. What can we hope to achieve? If we chose a negative base, such as −2, then we have logarithms of its powers, such as 4, −8, 16, −32… half of those are negative. But for a negative base we fail with all other numbers, that are not integer powers of the base. This is a valid topic for number theory, but useless in calculus.
Another possibility is to find a complex power of a positive base, that results in given negative number. That’s how logarithm is understood in complex analysis and calculus in general, but it is a multivalued function.
In neither case you can obtain log 0. Any power of a non-zero number is not zero, whereas log0 is ill-defined. | 2018-07-18 07:26:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8957201242446899, "perplexity": 341.99281496470377}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590069.15/warc/CC-MAIN-20180718060927-20180718080927-00194.warc.gz"} |
https://proofwiki.org/wiki/Abel%27s_Lemma | # Abel's Lemma
## Lemma
Let $\sequence a$ and $\sequence b$ be sequences in an arbitrary ring $R$.
### Formulation 1
$\displaystyle \sum_{k \mathop = m}^n a_k \paren {b_{k + 1} - b_k} = a_{n + 1} b_{n + 1} - a_m b_m - \sum_{k \mathop = m}^n \paren {a_{k + 1} - a_k} b_{k + 1}$
### Formulation 2
Let $\displaystyle A_n = \sum_{i \mathop = m}^n {a_i}$ be the partial sum of $\sequence a$ from $m$ to $n$.
Then:
$\displaystyle \sum_{k \mathop = m}^n a_k b_k = \sum_{k \mathop = m}^{n - 1} A_k \paren {b_k - b_{k + 1} } + A_n b_n$
## Also known as
Abel's Lemma is also known as:
Abel's transformation
Abel's partial summation formula
the technique of Summation by Parts.
## Source of Name
This entry was named for Niels Henrik Abel. | 2021-05-12 01:46:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9809144139289856, "perplexity": 3148.8624247383564}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991693.14/warc/CC-MAIN-20210512004850-20210512034850-00196.warc.gz"} |
https://forum.effectivealtruism.org/users/tetraspace-grouping | # Tetraspace
Software Engineer
Working (0-5 years experience)
328Joined Nov 2018
# Posts 5
Sorted by New
For fiction, AI Impacts has an incomplete list here sorted by what kind of failure modes they're about and how useful AI Impacts thinks they are for thinking about the alignment problem.
As of this comment: 40%, 38%, 37%, 5%. I haven't taken into account time passing since the button appeared.
With 395 total codebearer-days, a launch has occurred once. This means that, with 200 codebearers this year, the Laplace prior for any launch happening is 40% (). The number of participants is about in between 2019 (125 codebearers) and 2020 (270 codebearers), so doing an average like this is probably fine.
I think there's a 5% chance that there's a launch but no MAD, because Peter Wildeford has publicly committed to MAD, says 5%, and he knows himself best.
I think the EA forum is a little bit, but not vastly, more likely to initiate a launch, because the EA Forum hasn't done Petrov day before and qualitatively people seem to be having a bit more fun and irreverance over here, so I'm giving 3% of the no-MAD probability to EA Forum staying up and 2% to Lesswrong staying up.
I looked up GiveDirectly's financials (a charity that does direct cash transfers) to check how easily it could be scaled up to megaproject-size and it turns out, in 2020, it made $211 million in cash transfers and hence is definitely capable of handling that amount! This is mostly$64m in cash transfers to recipients in Sub-Saharan Africa (their Givewell-recommended program) and $146m in cash transfers to recipients in the US. Another principle, conservation of total expected credit: Say a donor lottery has you, who donates a fraction of the total with an impact judged by you if you win of , the other participants, who collectively donate a fraction of the total with an average impact as judged by you if they win of , and the benefactor, who donates a fraction of the total with an average impact if they win of . Then total expected credit assigned by you should be (followed by A, B and C), and total credit assigned by you should be if you win, if they win, and otherwise (violated by C). • Under A, if you win, your credit is , their credit is , and the benefactor's credit is , for a total credit of . If they win, your credit is , their credit is , and the benefactor's credit is , for a total credit of . • Your expected credit is , their expected credit is , and the benefactor's expected credit is , for a total expected credit of . • Under B, if you win, your credit is and everyone else's credit is , for a total credit of . If they win, their credit is and everyone else's credit is , for a total credit of . If the benefactor wins, everyone gets no credit. • Your expected credit is and their expected credit is , for a total expected credit of . • Under C, under all circumstances your credit is and their credit is , for a total credit of . • Your expected credit is and their expected credit is , for a total expected credit of . I've been thinking of how to assign credit for a donor lottery. Some ways that seem compelling: • A: You get X% credit for the actual impact of the winner • B: You get 100% credit for the impact if you win, and 0% credit otherwise • C: You get X% credit for what your impact would have been, if you won Some principles about assigning credit: • Credit is predictable and proportional to the amount you pay to fund an outcome (violated by B) • Credit depends on what actually happens in real life (violated by C) • Your credit depends on what you do, not what uncorrelated other people do (violated by A) Some actual uses of assigning credit and what they might say: • When I'm tracking my own impact, I use something kind of like C - there's a line on my spreadsheet that looks like "Donor lottery - £X", which I smile at a little more than the Long Term Future Fund, because C is how I estimate my expected impact ahead of time. • Impact certificates can't be distributed according to C because they correspond to actual impacts in the world, and are minted by the organizations that receive the grants and sold in exchange for the grants. You could kind of recover C by selling the rights to any impact certificates you would receive before the lottery is drawn. • A means that your credit is correlated with the decisions of other participants, which the CEA Donor Lottery is designed to avoid and which makes the decision whether to participate harder. What were your impressions for the amount of non-Open Philanthropy funding allocated across each longtermist cause area? I also completed Software Foundations Volume 1 last year, and have been kind of meaning to do the rest of the volumes but other things keep coming up. I'm working full-time so it might be beyond my time/energy constraints to keep a reasonable pace, but would you be interested in any kind of accountability buddy / sharing notes / etc. kind of thing? Simple linear models, including improper ones(!!). In Chapter 21 of Thinking Fast and Slow, Kahneman writes about Meehl's book Clinical vs. Statistical Prediction: A Theoretical Analysis and a Review, which finds that simple algorithms made by getting some factors related to the final judgement and weighting them gives you surprisingly good results. The number of studies reporting comparisons of clinical and statistical predictions has increased to roughly two hundred, but the score in the contest between humans and algorithms has not changed. About 60% of the studies have shown significantly better accuracy for the algorithms. The other comparisons scored a draw in accuracy [...] If they are weighted optimally to predict the training set, they're called proper linear models, and otherwise they're called improper linear models. Kahneman says about Dawes' The Robust Beauty of Improper Linear Models in Decision Making that A formula that combines these predictors with equal weights is likely to be just as accurate in predicting new cases as the multiple-regression formula that was ptimal in the original sample. More recent research went further: formulas that assign equal weights to all the predictors are often superior, because they are not affected by accidents of sampling. That is to say: to evaluate something, you can get very far just by coming up with a set of criteria that positively correlate with the overall result and with each other and then literally just adding them together. How has the landscape of malaria prevention changed since you started? Especially since AMF alone has bought on the order of 100 million nets, which seems not insignificant compared to the total scale of the entire problem. In the list at the top, Sam Hilton's grant summary is "Writing EA-themed fiction that addresses X-risk topics", rather than being about the APPG for Future Generations. Miranda Dixon-Luinenburg's grant is listed as being$23,000, when lower down it's listed as $20,000 (the former is the amount consistent with the total being$471k). | 2022-12-08 06:05:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.35871589183807373, "perplexity": 4977.414809736102}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446711278.74/warc/CC-MAIN-20221208050236-20221208080236-00813.warc.gz"} |
https://puzzling.stackexchange.com/questions/67493/what-is-a-croupiers-word | # What is a Croupier's Word™?
This puzzle is based off the What is a Word™ and What is a Phrase™ series started by JLee and their spin-off What is a Number™ series.
If a word conforms to a certain rule, I call it a Croupier's Word™. Use the following examples to find the rule:
$$% set Title text. (spaces around the text ARE important; do not remove.) % increase Pad value only if your entries are longer than the title bar. % \def\Pad{\P{1.0}} \def\Title{\textbf{ Croupier's }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\ \def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ }\displaystyle \smash{\lower{29px}\bbox[yellow]{\phantom{\rlap{rubio.2018.03.05}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{GOTHS}&\text{HIPSTERS}\\ \hline \text{FUTON}&\text{TATAMI}\\ \hline \text{TRASHED}&\text{SOBER}\\ \hline \text{CONSOLES}&\text{COMPUTERS}\\ \hline \text{OLDIE}&\text{GOLDIE}\\ \hline \text{HATERS}&\text{LOVERS}\\ \hline \text{TASER}&\text{MACE}\\ \hline \text{STRAYS}&\text{STAYS}\\ \hline \text{BASED}&\text{DEBASED}\\ \hline \text{GENRE}&\text{SUBGENRE}\\ \hline \text{WIDER}&\text{NARROWER}\\ \hline \text{FAULTS}&\text{STRENGTHS}\\ \hline \end{array}$$
The puzzle satisfies the series' inbuilt assumption, that each word can be tested for whether it is a Croupier's Word™ without relying on the other words.
These are not the only examples, there are more of both Croupier's Words™ and Not Croupier's Words™.
CSV version:
GOTHS,HIPSTERS
FUTON,TATAMI
TRASHED,SOBER
CONSOLES,COMPUTERS
OLDIE,GOLDIE
HATERS,LOVERS
TASER,MACE
STRAYS,STAYS
BASED,DEBASED
GENRE,SUBGENRE
WIDER,NARROWER
FAULTS,STRENGTHS
A Croupier's Word™
can be used to form a new word by cutting it in half (with the first half receiving the extra letter if the length is odd) and interleaving the two halves, similar to the way a croupier cuts a deck of cards and interleaves the halves to shuffle.
For example, TRASHED is one because
interleaving TRAS and HED yields THREADS.
For completeness,
the shuffled words are
GHOST
FOUNT
COOLNESS
OILED
HEARTS
TEARS
SATYRS
GREEN
WEIRD
FLATUS.
• Yup, that's it, exactly. Looking at the edit history of your answer, I'm super impressed: looks like you got the answer first, and only afterwards linked it with the title! That wasn't supposed to be possible at all! :-) – Bass Jun 25 '18 at 12:34
• @Bass If the correct answer has been posted, remember to accept it. ;-) (just posting this in case it was too early to do so back then) – EKons Jun 25 '18 at 22:30 | 2019-12-05 19:58:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3748224675655365, "perplexity": 1858.9353463634116}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540482038.36/warc/CC-MAIN-20191205190939-20191205214939-00061.warc.gz"} |
https://exeley.com/in_jour_smart_sensing_and_intelligent_systems/doi/10.21307/ijssis-2021-014 | Development of a computer-based simple pendulum experiment set for teaching and learning physics
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VOLUME 14 , ISSUE 1 (Feb 2021) > List of articles
### Development of a computer-based simple pendulum experiment set for teaching and learning physics
Citation Information : International Journal on Smart Sensing and Intelligent Systems. Volume 14, Issue 1, Pages 1-8, DOI: https://doi.org/10.21307/ijssis-2021-014
Received Date : 02-February-2021 / Published Online: 28-July-2021
### ARTICLE
#### ABSTRACT
The development of a cost-effective experiment set is essential for teaching and learning physics in educational institutes. We aim to develop a computer-based simple pendulum experiment set consisting of a simple pendulum, infrared phototransistor, and Arduino board for calculating the gravitational acceleration (g). We used 13 pendulum lengths with five angles for each length to measure the period of motion. We found linear relationships between lengths and period-squared. The g-value was 9.806 ± 0.025 (average ± standard error) m/s2. Since this experiment set is cost-effective, and more straightforward method to understand, it will benefit the physics learning in educational institutions.
## Introduction
Physics is one of the most fundamental scientific disciplines, and it forms the core of scientific development (Hartmann and Mittelstrass, 2002). Physics helps students to understand natural phenomena through observations, measurements, mathematics, and experiments (Falkenburg, 2011). However, the conventional teaching methods that include delivering traditional lectures in front of the passive students are often tedious and very difficult for the students to understand physics. Moreover, these methods do not provide adequate opportunities for the students to think critically to solve a problem (Adams et al., 2006; Schauer et al., 2009; Wieman and Perkins, 2005).
Along with the conventional teaching method, laboratory activities are essential as it allows the students to get involved in the learning process. Students start thinking critically while conducting laboratory works. Self-explored experience from laboratory activities helps the students understand and recognize laws of physics, enhance the physics’ conceptual thinking, and develop their scientific skills (Darrah et al., 2014; Sari et al., 2019).
It could be more helpful for the students if they get an opportunity to learn physics from the computer-based experiments in the physics laboratory. It helps the students better to understand physics than only lectures in the classroom. It allows the students to develop their skills, which makes physics more accessible (Brelsford, 1993; Darrah et al., 2014; Rutten et al., 2012; Sari et al., 2019; Zacharia and Anderson, 2003). It also increases the students’ motivation to collaborate and stay engaged with the learning process, which is very useful for them (Sari et al., 2019). The computer-based experiments have some more benefits for the students, such as teaching the students about data collection and data analysis, understanding the relationships among various variables through plotting graphs based on their collected data. This helps the students to gain knowledge about theory and experiments and develop their research skills (Amrani and Paradis, 2010; Beichner et al., 1999; David et al., 2007; Trumper and Gelbman, 2000).
A low-cost experimental set could be developed in computer-based experiments by using an Arduino board and a computer (Musik, 2017; Sanjaya et al., 2018; Sari and Kirindi, 2019; Tunyagi et al., 2018). This experimental set is cost-effective and easily handled. Students learn from real-time experiments and collect data continuously. Through this type of experiment, students obtain more accurate physics concepts compared to the conventional teaching method. These computer-based experimental sets can include various sensors, including photogate sensor (Yulkifli et al., 2018), ultrasonic sensor (Cutnell and Johnson, 2010; Galeriu et al., 2014; Pili and Violanda, 2019; Sanjaya et al., 2018; Tong-on et al., 2017), and infrared sensor (Musik, 2014, 2017), which makes physics learning more comfortable for the student.
The experiments about motion are fundamental in elementary or advanced physics, where the concept of position, time, speed, and acceleration is crucial. Gravity is known as the key to describe the motion of an object and pendulum experiment is an excellent way to demonstrate the gravity in high school, college, and university study.
In this study, a simple pendulum experiment is introduced which consists of an object with a small mass, also known as the pendulum bob, suspended from a light string. A simple pendulum period depends on the string’s length and the amplitude of the pendulum’s swing. An Arduino-based microcontroller and infrared phototransistor sensors are used to measure the period of oscillation and calculate the gravity. The aims of this study are (i) to develop a computer-based experiment set on a simple pendulum, and (ii) to measure the periodic motion and the acceleration of gravity (g) in Nakhon Si Thammarat province, southern Thailand. This proposed setup is cost-effective and easy to operate.
## Materials and methods
### Working principle of classical pendulum
A simple pendulum consists of a particle of mass m, attached to a frictionless pivot P by a cable of length L and negligible mass. When the particle is pulled away from its equilibrium position by an angle $θ$θ and released, it swings back and forth (Fig. 1) (Cutnell and Johnson, 2010). The period T of a simple pendulum for small angles depends on its length and the local strength of gravity as shown in the following equation:
##### (1)
$T=2πLg$
##### Figure 1:
A simple pendulum swinging back and forth about the pivot P. If the angle $θ$θ is small about 10° or less, the swinging is approximately simple harmonic motion.
For larger amplitudes, the period is longer than predicted by the small-angle approximation. T is calculated by using the following equations (Amrani et al., 2008; Beléndez et al., 2009; Simpson, 2010):
##### (2)
$T=2πLg(1+116θ02+113072θ04+173737280θ06+229311321205760θ08+...)$
and:
##### (3)
$T2=[4π2(1+116θ02+113072θ04+173737280θ06+229311321205760θ08+...)/g]L$
Here g is the acceleration of gravity, L is the length of the pendulum, and θ 0 is the angular displacement amplitude.
### Experimental setup
#### Mechanism of harmonic motion
The experimental setup is made of a stand (stainless steel) with a width of 0.30 m, length of 0.40 m, and a height of 0.16 m. A pole (1st pole in Fig. 2a) is fixed with the stand. The pole’s length is 1.00 m, but it can be increased up to 1.48 m by using a support system. A pendulum (stainless steel) is tied with the 2nd pole of the rigid support by using a nylon rope (Fig. 2a). The mass and diameter of the pendulum are 0.032 kg and 0.02 m, respectively. A screw lock is fixed with the 2nd pole to increase or decrease the nylon rope’s length along with the pendulum. Pendulum swing angle can be fixed by a projector as shown in Figure 2b (i.e., 35 degrees). An infrared LED and phototransistor sensor are fixed with the stand and the 1st pole, respectively (Fig. 2a).
##### Figure 2:
The structure of the experimental set; (a) experimental set, and (b) fix swing angle.
The infrared phototransistor circuit consists of a phototransistor, an infrared LED, and a resistor (Fig. 3). The phototransistor acts as a receiver, and the infrared LED acts as a transmitter. The resistor is 330 kΩ, 200 Ω, and 1/4 W (Musik, 2017) (Fig. 3). The power supply is 5 V of DC. During operating, when the infrared reaches the phototransistor, the output voltage becomes 0 V, and when an opaque object blocks the path of the light, the output voltage changes to 5 V. The signal of the output voltage is used to measure the swing period of the pendulum through using the Arduino program.
##### Figure 3:
Infrared phototransistor circuit.
The infrared transmitting circuit consists of four IR LEDs and four resistors of 220 Ω (Fig. 4a). Infrared LED is connected with four resistors (each infrared LED is 5 mm in diameter) in parallel, where the distance between each resister is 1.2 cm. The device is placed on a 3.0 cm × 6.5 cm printed circuit board (Fig. 4b).
##### Figure 4:
(a) Infrared LEDs circuit, (b) infrared LEDs board.
The phototransistor receiver circuit consists of four phototransistors in parallel. The diameter of each phototransistor is 5 mm. The distance between each phototransistor is 1.2 cm. This phototransistor receiver circuit is used for collecting the data of period (T) (Fig. 5a). This phototransistor receiver circuit is placed on a 3.0 cm × 6.5 cm printed board (Fig. 5b).
#### Computer interface on the simple pendulum
The computer interface experimental set consists of hardware and software, which are shown in Figure 6. An Arduino (model ET-EASY MEGA1280) is used as the hardware which is connected to the notebook PC via a USB port for sending simple pendulum motion data. The phototransistor is used as a signal detector. A simple pendulum motion test set is prepared by connecting a microcontroller with the notebook PC (Fig. 6). The pendulum moves through the infrared phototransistors which changes the output voltage from 0 to 5 volt. The output from the receivers is sent to microcontroller. The microcontroller receives the output voltage and calculates the g-value. Finally, Arduino development board has the ability to store the data for future reference. Arduino 1.8.12 is used to record the period of the pendulum motion. The codes used for data collection are shown in Figure 7.
##### Figure 6:
The computer-based experiment set on a simple pendulum.
##### Figure 7:
Arduino codes used for data collection.
### Experimental procedure
We took 13 pendulum lengths (0.20-0.80 m, with 0.05 m interval), and for each length, we used five angles (7, 10, 15, 20, and 25°). After confirming a length (i.e., 0.20 m), the first angle (i.e., 7°) was determined by using the projector. The pendulum was swung from the fixed angle 10 times (i.e.,10 periods, T) (see Pili, 2020; Yulkifli et al., 2018). During pendulum swing, the experimental data were recorded with the Arduino program and sent to the notebook PC. After finishing one angle, we selected the next angle (i.e., 10°) and swung the pendulum 10 times. In this way, we finished all angles (7-25°). Then we selected the next length (i.e., 0.25 m) and finished all five angles, and every time the Arduino program sent data to the notebook PC. In this way, we finished all five angles (7-25°) for all 13 lengths (0.20-0.80 m). After receiving all period (T), the square of the period (T 2) was calculated in the Microsoft Excel program. Afterward, graphs (i.e., relationships between lengths and square of periods for each angle) were plotted, and data were analyzed using Wolfram Mathematica program. Then, the value of gravitational acceleration (g) for each angle was calculated. Afterward, the average g-value ± standard error (SE) was calculated and compared this g-value with the theoretical (g) value.
