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https://www.slideserve.com/zubin/pre-calculus-chapter-7-outline | 1,642,883,872,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320303884.44/warc/CC-MAIN-20220122194730-20220122224730-00253.warc.gz | 1,021,304,686 | 19,491 | Pre Calculus Chapter 7 Outline
# Pre Calculus Chapter 7 Outline
## Pre Calculus Chapter 7 Outline
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##### Presentation Transcript
1. Pre CalculusChapter 7 Outline A Presentation By Cody Lee & Robyn Bursch
2. Section 7.1 : Inverse Sine, Cosine, and Tangent Functions • y= sin x means x= sin y where -1 ≤ x ≤ 1, - π/2 ≤ y ≤ π/2 • y= cos x means x= cos y where -1 ≤ x ≤ 1, 0 ≤ y ≤ π • y= tan x means x= tan y where -∞ < x < ∞, 0 < y < π • y= sec x means x= sec y where |x|≥1, 0 ≤ y ≤ π, y≠ π/2 • y= csc x means x= csc y where |x|≥1, - π/2 ≤ y ≤ π/2, y≠0 • y= cot x means x= cot y where -∞ < x < ∞, 0 < y < π See pg 489 for formulas, pg 429-442 for detailed explanation -1 -1 -1 -1 -1 -1
3. 7.1 Continued
4. Section 7.2 : Inverse Trigonometric Functions (Continued)
5. Ex: Find the exact value of: tan [cos (-1/3)] -1 • tan [cos (-1/3)] • Ѳ= cos (-1/3), so cos Ѳ = -1/3 and since cos Ѳ < O, Ѳ lies in quadrant II • Since cos is x/r, we let x=-1 and r=3 • Use pythagoream theorem to find y • (-1)²+ y² = 3² » 9-1=y² » y²=8 » y=2√2 • Since we have y=2√2 and r= 3, tan [cos (-1/3)] = tan Ѳ= (2√2)/-1 = - 2√2 -1 -1
6. Section 7.3 : Trigonometric Identities
7. Ex: Techniques to Simplify Trigonometric Expressions • Show that cosѲ / 1+ sin Ѳ = 1-sin Ѳ /cosѲ by multiplying the numerator and denominator by 1-sin • Solution: cosѲ/ 1+ sin Ѳ = cosѲ/ 1+ sin Ѳ x 1-sin Ѳ/ 1-sin Ѳ • = cosѲ (1-sin Ѳ)/1-sin² Ѳ • = cosѲ (1-sin Ѳ)/cos² Ѳ = 1-sin Ѳ/ cos Ѳ
8. Section 7.4 : Sum and Difference Formulas
9. Ex: Using Sum Formula to Find Exact Values • Find the exact value of cos(75°) • Solution: since 75° = 45°+30°, we use the formula for cos(α+β) • Cos 75° = (45°+30°) = cos 45°cos 30° - sin 45°sin 30° • = (√2/2)(√3/2)- (√2/2)( ½ ) • = ¼(√6-√2)
10. Section 7.5 : Double-Angle Formulas
11. 7.5: Double-Angle using Squares
12. Section 7.5: Half-Angle Formulas
13. Ex: Finding Exact Values Using Double-Angle • If sin Ѳ= 3/5 and π/2 < Ѳ < π, find the exact value of cos (2Ѳ) • Solution: because we are given sin Ѳ= 3/5, we can use the formula cos (2Ѳ)= 1 - 2sin²Ѳ. • cos (2Ѳ)= 1- 2(3/5)² » 1- 2(9/25) » 1- 18/25 • cos (2Ѳ)= 7/25
14. Ex: Finding Exact Values Using Half-Angle Formulas • Use a half-angle formula to find the exact value of: sin(-15°) • Solution: We use the fact that sin(-15°)= -sin(15°) and 15°= 30°/2 • Use the formula sin α/2= ± √(1 - cos α/2) • sin(-15°) = -sin(30°/2) = - √(1 - cos30°/2) » - √(1 –(√3/2)/2) » 2 (- √(1 –(√3/2)/2) » (- √(2 –√3)/4) • = - √(2 –√3)/2
15. Thanks for Watching! Good Luck on the Final… | 1,128 | 2,640 | {"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} | 4.59375 | 5 | CC-MAIN-2022-05 | latest | en | 0.546554 |
https://www.physicsforums.com/threads/find-the-equation-of-the-curve.548272/ | 1,695,983,114,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510501.83/warc/CC-MAIN-20230929090526-20230929120526-00527.warc.gz | 1,014,666,731 | 14,883 | # Find the equation of the curve
• aerin8
## Homework Statement
From the given sequence of numbers (11.25, 10, 9.25, 9, 9.25, 10, 11.25, 13, 15.25, 18 ...)
A) Graph the sequence
B) Find the equation of the curve
C) Determine the 100th term of the sequence
## The Attempt at a Solution
I know how to graph the sequence by setting the given numbers as y coordinates and their order as x coordinate but beyond there I'm stuck. Help please!
## Homework Statement
From the given sequence of numbers (11.25, 10, 9.25, 9, 9.25, 10, 11.25, 13, 15.25, 18 ...)
A) Graph the sequence
B) Find the equation of the curve
C) Determine the 100th term of the sequence
## The Attempt at a Solution
I know how to graph the sequence by setting the given numbers as y coordinates and their order as x coordinate but beyond there I'm stuck. Help please!
There is a certain pattern that jumps out here. Look at the difference of successive terms in this sequence.
Also, the second differences are constant.
I can see the pattern but I don't know how to apply it in the equation of the curve. Is there a formula I can plug the data into to find the equation?
is the curve the same thing as a parabola?
The curve might be a parabola. If so, you know where the vertex is.
In case it's not a parabola, there's an area of mathematics called Difference Equations (see http://en.wikipedia.org/wiki/Recurrence_relation) that might be helpful. See especially the section titled "Relationship to difference equations narrowly defined." | 391 | 1,516 | {"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} | 3.296875 | 3 | CC-MAIN-2023-40 | latest | en | 0.925386 |
https://profound-answers.com/what-is-another-name-for-a-french-curve/ | 1,695,494,610,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233506528.19/warc/CC-MAIN-20230923162848-20230923192848-00444.warc.gz | 553,735,777 | 43,160 | Collection of recommendations and tips
What is another name for a French curve?
What is another name for a French curve?
They were invented by the German mathematician Ludwig Burmester and are also known as Burmester (curve) set.
What is used for drawing irregular curves?
The large compass is used to draw circles or parts of circles, called arcs. Irregular curves (not circles or arcs) are drawn with special plastic instruments that are made in many different shapes. The most common of these instruments is called the French curve.
Why is it called French curve?
The French curve is a template used to draw different types of curve. It is called a cloud template in Japanese because of its resemblance to a cloud. The French curve enables the artist to draw curves that would be difficult to achieve with a compass.
What are irregular ellipses curves?
An ellipse French curve, or irregular curve, is used to draw short elliptical radius curves by using points.
What is a hip curve?
A Hip/Form curve is a large French curve that aids in pattern making by providing an elogated, curved edge for smoothing and correcting pattern lines.
What is French curve is used for shaping?
Answer: A French curve is a template usually made from metal, wood or plastic composed of many different curves. It is used in manual drafting and in fashion design to draw smooth curves of varying radii. The shapes are segments of the Euler spiral or clothoid curve.
What is a flexi curve?
A Flexi-curve is used to draw curves. It can be formed into almost any curve as it is flexible. They are used to draw curves by finding the section of curve that matches the desired shape on the profile of the curve. Some French Curves also have either circles or ellipses of various sizes cut out.
What is a French curve ruler?
1. French Curve Ruler. The French curve is the most common curved ruler used for fashion design. (It’s the translucent ruler shown above.) It’s especially handy for making common fitting or pattern adjustments.
What are irregular curves?
An irregular curve is a set of pixels that define a curve that does not fit the perimeter of a conic section. The ending point is excluded from a curve just as it is excluded from a line.
What are the 3 dots called?
ellipsis
You see those dots? All three together constitute an ellipsis. The plural form of the word is ellipses, as in “a writer who uses a lot of ellipses.” They also go by the following names: ellipsis points, points of ellipsis, suspension points.
What is French curve used for?
French curves are used in drafting (or were before computer-aided design) to draw smooth curves of almost any desired curvature in mechanical drawings. | 566 | 2,709 | {"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} | 2.6875 | 3 | CC-MAIN-2023-40 | latest | en | 0.973733 |
http://mathhelpforum.com/algebra/221258-dividing-mass-lifted-parties.html | 1,481,119,978,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698542112.77/warc/CC-MAIN-20161202170902-00361-ip-10-31-129-80.ec2.internal.warc.gz | 175,403,770 | 11,235 | # Thread: Dividing mass lifted by parties
1. ## Dividing mass lifted by parties
Say 4 men lift 200 kilos. Can I simply divide 200 by 4 to get 50kg each...So they lifted 50kilos each (given the same posture and dimensions of the lift)?
Or is the calculation more complex?
2. ## Re: Dividing mass lifted by parties
Originally Posted by Paze
Say 4 men lift 200 kilos. Can I simply divide 200 by 4 to get 50kg each...So they lifted 50kilos each (given the same posture and dimensions of the lift)?
Or is the calculation more complex?
50 kg is the average weight lifted. If add the assumption that they all lifted the same weight, then you can say they each lifted 50 kg.