## Results and discussion
The period squared achieved from each length, and each angle is shown in Table 1. The linear regressions between lengths and period squared for five angles are shown in Figure 8a-e. We observed significant positive relationships between lengths and period squared for each angle. The regression line, R 2 and p-value are shown in each figure.
##### Table 1.
Squared period form experimental data.
The slopes of the linear regressions in Figure 8 are 4.044, 4.035, 4.045, 4.044, and 4.070, respectively and represents by:
$4π2(1+116θ02+113072θ04+173737280θ06+229311321205760θ08+...)/g$
##### Figure 8:
Relationships of length and period squared for the angles (a) 7°, (b) 10°, (c) 15°, (d) 20°, (e) 25°.
Then, we calculated the gravitational acceleration (g) of Nakhon Si Thammarat province. We found that average gravitational acceleration ± standard error was 9.806 ± 0.025 m/s2 which is shown in Table 2. The true value of gravitational acceleration (g) of Nakhon Si Thammarat province was checked in SensorsONE (2021) by putting latitude (8.8297614) and height (20 m) and we found g-value as 9.781. The experimental value’s (9.806) accuracy to the true value (9.781) was calculated using the following relative error equation:
##### (4)
$Error(%)=|9.781‒gexp9.781|×100$
##### Table 2.
Values of gravitational acceleration (g).
Our results support the findings of other scientists (Khairurrijal et al., 2012; Pili and Violanda, 2019; Sanjaya et al., 2018; Sinacore and Takai, 2010; Yulkifli et al., 2018) who used simple pendulum motion experiment set to calculate the gravitational acceleration (g) in different places. One study in New York (USA) (Sinacore and Takai, 2010) used pendulum, telephone pickup, and sound card oscilloscope to calculate the g-value and their calculated g-value was 9.774 m/s2 with an error of 0.3%. A study in Indonesia (Khairurrijal et al., 2012) calculated g-value by using infrared transmitter and phototransistor receiver electronic circuit and their g-value was 9.77 ± 0.03 m/s2 with an error of 0.1%. Another study in Indonesia (Sanjaya et al., 2018) calculated g-value by using an HC-SR04 ultrasonic sensor, Arduino microcontroller, and the computer interface, and their calculated g-value was 9.811 ± 1.067 m/s2. Yulkifli et al. (2018) calculated g-value in the same country by using both manual and digital tools. They found that the g-value from manual and digital methods were 9.762 and 9.797 m/s2, respectively, where the accuracy (%) of the digital method was higher and relative error(%) was lower compared to the manual method. In the digital method, they used a photogate sensor and computer interface with Arduino pro mini. One more study in the Philippines (Pili and Violanda, 2019) used an ultrasonic sensor and an Arduino Uno board to calculate g-value and their calculated g-value was 9.82 ± 0.10 m/s2.
## Conclusion
The development of the computer-based experiment set on a simple pendulum in harmonic motion, which experiment apparatus based on a simple pendulum, infrared sensor, Arduino microcontroller, a computer, and Wolfram Mathematica has been successfully shown, the acceleration of gravity of pendulum motion measured g= 9.806 ± 0.025 m/s2 with an error of 0.253%. This experimental setup is a cost-effective and straightforward method. The advantage of this system is that it makes physics experiments easier than traditional lectures in the classroom. Students can better understand the physics theories, which help them to develop their learning skills (Brelsford, 1993; Darrah et al., 2014; Zacharia and Anderson, 2003). Significantly, the use of computer-based learning, along with sensors, might increase their motivation for learning physics. This might help them to achieve their expected learning outcomes (Karamustafaoğlu, 2012). Therefore, this system can be applied in real-time physics teaching, which may help students learn physics concepts and laws efficiently and effectively.
In the future, a matrix real-time simple pendulum method could be developed to test the relationships between displacement/velocity/acceleration and times of motion. This further study will help the physics students to understand the pendulum motion theory easily in the laboratory.
## Acknowledgements
This work was financially supported by the Ministry of Higher Education, Science, Research and Innovation (MHESI), Ministry of Education, and Nakhon Si Thammarat Rajabhat University, Thailand. We are grateful to Mr. Piyawit Jayangkool and Mr. Nattapol Jayangkool for assisting in developing the experiment set. Special thanks to Dr. Fahmida Wazed Tina (co-supervisor of the Ph.D. student Warawut Sukmak), faculty of Science and Technology, Nakhon Si Thammarat Rajabhat University, for editing the manuscript, and to Dr. Chitnarong Sirisathitkul, Walailak University, for providing valuable comments on this manuscript. Conflict of interest: the author declares that there is no conflict of interest.
## References
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2. Amrani, D. and Paradis, P. 2010. Use of computer-based data acquisition to teach physics laboratories: case study-simple harmonic motion. Latin American Journal of Physics Education 4: 511–514.
3. Amrani, D. , Paradis, P. and Beaudin, M. 2008. Approximation expressions for the large-angle period of a simple pendulum revisited. Revista Mexicana De Fi’Sica E, 54: 59–64.
4. Beichner, R. , Bernold, L. , Burniston, E. , Dail, P. , Felder, R. , Gastineau, J. , Gjersten, M. and Risley, J. 1999. Case study of the physics component of an integrated curriculum. Physics Education Research, American Journal of Physics Supplement 67(Suppl. 7): 16–24.
5. Beléndez, A. , Rodes, J. J. , Beléndez, T. and Hernández, A. 2009. Approximation for the large-angle simple pendulum period. European Journal of Physics 30: 1–6.
6. Brelsford, J. W. 1993. Physics education in a virtual environment Proceedings of The Human Factors and Ergonomics Society 37th Annual Meeting, pp. 1286–1290.
7. Cutnell, D. J. and Johnson, W. K. 2010. Introduction to physics USA: John Wiley & Sons.
8. Darrah, M. , Humbert, R. , Finstein, J. , Simon, M. and Hopkins, J. 2014. Are virtual labs as effective as hands-on labs for undergraduate physics? A comparative study at two major universities. Journal of Science Education and Technology 23: 803–814.
9. David, R. S. , Priscilla, W. L. and Ronald, K. T. 2007. Real Time Physics: active learning labs transforming the introductory laboratory. European Journal of Physics 28: S83–S94.
10. Falkenburg, B. 2011. What are the phenomena of physics? Synthese 182: 149–163.
11. Galeriu, C. , Edwards, S. and Esper, G. 2014. An Arduino investigation of simple harmonic motion. The Physics Teacher 52: 157–159.
12. Hartmann, S. and Mittelstrass, J. 2002. Physics is part of culture and the basis of technology, In Deutsche Physikalische Gesellschaft (Ed.), Physics–Physics Research: Topics, Significance and Prospects, pp. 195–198.
13. Karamustafaoğlu, O. 2012. How computer-assisted teaching in physics can enhance student learning. Educational Research and Review, 7: 297–308.
14. Khairurrijal, K. , Widiatmoko, E. , Srigutomo, W. and Kurniasih, N. 2012. Measurement of gravitational acceleration using a computer microphone port. Physics Education 47: 709–714.
15. Musik, P. 2014. Development of computer-based experimental set in physics for free falling object. The European Conference on Education 2014: 309–322.
16. Musik, P. 2017. Development of computer-based experiment set on simple harmonic motion of mass on springs. The Turkish Online Journal of Educational Technology 16: 1–11.
17. Pili, U. B. 2020. Sound-based measurement of g using a door alarm and a smartphone: listening to the simple pendulum. Physics Education 55: 1–4.
18. Pili, U. and Violanda, R. 2019. Measurement of the gravitational acceleration using a simple pendulum apparatus ultrasonic sensor and Arduino. Physics Education 54: 1–5.
19. Rutten, N. , van Joolingen, W. R. and van der Veen, J. T. 2012. The learning effects of computer simulations in science education. Computers & Education 58: 136–153.
20. Sanjaya, W. S. M. , Anggraeni, D. , Denya, R. , Pandriantama, H. , Iklimah, I. and Dewi, I. P. 2018. A low cost of simple pendulum experiment apparatus based on ultrasonic sensor and Arduino microcontroller. Jurnal Ilmiah Pengabdian Kepada Masyarakat 1: 51–54.
21. Sari, U. and Kirindi, T. 2019. Using Arduino in physics teaching: Arduino-based physics experiment to studytemperature dependence of electrical resistance. Journal of Computer and Education Research 7: 698–710.
22. Sari, U. , Pektaş, H. M. , Çelik, H. and Kirindi, T. 2019. The effects of virtual and computer based real laboratory applications on the attitude motivation and graphic skills of university students. International Journal of Innovation in Science and Mathematics Education 27: 1–17.
23. Schauer, F. , Cernansky, P. , Ožvoldová, M. and Lustig, F. 2009. Integrated e-learning-new strategy of the cognition of real world in teaching physics In Innovations 2009 (USA), World Innovations in Engineering Education and Research iNEER Special Volume 2009, 119–135.
24. SensorsONE. 2021. Local gravity calculator, available at: https://sensorsone.com/local-gravity-calculator/#height.
25. Simpson, D. G. 2010. The non linear pendulum, available at: http://pgccphy.net/ref/nonlin-pendulum.pdf.
26. Sinacore, J. and Takai, H. 2010. Measuring g using a magnetic pendulum and telephone pickup. The Physics Teacher 48: 448–449.
27. Tong-on, A. , Saphet, P. and Thepnurat, M. 2017. Simple harmonics motion experiment based on LabVIEW interface for Arduino. Journal of Physics: Conference Series 901: 1–6.
28. Trumper, R. and Gelbman, M. 2000. Investigating electromagnetic induction through a minicomputer-based laboratory. Physics Education, 35: 90–95.
29. Tunyagi, A. , Kandrai, K. , Fülop, Z. , Kapusi, Z. and Simon, A. 2018. Friction coefficient determination by electrical resistance measurements. Physics Education 53: 1–9.
30. Wieman, C. and Perkins, K. 2005. Transforming physics education. Physics Today 58: 26–41.
31. Yulkifli, Y. , Afandi, Z. and Yohandri, Y. 2018. Development of gravity acceleration measurement using simple harmonic motion pendulum method based on digital technology and photogate sensor. Materials Science and Engineering 335: 1–8.
32. Zacharia, Z. and Anderson, O. R. 2003. The effects of an interactive computer-based simulation prior to performing a laboratory inquiry-based experiment on students’ conceptual understanding of physics. American Journal of Physics 71: 618–629.
### FIGURES & TABLES
Figure 1:
A simple pendulum swinging back and forth about the pivot P. If the angle θ θ is small about 10° or less, the swinging is approximately simple harmonic motion.
Figure 2:
The structure of the experimental set; (a) experimental set, and (b) fix swing angle.
Figure 3:
Infrared phototransistor circuit.
Figure 4:
(a) Infrared LEDs circuit, (b) infrared LEDs board.
Figure 5:
Figure 6:
The computer-based experiment set on a simple pendulum.
Figure 7:
Arduino codes used for data collection.
Figure 8:
Relationships of length and period squared for the angles (a) 7°, (b) 10°, (c) 15°, (d) 20°, (e) 25°.
### REFERENCES
1. Adams, W. K. , Perkins, K. K. , Podolefsky, N. S. , Dubson, M. , Finkelstein, N. D. and Wieman, C. E. 2006. New instrument for measuring student beliefs about physics and learning physics. The Colorado Learning Attitudes about Science Survey. Physical Review Special Topics – Physics Education Research 2: 1–14.
2. Amrani, D. and Paradis, P. 2010. Use of computer-based data acquisition to teach physics laboratories: case study-simple harmonic motion. Latin American Journal of Physics Education 4: 511–514.
3. Amrani, D. , Paradis, P. and Beaudin, M. 2008. Approximation expressions for the large-angle period of a simple pendulum revisited. Revista Mexicana De Fi’Sica E, 54: 59–64.
4. Beichner, R. , Bernold, L. , Burniston, E. , Dail, P. , Felder, R. , Gastineau, J. , Gjersten, M. and Risley, J. 1999. Case study of the physics component of an integrated curriculum. Physics Education Research, American Journal of Physics Supplement 67(Suppl. 7): 16–24.
5. Beléndez, A. , Rodes, J. J. , Beléndez, T. and Hernández, A. 2009. Approximation for the large-angle simple pendulum period. European Journal of Physics 30: 1–6.
6. Brelsford, J. W. 1993. Physics education in a virtual environment Proceedings of The Human Factors and Ergonomics Society 37th Annual Meeting, pp. 1286–1290.
7. Cutnell, D. J. and Johnson, W. K. 2010. Introduction to physics USA: John Wiley & Sons.
8. Darrah, M. , Humbert, R. , Finstein, J. , Simon, M. and Hopkins, J. 2014. Are virtual labs as effective as hands-on labs for undergraduate physics? A comparative study at two major universities. Journal of Science Education and Technology 23: 803–814.
9. David, R. S. , Priscilla, W. L. and Ronald, K. T. 2007. Real Time Physics: active learning labs transforming the introductory laboratory. European Journal of Physics 28: S83–S94.
10. Falkenburg, B. 2011. What are the phenomena of physics? Synthese 182: 149–163.
11. Galeriu, C. , Edwards, S. and Esper, G. 2014. An Arduino investigation of simple harmonic motion. The Physics Teacher 52: 157–159.
12. Hartmann, S. and Mittelstrass, J. 2002. Physics is part of culture and the basis of technology, In Deutsche Physikalische Gesellschaft (Ed.), Physics–Physics Research: Topics, Significance and Prospects, pp. 195–198.
13. Karamustafaoğlu, O. 2012. How computer-assisted teaching in physics can enhance student learning. Educational Research and Review, 7: 297–308.
14. Khairurrijal, K. , Widiatmoko, E. , Srigutomo, W. and Kurniasih, N. 2012. Measurement of gravitational acceleration using a computer microphone port. Physics Education 47: 709–714.
15. Musik, P. 2014. Development of computer-based experimental set in physics for free falling object. The European Conference on Education 2014: 309–322.
16. Musik, P. 2017. Development of computer-based experiment set on simple harmonic motion of mass on springs. The Turkish Online Journal of Educational Technology 16: 1–11.
17. Pili, U. B. 2020. Sound-based measurement of g using a door alarm and a smartphone: listening to the simple pendulum. Physics Education 55: 1–4.
18. Pili, U. and Violanda, R. 2019. Measurement of the gravitational acceleration using a simple pendulum apparatus ultrasonic sensor and Arduino. Physics Education 54: 1–5.
19. Rutten, N. , van Joolingen, W. R. and van der Veen, J. T. 2012. The learning effects of computer simulations in science education. Computers & Education 58: 136–153.
20. Sanjaya, W. S. M. , Anggraeni, D. , Denya, R. , Pandriantama, H. , Iklimah, I. and Dewi, I. P. 2018. A low cost of simple pendulum experiment apparatus based on ultrasonic sensor and Arduino microcontroller. Jurnal Ilmiah Pengabdian Kepada Masyarakat 1: 51–54.
21. Sari, U. and Kirindi, T. 2019. Using Arduino in physics teaching: Arduino-based physics experiment to studytemperature dependence of electrical resistance. Journal of Computer and Education Research 7: 698–710.
22. Sari, U. , Pektaş, H. M. , Çelik, H. and Kirindi, T. 2019. The effects of virtual and computer based real laboratory applications on the attitude motivation and graphic skills of university students. International Journal of Innovation in Science and Mathematics Education 27: 1–17.
23. Schauer, F. , Cernansky, P. , Ožvoldová, M. and Lustig, F. 2009. Integrated e-learning-new strategy of the cognition of real world in teaching physics In Innovations 2009 (USA), World Innovations in Engineering Education and Research iNEER Special Volume 2009, 119–135.
24. SensorsONE. 2021. Local gravity calculator, available at: https://sensorsone.com/local-gravity-calculator/#height.
25. Simpson, D. G. 2010. The non linear pendulum, available at: http://pgccphy.net/ref/nonlin-pendulum.pdf.
26. Sinacore, J. and Takai, H. 2010. Measuring g using a magnetic pendulum and telephone pickup. The Physics Teacher 48: 448–449.
27. Tong-on, A. , Saphet, P. and Thepnurat, M. 2017. Simple harmonics motion experiment based on LabVIEW interface for Arduino. Journal of Physics: Conference Series 901: 1–6.
28. Trumper, R. and Gelbman, M. 2000. Investigating electromagnetic induction through a minicomputer-based laboratory. Physics Education, 35: 90–95.
29. Tunyagi, A. , Kandrai, K. , Fülop, Z. , Kapusi, Z. and Simon, A. 2018. Friction coefficient determination by electrical resistance measurements. Physics Education 53: 1–9.
30. Wieman, C. and Perkins, K. 2005. Transforming physics education. Physics Today 58: 26–41.
31. Yulkifli, Y. , Afandi, Z. and Yohandri, Y. 2018. Development of gravity acceleration measurement using simple harmonic motion pendulum method based on digital technology and photogate sensor. Materials Science and Engineering 335: 1–8.
32. Zacharia, Z. and Anderson, O. R. 2003. The effects of an interactive computer-based simulation prior to performing a laboratory inquiry-based experiment on students’ conceptual understanding of physics. American Journal of Physics 71: 618–629. | 2022-05-29 03:20:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 7, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5260486602783203, "perplexity": 4993.595485802307}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652663035797.93/warc/CC-MAIN-20220529011010-20220529041010-00409.warc.gz"} |
http://math.stackexchange.com/questions/98828/monotone-convergence-to-a-fixpoint-in-a-banach-space | # Monotone convergence to a fixpoint in a Banach space
Let $\mathscr X$ be a complete separable metric space and $\mathbb B$ be the Banach space of all real-valued bounded measurable functions on $\mathscr X$. The partial order on this space is introduced by $$f\leq g \text{ iff }f(x)\leq g(x)\text{ for all }x\in \mathscr X.$$ The operator $\mathscr A:\mathbb B\to\mathbb B$ is called monotone if $f\leq g$ implies $\mathscr Af\leq \mathscr Ag$, such operator is not necessary linear. Let us consider the function $f_0\in \mathbb B$ such that $\mathscr Af_0\geq f_0$ and construct the sequence $f_{n+1} = \mathscr A f_n$. Clearly, for any fixed $x\in \mathscr X$ the limit $\lim\limits_{n}f_n(x)$ exists (though it may be infinite) and the convergence is monotone.
Let us assume that for any $x\in\mathscr X$ the limit is finite and denote it by $f(x)$. Is it true that $$f = \mathscr Af\quad?$$
-
Is $\mathcal{A}$ assumed to be linear? – William Jan 13 '12 at 18:04
@WNY no, $\mathscr A$ only assumed to be monotone – Ilya Jan 13 '12 at 18:10
Maybe I misunderstand the problem, but what about $X=\mathbb R_+$, $Af(x)=\sup_{0\leq t\leq x}f(t)$. $A$ is monotone, $Af\geq f$ for all $f$ and $A^2f=Af$ so $f_n=A^nf=Af$ is converging, but we don't need to have $Af=f$. – Davide Giraudo Jan 13 '12 at 18:36
@Davide: You’ve misunderstood: Ilya’s asking whether the limit function has to be a fixed point. In your example the limit is $Af$, and indeed it’s true that $Af=A(Af)$. – Brian M. Scott Jan 13 '12 at 18:54
@BrianM.Scott You are right. Failed attempt... – Davide Giraudo Jan 13 '12 at 18:56
## 1 Answer
Let the metric space have one point, and identify $\mathbb B$ with $\mathbb R$. Let $\mathscr A(x)=\sqrt[3]{x}$ if $x<1$, $\mathscr A(x)=2$ if $x\geq 1$. Let $f_0=\frac{1}{2}$. Then $\mathscr Af_0\geq f_0$, and $\lim\limits_{n\to\infty}\mathscr A^nf_0=1=f$, but $\mathscr Af=2$.
In general $\mathscr A f\geq f$ is true, but this example shows that the equality need not hold.
-
Perfect answer! Thank you very much, Jonas. By the way, to make the operator monotone on the whole $\mathbb R$ I guess we should add something like $\mathscr A(x) = -1$ for $x< 0$. – Ilya Jan 14 '12 at 11:47
@Ilya: It already is monotone on $\mathbb R$. That's why I used $\sqrt[3]{x}$ instead of $\sqrt x$. – Jonas Meyer Jan 14 '12 at 17:45
isn't it that $\sqrt[3]{-1/3}<-1/3$? – Ilya Jan 15 '12 at 18:04
@Ilya: Increasing means $x\leq y\implies Ax\leq Ay$, not $\forall x,Ax\geq x$. It is true that $x\leq y\Longleftrightarrow x^3\leq y^3$. – Jonas Meyer Jan 15 '12 at 18:12
Oh, I mixed it up again. You're right, sorry – Ilya Jan 15 '12 at 18:57 | 2015-12-02 04:14:12 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.98121178150177, "perplexity": 173.04104093241003}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-48/segments/1448398538144.64/warc/CC-MAIN-20151124205538-00003-ip-10-71-132-137.ec2.internal.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/jimo.2012.8.41 | # American Institute of Mathematical Sciences
January 2012, 8(1): 41-49. doi: 10.3934/jimo.2012.8.41
## A note on the subtree ordered median problem in networks based on nestedness property
1 Faculty of Management and Administration, Macau University of Science and Technology, Avenida Wai Long, Taipa, Macau SAR, China 2 Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong, China 3 Department of Logistics and Maritime Studies, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong SAR, China
Received January 2011 Revised May 2011 Published November 2011
The nestedness property has become an increasingly important means for devising efficient algorithms for network location problems. In this paper we prove that the nestedness property holds for the tactical continuous, and strategic discrete and continuous subtree location problems in a tree network with the ordered median objective, where the $\lambda$-weights take at most two different values. These results extend some existing results in the literature. With these nestedness results, we solve the problems in polynomial time. Finally we pose an open problem on identifying the nestedness property for the $(k_1,k_2)$-trimmed problem.
Citation: Huajun Tang, T. C. Edwin Cheng, Chi To Ng. A note on the subtree ordered median problem in networks based on nestedness property. Journal of Industrial & Management Optimization, 2012, 8 (1) : 41-49. doi: 10.3934/jimo.2012.8.41
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2018 Impact Factor: 1.025 | 2019-12-14 14:00:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6766205430030823, "perplexity": 11228.680904413595}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541157498.50/warc/CC-MAIN-20191214122253-20191214150253-00196.warc.gz"} |
https://raspberrypi.meta.stackexchange.com/questions/641/should-we-have-mathjax | # Should we have MathJax? [closed]
We share some ground with Electrical Engineering - according to our on-topic rules - whenever it gets specific to the Pi. As such there are posts out there that could benefit from a readable typesetting of mathematical formulas.
Therefore the question is: Should we have MathJax enabled on our site?
A discussion should cover the relevance of a typeset mathematical notation for our site in terms of user experience and the question of effort vs. need (e.g. this old discussion hints that it is heavy).
MathJax of course requires additional formatting by the user. So it is definitely safe to assume that newcomers would need to be helped at this. However, the main use case would not be questions but comprehensive answers. I'd expect that our dedicated personnel giving such answers will pick up the notation in due time (see basic tutorial and quick reference to get a feeling).
Some examples:
## closed as primarily opinion-based by Ghanima♦Jan 17 '16 at 22:48
Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.
• How would MathJax work does it require extra formatting by the user? Can you proviide some examples where this would help. how would this interact with source code (which should (I assume not have this applied to it)? – Steve Robillard Dec 11 '15 at 14:31
• @SteveRobillard, find your comment addressed in edit and "answer" to illustrate the issue. – Ghanima Dec 11 '15 at 15:44
• I am not trying to be a jerk, but can you provide some example questions/answers from this site. Ideally with and without MathJax (I realize this may not be possible without having it enabled for the site). – Steve Robillard Dec 11 '15 at 15:54
• There you go. Looks cool, does it not? ("This is the mathematical notation you're looking for." "He can go about his business." "Move along.") – Ghanima Dec 11 '15 at 16:13
• I have one more question, if we enable this and it has negative effects (performance etc.) can we revert back without problems. – Steve Robillard Dec 11 '15 at 16:16
• Well. Text bodies will have things like $$something-something$$ in the clear, if reverting back. Nothing that could not be edited out of course. Can we query the data base for a string like "" to fix it? – Ghanima Dec 11 '15 at 16:23
• Adding answers so ppl can vote if needed :) I think the circuit schematic thing would be much more helpful though... – Wilf Dec 14 '15 at 1:08
• @Ghanima There's data SE for querying stuff data.stackexchange.com/raspberrypi/revision/415506/530422/… (involves SQL'ing) – Wilf Dec 24 '15 at 20:45
This does not seem to have wide community support, and the community has questioned the potential value this feature would add. As a result we will not be implementing this feature.
How would this interact with source code (which should (I assume not have this applied to it))?
Tested that on EE, seems to not collide with code. Before introduction of the feature this would have to be checked in detail of course.
• They have code blocks also on EE, they probably would notice... – Wilf Dec 14 '15 at 1:10
• @Wilf, so it would seem. – Ghanima Dec 14 '15 at 8:25
NO, this site is for the Raspberry Pi, not maths :)
• I agree. Schematics would be much more useful. I see some users use paint just to illustrate what they're doing. – Gene Dec 19 '15 at 6:41
• The Mathjax would only work in Questions and Answers - NOT in comments like this? I am not convinced that working just with HTML and Unicode would be any harder, and that is just as usable - if I have time I am quite happy to refer to an <b>I<sup>2</sup>C bus</b> or point out that V<sub>cc</sub> is <i>4.75.0±0.25 Volts</i> - it is just it doesn't actually work here. – SlySven Dec 24 '15 at 1:35
• You also have to allow java-script from mathjax.org to operate which is yet another site to enable if you use NoScript and allow cross-site requests to the same site if you use RedirectPolicy in Mozilla browsers! – SlySven Dec 24 '15 at 2:08
• @PandaLion98, I think both techniques have their merrit, and I don't think we have to pick one over the other. We can decide whether we need any or both of them. We'll get to the matter after christmas. – Ghanima Dec 25 '15 at 12:55
• @SlySven, heavy tagging does not work in the comments either way. But I think that both HTML tags and possibly mathjax are the most helpful in questions and answers only. Not having either in the comments section is only a very minor drawback. – Ghanima Dec 25 '15 at 12:57
In 45 years working as an Electrical Engineer I have rarely needed mathematical symbols. (I did once write a specification which used matrix algebra to explain the operation — this used Micro\$oft equation editor.)
The rest of the time I used standard mathematical notation (as used in FORTRAN), which most engineers can read.
I often use Unicode symbols e.g. Ω μ λ ² ± to make posts more readable but these need no special tools.
The vast bulk of users on raspberrypi.stackexchange seem to have problems with current and voltage. They don't need fancy mathematical notation.
YES, it's brilliant and would be useful here | 2019-05-25 00:26:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.40906664729118347, "perplexity": 1381.296327979609}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257781.73/warc/CC-MAIN-20190524224619-20190525010619-00374.warc.gz"} |
https://docs.scipy.org/doc/scipy/reference/generated/scipy.interpolate.RectBivariateSpline.__call__.html | # scipy.interpolate.RectBivariateSpline.__call__¶
RectBivariateSpline.__call__(self, x, y, dx=0, dy=0, grid=True)[source]
Evaluate the spline or its derivatives at given positions.
Parameters
x, yarray_like
Input coordinates.
If grid is False, evaluate the spline at points (x[i], y[i]), i=0, ..., len(x)-1. Standard Numpy broadcasting is obeyed.
If grid is True: evaluate spline at the grid points defined by the coordinate arrays x, y. The arrays must be sorted to increasing order.
Note that the axis ordering is inverted relative to the output of meshgrid.
dxint
Order of x-derivative
New in version 0.14.0.
dyint
Order of y-derivative
New in version 0.14.0.
gridbool
Whether to evaluate the results on a grid spanned by the input arrays, or at points specified by the input arrays.
New in version 0.14.0.
#### Previous topic
scipy.interpolate.RectBivariateSpline
#### Next topic
scipy.interpolate.RectBivariateSpline.ev | 2020-03-30 14:28:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.41049638390541077, "perplexity": 6677.472185452372}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-16/segments/1585370497042.33/warc/CC-MAIN-20200330120036-20200330150036-00344.warc.gz"} |
https://www.vedantu.com/question-answer/if-two-different-numbers-are-taken-from-the-set-class-12-maths-cbse-5fd741fa147a833c29ece1a4 | Question
If two different numbers are taken from the set $\left\{ {0,1,2,3,....,10} \right\}$; then the probability that their sum as well as absolute difference are both multiple of 4, isA.$\dfrac{{12}}{{55}}$B.$\dfrac{{14}}{{45}}$C.$\dfrac{7}{{55}}$D.$\dfrac{6}{{55}}$
Verified
94.5k+ views
Hint: Here, we are required to find the probability that if two different numbers are taken from the given set, then their sum as well as absolute difference are both multiple of 4. We will find the number of favorable outcomes which are possible i.e. the pair of numbers which satisfy the given conditions. Adding all such cases of the two possible numbers, we will get our favorable outcomes. The given set consists of 11 elements and we have to select 2 elements from this. Hence, we will use combinations to find the total possible outcomes. Dividing the favorable outcomes by the total outcomes, we will get the required probability.
Formula Used:
${}^n{C_r} = \dfrac{{n!}}{{r!\left( {n - r} \right)!}}$, where, $n$ represents the total number of terms and $r$represents the number of terms to be selected.
Probability of an event $=$ Number of favourable outcomes $\div$ Total number of outcomes.
We will solve this question by taking various cases from the given set.
According to the first case, let us take the number 0.
Now, let the second number to be chosen be $x$
According to the question, we have to choose the second number such that the sum as well as the absolute difference of the two numbers are both multiple of 4.
This means that $x + 0$ and $x - 0$, both are multiple of 4.
From the given set $\left\{ {0,1,2,3,....,10} \right\}$, the above situation is only possible when the value of $x$ is either 4 or 8
According to the second case, let us take the number 1.
Now, we have to think of the numbers from the given set $\left\{ {0,1,2,3,....,10} \right\}$ with which by adding and subtracting 1 we can get a number divisible by 4.
We will find that no such number exists. Also, this is true for all the odd numbers. Hence, no odd number from the given set paired with any other number will give us a number divisible by 4.
Therefore, we will check only for the even numbers present in the set.
Hence, we will make a table for the possible pairs:
First Number Second Number Total number of possible cases 0 4 or 8 2 2 6 or 10 2 4 0 or 8(But the case of 0 and 4 is already taken) 1 6 2 or 10 (Here, the case of 2 and 6 is already taken) 1 8 0 or 4 (Here, both the cases are already taken) 0 10 2 or 6 (Again, both the cases are already taken) 0
Hence, total number of possible cases $= 2 + 2 + 1 + 1 = 6$
Hence, total number of favourable outcomes are 6……………………………… $\left( 1 \right)$
Now, the total number of ways of choosing 2 numbers from the given set $\left\{ {0,1,2,3,....,10} \right\}$ where total elements are 11 are: ${}^{11}{C_2} = \dfrac{{11!}}{{2!\left( {11 - 2} \right)!}}$
This is because ${}^n{C_r} = \dfrac{{n!}}{{r!\left( {n - r} \right)!}}$, here, $n$ represents the total number of terms and $r$ represents the number of terms to be selected.
Hence, ${}^{11}{C_2} = \dfrac{{11!}}{{2!\left( {11 - 2} \right)!}} = \dfrac{{11!}}{{2! \times 9!}} = \dfrac{{11 \times 10}}{2} = 11 \times 5 = 55$
Hence, total number of possible outcomes are 55……………………………….. $\left( 2 \right)$
Now, Probability of an event is defined as the number of favourable outcomes divided by the total number of possible outcomes.
Hence, If two different numbers are taken from the set $\left\{ {0,1,2,3,....,10} \right\}$; then the probability that their sum as well as absolute difference are both multiple of 4 $= \dfrac{6}{{55}}$ (from $\left( 1 \right)$and $\left( 2 \right)$)
Therefore, option D is the correct answer.
Note: In mathematics, Probability is used to find how likely an event is to occur. The probability always lies between 0 and 1. Where, if the probability of an event is 0, then this means that it is an impossible event. For example, the probability of getting number 7 while tossing a coin is 0 because a coin will always give a head or a tail and not a number. Similarly, if the probability of an event is 1, then it shows the certainty of a specific event. For example, if there are only blue balls in a bag and hence, the probability of getting blue balls is always 1 because we will get only those balls from the bag as no other colour is present. | 2021-10-27 04:54:05 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8586507439613342, "perplexity": 123.51185443438874}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588053.38/warc/CC-MAIN-20211027022823-20211027052823-00216.warc.gz"} |
https://www.physicsforums.com/threads/the-vacuum-in-qft-what-is-it-why-have-it-does-everyone-believe-in-it.130683/ | The vacuum in QFT. What is it. Why have it. Does everyone believe in it?
1. Sep 3, 2006
CarlB
Any good references on the meaning of the vacuum in QM? What were you taught in school? What made sense? What did not? What did you discuss with the other graduate students? Any paradoxes regarding the vacuum? Any thoughts on why string theory is inundated with them?
Bring em on. I want to hear.
Carl
2. Sep 3, 2006
David Burke
Do you mean Maxwells EM wave length being of any size and therefore allowing for infinite energy zero point gravitational curvature which doesn't actually appear to happen in experiments, so we use Fermion/ Bosson equivalence to cancell the infinity values? I've known this to be called vacume energy.
3. Sep 3, 2006
Maaneli
This is actually a controversial issue in QM and QFT. I'll try to respond with detail later.
4. Sep 3, 2006
CarlB
I think that's on topic, but what I was really getting at is that odd thing that you hit with a creation operator in QFT.
Carl
5. Sep 4, 2006
Epicurus
In a quantum field theory, the vacuum state is the state with the most symmetry. The number of vacua is related to the symmetry group of the underlying lagrangian
6. Sep 5, 2006
Mike2
If we can only measure changes in the vacuum state and not the absolute value of the vacuum energy, then we cannot distinguish the false vacuum of inflation, responsible for mass, from the true vacuum of today. The vacuum may have just fallen to a lower vacuum energy, and it may fall to an even lower energy state in the future.
If the vacuum does have a physical consequential energy density, then wouldn't this have an equivalent mass density that would be attracted to gravitational fields (if it is not itself the gravitational field). Wouldn't this not tend to accummulate extra energy density around large gravitating bodies and act like dark matter?
If the vacuum does have an energy density, then wouldn't this behave in waves and have a momentum? I have to wonder, if the expansion of space is carried by momentum beyond that forced by the vacuum energy, then at some point wouldn't that expansion put a force on the vacuum energy to fall to a new level? And isn't this what happened during inflation? If so, then could this new round of acceleration cause the vacuum energy to fall to a new low?
Are there any more complete papers on all the various means of measuring the differences in the vacuum state?
Last edited: Sep 5, 2006
7. Sep 6, 2006
Mike2
Or again, why can it not be true that the calculated value of the cosmological constant and the globally measured value both be correct? Maybe I'm missing something here. Could it not be that there is an actual difference between the measured vacuum energy here on earth inside the deep gravity well of our large galaxy and the overall measured value which is weighted by the vast majority of empty intergalatic space? If the vacuum energy is indeed influenced by gravity, then shouldn't we expect a difference between empty space and the heart of galaxies? Or is it that if the vacuum energy were to change then other observation would also change which we could theoretically observer. But isn't it by definition that we cannot measure anything in vast regions of intergalatic space because there is nothing there to measure? Or would very small galaxies have observable contradiction if their vacuum energy were different than ours? Thanks.
8. Sep 7, 2006
Haelfix
Vacuum energy most definitely 'gravitates', indeed for any other QFT other than gravity, a simple field redefinition would suffice to make it vanish as there is usually no canonical choice of zero. Not so in gravity, which is why it is indeed important and why it has such profound implications for spacetime evolution.
9. Sep 7, 2006
Mike2
Obviously QFT is background dependent since it assume a metric of a spacetime to begin with. And particles take on new meaning in curved spacetimes. Doesn't this all mean that the vacuum energy also changes with the curvature of spacetime? I wonder how many orders of magnitude difference there is between the vacuum energy of intergalatic space and here on earth?
10. Sep 8, 2006
Chronos
Reminds me of the ultraviolet catastrophe in classical physics. Obviously the QFT prediction of ZPE conflicts with the GR model. I'm fairly confident QFT is the tortfeasor in this case.
11. Sep 8, 2006
CarlB
Okay, now I know what a "tortfeasor" is.
Almost all physicists seem to be divided into three groups. The first group thinks that QFT is wrong. The second group thinks that GR is wrong. The third group thinks that neither GR nor QFT is wrong. The set of measure zero thinks that both GR and QFT are wrong.
Lee Smolin's latest book lists various physicists, both amateur and professional, that believe either GR/SR or QM is wrong. But he didn't list any who think that both are defective. Get's lonesome out here on the fringe. I think that SR needs to be modified in order to make QM more natural, and that the secret to doing this is to make time more complicated. Eventually that gets around to the vacuum, but it's sort of off topic.
What I had in mind when starting this thread was Julian Schwinger's "fictitious vacuum" that he brings into an elegant foundation for QM in his book "Quantum Kinematics and Dynamics".
Carl
12. Sep 9, 2006
Careful
Perhaps one could redefine the fourth class as those people who think both GR and QFT could be approximations (of some kind) to a deeper theory in the low energy regime. QFT is incomplete (unless you believe in MWI), contains divergences (which indicate a lack of understanding), and basically we don't have a Hilbert space formulation of them. So, I guess it is better to ask first why QFT should be right. GR has other problems ... it occurs to me that those who desperately stick to one or the other (although GR is the better choice in that respect) merely do this for reasons which have little to do with scientific consistency and logic.
Careful
13. Sep 9, 2006
Staff Emeritus
There are those who want to preserve the "essential points" of QM and GR, the quantum principle and background independence respectfully, and combine themsome way. This is more than just the "effective theory" philosophy; it asssumes that each of QM and GR has seen some deep truth.
14. Sep 9, 2006
ZapperZ
Staff Emeritus
At what point do we bring in experimental verifications/consistency? For some odd reason, other than what Chronos has mentioned, this aspect seems to have been complete ignored. Does the fact that QFT methodology agrees with experimental measurement is completely meaningless?
Or what about its use in condensed matter physics where the QFT vacuum state is the ground state of a fermionic system at 0 K? A ton of phenomena, ranging from your popular conductors to magnetism, start off from such a scenario.
I can understand people having "philosophical" issues with QFT. However, to dismiss it as being "incorrect" dispite the wealth of agreement it has produced to various reproducible phenomena in condensed matter physics is simply astounding. I'd suggest those people derive the Kondo effect first, for example, using other alternative methodology. If they can do that, then they're welcome to give me a call.
Zz.
15. Sep 9, 2006
turbo
If you will audit any of Penrose's recent talks (streaming video - just google his name), you will see that he belongs in your "measure zero" set. I happen to agree with him, but I think that GR is going to take a much bigger "hit" than QFT.
Last edited: Sep 9, 2006
16. Sep 9, 2006
Staff Emeritus
The latest buzz is over Connes' spectral geometry with neutrino physics. It does not, as Urs Schreiber emphasises, do the detailed numbers of the standard model, but it is pretty good at doing its general features. And someone noted that many of the features that it is customary for quantum physicists to attribute to quantization are in this model explained by geometry.
This might be seen as the latest event in the long range program of Einstein and Schroedinger, to geometrize all of physics, not just gravity.
17. Sep 9, 2006
CarlB
Of course it's not at all meaningless. It gives a very broad hint as to what the approximate (i.e. < 20 digits accuracy), extremely low energy (i.e. much smaller than Planck mass) small particle number (i.e. far smaller than number of particles in universe) limited spatial extent (i.e. very small compared to observable universe), short time scale (i.e. very short compared to age of universe) behavior of the underlying theory should be. That's not nothing.