3. ## Re: Dividing mass lifted by parties
If the four men are evenly spaced around the edge of the object and if the center of gravity of the object is precisley in the middle (and hence equi-distant from all four men) then the 50 Kg/person calculation should be pretty accurate. But in the real world it often doesn't work out quite so ebevenly. Most objects are odd-shaped, so the center-of-gravity is not precisely in the middle. Plus it's possible that two men on opposite corners may do more lifting than the those on the other two corners. For example, it's quite possible for two men on opposite corners to lift 80 Kg each while the other two are lifting only 20 Kg each.
4. ## Re: Dividing mass lifted by parties
Thanks for verifying, guys!
For anyone who's wondering, I was doing some physics calculations on the blockbuster "Pacific Rim". I was wondering whether the choppers could hold the Jaegers (they can't) | 383 | 1,599 | {"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} | 3.40625 | 3 | CC-MAIN-2016-50 | longest | en | 0.940639 |
https://www.physicsforums.com/threads/solving-snells-law-problem-find-refractive-index-at-height-h.161756/ | 1,695,918,960,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510427.16/warc/CC-MAIN-20230928162907-20230928192907-00710.warc.gz | 997,127,012 | 14,309 | # Solving Snell's Law Problem: Find Refractive Index at Height h
• zell99
## Homework Statement
A man, height h, can see a mirage at angles less than a known angle $\theta$ to the horizontal. The refractive index of air is at ground level is known. Find the refractive index of air at height h.
## Homework Equations
Snell's law: $n1 sin(\theta 1)=n2 sin(\theta2)$ where angles are measured relative to the normal of the boundary.
I'm assuming it's a normal mirage, i.e. can see an image of the sky in the ground.
## The Attempt at a Solution
My plan was to split the air up into infintesimal stips at constant height, find $d\theta$ as a function of $d(refractive index)$ and integrate to find $\theta$ as a function of refractive index. The problem I have is I don't know what the initial value of theta is, and I obviously need to include h somewhere.
If anyone could point me in the right direction I'd really appreciate it.
Thanks
Last edited:
Has anyone got any ideas? I should have said theta is very small, so small angle approximations are fine where appropriate.
Thanks | 268 | 1,087 | {"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} | 3.171875 | 3 | CC-MAIN-2023-40 | latest | en | 0.942655 |
https://www.investorq.com/question/how-are-bonds-priced-in-the-market- | 1,597,127,098,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738735.44/warc/CC-MAIN-20200811055449-20200811085449-00309.warc.gz | 709,909,217 | 7,659 | A bond’s price equals the present value of its expected future cash flows. The rate of interest used to discount the bond’s cash flows is known as the yield to maturity (YTM.)
How are coupon-paying bonds priced?
A coupon-bearing bond may be priced with the following formula:
Where:
C = the periodic coupon payment
y = the yield to maturity (YTM)
F = the bond’s par or face value
t = time
T = the number of periods until the bond’s maturity date | 103 | 453 | {"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} | 2.546875 | 3 | CC-MAIN-2020-34 | latest | en | 0.870038 |
https://www.allinterview.com/interview-questions/532-14/ssc-general-studies.html | 1,620,379,263,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988775.80/warc/CC-MAIN-20210507090724-20210507120724-00401.warc.gz | 666,566,003 | 8,439 | Follow Our FB Page << CircleMedia.in >> for Daily Laughter. We Post Funny, Viral, Comedy Videos, Memes, Vines...
SSC General Studies Interview Questions
The average of a collection of 20 measurements was calculated to be 56 cm. But later it was found that a mistake had occurred in one of the measurements which was recorded as 64 cm, but should have been 61 cm. The correct average must be (a) 53 cm (b) 54.5 cm (c) 55.85 cm (d) 56.15 cm
3124
The average weight of 12 parcels is 1.8 kg. Addition of another new parcel reduces the average weight by 50 g. What is the weight of the new parcel? (a) 1.50 kg (b) 1.10 kg (c) 1.15 kg (d) 1.01 kg
4218
The average age of 20 boys in a class is 12 years. 5 new boys are admitted to the class whose average age is 7 years. The average age of the boys in the class becomes (a) 8.2 years (b) 9.5 years (c) 12.5 years (d) 11 years
2157
If 3x+3 + 7 = 250, the x is equal to (a) 5 (b) 3 (c) 2 (d) 1
5528
A die with faces numbered from 1 to 6 is thrown twice. The probability, that the numbers shown up differ by 2, is (a) 1/9 (b) 2/9 (c) 3/9 (d) 4/9
2160
In the sequence of numbers 5, 8, 15, 20, 29, 40, 53, one number is wrong. The wrong number is (a) 15 (b) 20 (c) 29 (d) 40
2797
1 + 2 + 3 + ??. + 49 + 50 + 49 + 48 + ??. + 3 + 2 + 1 is equal to (a) 1250 (b) 2500 (c) 2525 (d) 5000
4486
The surface area of a sphere is 64? cm2 its diameter is equal to (a) 16 cm (b) 8 cm (c) 4 cm (d) 2 cm
2661
Each of the height and base radius of a cone is increased by 100%. The percentage increase in the volume of the cone is (a) 700% (b) 400% (c) 300% (d) 100%
5748
A television and a refrigerator were sold for Rs. 12,000 each. If the television was sold at a loss of 20% of the cost and the refrigerator at a gain of 20% of the cost, then the entire transaction resulted in (a) No loss or gain (b) Loss of rs. 1,000 (c) Gain of rs. 1,000 (d) Loss of Rs. 1,200
4090
A person sells a table at a profit of 10%. If he had bought the table at 5% less cost and sold for Rs. 80 more, then he would have gained 20%. The cost price of the table is (a) Rs. 3,200 (b) Rs. 2,500 (c) Rs. 2,000 (d) Rs. 200
4410
By selling an article at 2/3 of the marked price, there is a loss of 10%. The profit percent, when the article is sold at the marked price, is (a) 20% (b) 30% (c) 35% (d) 40%
8676
A moving train, 66 metres long, overtakes another train 88 metres long, moving in the same direction in 0.168 minutes. If the second train is moving at 30 km/r, then at what speed is the first train moving ? (a) 85 km/hr (b) 50 km/hr (c) 55 km/hr (d) 25 km/hr
5956
A man observed that a train 120 m long crossed him in 9 seconds. The speed (in km/hr) of the train was (a) 42 (b) 45 (c) 48 (d) 55
3290
A constable is 114 metres behind a thief. The constable runs 21 metres and the thief 15 metres in a minute. In what time will the constable catch the thief ? (a) 19 minutes (b) 18 minutes (c) 17 minutes (d) 16 minutes
2717
Un-Answered Questions { SSC General Studies }
Please send me last 5 year solved question papers of Canara Bank as well as Bank of Baroda to my e mail id
1813
Can anybody tell me how to prepare for the interview of SSC Scientific assistants
1809 | 1,104 | 3,211 | {"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} | 4.03125 | 4 | CC-MAIN-2021-21 | longest | en | 0.913334 |
http://nomtbf.com/tag/failure/ | 1,590,378,476,000,000,000 | text/html | crawl-data/CC-MAIN-2020-24/segments/1590347387219.0/warc/CC-MAIN-20200525032636-20200525062636-00561.warc.gz | 91,738,599 | 14,248 | # Are the Measures Failure Rate and Probability of Failure Different?
Failure rate and probability are similar. They are slightly different, too.
One of the problems with reliability engineering is so many terms and concepts are not commonly understood.
Reliability, for example, is commonly defined as dependable, trustworthy, as in you can count on him to bring the bagels. Whereas, reliability engineers define reliability as the probability of successful operation/function within in a specific environment over a defined duration.
The same for failure rate and probability of failure. We often have specific data-driven or business-related goals behind the terms. Others do not.
If we do not state over which time period either term applies, that is left to the imagination of the listener. Which is rarely good.
## Failure Rate Definition
There at least two failure rates that we may encounter: the instantaneous failure rate and the average failure rate. The trouble starts when you ask for and are asked about an item’s failure rate. Which failure rate are you both talking about?
The instantaneous failure rate is also known as the hazard rate h(t)
$\displaystyle h\left( t \right)=\frac{f\left( t \right)}{R\left( t \right)}$
Where f(t) is the probability density function and R(t) is the relaibilit function with is one minus the cumulative distribution function. The hazard rate, failure rate, or instantaneous failure rate is the failures per unit time when the time interval is very small at some point in time, t. Thus, if a unit is operating for a year, this calculation would provide the chance of failure in the next instant of time.
This is not useful for the calculation of the number of failures over that year, only the chance of a failure in the next moment.
The probability density function provides the fraction failure over an interval of time. As with a count of failures per month, a histogram of the count of failure per month would roughly describe a PDF, or f(t). The curve described for each point in time traces the value of the individual points in time instantaneous failure rate.
Sometimes, we are interested in the average failure rate, AFR. Where the AFR over a time interval, t1 to t2, is found by integrating the instantaneous failure rate over the interval and divide by t2 – t1. When we set t1 to 0, we have
$\displaystyle AFR\left( T \right)=\frac{H\left( T \right)}{T}=\frac{-\ln R\left( T \right)}{T}$
Where H(T) is the integral of the hazard rate, h(t) from time zero to time T,
T is the time of interest which define a time period from zero to T,
And, R(T) is the reliability function or probability of successful operation from time zero to T.
A very common understanding of the rate of failure is the calculation of the count of failures over some time period divided by the number of hours of operation. This results in the fraction expected to fail on average per hour. I’m not sure which definition of failure rate above this fits, and yet find this is how most think of failure rate.