Funny thing. In condensed matter, QFT is only an "effective theory". The underlying theory is plain old QM. The implication is that the QFT of the standard model might very well be an effective theory of some deeper theory.
I don't think that they're saying that QFT is "incorrect" when used in condensed matter. You might try Smolin's recent book, "The Trouble With Physics", which discusses the matter better than I could:
Carl
18. Sep 9, 2006
ZapperZ
Staff Emeritus
As compared to what? The way you're describing it is as IF it was Newton's Laws and that we have already a better way to describe it. Again, I ask for the alternative. There is none that have come close.
All you have to counter QFT is speculation. In my book, THAT is what's nothing. We may (or may not) be able to accurately describe experimental observation in a very "limited" sense of our universe, but this is certainly better than making guesswork of a theoretical formulation that doesn't even exist yet. Or do you usually use such a thing everyday?
Please define "effective theory". In my book, if "it works", that is a very damn good thing, more than what most philosophical ideology can claim. Again, talk is cheap. Come up with something that can match QFT's astounding successes in condensed matter, then I'll pay attention. I gave one concrete example already of the Kondo effect.
And I truly don't understand the statement that the "underlying theory is plain old QM".
If QFT is not "incorrect" when used in CM, then why is it being accused of being wrong in your message #11? Or do you think something can be correct in condensed matter but not in others? Need I remind you how many theories came out of condensed matter that have permeated all over the rest of physics?
In addition, it seems that people somehow cannot separate an objection based on TASTES, versus a valid objection based on empiricial evidence. Last time I checked, we are still doing physics, aren't we?
Zz.
Last edited: Sep 9, 2006
19. Sep 9, 2006
CarlB
If a better alternative were available we wouldn't be having this discussion. Instead, you'd be defending THAT theory as having no alternative.
I don't mean to "counter" QFT. I think that QFT is THE path to the next theory, far more important than GR. But there are some features of QFT that I think need to be changed, which is why I started this thread.
If you haven't come across this term in your QFT textbooks, then look in the index. If you don't have any textbooks, look it up in wikipedia.
The foundation of the quantum theory of crystals begins with a multiparticle Schroedinger equation [edit: with spin of course]. It is multiparticle because crystals have lots of particles. The Schroedinger equation is sufficient because the particles are not relativistic. The resulting equations are difficult to solve.
The physics principles underlying the QFT theory of solids is identical to the physics principles for the QM theory of solids. They're the same theory, the only advantage of QFT is the ease of calculation. But if you go to high enough energies, the QFT model of solids breaks down and you are left with, yes you guessed it, the QM model (maybe relativistic).
These are subjects that should be covered in any elementary introduction to solid state theory. I guess it's possible to learn the practice without understanding the physical principles behind it, but that doesn't seem to me to be much of an education in physics. More like an engineering class.
The context is in looking at the foundations of physics, not "squalid mechanics" in particular. For example, Newton's equations are sufficient in their context.
I'm not stupid. Of course I think something can be correct in condensed matter theory and not in general. So does Smolin and a bunch of other physicists. Heck, condensed matter theory generally doesn't include gravitation. And the last time I looked, condensed matter didn't have much use for neutrinos.
You don't need to remind me. My whole point was that QFT came from solid state. Solid state physics suffers from the interesting assumption of a solid media [edit: or more generally, some sort of matter that is "condensed"]. That defines a preferred reference frame [edit: i.e. the center of mass of the "condensed" matter]. It's not at all obvious that this should be a good sandbox to test real unified theories out in, especially when they are based on an assumption of special relativity.
I agree with this, at least in a reciprocal manner. One of the points that Smolin makes over and over is that the way the standard model is put together is largely due to the taste of physicists. Here, let me quote him:
Carl
Last edited: Sep 10, 2006
20. Sep 10, 2006
Chronos
I agree with Zapper on this issue. QFT works fantastically well at the quantum level. And GR is equally impressive macroscopically. They were made for each other, but, refuse to date. I suspect there is a hidden realm that completes the trinity. I'm even willing to allow for the existence of one lousy extra dimension - so long as it is not spatial.
21. Sep 10, 2006
Careful
There is no more effective theory philosophy'' present in what I said than the stuff you are alluding to. First of all, I don't know what the quantum principle is : is it the one of Bohm, de Broglie, Bohr, Barut, 't Hooft, Everett, Dirac, Adler, Penrose, Feynman .. ??? Second, as far as I remember, background independance also is a fishy concept. Both theories will take a blow: (a) quantum mechanics needs to be undressed from it's operational formulation, meaning that you need a decent *local* theory of single events (b) GR will have to be build up from the vacuum.
Careful
Last edited: Sep 10, 2006
22. Sep 10, 2006
ZapperZ
Staff Emeritus
Then I don't get the point of your thread. You are hoping that we do a bunch of speculative arguments on what COULD, MIGHT, be the next better mouse trap? Do you not see, after all the years you've been on here, how futile such a thing is? Besides, how do you know which one is more 'valid' than another, or even if you're on the right path considering that experimental evidence, at least in this thread, is considered as almost non-existent.
Sorry, but when I see the words "wrong" and "incorrect", those do not indicate to me that one believes that it is still the right "path" on the way to a more complete theory. Again, I don't see how you can accomplish your mission in "changing" QFT when (i) you are basing it on speculation and (ii) you sweep away experimental evidence.
I have, but NOT in the degoratory form that you have implied. That is why I asked YOU for what you meant as an "effective theory".
"Theory of crystals"? Hum... what a strange concept to use for "condensed matter physics", considering that it includes (i) BE and Fermionic condensation of gasses (ii) glassy phases (what is the "crystal" there?), and (iii) granular/soft condensed matter.
And what you have described above regarding "multiparticle" is a rather strange explanation. You DO NOT go from the many-body Schrodinger Equation and then arrive at the QFT description of the system. You START, as the First Principle, the QFT ground state. However, to say that just because you can also write the system as a Schrodinger equation that you can't solve, does NOT mean that it is the "underlying" theory. That's like saying that Newton's Laws are the "underlying" theory of Lagrangian mechanics just because I can also write down all the force equations of a system but I can't solve it because it's too difficult. There is nothing in your argument here that proves that one is more "fundamental" than the other. I claim that they're equivalent.
"The physics principles underlying the QFT theory of solids is identical to the physics principles for the QM theory of solids. They're the same theory, the only advantage of QFT is the ease of calculation. But if you go to high enough energies, the QFT model of solids breaks down and you are left with, yes you guessed it, the QM model (maybe relativistic)."
Please show me an example where the QFT model in CM breaks down at "high enough energies".
OK, now you're trying very hard to be insulting. I suggest you drop that Gell-Mann's ignorant word unless you want this to deteorate into gutter discussion, or before I point out to you all the "squalid" stuff that you have taken for granted, and I don't mean just squalid electronics. Furthermore, just because I ASKED you to state something clearly and disagree with how you "interpret" my field of study to be doesn't mean I didn't get "much of an education in physics". Again, if you wish to play dirty, that is what you'll get.
But you don't mind assuming that I am.
That's like saying Newton's law didn't have "neutrinos" and so it sufers from a huge shortcoming. Well HELLO? What does "application" of the most general equations have anything to do with what it can and cannot include? And since you are not stupid, I will point out something VERY simple here. Look at the single-particle propagator in its most elementary form. In the self-energy term, I could include ANY (and I repeat, ANY) bosonic interaction to that particle to broaden its self energy. In condensed matter, we just happen to use the popular interactions that are present in the system, such as phonons, magnons, polarons, etc.. etc. However, there's NOTHING there to prevent ANY kind of bosonic interaction. You want a graviton of spin 2? Hey, knock yourself out!
And I have only described the most simplest formulation. I haven't yet included fermionic exchange in more complicted systems. This is what Peter Higgs got, from of all places, the formulation of a magnetic system. The point here isn't WHAT is included in the formulation. The point here is that the formulation is system independent. If you have issues with the origin of such a formulation, I'm surprised that you don't think that QM is "wrong" because it didn't include "neutrinos" or was solved mainly for "atoms".
Aren't you putting the cart WAY before the horses first? It is obvious to me that you're trying to find a falsification of SR. Yet, you are approaching it from trying to find a "unified theory" first, rather than working on your own fundamental assumption in which SR isn't completely valid. Shouldn't you be hunting for that first? And unless I've been asleep these part few years, all the more refined tests on SR so far would indicate to me that it is you who have more "incorrect" and shaky assumptions than QFT.
Except some tastes have more valid experimental support than others.
I don't think the Standard Model will survive intact. But how this somehow gets dragged into QFT, I have no clue. Maybe it's my lack of a deep physics education.
Zz.
23. Sep 10, 2006
CarlB
No, I was looking for arguments for and against the existence of the vacuum that are deeper then "shut up and calculate". That much I already knew. Obviously you can't provide further.
If you don't want a derogatory response, don't write one yourself. Let's begin over from now, okay? You won't ask rhetorical questions about the definitions of things that everyone understands and I won't give sarcastic responses.
Yes, you are correct. I've edited my response appropriately.
I don't think I've explained my point very well here. While I have said "condensed matter" physics, what I am thinking of is "solid state" physics. It is in the context of solid state physics that the spontaneous symmetry breaking of QFT was developed. But if you add enough energy to a solid, it eventually becomes something else, and solid state no longer applies to it.
One can say that the analogy in condensed matter is where a solid changes phase, and in fact that is how the problem is approached in elementary particles. But my point is that in solid state, the symmetry breaking of the vacuum was caused by a very obvious physical source. In elementary particles, there is no such obvious source. The elementary particle analogy of the vacuum of solid state is just an analogy.
What's more, obvious calculations for the vacuum energy gives results that are "the worst calculation in physics" in that the actual energy of the vacuum is very small while the natural calculations give extremely large numbers. This is a sign that the analogy is just that, an analogy.
I believe that as far as the particles and forces of the standard model go, SR is indistinguishable from perfect. I also think that under the same limitation, QFT is indistinguishable from perfect. Of course I could be wrong about this so I'm not saying that people looking for minor deviations from SR in stuff that is well explained by the standard model are wasting their time. For that matter, I think that in its own experimental regime, GR has at least not yet been distinguished from perfect.
You seem to be saying that a theorist should never work on a new theory until evidence against the old theory has arisen and is well known. That seems to me to be a little extreme. For example, was Einstein wasting his time working on relativity when there was no evidence for a lack of conservation of mass, and no evidence for the doubled bending of starlight near the sun? Was Dirac wasting his time when he predicted the positron in the absence of experimental evidence? Were the physicists who figured out SU(3) remiss in pointing out the missing element of the decuplet? Was Maxwell too early when he predicted radio waves? Is it your position that there are no worthwhile physics papers written except in the presence of confirming evidence?
I think that the history of physics shows that if you wait until the evidence is out there, well known and agreed upon by all, you will find that you have started too late and that there are 100 papers already written on it before your own.
Carl
Last edited: Sep 10, 2006
24. Sep 10, 2006
cesiumfrog
Surely the best way to understand the problems with QFT is to learn it (ie. carefully "shut up and calculate" its most important results again for yourself).
Nobody liked the crackpot who, rather than take the time for a single semester GR unit, shows up at conferences brandishing Schwarzschild's original paper (untranslated no less) and claiming that all of GR's results can be obtained using highschool math except for the conspiracy of closed-minded physicists..
Last edited: Sep 10, 2006
25. Sep 10, 2006
CarlB
At dinner I realized that this is the crux of the issue. Fermions get masses in the standard model as vacuum expectation values coming from the Higgs. If QFT and QM are equivalent, then what does the vev correspond to in QM.
The only reference I've got that talks about a vacuum state in QM is Julian Schwinger's "Quantum Kinematics and Dynamics". Of course I've had his book for ages and was thinking about these passages before starting this thread, but I hoped to see some other connections brought up by other people. Instead the thread seems to be getting off topic with insults and comments about special relativity. So let me quote from Schwinger's book in my next post.
Carl | 2018-06-24 13:01:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7226148843765259, "perplexity": 698.9780498630655}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-26/segments/1529267866937.79/warc/CC-MAIN-20180624121927-20180624141927-00458.warc.gz"} |
http://www.pratiyogi.com/assessment/test-on-probability/727 | # Test on probability
Total Questions:25 Total Time: 45 Min
Remaining:
## Questions 1 of 25
Question:If $$P\,(A) = 0.4,\,\,P\,(B) = x,\,\,P\,(A \cup B) = 0.7$$and the events A and B are mutually exclusive, then $$x =$$
### Answers Choices:
$$\frac{3}{{10}}$$
$$\frac{1}{2}$$
$$\frac{2}{5}$$
$$\frac{1}{5}$$
## Questions 2 of 25
Question:Let A and B be two events such that $$P\,(A) = 0.3$$ and $$P\,(A \cup B) = 0.8$$. If A and B are independent events, then $$P(B) =$$
### Answers Choices:
$$\frac{5}{6}$$
$$\frac{5}{7}$$
$$\frac{3}{5}$$
$$\frac{2}{5}$$
## Questions 3 of 25
Question:One card is drawn from a pack of 52 cards. The probability that it is a queen or heart is
### Answers Choices:
$$\frac{1}{{26}}$$
$$\frac{3}{{26}}$$
$$\frac{4}{{13}}$$
$$\frac{3}{{13}}$$
## Questions 4 of 25
Question:Let A and B be two events such that $$P\overline {(A \cup B)} = \frac{1}{6},P(A \cap B) = \frac{1}{4}$$ and $$P(\bar A) = \frac{1}{4},$$ where $$\bar A$$ stands for complement of event A. Then events A and B are
### Answers Choices:
Independent but not equally likely
Mutually exclusive and independent
Equally likely and mutually exclusive
Equally likely but not independent
## Questions 5 of 25
Question:If A and B are two independent events such that $$P\,(A) = \frac{1}{2},\,\,P(B) = \frac{1}{5},$$ then
### Answers Choices:
$$P\,\left( {\frac{A}{B}} \right) = \frac{1}{2}$$
$$P\,\left( {\frac{A}{{A \cup B}}} \right) = \frac{5}{6}$$
$$P\,\left( {\frac{{A \cap B}}{{A' \cup B'}}} \right) = 0$$
All of the above
## Questions 6 of 25
Question:A bag "A" contains 2 white and 3 red balls and bag "B" contains 4 white and 5 red balls. One ball is drawn at random from a randomly chosen bag and is found to be red. The probability that it was drawn from bag "B" was
### Answers Choices:
$$\frac{5}{{14}}$$
$$\frac{5}{{16}}$$
$$\frac{5}{{18}}$$
$$\frac{{25}}{{52}}$$
## Questions 7 of 25
Question:At least number of times a fair coin must be tossed so that the probability of getting at least one head is at least 0.8, is
7
6
5
None of these
## Questions 8 of 25
Question:The value of C for which $$P\,(X = k) = C{k^2}$$ can serve as the probability function of a random variable X that takes 0, 1, 2, 3, 4 is
### Answers Choices:
$$\frac{1}{{30}}$$
$$\frac{1}{{10}}$$
$$\frac{1}{3}$$
$$\frac{1}{{15}}$$
## Questions 9 of 25
Question:In a binomial distribution the probability of getting a success is 1/4 and standard deviation is 3, then its mean is
6
8
12
10
## Questions 10 of 25
Question:A card is drawn from a pack of 52 cards. If A = card is of diamond, B = card is an ace and $$A \cap B =$$card is ace of diamond, then events A and B are
### Answers Choices:
Independent
Mutually exclusive
Dependent
Equally likely | 2018-07-19 11:29:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.47237345576286316, "perplexity": 597.9569344969553}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676590866.65/warc/CC-MAIN-20180719105750-20180719125750-00474.warc.gz"} |
http://library.kiwix.org/ell.stackexchange.com_en_all_2020-11/A/question/243680.html | ## Why is it correct to say "me busy."?
27
3
I was playing Warcraft. I clicked on my peon.
He told me: "me busy. leave me alone."
Why is it OK to say it that way instead of just "I'm busy."?
34The specific construction of "*Me X. [You Y]" probably qualifies as a trope in and of itself to represent savage/unintelligent/uneducated characters. – chrylis -cautiouslyoptimistic- – 2020-04-06T09:18:08.637
8The expression demonstrates that the menial peon is uneducated, he speaks a funny illiterate english... – aliential – 2020-04-06T12:08:09.493
1It is acceptable informal English when used as a rhetorical question. "Are you busy?" "Me, busy? Not really!" – alephzero – 2020-04-06T13:01:25.553
6It's simply "Tarzan speak" from the famous character. – Fattie – 2020-04-06T16:44:36.017
22@alephzero "Me fail English? That's unpossible!" – JimmyJames – 2020-04-06T17:57:26.393
10It's not correct. That's the point. – Len – 2020-04-07T03:07:13.773
Me worry? :-) – Peter - Reinstate Monica – 2020-04-07T07:08:51.123
2Mesa Jar Jar binks. Mesa muy muy happy to be your friend! – paddotk – 2020-04-07T15:28:59.747
@aminabzz From Star Wars :) – paddotk – 2020-04-08T07:48:52.937
89
It's wrong. This is deliberate on the part of the game designers. Peons are not known for being highly educated or well-spoken.
However, babies sometimes speak this way before they learn the difference between objective pronouns (me) and subjective pronouns (I). For that reason, incorrect constructions like "me (verb)" or "me (adjective)" are associated with "baby talk."
1There are dialects in which it is correct. – phoog – 2020-04-06T14:16:33.790
@phoog Could you name a few? – Asteroids With Wings – 2020-04-06T15:03:41.037
4@phoog I am not aware of any dialects where this is actually considered correct. Do you have any specific examples? – Foogod – 2020-04-06T15:03:48.360
4
@Foogod Jamaican Patois comes to mind.
– phoog – 2020-04-06T15:26:38.757
1
@AsteroidsWithWings see my previous comment. Wiktionary has a general comment about "various types of pidgin English." I suppose it could be argued that these are different languages, but in the case of Jamaican Patois, at least, there appears to be a continuum with standard English, and whether the line between dialect and language can be drawn on one or the other side of where "me" is acceptable as a subject is probably difficult to determine.
– phoog – 2020-04-06T15:29:19.573
1Well, Patois is not really a dialect, but I believe generally classified as its own language (as that Wikipedia article also indicates). I will grant, though, that there might be some Patois-inspired English dialects in Jamaica which could use this construction (I'm not familiar enough to know). – Foogod – 2020-04-06T15:36:19.130
@phoog Okay thanks – Asteroids With Wings – 2020-04-06T16:54:59.223
3@Foogod of course the line between something being a separate language or a dialect of the same language is not strict. All I know for sure is that I hear people from the Caribbean using "me" as a (non-compound) subject from time to time, and I can understand what they're saying, and I recognize it as being (some version of) my native language, which is US English. Perhaps I would not understand everything they say in their dialect-or-language, but then again there are also varieties of English that are indisputably not different languages where I don't understand everything. – phoog – 2020-04-06T17:36:15.117
3I don't mean to detract from the answer, which is of course essentially correct. Rather, I want to underscore that native speakers of English (including languages derived from English) may in fact say certain things that learners of English have been taught are "wrong," so learners of English, especially advanced ones, will want to differentiate between things that are so wrong as to be unintelligible, things that they may hear but probably don't want to say, and things that they might want to say differently in different contexts. – phoog – 2020-04-06T17:44:38.197
2I would call it "caveman talk", personally. The line in the game is spoken by an orc, a race considered extremely dimwitted. – BlueRaja - Danny Pflughoeft – 2020-04-06T19:12:25.387
6@phoog I don't think the game designers intended to be suggestin' dat peons speak Jamaican patois, mon. – TypeIA – 2020-04-06T21:09:49.283
15@TypeIA Of course not, that's Trolls. – barbecue – 2020-04-06T21:29:41.070
2@TypeIA indeed not, which is why I said the answer is correct. In this case, it's the stereotype of limited language ability. – phoog – 2020-04-07T13:16:56.780
1
See this TV Tropes page and others it links to Hulk Speak - "The most important characteristic of Hulk Speak is its minimalism. The format is usually, "Me, (the person speaking) (verb) (subject).""