If we have 1,000 resistors that each operate for 1,000 hours, and then a failure occurs, we have 1 / (1,000 x 1,000 ) = 0.000001 failures per hour.
Let’s save the discussion about the many ways to report failure rates, AFR (two methods, at least), FIT, PPM/K, etc.
## Probability of Failure Definition
I thought the definition of failure rate would be straightforward until I went looking for a definition. It is with trepidation that I start this section on the probability of failure definition.
To my surprise it is actually rather simple, the common definition both in common use and mathematically are the same. There are two equivalent ways to phrase the definition:
1. The probability or chance that a unit drawn at random from the population will fail by time t.
2. The proportion or fraction of all units in the population that fail by time t.
We can talk about individual items or all of them concerning the probability of failure. If we have a 1 in 100 chance of failure over a year, then that means we have about a 1% chance that the unit we’re using will fail before the end of the year. Or it means if we have 100 units placed into operation, we would expect one of them to fail by the end of the year.
The probability of failure for a segment of time is defined by the cumulative distribution function or CDF.
## When to Use Failure Rate or Probability of Failure
This depends on the situation. Are you talking about the chance to failure in the next instant or the chance of failing over a time interval? Use failure rate for the former, and probability of failure for the latter.
In either case, be clear with your audience which definition (and assumptions) you are using. If you know of other failure rate or probability of failure definition, or if you know of a great way to keep all these definitions clearly sorted, please leave a comment below.
# Why Things Fail
Just a short note today about a great high level article in Wired magazine. Robert Capps did a nice summary and review of the significance of reliability engineering, product failure and what we can do about it.
And he doesn’t mention MTBF – which is appropriate.
http://www.wired.com/design/2012/10/ff-why-products-fail/all/
# International Day of Failure
In light of the International Day of Failure, Oct 13th, let’s consider failure from a reliability engineer’s point of view. We work to understand and avoid product failures. When a product fails to deliver the desired performance attribute it is tossed away, returned, replaced, repaired, or tolerated. This may occur before or after the value of the product has been achieved. Continue reading International Day of Failure | 1,239 | 5,740 | {"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": 4, "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} | 3.9375 | 4 | CC-MAIN-2020-24 | latest | en | 0.935899 |
https://www.jove.com/de/science-education/14177/electric-field-of-a-non-uniformly-charged-sphere | 1,722,737,987,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640388159.9/warc/CC-MAIN-20240804010149-20240804040149-00039.warc.gz | 661,510,941 | 38,103 | Electric Field of a Non Uniformly Charged Sphere
JoVE Core
Physik
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JoVE Core Physik
Electric Field of a Non Uniformly Charged Sphere
Nächstes Video23.12: Electric Field of Parallel Conducting Plates
Consider a non-conducting sphere of radius R. The sphere has a radially varying non-uniform charge density. Therefore, it has spherically symmetric charge distribution.
Since the charge density is non-uniform, consider an infinitesimal spherical shell of thickness 'dr' within the sphere.
The charge enclosed in the shell is the product of the charge density and the volume of the shell.
To determine the electric field at a point P, outside the charge distribution, consider a Gaussian surface of radius r'.
Here, the region between the Gaussian surface and the sphere is devoid of charge carriers. So, the net charge enclosed by the Gaussian surface is obtained by integrating the charge enclosed in the shell over the sphere's radius.
Substituting the net charge in the electric field equation gives the field at a point outside the sphere.
Similarly, for a point inside the charge distribution, the net charge enclosed is the integral of the charge enclosed in the Gaussian surface. Substituting the net charge in the field equation gives the electric field at a point inside the sphere.
Electric Field of a Non Uniformly Charged Sphere
Gauss's law states that the electric flux through any closed surface equals the net charge enclosed within the surface. This law is beneficial for determining the expressions for the electric field for a particular charge distribution if the electric flux is known.
Consider a non-uniformly charged sphere, for which the density of charge depends only on the distance from a point in space and not on the direction. Such a sphere has a spherically symmetrical charge distribution. Here, the electric field at any point is radially directed because of the charge; hence, the field is invariant under rotation. The electric field at point P at a distance r from the center of a spherically symmetrical charge distribution is given by,
To determine the electric field inside and outside the non-uniformly charged sphere, first, the charge enclosed within an infinitesimal shell is determined. The charge enclosed in such a shell is the product of the charge density and volume of the shell. The entire sphere can be considered to be made up of combinations of these shells.
A Gaussian surface with the same symmetry as the charge distribution is considered to find the electric field for a point outside the sphere. The Gaussian surface's radius equals the distance to the field point. The net charge inside the Gaussian surface is then calculated by integrating the charge enclosed in the shell over the entire charge distribution. Here, since the observation point is outside the charge distribution, the region between the sphere and the Gaussian surface has no charge and does not contribute to the net charge. The obtained value of the net charge is substituted into the electric field equation to obtain the electric field outside the sphere, which is given by,
If the point of observation lies within the sphere, the Gaussian surface lies within the sphere, and hence, the net charge enclosed in it contributes to the electric field. The electric field at a point inside the non-uniformly charged sphere is given by, | 690 | 3,506 | {"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} | 3.046875 | 3 | CC-MAIN-2024-33 | latest | en | 0.855083 |
https://lovinthings.com/what-dimension-are-we-in/ | 1,632,241,819,000,000,000 | text/html | crawl-data/CC-MAIN-2021-39/segments/1631780057225.57/warc/CC-MAIN-20210921161350-20210921191350-00485.warc.gz | 409,514,716 | 24,050 | # What Dimension Are We In
Dimensions are misunderstood by most people but it’s not your fault. Mathematicians know only the 3-spatial dimensions, up-down. Left-right, and in-out. If you measure an object like a chair it’s a certain width, height, and depth. In math and in science there are never more than the 3-spatial dimensions that I just mentioned. What dimension are we in?
How many dimensions exist and which one are we in now?
## What is a Dimension
We need a new definition of a dimension or a new word to describe the space (dimension) that we live in.
Think of a fly living in a glass jar. A mathematician could measure the size of the fly and the size of the jar (container).
It’s possible to plot the position of the fly inside the container similar to the GPS system that tells us where we are on the Earth.
Now try to plot the position of the fly in the universe. It was easy to find its position in the jar but the container of space is too large and has no borders that we know of.
We could say it’s on a rotating blue planet the 3rd planet in a solar system in the Milky Way Galaxy at the time of April 27th in the Earth year 2020.
An alien would ask where is the Milky Way Galaxy, where is the solar system that this planet is in. and what time are you talking about?
What I’m trying to point out is that space isn’t the same kind of container as a jar.
We often call this space we live in as the universe, which is everything we know.
But the alien might get lost if he doesn’t know what dimension of the universe has this fly in a jar.
You indicate that it’s the 3rd dimension because there is only one dimension in the universe.
Well, that’s funny because in math we use 3 dimensions. So is it one dimension or the 3rd dimension?
## Our Dimension
Did you mention that time is the 4th dimension? Please don’t confuse the alien. Time is not a dimension and our time means nothing to an alien.
How do we describe our space as a dimension? We need a new word or a new definition of space.
Maybe the 3rd realm of the universe and once other realms are known they become the 4th realm, the 5th realm and the 6th realm.
However, the definition of the container of space needs a name.
If we continue to use the term the 3rd dimension will scientists and aliens know what we mean?
Suppose that we are in the 4th dimension now? How would we know?
What are the attributes and descriptions of the 4th dimension?
One of the main differences between dimensions is the frequency of the energy.
We see this new energy in global warming and climate change. We might see new species of viruses or animals and we might see other ones going extinct
We would feel different and it seems that time is going faster. We don’t get as much done in a day as we used to.
If you are at least 40 years old you know what I’m talking about.
## Do Other Dimensions Exist
If other dimensions exist they have the same 3-spatial dimensions and time.
Do we think that there are other levels of energy in the universe that might be different?
We know that the universe started at the Big bang event with energy entering the 3rd dimension.
This is a possible structure of the universe with matter and antimatter dimensions
This is proof that other dimensions (realms) exist.
Another realm that exists is where the dark matter is since we can’t find dark matter it must be in another dimension.
My last reason for other realms is that the antimatter from the Big bang event is missing. Multiple dimensions answer all the questions that we are seeking, so it looks like other dimensions do exist.
But what dimension are we in now? My guess is the 4th dimension.
The universe is divided into levels or realms that have certain frequencies.
Consider that there is an evolution of energy into life and consciousness.
Humans on various galaxies and various dimensions (realm) are evolving as they move with the flow of energy.
The only thing that should concern us is the question. Am I experiencing life in a way that will evolve my consciousness during this lifetime?
That’s my question for you.
Thanks for being here and as always be well.
### About the Author Erik Lovin
Erik has a BSc degree and is a retired professional photographer who is now a published Author of many books. His passion is understanding how life and the universe works. He is currently blogging about the science of the Big Bang and the science of cosmology. Erik is helping his tribe with questions about the universe. His goal is to help find a theory of everything (TOE). In order to do that, he is trying to prove light has mass and that the fabric of spacetime is a false theory. We are welcoming questions and answers that you might have about the universe. | 1,036 | 4,762 | {"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} | 3.671875 | 4 | CC-MAIN-2021-39 | longest | en | 0.9298 |
http://mathhelpforum.com/pre-calculus/170720-graph-y-x-5-2-2x-1-2-a.html | 1,527,056,393,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794865450.42/warc/CC-MAIN-20180523043959-20180523063959-00127.warc.gz | 194,419,033 | 9,996 | # Thread: Graph of y=x^(5/2) and -2x^(1/2)
1. ## Graph of y=x^(5/2) and -2x^(1/2)
Any procedure or guidelines on how to sketch the graph y=x^(5/2) and -2x^(1/2)? I know how it looks like but i had no ideas on the proper procedure of drawing them. Any tips? Thanks.
Sorry, its y=x^(1/3) and not y=x^(5/2)... ^^
2. Try an xy table. Choose values for x, calculate the corresponding y values, and plot the points. You should be able to sketch the graph reasonably.
3. Originally Posted by MichaelLight
Any procedure or guidelines on how to sketch the graph y=x^(5/2) and -2x^(1/2)? I know how it looks like but i had no ideas on the proper procedure of drawing them. Any tips? Thanks.
Sorry, its y=x^(1/3) and not y=x^(5/2)... ^^
$\displaystyle f(x)=x^{\frac{1}{3}}$ is the inverse function of $\displaystyle y=x^3$
Sketch $\displaystyle y=x^3$.
What is the relationship between the graph of $\displaystyle y=f(x)$ and $\displaystyle y=f^{-1}(x)$? | 292 | 951 | {"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} | 3.59375 | 4 | CC-MAIN-2018-22 | latest | en | 0.882322 |
https://math.answers.com/Q/What_is_10_over_25_as_a_percent | 1,695,839,889,000,000,000 | text/html | crawl-data/CC-MAIN-2023-40/segments/1695233510319.87/warc/CC-MAIN-20230927171156-20230927201156-00874.warc.gz | 415,519,500 | 46,108 | 0
# What is 10 over 25 as a percent?
Updated: 8/19/2019
Wiki User
12y ago
10/25 x 100 = 40
Therefore, 10 is 40 percent of 25.
Wiki User
12y ago
Study guides
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225 Reviews | 81 | 209 | {"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} | 2.90625 | 3 | CC-MAIN-2023-40 | latest | en | 0.828139 |
http://www.slate.com/articles/news_and_politics/polling/2010/09/can_the_republicans_takeback_congress.single.html | 1,529,832,359,000,000,000 | text/html | crawl-data/CC-MAIN-2018-26/segments/1529267866926.96/warc/CC-MAIN-20180624083011-20180624103011-00185.warc.gz | 491,371,849 | 19,960 | Try to predict how many seats the GOP will have in the House and Senate.
# Try to predict how many seats the GOP will have in the House and Senate.
Slate readers predict the future.
Oct. 7 2010 9:59 AM
# Can the Republicans Take Back Congress?
## Try to predict how many seats the GOP will have in the House and Senate.
As you read this, there are 255 Democrats and 178 Republicans in the House of Representatives. In January, when the 112th Congress takes office, there will almost certainly be fewer Democrats and more Republicans. On second thought, strike that "almost." As any casual Web surfer can quickly learn, the 2010 election looks great for Republicans and very bad for Democrats. The question is not how many seats Republicans will win, but whether they will win enough to gain control of the House for the time since way back in 2007 (they need 40 more seats). Which leads to the question: How many seats will the Republicans control in the House in the next Congress?
Remember: we're not looking for how many seats the Republicans will gain in November. We're looking for the total number of seats they will control. You can choose any number between 0 and 435.
Currently, the Democrats also control the Senate: There are 57 Democrats and 41 Republicans. (Two senators are technically independents, though they caucus with the Democrats.) No one believes those numbers will be the same come January. Can Republicans gain enough seats—for those of you scoring at home, that number would be 10—to win control of the Senate? So far at least, it looks to be a pretty good year for Republican Senate candidates. How many seats will the Republicans control in the Senate in the next Congress?
Remember: we're not looking for how many seats the Republicans will gain in November. We're looking for the total number of seats they will control. You can choose any number between 0 and 100. | 410 | 1,903 | {"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} | 2.640625 | 3 | CC-MAIN-2018-26 | latest | en | 0.955253 |
http://dtsheet.com/doc/1380582/an842---silicon-labs | 1,498,308,469,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320261.6/warc/CC-MAIN-20170624115542-20170624135542-00295.warc.gz | 115,465,167 | 6,200 | ### AN842 - Silicon Labs
```AN842
Use a Self-Powered Op Amp to Create a Low-Leakage Rectifier
An Amplifier that Works at 0.8 V is Key
1. Introduction
Figure 1.
You can combine a carefully chosen op amp, a low-threshold P-channel MOSFET, and two feedback resistors to
make a rectifier circuit with less forward drop than a diode (Figure 1). The rectified output voltage powers the active
circuitry, so no additional power supply is necessary. The circuit’s quiescent current is lower than most Schottky
diodes’ reverse-leakage current. This circuit provides active rectification at voltage drops as low as 0.8V. At lower
voltages, the MOSFET’s body diode takes over as an ordinary diode.
The op-amp circuit turns on the MOSFET as a forward voltage develops between the input and the output voltages,
according to the following equation:
where VGATE is the MOSFET’s gate drive, VIN is the input voltage, and VOUT is the output voltage. You can
relate the input and the output voltages to the MOSFET’s drain-to-source and gate-to-source voltages, according
to the following equations:
Rev. 1.0 7/14
AN842
AN842
where VDS is the drain-to-source voltage and VGS is the gate-to-source voltage. Combine these equations to
relate the MOSFET’s gate drive to a function of the drain-to-source voltage:
Figure 2.
If you make R2 12 times larger in value than R1, a 40 mV voltage drop across the MOSFET’s drain-to-source
voltage is sufficient to turn on the MOSFET at low drain currents (Figure 2). You could choose a higher ratio to
further reduce the voltage drop within the limits of the op amp’s worst-case input-offset voltage of 6 mV. The op
amp is powered from output-reservoir capacitor C1. The amplifier has rail-to-rail inputs and outputs and no phase
inversion when operating near the rails. The amplifier operates at power-supply voltages as low as 0.8 V. You
directly connect the op amp’s non-inverting input to the VDD rail and the amp’s output to the gate of the MOSFET.
The circuit consumes slightly more than 1 µA when actively rectifying a 100 Hz sine wave, less current leakage
than that of most Schottky diodes. The BSH205 supports milliamp-level currents at a gate-to-source voltage of
0.8 V.
2
Rev. 1.0
AN842
Figure 3.
The op amp’s bandwidth limits the circuit to lower-frequency signals. At bandwidths higher than 500 Hz, the
amplifier’s gain begins to decline. As the signal frequency increases, the MOSFET remains off, and the body diode
of the MOSFET takes over the rectification function. An input with a fast fall time could potentially drag the output
with reverse current through the MOSFET. However, for small currents, the MOSFET operates in its sub-threshold
range. The amplifier quickly turns off due to the exponential relationship of the gate-to-source voltage to the drainto-source current in the sub-threshold range. The limiting factor is the amplifier’s slew rate of 1.5V/msec. As long
as you don’t load the circuit so heavily that you drive the MOSFET into its linear range, reverse currents won’t
exceed forward currents.
You can use the circuit in a micropower solar-harvesting application (Figure 3). Depending on the light, the BPW34
cells generate 10 to 30 µA at 0.8 to 1.5 V. The active-diode circuit rectifies the peak harvested voltage in conditions
of rapidly changing light and minimizes reverse leakage to the cells.
Please see the documentation for the TS1001 Op Amp. For additional information, contact Silicon Labs.
Rev. 1.0
3
AN842
CONTACT INFORMATION
Silicon Laboratories Inc.
400 West Cesar Chavez
Austin, TX 78701
Tel: 1+(512) 416-8500
Fax: 1+(512) 416-9669
Toll Free: 1+(877) 444-3032
Please visit the Silicon Labs Technical Support web page:
https://www.siliconlabs.com/support/pages/contacttechnicalsupport.aspx
and register to submit a technical support request.
Patent Notice
Silicon Labs invests in research and development to help our customers differentiate in the market with innovative low-power, small size, analogintensive mixed-signal solutions. Silicon Labs' extensive patent portfolio is a testament to our unique approach and world-class engineering team.
The information in this document is believed to be accurate in all respects at the time of publication but is subject to change without notice.
Silicon Laboratories assumes no responsibility for errors and omissions, and disclaims responsibility for any consequences resulting from
the use of information included herein. Additionally, Silicon Laboratories assumes no responsibility for the functioning of undescribed features or parameters. Silicon Laboratories reserves the right to make changes without further notice. Silicon Laboratories makes no warranty, representation or guarantee regarding the suitability of its products for any particular purpose, nor does Silicon Laboratories assume any
liability arising out of the application or use of any product or circuit, and specifically disclaims any and all liability, including without limitation
consequential or incidental damages. Silicon Laboratories products are not designed, intended, or authorized for use in applications intended to support or sustain life, or for any other application in which the failure of the Silicon Laboratories product could create a situation where
personal injury or death may occur. Should Buyer purchase or use Silicon Laboratories products for any such unintended or unauthorized
application, Buyer shall indemnify and hold Silicon Laboratories harmless against all claims and damages.
Silicon Laboratories and Silicon Labs are trademarks of Silicon Laboratories Inc.
Other products or brandnames mentioned herein are trademarks or registered trademarks of their respective holders.