– Michael Harvey – 2020-04-07T20:18:37.070
1@phoog Creoles and pidgins are not English. A monolingual English speaker can't speak or understand Jamaican Patios due to the vocabulary difference. – CJ Dennis – 2020-04-08T12:44:42.620
@CJDennis then I can only conclude that the language I have heard people speaking in which they used "me" as the subject was English rather than Jamaican Patois, because I understood what they were saying, and I have not had any training in nor particularly significant exposure to Jamaican Patois. – phoog – 2020-04-08T14:59:43.457
@phoog You might be able to understand one or two sentences, but if you look at translation guides, you'll see that English and Jamaican Patois are quite different. "Fi alla oo a carry belly fi mi, low mi." "My yute, why u waah loud up di thing?" – CJ Dennis – 2020-04-09T02:35:02.233
@CJDennis vocabulary isn't a great way to distinguish languages. That there are words in Jamaican Patois that I don't know doesn't convince me that it isn't English: similar examples can be had for the English used in Australia, South Africa, England, and probably Texas. Jabberwocky, for example, is English. Furthermore, and this is the main point, even if Jamaican Patois is a distinct language, it does not preclude the existence of a point on the dialect continuum between Jamaican Patois and standard Jamaican English where people use "me" as a subject but are speaking a dialect of English. – phoog – 2020-04-09T03:58:12.493
23
Imagine a man who was raised in the jungle by animals ever since he was a child. He was not taught English since animals don't speak English. He has only recently met his first human, and is currently being exposed to speaking English (or any civilised language, for that matter) Which statement would make more sense to come from him, in this context:
• "Me Tarzan, you Jane"
• "Salutations! I am called Tarzan, and I surmise your name to be Jane?"
Your question seems to assume that Tarzan should have a grammatical (and thus educational) level equivalent to that of either the reader or the person he is speaking to - but Tarzan is inherently defined as a character who is lacking any education. It makes sense for him to not have a good handle on grammar. It literally defines his character and the entire narrative - a man who is learning about civilization for the first time.
Peons, by their very nature of being a peon, lack the same grammatical skill that Tarzan does. They are defined by their lack of refinement. Their statements specifically reveal that these are not highly trained individuals.
2
I think it's safe to assume that Tarzan, a.k.a. John Clayton II, Viscount Greystoke, would know the correct usage of first and second person pronouns.
– Lee Mosher – 2020-04-06T14:05:22.653
4@LeeMosher but that's not the story told in the movie. Flater: Tarzan uttered these lines in a language lesson scene, not as a greeting, so this translation into more verbose English is probably incorrect. – phoog – 2020-04-06T14:17:54.807
18
"Me busy" is not standard English. It's an example of "caveman speak", which is a form of English used in fiction when depicting characters who are capable of speech, but who are very stupid, brutish or "primitive".
Your character in Warcraft is probably an orc or some species like that. The game has your character speaking in "caveman speak" in order to show that he is unintelligent.
I don't know of any real-world varieties of English that are similar to "caveman speak". In my experience, it's not similar to the speech of children, non-native speakers, or people with language disabilities.
2Well, I think it's quite common to see "me x" sentences on discord, not sure if gamers qualify as caveman, but it is used as cute/short/distancing form in those subcultures as well. – None – 2020-04-07T18:23:13.110
2@eckes that may be connected to /me which is a common emote command on a lot of platforms devolving into use in plain language. As for Tanner, you're correct, peons are an orc character and thus the low level of english. – Andrew – 2020-04-07T20:17:43.387 | 2021-03-07 21:28:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3692834973335266, "perplexity": 3195.9333657168345}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-10/segments/1614178378872.82/warc/CC-MAIN-20210307200746-20210307230746-00340.warc.gz"} |
https://physics.stackexchange.com/questions/242499/is-there-an-underlying-physical-reason-why-the-coriolis-force-is-similar-to-the/242971 | # Is there an underlying physical reason why the Coriolis force is similar to the magnetic component of the Lorentz force?
I couldn't help but notice that the expression for the magnetic component of the Lorentz force,
$$\mathbf F = q\,\mathbf v \times \mathbf B\,,$$
is very similar in its mathematical form to the Coriolis force,
$$\mathbf F = 2m\mathbf v \times \mathbf ω\,,$$
providing that we replace electric charge with mass, and angular velocity with the magnetic induction.
Even though I am aware of the physical differences between those two forces (Coriolis is a fictitious force, which acts on objects that are in motion relative to a rotating frame of reference, whereas the magnetic force is caused by a magnetic field), I do remember reading that magnetism is a "relativistic effect of electricity" (Feynman lectures), and wonder whether this analogy is pure coincidence or could obey to a deeper connection. Could it have something to do with Lorentz transformations?
On a more general level, could the magnetic force be viewed as "fictitious", and may this have some relation with the apparent non-existence of magnetic monopoles?
Edit:
I would like to point out that the analogy can be extended to the two other inertial forces, the centrifugal force and the Euler force, as is shown here and here.
My question could then be restated as:
Why is there an analogy between inertial and electromagnetic forces?
• – Qmechanic Mar 9 '16 at 20:23
• I apologize, I didn't notice this had been asked before. I am still curious about the last part of my question, though. – David Herrero Martí Mar 9 '16 at 20:55
• @David. I was wondering, did my answer address your questions? – Giorgio Comitini Mar 15 '16 at 14:53
• I was worried that the formalism might have hidden the intuition behind the argument I was advancing. Glad I was able to help. Feel free to ask for clarification, if needed. – Giorgio Comitini Mar 15 '16 at 16:41
• My question did not cause this kind of a response, I know why...because this is much nicer one. Great question and great answers too. Just...great. – Žarko Tomičić Mar 16 '16 at 19:49
As nobody has done this yet, let's try to give an answer to your question in the right framework, i.e. through the formalism of differential geometry (and of action principles, as far as the physics is concerned). This formalism has the advantage of allowing for the use of arbitrary coordinate systems, so that the problem of the arising of "fictitious" force terms such as the Coriolis force can be addressed in a rigorous way. Moreover, it allows to generalize the standard description of electromagnetism in such a way that magnetic monopoles indeed are permitted to exist. I will show and motivate why in my opinion there is no connection between the Coriolis force and the magnetic force, explain what it means for the magnetic force to be a relativistic effect of the electric force and show how to introduce monopole fields in the magnetic field. I'll try to make myself as clear as possible, as I understand that you are not familiar with the formalism.
First of all, the Lagrangian for a point-like, massive particle in an arbitrarily curved spacetime, subject to the electromagnetic field, can be expressed as
$$\mathscr{L}=-m\sqrt{g_{\mu\nu}\frac{dx^{\mu}}{ds}\frac{dx^{\nu}}{ds}}-e\,A_{\mu}(x^{\mu})\frac{dx^{\mu}}{ds}$$
(factors of $c$ missing). Here $g_{\mu\nu}$ is the spacetime metric, the object which encodes the spacetime curvature, $A_{\mu}$ is the covariant form of the electromagnetic four-potential, $A_{\mu}=(\phi,-\vec{A})$, $s$ is an arbitrary parameter, $m$ and $e$ the mass and charge of the particle, $x^{\mu}(s)$, with $\mu=0,1,2,3$, the trajectory of the particle in spacetime. We will be interested in flat spacetimes, i.e. Minkowski spacetime, but one needs the full generalization to extract useful results from the formalism. One finds the equations of motion for the particle by minimizing the action integral $S$, that is
$$S[x]=\int_{a}^{b}\mathscr{L}(x^{\mu}(s),\dot{x}^{\mu}(s))\ ds$$ where the dot denotes a derivation with respect to the parameter $s$. Finding a minimum for $S$ is completely equivalent to the procedure shown in Frédéric's answer: the curve which minimizes the action is the curve which solves the Euler-Lagrange equations, or equivalently the Hamilton equations (those in the cited answer). Notice that the action
$$S=\int_{a}^{b}\bigg\{-m\sqrt{g_{\mu\nu}\frac{dx^{\mu}}{ds}\frac{dx^{\nu}}{ds}}-e\,A_{\mu}\frac{dx^{\mu}}{ds}\bigg\}\ ds$$ is invariant with respect to three different kinds of transformation. The first one is a monotone, increasing change of parametrization $s\to s'$ (i.e. one with $ds'/ds>0$), as the transformation gets absorbed in the measure of integration $ds$. The second one is an arbitrary change of coordinates: every time you see two indices contracted, as the two objects involved in the contraction transform in opposite ways (this is symbolically expressed by the positioning of the indices), the overall object remains invariant under a change of coordinates. The last one is the transformation
$$A_{\mu}\to A_{\mu}+\partial_{\mu}\chi$$ where $\chi$ is an arbitrary function of the variables $x^{\mu}$, known as a gauge transformation of the electromagnetic potential. Under such a transformation, the action gains the additional term
$$\delta S=\int_{a}^{b}-e\ \partial_{\mu}\chi\ \frac{dx^{\mu}}{ds}\ ds=\int_{a}^{b}-e\ \frac{d\chi}{ds}\ ds=-e\ \bigg[\chi(b)-\chi(a)\bigg]$$ which is a constant. So the action may not actually be invariant under such a transformation, but as $S$ only gets shifted by a constant amount, its minima are preserved by the transformation. The property of $S$ being invariant under such transformations has one important consequence: the general form of the dynamical equations one gets from the minimization of $S$ is valid with respect to any parametrization of the curve of the particle, which in turn can be expressed in any coordinate system you like, and the equations are not changed by a gauge transformation. To give the equations a simpler look, I will use the parametrization in which
$$\sqrt{g_{\mu\nu}\frac{dx^{\mu}}{ds}\frac{dx^{\nu}}{ds}}=1$$
Please notice that this condition does not affect the choice of the coordinates through which you express the dynamical curve: the condition itself is unaffected by a change of coordinates. From the above action $S$ and given the former condition on $s$, it can be shown that the dynamical equations have the following form:
$$\frac{d^{2} x^{\mu}}{ds^{2}}=-\Gamma^{\mu}_{\nu\tau}\ \frac{dx^{\nu}}{ds}\frac{dx^{\tau}}{ds}+\frac{e}{m}\ F^{\mu}_{\ \nu}\ \frac{dx^{\nu}}{ds}$$
Here $$F^{\mu}_{\ \nu}=g^{\mu\sigma}(\partial_{\sigma}A_{\nu}-\partial_{\nu} A_{\sigma})$$ with $g^{\mu\sigma}$ the inverse of the matrix $g_{\mu\sigma}$, is the electromagnetic field tensor and the functions $$\Gamma^{\mu}_{\nu\tau}=\frac{1}{2}g^{\mu\sigma}\ \big[\partial_{\nu}g_{\sigma\tau}+\partial_{\tau}g_{\sigma\nu}-\partial_{\sigma}g_{\nu\tau}\big]$$ are called the "Christoffel symbols" related to the metric $g$ in the $x^{\mu}$ coordinate system. The Christoffel symbols encode two kinds of information: first of all, if the metric $g$ describes a curved spacetime, they encode the effect of curvature on the particle, i.e. they encode the gravitational field; second of all, they encode the fictitious forces due to the choice of a specific coordinate system. It can be shown that, when spacetime is not curved, there exist coordinates with respect to which every $\Gamma$ is zero. These are the (in)famous intertial frames, in which $\eta_{\mu\nu}=\text{diag}(1,-1,-1,-1)$ and the equations take the form
$$\frac{d^{2} x^{\mu}}{ds^{2}}=\frac{e}{m}\ F^{\mu}_{\ \nu}\ \frac{dx^{\nu}}{ds}$$ $$F^{i}_{\ 0}=-\vec{\nabla}\phi-\partial_{0}\vec{A}=\vec{E}$$ $$F^{i}_{\ j}=-\partial_{i}A_{j}+\partial_{j}A_{i}=\epsilon_{ijk}(\vec{B})_{k}$$ If we substitute $ds$ with $dt ds/dt$, where $t$ is the time coordinate of the inertial observer, i.e. $t=x^{0}$, we find for the $\mu=1,2,3$ equations $$\frac{d}{dt}\bigg(\frac{dt}{ds}\frac{d\vec{x}}{dt}\bigg)=\frac{e}{m}\ \left(\vec{E}+\vec{v}\times\vec{B}\right)$$ As $ds/dt$ turns out to be $\sqrt{1-v^{2}/c^{2}}$, the former is exactly the Lorentz equation for a relativistic particle. Now let's work in more general coordinates. Let's call these coordinates $y^{\mu}$, with equations of motion $$\frac{d^{2} y^{\mu}}{ds^{2}}=-\Gamma^{\mu}_{\nu\tau}\ \frac{dy^{\nu}}{ds}\frac{dy^{\tau}}{ds}+\frac{e}{m}\ F^{\mu}_{\ \nu}\ \frac{dy^{\nu}}{ds}$$ It can be shown that the general relation between the Christoffel symbols wrt the $y$ and the $x$ coordinates is
$$\Gamma^{\mu (y)}_{\nu\tau}=\frac{\partial x^{\sigma}}{\partial y^{\nu}}\frac{\partial x^{\lambda}}{\partial y^{\tau}}\Gamma^{\alpha\ (x)}_{\sigma\lambda}\frac{\partial y^{\sigma}}{\partial x^{\alpha}}+\frac{\partial y^{\mu}}{\partial x^{\alpha}}\frac{\partial^{2} x^{\alpha}}{\partial y^{\nu}\partial y^{\tau}}$$ where $\partial y/\partial x$ and its inverse are the matrices of the change of coordinates. In our specific case ($\Gamma^{\alpha\ (x)}_{\sigma\lambda}=0$), $$\Gamma^{\mu}_{\nu\tau}=\frac{\partial y^{\mu}}{\partial x^{\alpha}}\frac{\partial^{2} x^{\alpha}}{\partial y^{\nu}\partial y^{\tau}}$$ So the dynamical equations can be written as $$\frac{d^{2} y^{\mu}}{ds^{2}}=-\frac{\partial y^{\mu}}{\partial x^{\alpha}}\frac{\partial^{2} x^{\alpha}}{\partial y^{\nu}\partial y^{\tau}}\ \frac{dy^{\nu}}{ds}\frac{dy^{\tau}}{ds}+\frac{e}{m}\ F^{\mu\ (y)}_{\ \nu}\ \frac{dy^{\nu}}{ds}$$ Now let's focus on each term of the equation. $\frac{d^{2} y^{\mu}}{ds^{2}}$ plays the role of an acceleration wrt to the parameter $s$ (which does not need to be time). $\frac{e}{m}\ F^{\mu (y)}_{\ \nu}\ \frac{dy^{\nu}}{ds}$ is the ordinary electromagnetic acceleration, expressed in an arbitrary coordinate system and wrt to the parameter $s$. But what about the functions $-\frac{\partial x^{\alpha}}{\partial y^{\nu}\partial y^{\tau}}\ \frac{dy^{\nu}}{ds}\frac{dy^{\tau}}{ds}$? It is useful to notice that these functions depend on second derivatives, i.e. they do not appear if the relation between the coordinates $y$ and $x$ is linear, of the form
$$x^{\mu}=\Lambda^{\mu}_{\ \nu}y^{\nu}+a^{\mu}$$ It is easy to realize that the former is the correct relation between two inertial coordinate systems. In a special-relativistic setting, we choose $\Lambda$ to be a Lorentz transformation, in order to keep the metric $g_{\mu\nu}=\text{diag}(1,-1,-1,-1)$, and in turn the $g^{\mu\nu}$ in the definition of tensor $F^{\mu}_{\nu}$, invariant. Following a Lorentz transformation then, the equations of motion do not change, as advised by the theory of special relativity. But if we were to make different coordinate changes, the equations would indeed be different. In particular, new terms proportional to the velocities $dy^{\mu}/ds$ would arise. This is how Coriolis and fictitious forces arise: $\vec{v}\times\vec{\omega}$ is none other than the product between a velocity and a reference frame parameter $\vec{\omega}$, which you can see in the general equation given above. The other velocity disappears when you choose $s$ to be time.
Now that we have the needed machinery and conceptual rigour, let's go back to your questions. First of all, what does it mean for the magnetic force to be a relativistic effect of the electric force? The electric and magnetic fields are related by coordinate transformations through the equations
$$F_{\mu\nu}^{(y)}=\frac{\partial x^{\sigma}}{\partial y^{\mu}}\frac{\partial x^{\lambda}}{\partial y^{\nu}}\ F_{\sigma\lambda}^{(x)}$$ On the right side of the equation, the electric and magnetic fields get mixed due to the change of coordinates. Are there coordinate systems in which the field is entirely electric or magnetic? Yes (and in principle they can even be inertial frames). This is because if the electric source is static in some reference frame, then in that frame the field is entirely electric. Thus, for example, in any frame related to this frame by a space rotation or translation the field will remain totally electric (Lorentz boosts, on the other hand, mix the two). On the other hand, imagine setting the source into motion. Then the field produced by the force in that frame is both electric and magnetic, but the source itself hasn't changed a bit! This means that the splitting of the EM field between an electric component and a magnetic component is not an intrinsic property of the source, but rather an artifact of the choice of a coordinate system, relative to the state of motion of the source itself. This is seen by the very definition of the E and B fields, which are deduced from the tensor $F_{\mu\nu}$, which in turn depends on the choice of coordinates. So in this case "relativistic effect" means "relative wrt the state of motion of the source, wrt to a chosen coordinate system". (The question of magnetic fields due to spin currents, on the other hand, must be addressed in a different, quantum-mechanical, setting).