4
Rev. 1.0
``` | 1,295 | 5,713 | {"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} | 2.75 | 3 | CC-MAIN-2017-26 | longest | en | 0.86648 |
https://physicscomputingblog.com/tag/wavepacket/ | 1,597,002,540,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439738573.99/warc/CC-MAIN-20200809192123-20200809222123-00156.warc.gz | 448,754,930 | 27,647 | Numerical solution of PDE:s, Part 7: 2D Schrödinger equation
Haven’t been posting for a while, but here’s something new… Earlier I showed how to solve the 1D Schrödinger equation numerically in different situations. Now I’m going to show how to calculate the evolution of a 2D wavepacket in a potential energy field that has been constructed to mimic the classical “two-slit experiment” which shows how the mechanics of low-mass particles like electrons can exhibit interference similar to the mechanics of classical waves (sound, light, water surface, and so on).
A 2D Schrödinger equation for a single particle in a time-independent background potential V(x,y) is
Where the particle mass has been set to 1 and the Planck’s constant to $2\pi$.
To solve this numerically, we need the Crank-Nicolson method, as was the case when solving the 1D problem. More specifically, the linear system to be solved is
with
where the wavefunction now has two position indices and one time index, and the potential energy has only two position indices.
To form a model of the two-slit experiment, we choose a domain 0 < x < 6; 0 < y < 6 and make a potential energy function defined by
IF (x < 2.2 OR x > 3.8 OR (x > 2.7 AND x < 3.3)) THEN IF (3.7 < y < 4) THEN V(x,y) = 30
IF (x < 0.5 OR x > 5.5 OR y < 0.5 OR y > 5.5) THEN V(x,y) = 30
Otherwise V(x,y) = 0.
which corresponds to having hard walls surrounding the domain and a barrier with two holes around the line y = 3.85
For an initial condition, we choose a Gaussian wavepacket that has a nonzero expectation value of the momentum in y-direction:
An R-Code that solves this problem for a time interval 0 < t < 1 is
library(graphics) #load the graphics library needed for plotting
lx <- 6.0 #length of the computational domain (both x and y)
lt <- 1.0 #length of the simulation time interval
nx <- 47 #number of discrete lattice points in x and y directions
nt <- 60 #number of timesteps
dx <- lx/nx #length of one discrete lattice cell, same in x and y directions
dt <- lt/nt #length of timestep
V = matrix(nrow=nx,ncol=nx) #potential energies at discrete xy points
for(j in c(1:nx)) { #construct the potential field with a double-slit barrier
for(k in c(1:nx)) {
V[j,k] = 0+0i
if((j*dx<2.2)||(j*dx>3.8)||((j*dx>2.7) && (j*dx<3.3))) {
if((k*dx>3.7) && (k*dx<4.0)) {
V[j,k] = 30+0i #No significant density is going to go through these barriers
}
}
if((j*dx>5.5) || (j*dx<0.5) || (k*dx>5.5) || (k*dx<0.5)) {
V[j,k] = 30+0i
}
}
}
kappa1 = (1i)*dt/(2*dx*dx) #an element needed for the matrices
kappa2 <- c(1:(nx*nx)) #another element
for(j in c(1:nx)) {
for(k in c(1:nx)) {
kappa2[(j-1)*nx+k] <- kappa1*2*dx*dx*V[j,k]
}
}
psi = c(1:(nx*nx)) #array for the wave function values
for(j in c(1:nx)) {
for(k in c(1:nx)) {
psi[(j-1)*nx+k] = exp(-2*(k*dx-1.7)*(k*dx-1.7)-2*(j*dx-3)*(j*dx-3)+(2i)*k*dx) #Gaussian initial wavefunction
if((j*dx > 5.5)||(j*dx < 0.5)||(k*dx > 5.5)||(k*dx < 0.5)) {
psi[(j-1)*nx+k] = as.complex(0)
}
}
}
xaxis <- c(1:nx)*dx #the x values corresponding to the discrete lattice points
yaxis <- c(1:nx)*dx #the y values
A = matrix(nrow=nx*nx,ncol=nx*nx) #matrix for forward time evolution
B = matrix(nrow=nx*nx,ncol=nx*nx) #matrix for backward time evolution
P = matrix(nrow=nx,ncol=nx) #matrix for the solution after time stepping
IP = matrix(nrow=4*nx,ncol=4*nx) #matrix for the higher resolution image obtained by interpolation
for(j in c(1:(nx*nx))) { #Set the values for time evolution matrix elements
for(k in c(1:(nx*nx))) {
A[j,k]=0
B[j,k]=0
if(j==k) {
A[j,k] = 1 + 4*kappa1 + kappa2[j]
B[j,k] = 1 – 4*kappa1 – kappa2[j]
}
if((k==j+1) || (k==j-1)) {
A[j,k] = -kappa1
B[j,k] = kappa1
}
if((k==j+nx)||(k==j-nx)) {
A[j,k] = -kappa1
B[j,k] = kappa1
}
}
}
for(k in c(1:nt)) { #main time stepping loop
sol <- solve(A,B%*%psi) #solve the system of equations
for(l in c(1:(nx*nx))) {
psi[l] <- sol[l]
}
for(l in c(1:nx)) {
for(m in c(1:nx)) {
P[l,m] = abs(psi[(l-1)*nx + m])*abs(psi[(l-1)*nx + m]) #square of the absolute value of wave function
if(abs(V[l,m]) > 5) P[l,m] = 2
}
}
for(l in c(1:(nx-1))) {
for(m in c(1:(nx-1))) { #make a bitmap with 4 times more pixels, using linear interpolation
IP[4*l-3,4*m-3] = P[l,m]
IP[4*l-2,4*m-3] = P[l,m]+0.25*(P[l+1,m]-P[l,m])
IP[4*l-1,4*m-3] = P[l,m]+0.5*(P[l+1,m]-P[l,m])
IP[4*l,4*m-3] = P[l,m]+0.75*(P[l+1,m]-P[l,m])
}
}
for(l in c(1:(4*nx))) {
for(m in c(1:(nx-1))) {
IP[l,4*m-2] = IP[l,4*m-3]+0.25*(IP[l,4*m+1]-IP[l,4*m-3])
IP[l,4*m-1] = IP[l,4*m-3]+0.5*(IP[l,4*m+1]-IP[l,4*m-3])
IP[l,4*m] = IP[l,4*m-3]+0.75*(IP[l,4*m+1]-IP[l,4*m-3])
}
}
jpeg(file = paste(“plot_abs_”,k,”.jpg”,sep=””)) #save the image
image(IP, zlim = c(0,0.15))
dev.off()
}
The code produces a sequence of image files, where the probability density is plotted with colors, as an output. Some representative images from this sequence (converted to grayscale) is shown below:
A video of the time evolution is shown below:
The treshold for maximum white color has been chosen to be quite low, to make the small amount of probability density that crosses the barrier visible.
The discrete grid of points has been made quite coarse here to keep the computation time reasonable, and the resolution has been increased artificially by using linear interpolation between the discrete points.
So, now we’ve seen how to solve the motion of 2D wavepackets moving around obstacles. In the next numerical methods post, I’ll go through the numerical solution of a nonlinear PDE.
Numerical solution of PDE:s, Part 4: Schrödinger equation
In the earlier posts, I showed how to numerically solve a 1D or 2D diffusion or heat conduction problem using either explicit or implicit finite differencing. In the 1D example, the relevant equation for diffusion was
and an important property of the solution was the conservation of mass,
i.e. the integral of the concentration field over whole domain stays constant.
Next, I will show how to integrate the 1D time-dependent Schrödinger equation, which in a nondimensional form where we set $\hbar = 1$ and $m = 1$ reads:
Here $i$ is the imaginary unit and $V(x)$ is the potential energy as a function of $x$. The solutions of this equation must obey a conservation law similar to the mass conservation in the diffusion equation, the conservation of norm:
where the quantity $|\Psi (x,t)|$ is the modulus of the complex-valued function $\Psi (x,t)$ . This property of the solution is also called unitarity of the time evolution.
Apart from the TDSE, another way to represent the time development of this system is to find the normalized solutions $\psi_0 (x)$, $\psi_1 (x)$, $\psi_2 (x) \dots$ of the time-independent Schrödinger equation
and write the initial state $\Psi (x,0)$ as a linear combination of those basis functions:
This is possible because the solutions of the time-independent equation form a basis for the set of acceptable wave functions $\psi (x)$. Then, every term in that eigenfunction expansion is multiplied by a time dependent phase factor $\exp(-iE_n t)$:
The numbers $E_n$ are the eigenvalues corresponding to the solutions $\psi_n (x)$ and the function $\psi_0 (x)$ is called the ground state corresponding to potential $V(x)$, while the functions $\psi_1 (x)$ is the first excited state and so on.
The Schrödinger equation can’t be discretized by using either the explicit or implicit method that we used when solving the diffusion equation. The method is either numerically unstable or doesn’t conserve the normalization of the wave function (or both) if you try to do that. The correct way to discretize the Schrödinger equation is to replace the wave function with a discrete equivalent
and the potential energy function $V(x)$ with $V_{i;j}$ (or $V_i$ in the case of time-independent potential), and write an equation that basically tells that propagating the state $\Psi_{i;j}$ forward by half a time step gives the same result as propagating the state $\Psi_{i;j+1}$ backwards by half a time step:
Here we have
and
This kind of discretization is called the Crank-Nicolson method. As boundary conditions, we usually set that at the boundaries of the computational domain the wavefunction stays at value zero: $\Psi (0,t) = \Psi (L,t) = 0$ for any value of $t$. In the diffusion problem, this kind of a BC corresponded to infinite sinks at the boundaries, that annihilated anything that diffused through them. In the Schrödinger equation problem, which is a complex diffusion equation, the equivalent condition makes the boundaries impenetrable walls that deflect elastically anything that collides with them.
An R-Code that calculates the time evolution of a Gaussian initial wavefunction
in an area of zero potential:
for a domain 0 < x < 6, a lattice spacing $\Delta x = 0.05$, time interval 0 < t < 2 and time step $\Delta t = 0.01$, is given below:
library(graphics) #load the graphics library needed for plotting
lx <- 6.0 #length of the computational domain
lt <- 2.0 #length of the simulation time interval
nx <- 120 #number of discrete lattice points
nt <- 200 #number of timesteps
dx <- lx/nx #length of one discrete lattice cell
dt <- lt/nt #length of timestep
V = c(1:nx) #potential energies at discrete points
for(j in c(1:nx)) {
V[j] = 0 #zero potential
}
kappa1 = (1i)*dt/(2*dx*dx) #an element needed for the matrices
kappa2 <- c(1:nx) #another element
for(j in c(1:nx)) {
kappa2[j] <- as.complex(kappa1*2*dx*dx*V[j])
}
psi = as.complex(c(1:nx)) #array for the wave function values
for(j in c(1:nx)) {
psi[j] = as.complex(exp(-2*(j*dx-3)*(j*dx-3))) #Gaussian initial wavefunction
}
xaxis <- c(1:nx)*dx #the x values corresponding to the discrete lattice points
A = matrix(nrow=nx,ncol=nx) #matrix for forward time evolution
B = matrix(nrow=nx,ncol=nx) #matrix for backward time evolution
for(j in c(1:nx)) {
for(k in c(1:nx)) {
A[j,k]=0
B[j,k]=0
if(j==k) {
A[j,k] = 1 + 2*kappa1 + kappa2[j]
B[j,k] = 1 - 2*kappa1 - kappa2[j]
}
if((j==k+1) || (j==k-1)) {
A[j,k] = -kappa1
B[j,k] = kappa1
}
}
}
for (k in c(1:nt)) { #main time stepping loop
sol <- solve(A,B%*%psi) #solve the system of equations
for (l in c(1:nx)) {
psi[l] <- sol[l]
}
if(k %% 3 == 1) { #make plots of |psi(x)|^2 on every third timestep
jpeg(file = paste("plot_",k,".jpg",sep=""))
plot(xaxis,abs(psi)^2,xlab="position (x)", ylab="Abs(Psi)^2",ylim=c(0,2))
title(paste("|psi(x,t)|^2 at t =",k*dt))
lines(xaxis,abs(psi)^2)
dev.off()
}
}
The output files are plots of the absolute squares of the wavefunction, and a few of them are shown below.
In the next simulation, I set the domain and discrete step sizes the same as above, but the initial state is:
Which is a Gaussian wave packet that has a nonzero momentum in the positive x-direction. This is done by changing the line
for(j in c(1:nx)) {
psi[j] = as.complex(exp(-2*(j*dx-3)*(j*dx-3))) #Gaussian initial wavefunction
}+(1i)*j*dx
into
for(j in c(1:nx)) {
psi[j] = as.complex(exp(-2*(j*dx-3)*(j*dx-3)+(1i)*j*dx)) #Gaussian initial wavefunction
}
The plots of $|\Psi (x,t)|^2$ for several values of $t$ are shown below
and there you can see how the wave packet collides with the right boundary of the domain and bounces back.
In the last simulation, I will set the potential function to be
which is a harmonic oscillator potential, and with the nondimensional mass $m =1$ and Planck constant $\hbar = 1$ the ground state $\psi _0 (x)$ of this system is
If I’d set the initial state to be $\Psi (x,0) = \psi_0 (x)$, or any other solution of the time-independent SE, the modulus of the wavefunction would not change at all. To get something interesting to happen, I instead set an initial state that is a displaced version of the ground state:
The solution can be obtained with the code shown below:
library(graphics) #load the graphics library needed for plotting
lx <- 6.0 #length of the computational domain
lt <- 3.0 #length of the simulation time interval
nx <- 360 #number of discrete lattice points
nt <- 300 #number of timesteps
dx <- lx/nx #length of one discrete lattice cell
dt <- lt/nt #length of timestep
V = c(1:nx) #potential energies at discrete points
for(j in c(1:nx)) {
V[j] = as.complex(2*(j*dx-3)*(j*dx-3)) #Harmonic oscillator potential with k=4
}
kappa1 = (1i)*dt/(2*dx*dx) #an element needed for the matrices
kappa2 <- c(1:nx) #another element
for(j in c(1:nx)) {
kappa2[j] <- as.complex(kappa1*2*dx*dx*V[j])
}
psi = as.complex(c(1:nx)) #array for the wave function values
for(j in c(1:nx)) {
psi[j] = as.complex(exp(-(j*dx-2)*(j*dx-2))) #Gaussian initial wavefunction, displaced from equilibrium
}
xaxis <- c(1:nx)*dx #the x values corresponding to the discrete lattice points
A = matrix(nrow=nx,ncol=nx) #matrix for forward time evolution
B = matrix(nrow=nx,ncol=nx) #matrix for backward time evolution
for(j in c(1:nx)) {
for(k in c(1:nx)) {
A[j,k]=0
B[j,k]=0
if(j==k) {
A[j,k] = 1 + 2*kappa1 + kappa2[j]
B[j,k] = 1 - 2*kappa1 - kappa2[j]
}
if((j==k+1) || (j==k-1)) {
A[j,k] = -kappa1
B[j,k] = kappa1
}
}
}
for (k in c(1:nt)) { #main time stepping loop
sol <- solve(A,B%*%psi) #solve the system of equations
for (l in c(1:nx)) {
psi[l] <- sol[l]
}
if(k %% 3 == 1) { #make plots of Abs(psi(x))^2 on every third timestep
jpeg(file = paste("plot_",k,".jpg",sep=""))
plot(xaxis,abs(psi)^2, xlab="position (x)", ylab="Abs(Psi)^2",ylim=c(0,2))
title(paste("|psi(x,t)|^2 at t =",k*dt))
lines(xaxis,abs(psi)^2)
lines(xaxis,V)
dev.off()
}
}
and the solution at different values of $t$ look like this (images and video):
Here the shape of the Hookean potential energy is plotted in the same images. So, here you see how the center of the Gaussian wavefunction oscillates around the point $x = 3$, just like a classical mechanical harmonic oscillator does when set free from a position that is displaced from equilibrium.
By changing the code that produces the output images, we can also get a sequence of plots of the imaginary part of the wavefunction:
if(k %% 3 == 1) { #make plots of Im(psi(x)) on every third timestep
jpeg(file = paste("plot_",k,".jpg",sep=""))
plot(xaxis,Im(psi), xlab="position (x)", ylab="Im(Psi)",ylim=c(-1.5,1.5))
title(paste("Im(psi(x,t)) at t =",k*dt))
lines(xaxis,Im(psi))
lines(xaxis,V)
dev.off()
}
and the resulting plots look like this: | 4,431 | 14,241 | {"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": 36, "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} | 3.28125 | 3 | CC-MAIN-2020-34 | latest | en | 0.886203 |
https://classbasic.com/2021/05/25/third-term-examination-mathematics-primary-5-basic-5-exam-questions/ | 1,624,274,887,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488269939.53/warc/CC-MAIN-20210621085922-20210621115922-00486.warc.gz | 167,836,979 | 35,276 | # Third Term Examination Mathematics Primary 5 (Basic 5) – Exam Questions
Last Updated on May 25, 2021 by Alabi M. S.
MATHEMATICS
THIRD TERM EXAMINATION
PRIMARY 5 (BASIC 5)
SECTION A
Attempt all the questions.
Choose the correct answer from the options.
1. ______________ is the degree of hotness or coldness of the body.
[a] Power
[b] Temperature
[c] Celsius
2. Convert 30º C to degree Fahrenheit.
[a] 86º
[b] 76º
[c] 66º
3. Each of the angles of an equilateral triangle measure ______________.
[a] 80º
[b] 60º
[c] 45º
4. Which of the plane shapes has four lines of symmetry?
[a] Rectangle
[b] Square
[c] Triangle
5. Two lines are said to be ______________ if they intersect at a right angle.
[a] parallel lines
[b] perpendicular lines
[c] diagonal lines
6. Calculate the lettered angle in the figure below:
[a] 55ª
[b] 45ª
[c] 35ª
7. Name these 3 – dimensional shape?
[a] Prism
[b] Cylinder
[c] Net cylinder
8. How many edges are there in the shape of a cuboid?
[a] 6 edges
[b] 9 edges
[c] 12 edges
9. The distance round a circle or its boundary called ______________.
[a] diameter
[c] circumference
10. The measurement from base to top is called ______________.
[a] distance
[b] height
[c] perimeter
11. Convert 1001two to base 10?
[a] 910
[b] 1410
[c] 1210
12. Evaluate 11101two – 1011two
[a] 10010two
[b] 10010two
[c] 10011two
13. ______________ means the collection, classification analysis, presentation and interpretation of data.
[a] Graph
[b] Tally
[c] Statistics
Study this data and answer and answer the 2, 2, 2, 4, 8, 5, 6, 4, 3, 4
14. What is the mode of the data?
[a] 2
[b] 5
[c] 5
15. The mean is
[a] 40
[b] 15
[c] 4
Get more Mathematics Exam Questions – Third Term Examination Mathematics Link
SECTION B
Attempt all questions in this section.