Coriolis forces are too an effect of the choice of a specific coordinate system. As seen, they arise from second derivatives of the coordinate transformation from inertial coordinates. Their "coordinate dependence" status, however, is quite different from that of the E/M splitting. First of all, they do not depend upon the state of motion of any kind of source relative to a specific coordinate system (here we don't regard spacetime itself as one). Second of all, they only appear in non-inertial frames, whereas the E/M splitting is an issue even in inertial frames. Last but not least, Coriolis forces depend upon the mass of the particle, whereas the magnetic force does not. This means that particles with different masses whose motion is described in the same coordinate system will experience different Coriolis forces, but they will experience the very same E/M splitting (the opposite happens with respect to the accelerations). So magnetic forces and Coriolis forces should not be compared to one another: they are two very different objects, and as such no deep connection can exist between them. You noticed, though, that their mathematical form is similar. The mathematical form of a dynamical equation (apart from general covariant equations such as those I wrote above, but this is not the case), though, depends very much on the choice a coordinate system, so one must be careful when comparing force terms of dynamical equations, especially when one is going from one coordinate system to another. The choice of coordinates is unphysical, in the sense that it needn't be connected to underlying physical principles, nor it affects the physics of the system. In this case, though, a comparison can be made on a solid basis and turns out to be useful to answer your question. Now, a Coriolis force term of the form $2m\vec{v}\times\vec{\omega}$ appears in coordinate systems (rotating coordinates wrt a given inertial frame) where the magnetic force can as well not be of the form $e\,\vec{v}\times \vec{B}$. Consider a non-relativistic charged particle in a uniform, constant magnetic field (description given in an inertial frame). The particle will spin around some axis parallel to the magnetic field with frequency $\omega=\frac{eB}{m}$ (factors of $c$ missing, depending on convention on the definition of the magnetic field). If you go to a frame which uniformly rotates around that axis with angular frequency $\omega=\frac{eB}{m}$, there will seem to be no magnetic field at all acting on the particle. This is because the frame is moving together with the component of the motion of the particle which changes due to the magnetic field, thus no motion induced by the magnetic field can be observed in that frame. This does not signal a deep connection between the Coriolis and the magnetic force, it only confirms that there exist specific frames in which specific forces do not appear to act on specific systems. This, of course, is valid for any kind of force, if you don't restrain yourself to simple inertial frames. In this case, magnetic fields make electrically charged particles spin, so it is obvious that the coordinate systems in which the magnetic field does not appear must be a rotating coordinate system. Let us see this for the case of interest. I'll use the same formulas as in Wikipedia's "Rotating reference frame" article (with $\vec{\omega}$ taken in the opposite direction). The acceleration for a charged particle in a uniformly rotating frame about the center of the trajectory, subject to a uniform constant magnetic field, takes the form: $$\vec{a}_{r}=-\vec{\omega}\times\vec{\omega}\times \vec{r}_{i}+2\vec{\omega}\times\vec{v}_{r}+\frac{e}{m}\ \vec{v}_{i}\times \vec{B}$$ where the subscript $r$ denotes a quantity in the rotating reference frame, while the subscript $i$ denotes the same quantity in an inertial frame. We have: $$\vec{v}_{i}=\vec{v}_{r}-\vec{\omega}\times\vec{r}_{i}$$ so that $$\frac{e}{m}\ \vec{v}_{i}\times \vec{B}=\frac{e}{m}\ \vec{v}_{r}\times \vec{B}-\frac{e}{m}\ \vec{\omega}\times\vec{r}_{i}\times \vec{B}$$ As you can see, the mathematical form of the magnetic force changes in a uniformly rotating reference frame. Moreover, as $$-\vec{\omega}\times\vec{\omega}\times \vec{r}_{i}=-\vec{\omega}(\vec{\omega}\cdot\vec{r}_{i})+\vec{r}_{i}(\vec{\omega}\cdot\vec{\omega})=\frac{e^{2}B^{2}}{m^{2}}\ \vec{r}_{i}$$ where the last identity follows from
$$\vec{\omega}=\frac{e}{m}\ \vec{B}\ ,\qquad\quad \vec{\omega}\cdot\vec{r}_{i}=0$$ and $$-\frac{e}{m}\ \vec{\omega}\times\vec{r}_{i}\times \vec{B}=-\frac{e}{m}\ \vec{r}_{i}(\vec{\omega}\cdot\vec{B})+\frac{e}{m}\ \vec{B}(\omega\cdot \vec{r}_{i})=-\frac{e^{2}B^{2}}{m^{2}}\ \vec{r}_{i}$$ we have $$\vec{a}_{r}=-2\vec{v}_{r}\times \vec{\omega}+\frac{e}{m}\ \vec{v}_{r}\times\vec{B}=-2\vec{v}_{r}\times \vec{\omega}+\vec{v}_{r}\times\vec{\omega}=-\vec{v}_{r}\times \vec{\omega}$$ Again, $$\vec{a}_{r}=-\vec{v}_{r}\times \vec{\omega}=-\vec{v}_{i}\times\vec{\omega}-\vec{\omega}\times\vec{r}_{i}\times\vec{\omega}$$ which is zero due to the fact that, having solved the equation in the inertial system, $\vec{v}_{i}=\vec{r}_{i}\times\vec{\omega}$. Hence no uniform constant magnetic field nor Coriolis forces appear in the equations expressed in the uniformly rotating reference frame. This is why the form of the magnetic force term in the inertial frame coincides with the form of the Coriolis force term in the rotating frame: one must compensate the other (together with the centrifugal force) in the transition between the two coordinate systems, given the right rotation frequency.
The same can be done for the electric force: it can be made to disappear in simple accelerating coordinate systems, as the force term has the form of a simple acceleration (in contrast with the $\vec{v}\times$ form of the magnetic force).
A magnetic force is not fictitious in the following sense. Magnetic and electric forces have very different effects on the motion of point-like charges. This statement is supported by the very form of the Lorentz equation. Thus, as previously stated, one may find a coordinate system such that the magnetic force does not appear in the equations, but one cannot remove the effect of the magnetic field on the trajectories of charged particles: the trajectories themselves do not depend on the description you give of them. The curve $x^{\mu}(s)$ is an actual collection of points in spacetime, and the location of these points does not depend on the way in which you parametrize it. The equations will change in such ways as to produce the very same effect on the dynamical trajectories, only through a different coordinate description of the dynamics. This is the statement of the coordinate-transformation invariance of the action $S$. It is the description which changes, not the physics. Thus a magnetic field will always have an influence on the system, whether you call it magnetic or (in a different description, i.e. in a different coordinate system) not. One should though keep in mind that magnetic fields arise from the perturbation of the EM field by non static (wrt to some inertial frame) electric charges, with emphasis on the electric (i.e. non-magnetic) nature of the charges. (Again, we are totally underlooking the role of spin currents on the production of magnetic fields).
As a bonus, here is the potential for a monopole magnetic field. Define a coordinate system that covers the entire $\Bbb{R}^{4}$ spacetime except for the non-positive $z$ axis and take $\vec{A}$ to be
$$\vec{A}^{N}=\left(g\ \frac{y}{r(r+z)},-g\ \frac{x}{r(r+z)},0\right)$$ Then define a coordinate system that covers $\Bbb{R}^{4}$ except for the non-negative $z$ axis and take $\vec{A}$ to be $$\vec{A}^{S}=\left(-g\ \frac{y}{r(r-z)},g\ \frac{x}{r(r-z)},0\right)$$
$g$ is the magnetic coupling constant, and the magnetic field which corresponds to $\vec{A}^{N}$ and $\vec{A}^{S}$ is the same; it equals
$$\vec{B}=\vec{\nabla}\times\vec{A}=-g\frac{\vec{r}}{r^{3}}$$ and it is a monopole field. Differential geometry teaches us that it is ok to choose local coordinate systems, i.e. coordinate systems which cover spacetime only in part. It also teaches us that, thanks to the gauge invariance of the action, we can choose potentials to be different in those local coordinate systems, as long as they are related by a gauge transformation in the overlapping regions. In this case, we have
$$\vec{A}^{N}=\vec{A}^{S}+2g\vec{\nabla} \arctan\frac{y}{x}$$
so that an overall gauge potential is well defined, and it correctly reproduces a monopole field. So no, magnetic monopoles are not forbidden, not even in a classical setting.
• (1/2) Thank you for this thoughtful response- for what's it's worth, I enjoyed reading it quite a bit! I appreciate your point about not mixing up artifacts of the coordinates with physical phenomena, but I have a doubt about this argument in this instance. If you will permit me to generalize the OP's question slightly, it is a coordinate-independent statement that if one takes an interferometer and sets it into circular motion, a phase shift results. This is the Sagnac effect. For charged particles, an analogous phase shift occurs in a uniform magnetic field: the Aharonov-Bohm effect. – Rococo Mar 16 '16 at 7:52
• (2/2) The relation between these two effects involves the same substitution of terms as in the OP’s question (see, for example, PRD 21, 2993), and I think it is reasonable to claim that both are manifestations of the same physical analogy. So one might reformulate the OP’s question as: what is the underlying reason for the resemblance between the Aharonov-Bohm and Sagnac effects? And it is not clear to me that this question is an unphysical artifact of a choice of coordinates. – Rococo Mar 16 '16 at 7:52
• Sure. I addressed this point, but I may not have given it the emphasis it deserved. I will modify that paragraph later. Now, first of all, there is a problem with wave and quantum mechanics in that the dynamical equations for wave and quantum systems (Maxwell, Schrödinger, Heisenberg, path integral kernel of the evolution operator) are quite different from those of geometric mechanics (i.e. particle mechanics). Specifically, the Aharonov-Bohm effect cannot be observed in geometric mechanics, while it is in quantum mechanics. – Giorgio Comitini Mar 16 '16 at 10:37
• I was not aware about the Sagnac effect, but the same applies in this case, as it is manifestly a wave-like phenomenon. Moreover, I don't think that comparison with wave/quantum mechanics clarifies the problem. Geometric mechanics is a self-consistent theory and thus need not be given a foundation/interpretation in terms of a wave/quantum theory (though it is possible to do so, of course, especially when one starts from an action principle). – Giorgio Comitini Mar 16 '16 at 10:42
• The reason why the Coriolis force and the magnetic force for a uniform, constant magnetic field have a similar mathematical form in two different, specific coordinate systems (the rotating frame and the inertial frame), as I wrote in the third-last paragraph, is that a uniform constant magnetic field has the effect of producing a uniform circular motion on the particles subject to it. This, of course, is a coordinate-invariant (i.e. physical) statement. One can even measure the geometrical features of the trajectory, with no reference to a specific coordinate system. – Giorgio Comitini Mar 16 '16 at 10:48
I came across this wonderful paper on arXiv.org which exactly answers what you asked for.
"Why is the magnetic force similar to a Coriolis force?" - Antoine Royer
Abstract from the paper:
In this paper, it is pointed out that the underlying reason why the magnetic force is similar to a Coriolis force is that it is caused by Thomas rotations, induced by successions of non-collinear Lorentz boosts. The magnetic force may even be viewed as a kind of Coriolis force (making perhaps more acceptable the apparent non-existence of magnetic monopoles). We also show that under a change of inertial frames, Faraday lines of force Lorentz contract as if ‘etched’ in space, while ‘Coriolis’ terms get added on.
Please read the full paper. Something I noticed was that the question you asked and the description you gave, like the lecture by Feynman, is also described in this paper.
PS:
"What led me more or less directly to the special theory of relativity was the conviction that the electromotive force acting on a body in motion in a magnetic field was nothing else but an electric field." - A. Einstein
"This magnetic force has a strange directional character […] Magnetism is in reality a relativistic effect of electricity." - R. P. Feynman
The paper describes that magnetic forces have their strange Coriolis-like character because they enact Thomas rotations, induced by successions of non-collinear boosts. So if one views magnetism as a “relativistic effect of electricity” (Feynman), as was apparently also the initial idea of Einstein, then magnetic forces are a kind of Coriolis force. More generally, any Newtonian force (i.e. depending on the positions, but not on the velocities of particles) in some inertial frame, is necessarily accompanied by a ‘Coriolis’ force in another inertial frame.
It is recommended to check the "conclusion" part of the paper.
• This does look like an interesting argument. It would be nice if you could provide more description than just reposting the abstract though. – Rococo Mar 14 '16 at 4:57
A comment about this answer: as I now think about it, this answer really gives a motivation, starting from some gauge theory assumptions, for why a uniform magnetic field should cause a moving charged particle to rotate in a circle. The answer of Giorgio, on the other hand, explains quite nicely why any force that causes circular motion (in an inertial frame) must have a form analogous to the Coriolis force (in a rotating frame).
I have wondered about this myself (and I don't regard the answer to the linked question as particularly helpful). This analogy appears strikingly in, for example, the comparison between the response of a super-fluid to rotation and of a superconductor to a uniform magnetic field, as I mentioned in a recent answer.
I don't see myself as very qualified to give a definitive answer about this, but I will put something down in the hope of encouraging discussion. I think the root of this comparison lies not in Lorentz transformations, but in the structure and meaning of gauge theory. This will require a deep dive into quantum physics, so if you haven't studied that I apologize in advance...
One way that the laws of electromagnetism can be derived is by starting with the regular expression for the Lagrangian of a charged particle, then demanding that it be invariant under a local gauge transformation. This ends up requiring that you introduce the vector potential $A_{\mu}$ and modify the kinetic energy term in the minimal coupling way: $\partial_{\mu}\rightarrow(\partial_{\mu}-\frac{ie}{\hbar c}A_{\mu})$.
One way to think about this is that $A_{\mu}$ describes how the phase of the particle's wavefunction changes as one moves from point to point. Indeed, Chen-Ning Yang, among others, has remarked that a 'gauge field' really ought to be called a 'phase field' instead. If you're not familiar with this set of ideas, relevant phrases to start looking at are 'fiber bundle,' '(gauge) covariant derivative,' 'parallel transport,' and 'connection.'
Okay, so to recap: when we look at the evolution of the wavefunction of a charged particle in a region with some EM field, taking a spinless particle for simplicity, the Hamiltonian has a term like: $(\partial^{\mu}+\frac{ie}{\hbar c}A^{\mu})(\partial_{\mu}-\frac{ie}{\hbar c}A_{\mu})\phi$ . We can view the terms with $A$ as telling us how the phase changes in space, in much the same way that a curvature tensor could tell us how to transport a vector along a curved surface. But, in practice, we invariably instead think of the phase of the wavefunction as being connected in the same way it would be in the absence of an EM field, and then add a new influence to the wavefunction (aka the electromagnetic field) to 'correct' the behavior. Therefore, I suspect (and I say suspect because I haven't quite seen anyone else say this explicitly) that this process of ignoring the non-trivial phase field, then adding in some term to reproduce the same behavior, is fundamentally in the same spirit as ignoring that you are really rotating and putting in a fictitious Coriolis force to make things work out.
For example, in a uniform magnetic field along the $\hat{z}$ direction, one may write $A$ as: $A=\frac{1}{2}(Bx\hat{y}-By\hat{x})$. Now think of $(\hat{r}\cdot\vec{A}(x,y))$ as the rate of change of the phase at (x,y) for an infinitesimal step along $\hat{r}$, which is in fact (up to some constants) exactly what it means. One can see that the phase is in a sense spiralling around in a circle, so it makes sense that when we ignore this spiralling and then try to add some force to duplicate its effect, we end up getting something that closely resembles a fictitious force for uniform circular motion.
One obvious complication is that the gauge of $A$ is not unique- for example, we can just as easily say that $A=Bx\hat{y}$. But although this no longer looks like a whorling pattern, it is still true, of course, that it has the same curl with value $\vec{B}$.
Although I know even less about this, my understanding is that Kaluza-Klein theory was an attempt to unify EM and gravity around the '30s by adding an extra tiny 5th dimension at every point in space. This tiny space would basically be a physical place for the phase (or, in other words, the U(1) symmetry) to be manifest. I therefore suspect (although I would appreciate any comments from more knowledgeable people on this subject) that in Kaluza-Klein the magnetic field really does literally correspond to the fictitious force that results from pretending that you aren't spinning around in the little 5th dimension when you actually are. Sadly, this didn't quite work out, so at least in the Standard Model one should regard all these phases of the field as a purely internal property.
I think it is fair to say that, in this picture, the difference between a fictitious and non-fictitious force becomes somewhat fuzzy, as is the case in GR. I don't see any connection with monopoles, and since this formulation takes care of both electricity and magnetism, I don't think it is getting at some deep difference between the two of the type you have in mind.
Edit: in response to the comments of ACuriousMind, I will go into some more depth.
As mentioned above, one way to think about the effect of the magnetic field (or, more generally, a non-trivial vector potential) is that it modifies the phase accumulated by a charged particle. The minimum set of observables needed to describe the effects of this field, as mentioned above, are the so-called non-integrable phase factors:
$$I(C)=e^{\frac{ie}{\hbar c} \oint_C A_{\mu} dx^{\mu}}$$
Note that these are gauge-invariant quantities. In a uniform magnetic field this expression simplifies to (setting $\hbar$,$c$, and $e$ to one):
$$I(C)=e^{i BA}$$
where $A$ is the area enclosed by the path. These phase factors contain all the information about the dynamics in the field. In particular, they imply the Lorentz force. Instead of giving a derivation, I will give a heuristic argument that will be useful later: by definition, these phase factors mean that a charged particle transported in a loop gets an extra phase of $BA$. As a result, the free particle phase of $(\vec{p}\cdot \vec{x}-\omega t)$ must be modified, and since this phase is only dependent on the spatial path taken we must modify $\vec{p}\cdot \vec{x}$. There are various equivalent choices of how to do this. For example, if the path taken is a circle with radius $r$, one may modify the momentum: $\vec{p} '=\vec{p}-xB\hat{y}$, and this will get the phase right. Of course, this is a special case of the minimal coupling expression given above. This modification of the momentum necessarily implies a velocity-dependent force of the Lorentz form, as is shown in any course covering QM in a magnetic field.
We normally think about the magnetic field (or, more precisely, the vector potential) as modifying the expression for the momentum, but one could also interpret it as modifying the $\vec{x}$ term in $\vec{p}\cdot \vec{x}$ instead. In this interpretation, the magnetic field effectively changes the path length for a given charged particle. This is an unusual perspective to take, but it is completely identical: it results in the same phase factors, which completely describe the effects of the magnetic field. In this perspective, the path length for the same circular trajectory becomes longer by $\Delta x=B \pi r^2/p$.
With all this in place, the comparison with a rotating frame is straightforward. An object traveling along a rotating disc (as in the picture) really does travel a longer path than one measures in the frame that rotates along with the disc. In particular, something that travels in a circle at radius $r$ and velocity $v$, in the same direction as the overall rotation, travels an extra distance of $\Delta x=2\pi d^2 \omega/v=2 m \omega \pi r^2/p$. As expected, this is the same expression with the substitution $B\rightarrow2m\omega$.
To summarize this argument: the phase factor formulation of electromagnetism implies that a non-zero vector potential may just as easily be interpreted as modifying the spatial structure that a given charged particle travels through as it may be interpreted as modifying the momentum in the usual prescription. Upon taking this perspective, one sees that the expression for the change in path length in this system is analogous to that of a system in uniform rotation. Therefore, if one attempts to correct for the dynamics caused by this path length change by introducing a force, the force in either case has the same form. The fact that it is called a fictitious force in one case and not the other is, in my view, somewhat arbitrary.
• Thank you for your answer! Although I unfortunately can't follow the entire explanation –I'm still an undergraduate and haven't studied those subjects yet–, I think I somehow managed to grasp some of the ideas. At least, it is helpful to have some clues on where to keep looking for further information. – David Herrero Martí Mar 10 '16 at 23:19
• I glad you liked it. I think it would be nice for this to get a more definitive answer than mine, though, so I'm going to put a bounty on the question and see what kind of competition I can attract. – Rococo Mar 11 '16 at 23:55
• I believe you are taking the "geometrical" analogy too far here. The geometrical space in which a gauge theory acts is not a physical space, the gauge choice acts purely on unphysical degrees of freedom, while a spatial rotation is manifestly a physical choice. Also, the Lorentz force involves only gauge invariant quantities, so I don't see the analogy you claim. Newton's law actually changes under non-inertial coordinate changes, but the Lorentz law does not change under the change of gauge. How do you think the Lorentz law corresponds to a fictitious force in the sense of Coriolis? – ACuriousMind Mar 12 '16 at 0:26
• Please see my edit on the original question, as it may be relevant to the discussion. – David Herrero Martí Mar 13 '16 at 13:38
• Some random remarks: 1. The phrase "non-integrable phase factor" sounds archaic to me, it's just the parallel transport operator associated to the connection that is the gauge field. 2. The modification of $x$ instead of $p$ works for a single particle, but fails to generalize to a more general gauge theory. 3. The answer seems to freely switch between quantum viewpoint ("free particle phase") and classical viewpoint ("rotating disk"). In particular, the argument for the classical Lorentz force being a fictitious force relying on the quantum notion of particle phase seems a bit strange. – ACuriousMind Mar 14 '16 at 10:34
The formal identity in the two expression is maybe just due to the fact that it is the easiest way to add a velocity dependent force in a Lagrangian. Let’s look at this more formally, in the framework of Lagrangian and Hamiltonian mechanics.
If one want a velocity-dependent force (like Coriolis of Lorentz forces) coming from a Lagrangian, the simplest way is to add a term which varies linearly on the velocity $\dot{\mathbf r}$. Such a term can always take the form ${\mathbf a}(\mathbf r)⋅\dot{\mathbf r}$. That would give the following Lagrangian for a single particle $$\mathcal L=\frac12 m\dot{\mathbf r}² - V(\mathbf r) + {\mathbf a}(\mathbf r)⋅\dot{\mathbf r}.$$
If you are not familiar with Lagrangian mechanics,
• The independence of this Lagrangian with respect to $t$ ensures energy conservation
• The first two terms correspond to the kinetic energy and the potential energy of the other forces present in this sytem
• As shown in the appendix, the last term creates a Coriolis/magnetic-like force, and ${\mathbf a}$ plays a role similar to the vector potential, and $m\mathbf Ω$ or $q \mathbf B$ is given by $∇×\mathbf a$.
Since a linear dependence in $\dot{\mathbf r}$ is the simplest, the linearity can arise for many reasons, and the common cause is that both force velocity dependent Lagrangian forces. Of course, to have a velocity dependence, one need a “non-Galilean” reference frame change (non-inertial for Coriolis, relativistic for $\mathbf B$, since magnetism is explained by electrostatic + relativity.) In the latter case, the linearity might be explained by a first order approximation in $\dot{\mathbf r}/c$.