QUESTION 1
A. Convert 30º C to degree Fahrenheit.
B. Convert 35º F to degree Celsius.
C. Indicate the type of lines in each case?
QUESTION 2
A. State 2 each properties of the following plane shapes.
I. Rhombus
II. Square
III. Kite
B. Write these angle sizes in degrees:
I. 1½ right angle
II. Two third of a right angle
III. 80% of 3 right angle
QUESTION 3
A. How many edges are there in the following 3 – dimensional shapes:
I. Cylinder
II. Prism
III. A matches box
B. A wheel of circumference 40cm is for 200 times, what was the distance covered?
QUESTION 4
A. Express each of the following in metres:
I. 500 cm
II. 480 cm
III. 10,000 cm
B. Convert 1110two to base 10.
QUESTION 5
A. In a class the number of pupils who passed English is 40, mathematics 90, science 50, and literature 45. Represent this information in a pictogram.
B. Find the simple interest on ₦600.00 for 4 years at 6% per annum. | 826 | 2,757 | {"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} | 4 | 4 | CC-MAIN-2021-25 | latest | en | 0.789617 |
www.lothar.com | 1,722,882,386,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640454712.22/warc/CC-MAIN-20240805180114-20240805210114-00295.warc.gz | 38,136,069 | 8,122 | Many cryptographic protocols, like Diffie-Hellman and SPAKE2, require a way to choose a uniformly random scalar from some prime-order range. Why? What is the best way to do this?
## What (is a scalar)?
Classic Diffie-Hellman Key Exchange starts with each side chosing a random scalar. This is kept secret, but is used to derive a "public ephemeral element" that is sent to the other side. It is also used upon the peer's ephemeral element to build the shared secret element, from which the final secret key is derived. SPAKE2, as a modified DH protocol, relies on this secret random scalar too.
Scalars are basically integers in a specific range, bounded by the order of an Abelian group, and the order is generally a big prime number P. To be precise, scalars are "equivalence classes of integers modulo P", meaning that you're choosing a class of integers, all of which are equal to each other if your idea of "equal" is modulo P. If P is 5, then one such equivalence class is the integers 2, 7, 12, -3, -8, -13, etc. Each of these classes can be represented by a single member, which is an integer between 0 and P, so we usually pretend that scalars are just integers with the constraint that `0 <= x < P`. We say "2" instead of "the class that includes 2, 7, 12, etc".
Also note: there is some confusion, at least in my mind, about the precise range of scalars. Some references (including the original SPAKE2 paper) say `Zp`, which means any positive integer less than P (```0 <= x < P```). The Handbook of Applied Cryptography section on Diffie-Hellman (protocol 12.47, page 516) says scalars should be `1 <= x <= P-2` (excluding both 0 and -1). I'm pretty sure that 0 is a bad choice: in DH it will cause the resulting shared element to always be the same thing (the identity element), independent of the other party's message. It's a bit like a weak key in symmetric ciphers. But P is huge, so the chance of accidentally getting a scalar of 0 (or any other specific value) is effectively nil. As long as the protocol only uses scalars from trusted sources (i.e. ourselves, not the network), we don't need to worry about it.
So for simplicity, I'll define our task to be generating an integer `x`, where `0 <= x < P` for some large (prime) P, such that the value is uniformly randomly distributed in that range (all values are equally likely).
## Why (do we need a random one)?
The DSA and ECDSA signature algorithms also use a unique secret random scalar (known as a "nonce", or just `k`), and are vulnerable to attack if this nonce is biased. If you know the first or last few bits of each nonce, and you have multiple signatures to work with, then a brute-force search for the signer's private key is much easier than it should be. In some cases, the private key can be recovered in a couple of hours.
Of course, if the implementation doesn't even try to be random, then you wind up with things like the Playstation 3 where they used the same hard-coded value of `k` for every single message, allowing the private key to be recovered trivially with just two signatures.
It isn't clear if other protocols (like DH) are quite this vulnerable. The Logjam paper, in section 3.5, mentions attacks on small-exponent DH in poorly-chosen integer groups, and this email about Curve25519 scalars points out the attack-resistance provided by their specific clamping decisions (which constrain the scalar to certain values). But in general, our security proofs are built around the assumption that the scalar is unique and uniformly random, so to be safe we must follow those rules.
## How (do we create one)?
We can assume that our operating system gives us a source of random bytes. `/dev/urandom` on a fully-initialized unix-like host will give us as many as we need.
If our target range `0 <= x < 256`, or `0 <= x < 65536`, or some other power of 256, that'd be trivial. It would also be easy to produce integers in a range that's any integral power of two (you just mask off the extra bits, and treat the result as an integer). But since P is a prime, we're never going to have a nice round size for truncation.
So we need to use `/dev/urandom` to get a seed, and then convert some number of these seed bytes to an integer. This is pretty easy: just treat the array of bytes as a base-256 number. In Python2, we can exploit the `hexlify()` and `int()` functions to make this really fast (python3 adds `int.from_bytes()`, which is even better):
```def bytes_to_integer(seed_bytes):
return int(binascii.hexlify(seed_bytes), 16)
```
What's the range of this number? It will be 0 to `2**len(seed_bytes)`. If we use too few bytes, then it will obviously not even cover the entire target range, so our first step is to make the seed larger than the total range. This introduces the possibility of getting a number that's too big, so we'll have to modulo down:
```def make_random_scalar_with_bytes(seed_length_bytes, P):
# check that our seed will produce sufficiently-large integers
# the right-hand side is roughly equal to ln2(P)
assert 8*seed_length_bytes > (4*len("{:x}".format(P)))
seed_bytes = os.urandom(seed_length_bytes)
hash_int = bytes_to_integer(seed_bytes)
scalar = hash_int % P
return scalar
```
What's a reasonable choice of seed length? For the Curve25519 group, P is `2**252 + 27742317777372353535851937790883648493`, which lies on the low end of the range between `2**252` and `2**253`. If we use 253 random bits (which you get from 32 random bytes by doing something like ```seed_bytes[0] &= 0x1F``` to mask out the top three bits), then we'll get a suitable value slightly more than half the time, and the modulo function will kick in (i.e. "aliasing" occurs) slightly less than half the time.
But that's pretty badly biased. Each time aliasing happens (e.g. `hash_int >= P`) means that two values of `hash_int` (which is uniform) are mapping to the same value of `scalar` (which therefore is not uniform). Consider the simple case of `P = 2**8 - 1 == 255` (so we want outputs from 0 to 254, inclusive, and exclude only 255), and our `seed_length` is 1 byte. Seeds of 0 and 255 will both map to an output of 0, so zeros will appear in the output twice as frequently as any other value. The one case of aliasing will induce a bias in our output.
The amount of bias, in a statistical sense, depends upon how many extra bits we start with, and how close our target `P` is to a power of 2, so it's something like `ln2(P) - floor(ln2(P))`, using the base-2 logarithm of our target P.
## The Best Good-Enough Solution
The simplest solution that yields a minimal bias is to throw more bits at the problem. Using a `seed_length` that's 32 bytes (128 bits) larger than we really need reduces the bias to a statistically insignificant level. In this case, we're aliasing almost all the time:
```def make_random_scalar(P):
# conversion that reduces the bias to a fraction of a bit
minimal_length_bits = 4*len("%x" % P)
safe_length_bits = minimal_length_bits + 128
safe_length_bytes = safe_length_bytes // 8
# that gets us between 121 and 128 bits of safety margin
return make_random_scalar_with_bytes(safe_length_bytes, P)
```
This is the approach used by the Ed25519 codebase to compute unbiased deterministic nonces from the private key and the message being signed. These nonces have the same requirements as ECDSA: they must be unique and unbiased. The Ed25519 signing function creates a 512-bit hash and then reduces it down to the ~252-bit group order: see the bottom of page 6 of the Ed25519 paper, where `r` is the nonce, and computations end up being performed mod `P` (which they call `l`). They use about 258 extra bits.
FIPS 186-4, which defines DSA and ECDSA, says that 64 extra bits are sufficient (in appendix B.2.1).
## The Exact Solution: Try-Try-Again
There is a way to remove all the bias, but you might not like it. To achieve zero bias, you remove the modulo-P step (so there's no chance of aliasing), and you add a loop that keeps trying new random seeds over and over again until the integer just happens to be in the right range.
```def try_try_again(P):
length_in_bits = 4*len("%x" % P)
seed_length_bytes = round_up_to_multiple_of_eight(length_in_bits)
while True:
candidate = bytes_to_integer(seed_bytes)
if candidate < P:
return candidate
# else, try again
```
This takes an unpredictable amount of time, but provides a perfectly uniform output. The number of trials that you'll need depends upon the same bias that we're removing. If you mask the bytes down to the minimum number of bits, then the worst case (where P is just slightly larger than some power of 2) is an average of two passes. If you don't bother masking individual bits, then the worst case is 255 average passes. If P is just slightly smaller than a power of 2, the average is a single pass.
But this is an exponential distribution: if you're really unlucky, it could take thousands of iterations before you find a suitable integer, or worse. The mean is small, but the maximum is infinite.
I used this "try-try-again" algorithm as an option in python-ecdsa. But unbounded runtime is a drag, so the recommended approach is to use the extra-128-bits scheme described above (in `make_random_scalar()`).
This technique is also used (since around 2003 for large ranges, and since 2010 for all ranges) in Python's `random.SystemRandom.randrange()` function, and `secrets.randbelow()` in Python3.6.