### Appendix: Formal derivation of the Coriolis/magnetic forces from $\mathcal L$
Here, I derive the magnetic/Coriolis force expression from the Lagrangian introduced above. It is just straightforward and standard Hamiltonian mechanics, and it does not need to be read if you accept that a simple linear term added in the Hamiltonian creates the desired force.
For this $\mathcal L$, the generalised momentum $\mathbf p$ is ${\mathbf p}:=\frac{∂\mathcal L}{∂\dot{\mathbf r}}=m\dot{\mathbf r}+\mathbf a$. The Hamiltonian $\mathcal H$ is then given by \begin{align} \mathcal H &:=\dot{\mathbf r}⋅\mathbf p-\mathcal L=\frac{(\mathbf p - \mathbf a({\mathbf r}))^2}{2m} + V({\mathbf r}). \end{align}
the expression of the momentum allows us to compute its change rate $$\dot{\mathbf p}=m\ddot{\mathbf r}+\dot{\mathbf r} ⋅\frac{∂\mathbf a}{∂{\mathbf r}} =m\ddot{\mathbf r}+ \begin{bmatrix} \dot x \frac{∂a_x}{∂x}+\dot y \frac{∂a_x}{∂y}+\dot z\frac{∂a_x}{∂z}\\ \dot x \frac{∂a_y}{∂x}+\dot y \frac{∂a_y}{∂y}+\dot z\frac{∂a_y}{∂z}\\ \dot x \frac{∂a_z}{∂x}+\dot y \frac{∂a_z}{∂y}+\dot z\frac{∂a_z}{∂z} \end{bmatrix}.$$
On the other hand, Hamilton’s equations give us $$\dot{\mathbf p} = -\frac{∂\mathcal H}{∂{\mathbf r}} = -\frac{∂}{∂{\mathbf r}}\frac{(\mathbf p - \mathbf a)^2}{2m} -\frac{∂V}{∂{\mathbf r}} =\begin{bmatrix} \dot x \frac{∂a_x}{∂x}+\dot y \frac{∂a_y}{∂x}+\dot z\frac{∂a_z}{∂x}\\ \dot x \frac{∂a_x}{∂y}+\dot y \frac{∂a_y}{∂y}+\dot z\frac{∂a_z}{∂y}\\ \dot x \frac{∂a_x}{∂z}+\dot y \frac{∂a_y}{∂z}+\dot z\frac{∂a_z}{∂z} \end{bmatrix}-\frac{∂V}{∂{\mathbf r}}.$$ Puting the equations together, we obtain the following expression for the acceleration (and the forces): \begin{align}\ddot{\mathbf r} &=\begin{bmatrix} \dot x \frac{∂a_x}{∂x}+\dot y \frac{∂a_y}{∂x}+\dot z\frac{∂a_z}{∂x}\\ \dot x \frac{∂a_x}{∂y}+\dot y \frac{∂a_y}{∂y}+\dot z\frac{∂a_z}{∂y}\\ \dot x \frac{∂a_x}{∂z}+\dot y \frac{∂a_y}{∂z}+\dot z\frac{∂a_z}{∂z} \end{bmatrix}-\frac{∂V}{∂{\mathbf r}} - \begin{bmatrix} \dot x \frac{∂a_x}{∂x}+\dot y \frac{∂a_x}{∂y}+\dot z\frac{∂a_x}{∂z}\\ \dot x \frac{∂a_y}{∂x}+\dot y \frac{∂a_y}{∂y}+\dot z\frac{∂a_y}{∂z}\\ \dot x \frac{∂a_z}{∂x}+\dot y \frac{∂a_z}{∂y}+\dot z\frac{∂a_z}{∂z} \end{bmatrix}\\ &=\begin{bmatrix} \dot y (\frac{∂a_y}{∂x}-\frac{∂a_x}{∂y})+\dot z(\frac{∂a_z}{∂x}-\frac{∂a_x}{∂z})\\ \cdots\\ \cdots \end{bmatrix}-\frac{∂V}{∂{\mathbf r}}\\ &=\begin{bmatrix} \dot y (∇×\mathbf a)_z-\dot z(∇×\mathbf a)_y\\ \cdots\\ \cdots \end{bmatrix}-\frac{∂V}{∂{\mathbf r}}\\ &=\dot{\mathbf r}×(∇×\mathbf a) -\frac{∂V}{∂{\mathbf r}} \end{align} The first term is the magnetic/Coriolis force, and the second the usual potential derived forces.
• Thank you for your answer! I find this approach interesting, too. However, please see my recent edit on the original question: could the two other analogies between inertial and electromagnetic forces also be explained by this approach? – David Herrero Martí Mar 15 '16 at 21:40 | 2019-12-14 15:45:17 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 2, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8900052309036255, "perplexity": 229.0168907569717}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575541281438.51/warc/CC-MAIN-20191214150439-20191214174439-00228.warc.gz"} |
http://openstudy.com/updates/4dd96341d95c8b0b98f564c4 | ## anonymous 5 years ago Definite integral gives you the area, and area can't be negative. But while doing exercises, i cam across a lot of definite integrals, which after integrating, were giving negative answers. Why is it so?
1. amistre64
Area in a direction can be negative; maybe
2. amistre64
its either that or youve got your numbers backwards and are subtracting the smaller from the larger
3. amistre64
15 - 3 = 12 3 - 15 = -12
4. angela210793
well sometimes the area equals 0...so...that may b true...
5. anonymous
For example, when you integrate this definite integral, $\int\limits_{-1}^{-3} (x-1)^{-3} dx$ the answer is -3/32 is it so because of the negative limits?
6. anonymous
hullo?
7. amistre64
You are simply on the "other side" of normal
8. anonymous
Ummm?
9. amistre64
you can flip your bounds and it makes a (-) in front
10. amistre64
it simply means that the area that you want is to the left of x=0
11. amistre64
since you are working in a region that is "negative" to begin with, it gonne be a "negative" area
12. anonymous
Alright, thank you...
13. anonymous
Are you a teacher in some college?
14. amistre64
nope...
15. anonymous
You're a student? Whoa, man than your genius.
16. amistre64
:)
17. anonymous
then **
18. anonymous
No, really, are you a student?
19. amistre64
I am a college student yes; 35 years old tho so that might account for some wits lol
20. anonymous
of which year then?
21. anonymous
then you must be a Master's student, Well anyways thank you. Take care.
22. anonymous
Well, I'm a 12th year student, just to tell you, by the way.
23. amistre64
:) youll grow into it | 2016-10-22 23:52:58 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7201781868934631, "perplexity": 4097.329664239325}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719079.39/warc/CC-MAIN-20161020183839-00197-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://forum.zettelkasten.de/discussion/2416/determine-the-most-and-least-connected-book | # Determine the most and least connected book
I'm moving this discussion from Sascha's thread "Graph view with older Zettelkastens" so as not to spoil their fun, and we can run on off-topic.
@r1tger said over on another post:
@Will said:
Why have you settled on incoming links as the indicator for note ranking? What about considering outbound links, the number of tags, or the number of links to structure notes?
Mainly pragmatism :-). I figure that if I reference a note a lot in other notes, the information in the note being referenced is "more valuable", since I keep coming back to it. I don't do tagging, and structure notes are a later addition to my Zettelkasten, and are treated as regular notes, but with a lot of outgoing links. So those two are out too. Does either of those help you in using your Zettelkasten? I'm always looking to improve this metric.
I completely understand the need for pragmatism. I tag most notes and sometimes use a tag in a search, for example, if I want to limit my search query to #coding or #ENGL463. I'm still waiting for the logic of tagging to light a fire in my ZK, and maybe it won't. I'm keeping an open mind. We'll see. I treat my structure notes much like you do, as regular notes.
Together, tags and structure notes don't help considerably, but they are indispensable with some questions. I'm starting to get a clue that my structure notes want me to give them more attention and love.
A weighted system would capture all the values of a particular zettel. For example, 1 point for each inbound and .75 for each outbound link, maybe .5 for each tag, and .25 for each link on a structure note. What do you think of this idea?
The zsh script I use for the output below is an early attempt but is sloooow. Here we are looking at a small sample of my top nine book notes and how well or not so well they are connected.
B-Quintessential Dzogchen 201901301240 - Total Links: 113 : (In 73 - Out 40) Score 103
B-Ecodharma 202007050647 - Total Links: 80 : (In 42 - Out 38) Score 70.5
B-Meditations on Self-Discipline 201901021303 - Total Links: 78 : (In 45 - Out 33) Score 69.75
B-Rationality: From AI to Zombies 201910281639 - Total Links: 69 : (In 30 - Out 39) Score 59.25
B-Environmental And Nature Writing 202008061944 - Total Links: 62 : (In 13 - Out 49) Score 49.75
B-The Extended Mind 202203031429 - Total Links: 53 : (In 13 - Out 40) Score 43
B-The Zen Teaching of Huang-Po 201903141853 - Total Links: 52 : (In 8 - Out 44) Score 41
B-Techniques For Producing Ideas 202206251631 - Total Links: 51 : (In 26 - Out 25) Score 51.75
B-Haiku Book One 202001011457 - Total Links: 50 : (In 9 - Out 41) Score 39.75
I also use the incoming links metric to programmatically ask my Zettelkasten how to find the least number of related notes between two separate ideas, but that's getting off-topic.
This is intriguing. I'm not sure how you'd use this metric. Why would I want to know "the least number of related notes between two separate ideas?" Please tutor me.
Will Simpson
“Read Poetry, Listen to Good Music, and Get Exercise”
kestrelcreek.com
• @Will said:
Together, tags and structure notes don't help considerably, but they are indispensable with some questions. I'm starting to get a clue that my structure notes want me to give them more attention and love.
I'm still figuring out if I like structure notes. I really like linking notes to one another and being able to query that graph. I'm a bit limited in available time, so I'd rather not do manual maintenance on structure notes. Without structure notes I tend to focus on maintenance as part of adding and linking new notes, which I find more fun.
A weighted system would capture all the values of a particular zettel. For example, 1 point for each inbound and .75 for each outbound link, maybe .5 for each tag, and .25 for each link on a structure note. What do you think of this idea?
I like it, should be easy enough to implement. Excluding structure notes is important though, otherwise each lattice will always revolve around as many interconnected structure notes as the algorithm can possible find. However, such a rating is really just a very small starting point. How interesting a note is to me depends on what I'm doing with my Zettelkasten (explaining something, jog-my-memory, writing an article, preparing a presentation, etc.). That is practically impossible to express in just single number on a note. It's all imperfect, but every bit helps.
This is intriguing. I'm not sure how you'd use this metric. Why would I want to know "the least number of related notes between two separate ideas?" Please tutor me.
I talk too much :-). One of the things I really use my Zettelkasten for is preparing presentations. As part of my presentations I like include something surprising. This is where my Zettelkasten really shines. Being able to quickly see there's an indirect link between "Information Risk Management" and "Mise-en-place for Knowledge Workers" (the culinary practice) and having the least number of notes needed to get there is an awesome starting point to start exploring in/talking to my notes, without being overwhelmed by all available links. It gives me a broad outline for my presentation, with most of the ideas already available for further processing.
Also, finding the shortest path across weighted nodes is something that came standard in the graph library I'm using. So a win-win basically, since it was quick to build.
• NetworkX looks interesting. Python is my first language; I'll have to explore it to see if I can grasp what you suggest. Can you help me if I get stuck?
Yes, time is limited and time spent on building/refactoring structure notes takes away from the fun parts of zettelkasting.
• Giving neglected notes, love, and attention is always fun and rewarding. Some of my most rewarding interactions with my ZK have been refactoring old notes and finding connections with my current work. Rethinking these ideas and reminiscing brings warmth to my heart and excites my brain—a powerful spaced repetition learning opportunity.
• In the last couple of weeks, I glimpsed what I think is some of the magic of structure notes. I came to this via my rededication to refactoring notes in what I'd consider a poorly neglected condition. Giving structure notes the same love as I give individual zettel produces the same feelings. The question is, do I have the time to dedicate to this? From an opportunity cost perspective, loving on notes is where I should concentrate. It takes more time and cognitive energy to refactor a structure note properly than an atomic zettel.
• But I see the value in the exercise. A whole idea stream is looked at instead of one or two branches and put in order, mentally fitting it with current and past knowledge. Some of my structure notes are in great shape. Some are a mess. I have 75! Way too many. Some need combining, and a few have grown unwieldy.
• How to divide zettelkasting time?
• 50% input of new ideas
• 50% writing
• 50% refactoring of notes
• 50% investigating and interrogating
• 50% sharing experience with others
• 50% looking at workflow
• 50% refactoring structure notes
THERE IS NOT ENOUGH TIME AVAILABLE!
Will Simpson
“Read Poetry, Listen to Good Music, and Get Exercise”
kestrelcreek.com
• @Will said:
NetworkX looks interesting. Python is my first language; I'll have to explore it to see if I can grasp what you suggest. Can you help me if I get stuck?
Sure! Implementing NetworkX can be kinda rough. I think there's some examples to get started hidden in the documentation. The stuff that was harder to do for me were (in no particular order):
• Figuring out how to parse Markdown for links (there's another library for this!);
• Figuring out the various data structures returned by NetworkX. These can be poorly documented, requiring the help of a debugger or lots of pprint() statements;
• How to render my Markdown notes to HTML, so I can generate an entire web browser version of my Zettelkasten that only requires a browser and a place on the web to put the HTML files.
Not all of these may be interesting to you, but to get you started: my implementation is on Github. I don't think your Zettelkasten Markdown files are parseable by my script though, but having an example implementation that's a bit bigger than the NetworkX examples might be useful.
• How to divide zettelkasting time?
THERE IS NOT ENOUGH TIME AVAILABLE!
I completely agree. Only do what's fun :-). | 2022-12-10 08:37:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4195767939090729, "perplexity": 2018.3710412861922}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710421.14/warc/CC-MAIN-20221210074242-20221210104242-00539.warc.gz"} |
https://www.animaltags.org/doku.php?id=tagwiki:tools:plotting:c_line | Plots a line at points specified by inputs x and y, and colored according to factor input z
[p] = c_line(x, y, z, color_vector)% Matlab & Octave
cline(x, y, z, color_vector) #R
Plots a line at points specified by inputs x and y, and colored according to factor input z (with one color for each level of z).
Input var Description Default value
x x positions of points to be plotted N/A
y y positions of points to be plotted N/A
z a factor, the same length as x and y. Line segments in the resulting plot will be colored according to the levels of z. N/A
color_vector a list of colors to use (length should match the number of levels in z). N/A
Output var Description Units
p plot of x and y with the color changes specified by color_vector between levels of z N/A
• This function adds colored line segments to an existing plot.
• The line is plotted at points specified by inputs x and y, and colored according to factor input z (with one color for each level of z).
### Matlab & Octave
c_line(1:5, 1:5, 1:5, {[.1 .2 .3], [.1 .4 .5], [.1 .2 .6] [.1 .8 .9] [.5 .4 .5]})
### R
graphics::plot(NA, xlim = c(0, 30), ylim = c(0, 400))
cline(x=ChickWeight$Time, y=ChickWeight$weight,
z=as.factor(ChickWeight\$Diet),
color_vector=c('black', 'grey20',
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https://electronics.stackexchange.com/tags/fpga/new | # Tag Info
## New answers tagged fpga
3
You are mostlikely looking for the "Hierarchy – Post Synthesis Resources" view. In my version it is "hidden" as a tab next to the "File List" and "Process" views.
1
The BSS138 rise and fall times look in MHz range, but to be honest I always used them on slow signals. If you have oscilloscope it would be nice to measure what is going from the FPGA pin, what is going after BSS138 when the L298, is there some capacitance, would a big pull down resistor change the characteristics? When checking the L298 PDF: https://www.st....
1
I thought a BSS138 was just a single Nch FET. You don't have any pullup R's but you don't need it anyways. The L298 works off of 2.3V logic to 5V logic Vil <= 1.5 V Vih >= 2.3V Also with Vce(sat) on hi/lo outputs you need at least 2.5V more than motor rated voltage for full RPM + torque. CMOS or FET power half or full H bridge drivers are better This ...
2
There are two methods: period and frequency measurement. You have chosen the frequency method. My old books say: $$f_x = \dfrac{N}{T_M} \pm \dfrac{1}{T_M}$$ Where $T_M$ is a measuremnt period (0.1s in your case) and $N$ is the number of counts. $$f_x = \dfrac{RPM_x}{60s}\cdot 4000\ inc$$ $$RPM = \dfrac{60}{4000}\lbrace \dfrac{N}{0.1} \pm \dfrac{1}{0.1} \... -1 The power consumption is not going to be a strong function of the number of LUTs and FFs used. What will have a large influence on power consumption is the activity level of the logic and flip-flops, and this is highly dependent on the specific design that is implemented in the FPGA. If you use a design that "does not perform any specific useful ... 1 As others have noted, classical circuit theory effects (RLC) will overwhelm relativistic effects, making direct measurement from the FPGA impossible. If you want to experiment, you can try building a Nutt interpolator. Background: here. Basically, create ratioed current sources and use the FPGA (asynchronously!) to control them, based on input events. The ... -1 You'd implement a block for the low-level parts of the I2C protocol, and a block that schedules the data transfers, and then evolve from there. I2C has a gated clock and a bidirectional data pin, these are your first steps on the low level block, and both are great learning experiences as well: The clock isn't very fast, so you can in theory generate the ... 6 You're measuring how long The source current of your output pin takes to charge up The capacitance of your input pin through The inductance of your coil of wire until it reaches The threshold voltage of your input pin. Number 3 is related to the length of your wire, but not as directly as you would think. It's also influenced by the geometry of the ... 3 Does an always block, that runs at posedge of a 100MHz clock, occur at 100MHz Yes, a 100MHz clock has 100M rising edges and 100M falling edges per second. Is it legit to measure very short time intervals The resolution is one clock cycle, or 10ns here, so how legit it is is up to you to decide, depending on the accuracy and resolution you need. Does the ... 5 Just using a single wire isn't going to work for this -- basically, layer of winding on the spool talks to the next. Typically, you conduct this experiment with a good long length of coax cable; the measuring instrument can be a plain old oscilloscope. Then it's just a matter of trading off how much the measuring instrument costs vs. how much the roll of ... 3 I think the term for this is a "gearbox". They are used all the time when interfacing with serializers - converting between 66 and 64 bits, 66 and 16 bits, etc. Not sure about the proper way to do it aside from whatever gets the job done, although there may be more efficient techniques that I'm not currently aware of. Personally, I wouldn't ... 1 If you really want something based on an assign statement, your version can be improved: // yours is below assign out = sel[1] ? (sel[0] ? d : c) : (sel[0] ? b : a); // but you can decode two bits at a time: assign out = (sel==2'b00) ? a : (sel==2'b01) ? b : (sel==2'b10) ? c : (sel==2'b11) ? d : 2'bx; // ... 4 You can simplify the procedural block by using an implicit sensitivity list, always @* in Verilog and preferably always_comb in SystemVerilog. And you should not be using non-blocking assignments in combinational logic. always_comb case (sel) 2'b00 : out = a; 2'b01 : out = b; 2'b10 : out = c; 2'b11 : out = d; endcase Almost the same amount of typing ... 0 Couple of things to consider. First, I'm not an expert on RDMA. But I think there are a few options for your setup. One option could be to use the Xilinx RDMA IP core, which means the FPGA can directly communicate via RDMA without a host system. However, I'm not sure if that supports IB or only Ethernet (RoCE). Another option is what you describe, bouncing ... 0 For CONNECT-X type speeds up to 50Gbps/lane at present, RDMA must be used with non+volatile(UPS) DDR hybrid NDRAM to achieve lowest latency. (Snip) . RDMA also facilitates a faster data transfer rate and low-latency networking. It can be implemented for networking and storage applications. How RDMA works RDMA enables more direct data movement in and out of a ... 2 This has been researched by UofT and Umass in the link below. “ In between these extremes is a spectrum of logic block choices ranging from fine to coarse-grain logic blocks. FPGA architects over the last two decades have selected basic logic blocks made of transistors (noted above) [144], NAND gates [160], an interconnection of multiplexers [79], lookup ... 1 There are two approaches. One is a ROM or external RAM big enough to hold multiple images, each starting at a different base address. Simply change the base address each frame period... If your FPGA allows a large enough ROM, you can decode the MP4 file into a series of RGB images on the host computer and generate a very big .coe file from that. The other ... 0 You should unencode, that is decompress, your MP4 stream. Step 1 Decompress, your MP4 stream which is made up of GOP's, in a sequence of 13 JPG pictures. A GOP is a group of 13 pictures. This is the toughest part. You can do it in software using some open source library. You can do it in hardware if you find an open source VHDL or Verilog library. ... 1 Code just a single input capture block that records the value of a counter/timer input upon an incoming pulse and also sends an output trigger when it does so. Then generate a bunch of them and connet their time base input to a master timer block (that you also write) that is in turn triggerable by all the capture blocks via ORing, but only once (non-... 0 You are in essence creating a a logic analyzer with a fixed trigger condition: any input making a 0-to-1 transition. Trigger on that, store successive samples with time stamps in a FIFO, then measure the time between changes of state, noting what bits have changed between samples. Then you have a list of arrival times and bits. If you're using an FPGA that ... 3 One simple approach would be to have a free-running counter that measures time in units of its clock period. Each channel, when it receives a pulse, captures the value of the counter into a register. The counter must be big enough so that it doesn't overflow in the expected total time between the first and last pulses. Once all of the channels have triggered,... 3 My constraints now look like this: set_max_delay -to [get_pins -nocase -hierarchical s_rst_sync_ff[*]|CLRN] 10.000 set_max_delay -from [get_cells -nocase -hierarchical s_rst_sync_ff[*]] -to [get_cells -nocase -hierarchical s_rst_sync_ff[*]] 2.500 Besides, I enabled synchronizer identification in the Quartus qsf file: set_global_assignment -name ... 0 One possibility is that your mentor is considering that signal declarations are needed to provide the "storage" for the register. Just as an example, they are declared in this document from Xilinx: The flip-flops are not synthesized because of the signal declarations. It is the edge triggered part of the code you have shown that implies the flip-... 0 Color swap: you read with one byte delay and the YUV decoder produces wrong results. Black bar on the left: The horizontal synch is correct but your controller starts reading zeros before the CMOS camera opens the rolling shutter. 1 Your code is so badly formatted that it's making my eyes bleed, but the main problem is that the process that's generating your memory addresses is not actually regulated by any clock. As a result, it's generating essentially random numbers as far as the rest of the design is concerned. This wouldn't show up in the simulation because there is a clock listed ... 1 I answered a similar question regarding optical encoder accuracy here: PWM accuracy vs speed control accuracy Minimum resolvable angle: $$\theta(1) = \frac{360}{4000}=0.09deg\\$$ Sampling Period: $$T=0.001s$$ Expected error bounds: \omega_{error} = \frac{\theta(1)}{T} = \frac{0.09}{0.... 3 The safest time to capture data is ... immediately before the SCLK falling edge. If you are rolling your own SDI interface, you can arrange this any way you like. It is tempting to capture data on the positive SCLK edge ... but... with the maximum SCLK frequency of 20MHz, an SCLK period of 50 ns assures the SCLK rising edge is 25 ns after the falling edge. ... 6 Here's a good clue: - And, if you look at the value for $t_4$ it is quoted here: - So, a new data bit is available between 0 and 40 ns of the falling edge of SCLK. This means you can't rely on the falling edge of SCLK to read valid data. Of course, if you look at $t_7$ it tells you that current data is valid for maybe 7 ns should you attempt to read it ... 0 The Xilinx support page has a Q/A for this: Vivado - How to get resource utilization of one sub module? When button to get the utilization report is greyed out, you can't get to the reports via the nice GUI. But you can still have it dumped to a file using the TCL console command: report_utilization -hierarchical -file path_to_output_text_file Navigate to ... 3 Get an optocoupler which is designed for high enough speed. Its receiving end is a complex amplifier circuit instead of pull-up with a resistor. For high speed an ordinary opto-coupler could be used if there's very low resistance pull-up resistor and an amplifier or a cascode amp is used to prevent Vce voltage changes of the opto transistor during the state ... 1 The opto-transistor is fast when switching from OFF to ON that is from FPGA input 1 to FPGA input 0. The problem here is that R has the responsibility to pull from 0 to 1 the FPGA input and it's really slow. You need either: A totem pole optocoupler like this: https://uk.rs-online.com/web/p/optocoupler-ics/6258413/ or To review your design and possibly ... 4 No, this will not work with the 10kohm load resistor. Look at datasheet diagram 13, at 10kohm load resistor, it takes about 50us for the signal rising edge to propagate from input to output, while falling edge propagation is below 2us. As 75kHz is about 13us period, you need signal rising edge propagation time much faster than that, and you can go down to ... 1 With "implementing a neural network" I reckon you mean the inference part. This mathematically means that you want to do a lot of matrix multiplication, possibly at low precision. The DSP blocks on Fpga are not that helpful as they target higher precision calculations. Using fabric logic to implement such matrix multiplication is quite expensive ... 1 We also needed to update the firmware without opening the products. Now we use this remote programmer from FPGA Cores: The programming is done over Ethernet and you need to add one of these Ethernet cores. It works very good and we can also do remote debugging. We mostly use Artix from Xilinx. 1 Should I add an interrupt capability to my processor to only run the PID code every 1ms as the speeds are refreshed? Yes. Also in your opinions, is every 1ms too fast or too slow to refresh the values? This is a motor and encoder on a bench with no load so it probably doesn't even matter, I am just unsure. That sounds about right for a motor control. ... 1 There is a rule of thumb for digital control loops :$$ f_s >= 20 B_w Basically, the sampling rate should be at least 20 times the desired closed-loop bandwidth. So in your case, the closed-loop bandwidth should be less than 50 Hz. For example, if you want a stabilization time of 1 ms, you need more bandwidth. It's up to you to determine what your ...
1
1st write a spec with the Current vs acceleration vs RPM then repeat with an inertial load as the optimal PID parameters will change especially with reverse. Create an algorithm for it. Also determine the power dissipation for such duty cycles of acceleration and create an algorithm for that. You ought to know that no-load = kV or RPM/V is a constant and ...
1
Re: 2.: This is a question that control theory and the properties of your system will have to define. We can't tell you that! Re: 1.: Yeah, that sounds like the standard way of doing that: add a timer unit, give it a couple easy registers (or memory-mapped registers) to control it, and an interrupt controller. That thing doesn't have to be fancy, honestly - ...
0
Yes, unchanged registers are implicitly "latched", which may require the compiler to dedicate additional resources to ensuring these semantics (usually you will get a warning here). If your logic doesn't depend on this behavior, you can explicitly assign an undefined value, which allows for better optimization during synthesis and also shows subtle ...
1
Present (series 7) Xilinx FPGAs support a number of methods to load the bitstream: Master-Serial configuration mode Slave-Serial configuration mode Master SelectMAP (parallel) configuration mode (x8 and x16) Slave SelectMAP (parallel) configuration mode (x8, x16, and x32) JTAG/boundary-scan configuration mode Master Serial Peripheral Interface (SPI) flash ...
1
If you want to program the FPGA directly, such as when you are doing development work, you will use JTAG. If you want to program an FPGA that uses external memory (which was the norm until recently) then you need only program the external memory device (which generally have their own programming protocols not using JTAG) and then reset the FPGA so that it ...
4
A good practice is creating a package with a set of global parameters used by your project that you can import. Putting them in a package avoids namespace collisions with other projects or external IP that you might have to integrate later. `define macros are global and have the problem with namespace collisions and file compilation order dependancies. const ...
2
The downside is that you obviously are adding more terms to the namespace (although these are probably names you would treat as reserved, just by habit). There's also the issue of active low signals, so you might need an nENABLE for example. Up to you though, wouldn't say it's best/worst practice. If you think it improves maintainability or readability then ...
0
I would have just commented on @bFig8's answer (But I haven't got enough credits). So, since we dragged the variables as shown in above answer, they are shown as -No Data-. To get these new wave information, we'll restart the simulation! This can be done from the ModelSim interface itself. Read this, to find out how to restart the simulation: https://www....
0
Well, you need to have some sort of buffer if you want to convert interleaved video (PAL,NTSC) to full-frame video (VGA) at full resolution. That is the SDRAM. (I don't know what the project does, probably something else than just displaying PAL video on a VGA display, but you don't tell). The SDRAM has to run at a higher clock frequency than your pixel ...
2
The incoming video clock is asynchronous to the FPGA clock. That is why it needs synchronization between video pixel clock domain and FPGA clock domain. And it might make no sense to send video data to DRAM at one byte at a time but many bytes at a time, a FIFO makes perfect sense to transfer data in bursts of few bytes at a time. The DRAM is required for a ...
6
Justme gave the answer, you have to clock it. continuous conversion without having to initialise and command the conversion? That would mean the ADC would change the level of its output pins every time it does a new conversion. Counting uneven propagation delays, skew, etc, if the device that reads these pins reads them at the wrong time, it will get some ...
4
Holding CS and RD low permanently will force the ADC to make one single conversion right after power is applied. That value will be presented to the output bus until you remove power. No further conversions will be performed: -
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No it won't work like that, page 15 of the datasheet describes how the chip bus works. At least some of the control signals need to have transitions, this chip is intended to be sitting on a memory bus so it looks like RAM or ROM chip.
2
With this: bit [63:0] tab [256]; Your second dimension is not a range, so if the syntax were valid, it would be trying to declare a single 64-bit value called tab. The correct syntax is: bit [63:0] tab [255:0]; Which is an array of 256 x 64-bit values
Top 50 recent answers are included | 2021-04-15 15:27:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 2, "x-ck12": 0, "texerror": 0, "math_score": 0.3541826903820038, "perplexity": 2328.876138712754}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038085599.55/warc/CC-MAIN-20210415125840-20210415155840-00147.warc.gz"} |
http://mathhelpforum.com/trigonometry/142551-couple-tricky-trig-function-problems.html | # Math Help - a couple tricky trig function problems
1. ## a couple tricky trig function problems
1) express as a sum or difference as it applies to: sin(5x)sin(3x)
2) find the exact value in radical form for: cos(45)cos(15)
I'm not sure if I'm supposed to put two questions in one thread, but i thought that maybe they were worked similarly so I could lump them together. Also, the integers in problem two are in degrees, not radians. And I think that I'm supposed to use identities to solve these but I'm not sure which one.
2. Originally Posted by GUNSLINGAZ
1) express as a sum or difference as it applies to: sin(5x)sin(3x)
2) find the exact value in radical form for: cos(45)cos(15)
I'm not sure if I'm supposed to put two questions in one thread, but i thought that maybe they were worked similarly so I could lump them together. Also, the integers in problem two are in degrees, not radians. And I think that I'm supposed to use identities to solve these but I'm not sure which one.
For Q1, you should have a formula somewhere which gives an expression for sin A x sin B. Find that first then sub in 5x for A and 3x for B.
For Q2, use a similar expression for cos A x cos B, sub in appropriate values and then simplify.
You should know sin, cos, tan of 30, 45 and 60 off by heart.
If you don't, I suggest you do this:
Draw an equilateral triangle - let each side be length 2 - slice it down the middle - you now have a 30, 60, 90 triangle with the hypotenuse 2, base 1 - use Pythagoras to work out the other side is sqrt(3) - mark in your angles. You can then read off sin, cos, tan of 30 and 60 degrees.
For 45 degrees, draw a right-angled isoceles triangle with side lengths and (by Pythagoras) hypotenuse is sqrt(2). Label angles - read off sin, cos tan of 45 degrees.
3. Originally Posted by GUNSLINGAZ
1) express as a sum or difference as it applies to: sin(5x)sin(3x)
2) find the exact value in radical form for: cos(45)cos(15)
I'm not sure if I'm supposed to put two questions in one thread, but i thought that maybe they were worked similarly so I could lump them together. Also, the integers in problem two are in degrees, not radians. And I think that I'm supposed to use identities to solve these but I'm not sure which one.
hi
in general ,
sin A sin B = -(1/2)[cos (A+B)-cos (A-B)]
cos A cos B=(1/2)[cos (A+B)+cos (A-B)]
4. thanks so much. in looking at my handout, i know see the identities you mention under "product to sum identities." thanks.
5. find the exact value in radical form for: cos(45)cos(15)
$cos(a-b) = cosacosb+sinasinb$
= cos(45)*(cos(45-30))
= cos(45)*(cos45cos30+sin45sin30)
rest is numerical | 2015-05-28 06:23:34 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 1, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8998607397079468, "perplexity": 801.2615971807115}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-22/segments/1432207929256.27/warc/CC-MAIN-20150521113209-00331-ip-10-180-206-219.ec2.internal.warc.gz"} |
https://blog.audio-tk.com/2020/06/23/should-i-invert-my-matrix-or-not/ | ### Should I invert my matrix or not?
In almost all analog modeling algorithms, we solve a (non-)linear system they require at some point to solve $A x=y$, with given $A$ and $y$. Depending on the size of the matrix and its characteristics, computing an inverse can be costly and may incur numerical problems. Let’s tackle cost in this discussion.
#### The case for an inverse
When we have a small matrix, inverses can be very efficient to compute. The simplest case is a division (1×1 case) and with some knowledge of the matrix structure, the inverse can be simplified instead of using a general algorithm like the determinant of the comatrices.
When you have a linear system (this would occur with an analog modelling of a circuit with only linear components like resistors, inductors and capacitors), the case is even bigger because the matrix is constant, so the inverse computation is a one-off cost. Even if the matrix is now dense when the original $A$ was sparse, the one-off cost is still worth it, until you get to high dimension matrices.
#### The case for solving the equation
Solving the equation means not inverting the matrix. Not inverting the matrix means using another algorithm like a pivot (QR, Householder…) to get the answer. These can works very well with large sparse matrices, and you can tailor them to the specifics of the matrices structure, just like for the inverse.
When the equations are non-linear, the cost of inverting the matrix all the time quickly becomes higher than using a numerical solver.
#### Wrapping up
In the end, choosing between inverting a matrix or solving equations depends on linearity/non-linearity and the size of your matrix. Each system will have a limit where one will be better than the other, and we need to measure to get to this limit. But basically the solution is the following one:
Type Small-size matrix Medium-size matrix Big-size matrix Linear system Invert Invert Solve Non-linear system Invert Solve Solve
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http://crypto.stackexchange.com/tags/schnorr-signature/hot | # Tag Info
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On a general basis, you want to keep encryption and signature keys disjoint, because they tend to have distinct life cycles. In broad terms, an encryption key should be escrowed, because loss of the private key implies loss of the data which is encrypted relatively to the public key. However, a signature key must not be escrowed, since the proof value of a ...
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Apparently, Schnorr was quite adamant, at that time, about the applicability of his patent to DSS. See this message and that one. These are from 1998, but the controversy had begun earlier; see for instance this bulletin from NIST, from late 1994, where references to it can be found in the "Patent Issues" section. Interestingly, NIST not only tried to avoid ...
7
Despite their theoretical security advantages, Schnorr signatures aren't very popular. Probably because they were patented. Since the patents expired in 2008 they might rise a bit in popularity. But probably only in the elliptic curve form, and not in finite fields. I don't know of any application actually using Schnorr signatures, but I know several that ...
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In the other answers, you'll find how to simulate a proof if you know $e$. This answer is meant to provide some "color commentary" on the other answers. It is a companion piece. Notation In step 1, Alice sends $g^r$. Call this value $a=g^r$. In step 3, Alice sends $r+se$. Call this value $b=r+se$. In step 1-3, one value is sent in each step: {$a,e,b$}. ...
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This scheme is insecure, as anyone with the public key can generate a forgery of an arbitrary message. To do this, the forger would take the message $M$, the public key $y$, pick an arbitrary $z$, and compute $r = y^{-H(M)} g^{z} \bmod p$ and output $(r,z)$
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The paper "On the Joint Security of Encryption and Signature in EMV" shows that ECIES and EC-Schnorr signatures can be used together without compromising security: In the random oracle model ECIES-KEM and EC-Schnorr are jointly secure if the gap-DLP problem and gap-DH problem are both hard Ed25519 is extremely similar to EC-Schnorr, and both ECIES ...
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If Alice guesses $e$ then she chooses a random value $x$ and computes $h = g^x v^{-e}$, a value which she sends to Bob at step 1. At step 3, Alice sends $x$. When Bob does step 4, he recomputes $g^x v^{-e}$ and finds $h$, and he is happy. However, Alice does not know $s$. The "commitment" at step 1 is a way for Alice to say: "I know a $r$ corresponding to ...
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Suppose that we have Eve, that knows what $e$ is going to be, and does not need to know the prover's private key $a$, just the public one $v$. She then sends $g^k \cdot v^{-e}$ as her first "move", where she can choose her own $k$ (you can modify the $k$ in different plays to make it all look nice and random...). The verifier sends $e$ as expected, of ...
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Schnorr can be proven zero knowledge when the challenge $e$ is restricted to a small set (typically $0$ and $1$). Recall that in the Schnorr protocol, the prover knows the logarithm $u$ of $y$ to base $g$. He chooses a random value $r$, computes $a = g^r$ and sends $a$ to the verifier. The verifier chooses a random challenge $e$ from some set and sends it ...
4
Well, if fake-Alice guesses the challenge exponent $e$ in step 1, then she can guess the value of $v^{-e}$. That means she can pick an arbitrary value to stand in for $r+se$, compute $g^{r+se}v^{-e}$, and send that as her commitment in step 1. Then, assuming Bob sends the guessed exponent in step 1, fake-Alice sends the value $r+se$ that she picked above. ...
3
First of all, while Schnorr Signatures are usually described that way, the two primes are not necessary for it to work. In principle, Schnorr works in any cyclic group. However, to achieve security we need that the discrete logarithm problem in that group is hard. So the reason for the choice of $q$ (which is the group order) is that DL is believed to be ...
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Here and in many other signature schemes, $f$ is modeled as a "random oracle." This means that on each distinct input, $f$ outputs a uniformly random value in $\mathbb{Z}_q$ that is independent of all other outputs. (When queried on the same input multiple times, it always returns the same answer.) The trick here is that the simulator has the power to ...
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A small message space is no problem and I do not really know what you mean by "signature length is very small". However, it is not only a good idea to choose independent and fresh randomness for every signature, it is (as Alex mentioned in his comment) necessary. Otherwise anyone who gets two signatures of you computed with same randomness for different ...
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Yes, there are some examples of Schnorr signature in real world applications, although I can not provide you the names of the products. (Edit: OpenSSH contains a reference implementation in schnorr.c). The good feature of Schnorr signature is that by design it does not require lot of computations on the signer side. Therefore, you can use it even on a ...
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As noted by Perseids in a comment to this answer, the formula $s = r + c + x$ would allow an adversary (who has completed the protocol once in the role as verifier with $P$ and already got one valid triplet $t_1,c_1,s_1$) to compute responses to any arbitrary challenge, simply using the formulas $t_2 = t_1$, $s_2 = s1 + c_2 - c_1$. Your other alternative $s ... 2 Given the definition of a zero-knowledge proof, it must satisfy three properties: Completeness: if the statement is true, the honest verifier (that is, one following the protocol properly) will be convinced of this fact by an honest prover. Soundness: if the statement is false, no cheating prover can convince the honest verifier that it is true, ... 2 You have to look at the response from the perspective of the verifier. This specific construction allows him/her to verify the$P$'s knowledge of$x$: If$P$could answer two different request$c_1,c_2$in step 2) then we would have$g^{s_1}=ty^{c_1}$and$g^{s_2}=ty^{c_2}$. Dividing one equation by the other we get$g^{s_1-s_2}=y^{c_1-c_2}\$. Let ...
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Threshold (robust) m-of-n variant of Schnorr signature scheme is known: Douglas R. Stinson, Reto Strobl - Provably Secure Distributed Schnorr Signatures and a (t, n) Threshold Scheme for Implicit Certificates Major hints on intended usage are from Ripple page mentioned. Points 4 and 3 are explicit: produce a signature, in a theshold m-of-n way. This could ...
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Well, the goal of their reductionists proof is to show that if there is an adversary against the signature scheme one is can use this adversary to extract the unknown secret key. Now, if the reduction would already know the secret key from the start this would make no sense. But how should the reduction then answer the signing queries of the adversary ...
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