Before that point, python2.4 had a bug (reported by none other than Ron Rivest, the R in RSA!) in which `random.SystemRandom` used `/dev/urandom` as a seed correctly, but `randrange()` used that seed to create a floating point number, then multiplied it out to the desired range (and rounded the result to an integer). As a result, no matter how large a range you asked for, the number could never have more than about 53 bits of entropy (and in fact the low-order bits were always zero, which is exactly where ECDSA is vulnerable).
That bug was fresh in my mind when I wrote the python-ecdsa code, which is why I avoided using the standard library functions. But at this point it's probably safe to just use the following (though be sure to check what the underlying functions are really doing, especially if you're porting this to some other language which might have made the same mistake as Python):
```import secrets
def make_random_scalar(P):
return secrets.randbelow(P)
```
or, on python2.7:
```from random import SystemRandom
def make_random_scalar(P):
return SystemRandom().randrange(P)
```
## Scalars From Seeds
For testing, it may be useful to break the function up into two pieces. The private inner function is deterministic, and accepts the seed bytes as an argument. The externally-visible outer function is where `/dev/urandom` is sampled. The inner function can be unit tested.
```def _bytes_to_integer(seed_bytes):
return int(binascii.hexlify(seed_bytes), 16)
def _map_bytes_to_scalar(seed_bytes, P):
# check that our seed will produce sufficiently-large integers
# the right-hand side is roughly equal to ln2(P)
assert 8*len(seed_bytes) > (4*len("{:x}".format(P)))
hash_int = _bytes_to_integer(seed_bytes)
scalar = hash_int % P
return scalar
def make_random_scalar(P):
# conversion that reduces the bias to a fraction of a bit
minimal_length_bits = 4*len("%x" % P)
safe_length_bits = minimal_length_bits + 128
safe_length_bytes = safe_length_bytes // 8
# that gets us between 121 and 128 bits of safety margin
seed_bytes = os.urandom(seed_length_bytes)
return _map_bytes_to_scalar(seed_bytes, P)
```
This can also be used in a related function: mapping seeds to scalars. This function is needed for protocols like SPAKE2, where the `password` input must be converted into a scalar for the blinding step. In this case, uniformity is not strictly necessary (the SPAKE2 password isn't randomly distributed, so any deterministic function of it will have the same non-random distribution). But if your library already has `_map_bytes_to_scalar()`, then it may be easiest to build on top of that:
```def password_to_scalar(pw, P):
seed = sha256(pw).digest()
return _map_bytes_to_scalar(seed, P)
```
In addition, you might want the seed-to-scalar function to behave differently for different protocols, so the same password used in two different places doesn't produce values which could be mixed/matched in an attack. The usual way to accomplish this is to feed some sort of algorithm identifier into the hash function. Some options are:
• a simple prefix string: `sha256("my algorithm name" + pw)`
• a real key-derivation function: ```HKDF(context="my algorithm name", secret=pw)```. This also gives you exact control over the number of bytes, not limited to the native output size of the hash function.
• some modern hash functions like BLAKE2 have dedicated "personalization" inputs: ```blake2(input=pw, personalize="my algorithm name")```
## Use in python-spake2
All of this is an attempt to explain why the password-to-scalar function in my python-spake2 library is so over-complicated. When I wrote that function, I was worried that the blinding scalar needed to be uniformly random (like most other scalars in cryptographic protocols). So I combined all the techniques above: both algorithm-specific hash personalization and using an oversized hash output.
In retrospect, it would probably have been ok to just truncate a plain SHA256 output to something less than the Curve25519 group order. In fact, just using 128 bits would have been enough, which removes the need for the modulo step.
```def password_to_scalar(pw, P):
return _bytes_to_integer(sha256(pw).digest()[:16])
```
So if you're looking at the `password_to_scalar` function in python-spake2 and think it's unnecessarily complicated, that's why.
## Conclusions
Thanks to Thomas Ptáček, Sean Devlin, Thomas Pornin, and Zaki Manian for their advice and feedback. | 3,314 | 13,886 | {"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} | 3.171875 | 3 | CC-MAIN-2024-33 | latest | en | 0.914077 |
https://www.coursehero.com/file/6161450/Lecture23/ | 1,513,194,189,000,000,000 | text/html | crawl-data/CC-MAIN-2017-51/segments/1512948530668.28/warc/CC-MAIN-20171213182224-20171213202224-00505.warc.gz | 761,046,062 | 374,861 | # Lecture23 - ECO220Y Lecture 23 Estimation of when 2 is...
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ECO220Y Lecture 23 CO220 ectu e 23 Estimation of μ when σ 2 is unknown Migiwa Tanaka Reading: 8.4 (pp. 281 – 285), and 12.1 (pp.381 – 383, 386 – 391) 1
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utline Outline Introduction: Estimation of μ when σ 2 is unknown Student t Distribution Application – Estimation of weekly sales 2
stimation of μ when unknown Estimation of μ when σ 2 is unknown Lecture 21 & 22: Estimation of mean of X, μ when σ 2 is known: Under a certain condition, 2 X 1- α CI estimator of μ: ) 1 , 0 ( ~ , ~ N N X n n z X This lecture: Estimation of mean of X, μ when σ 2 is n 2 / unknown . Since σ is unknown, need to estimate it. A natural candidate estimator: sample standard deviation, s . X No! The complication is that 3 ? ) 1 , 0 ( N n s s is r.v. while σ is constant.
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sing s as an estimator of Using s as an estimator of X is r.v. with mean μ and variance 2 , ~ 2 N X n , ~ 2 N X n X Z X Y / n / 2 n s n ) 1 , 0 ( N Z where 1 X X s i i ? ~ 1 Y n 4
sing s as an estimator of Using s as an estimator of X ) 1 , 0 ( ~ / N n s It was found by British Statistician, William S. Gosset, who worked for a brewery in Ireland. Moreover, he found following: If X is normally distributed , called “t statistics” follows Student t istribution with egree of freedom n s X / distribution with degree of freedom, ν . ) ( ~ t X t 5 / n s
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tudent t Distribution (Recap Lecture16) Student t Distribution (Recap, Lecture16) Student t density function is give by: 2 ) 1 ( 2 ! 2 1 y 1 !
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Ask a homework question - tutors are online | 658 | 2,212 | {"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} | 3 | 3 | CC-MAIN-2017-51 | latest | en | 0.804927 |
https://tolstoy.newcastle.edu.au/R/help/04/05/0220.html | 1,550,650,067,000,000,000 | text/html | crawl-data/CC-MAIN-2019-09/segments/1550247494485.54/warc/CC-MAIN-20190220065052-20190220091052-00212.warc.gz | 702,431,086 | 2,133 | # Re: [R] anyone know how to combine two vector with some # overlaped?
From: Richard A. O'Keefe (ok@cs.otago.ac.nz)
Date: Wed 05 May 2004 - 18:08:01 EST
```Message-id: <200405050808.i45881t1115500@atlas.otago.ac.nz>
```
If you want this:
> Suppose I have two vector say x=c(1 2 3 4 5) and y=(2
> 3 6 7). Then I want to combine these two vector
> together and get z=c(1 2 3 4 5 6 7) with 2 and 3 only
> appear once.
x <- c(1,2,3,4,5)
y <- c(2,3,6,7)
z <- c(x,y)[!duplicated(c(x,y))]
But you can do it in one step:
z <- unique(c(x,y))
I don't know how unique() is implemented, but using a hash table it
_could_ be done in linear expected time, and in practice it seems to
be pretty quick, more than quick enough for a few hundred elements.
______________________________________________
R-help@stat.math.ethz.ch mailing list
https://www.stat.math.ethz.ch/mailman/listinfo/r-help | 294 | 885 | {"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} | 2.515625 | 3 | CC-MAIN-2019-09 | latest | en | 0.775961 |
https://nl.mathworks.com/matlabcentral/answers/142664-how-to-find-standard-deviation-of-a-linear-regression | 1,713,959,121,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296819273.90/warc/CC-MAIN-20240424112049-20240424142049-00827.warc.gz | 374,227,134 | 28,622 | # How to find standard deviation of a linear regression?
79 views (last 30 days)
Ronny on 20 Jul 2014
Commented: star on 28 Jun 2016
Hi everybody
I have an actually pretty simple problem which is driving me crazy right now. There are two sets of data: one for O2 and one for Heat. I made a linear regression in the plot of those two data sets which gives me an equation of the form O2 = a*Heat +b. So now I need to find the confidance interval of a. That for I need to find the standard deviation of a which I somehow just can't find out how to get it. Of course it would also work for me if there is a function that returns the confidance interval directly.
Cheers Ronny
Star Strider on 20 Jul 2014
Edited: Star Strider on 21 Jul 2014
With absolutely no humility at all I direct you to polyparci. It calculates the confidence intervals for you for both parameters:
[p,S] = polyfit(Heat, O2, 1);
CI = polyparci(p,S);
If you have two vectors, Heat and O2, and a linear fit is appropriate to your data, this code should work.
Ronny on 21 Jul 2014
Thanks. That works.
Star Strider on 21 Jul 2014
My pleasure!
Shashank Prasanna on 21 Jul 2014
Ronny, it is fairly easy to calculate in few lines of code, however it is easier to use functions such as fitlm to perform linear regression. fitlm gives you standard errors, tstats and goodness of fit statistics right out of the box:
If you want to code it up yourself, its 5 or so lines of code, but I'll let you give it a shot first.
##### 3 CommentsShow 1 older commentHide 1 older comment
Shashank Prasanna on 21 Jul 2014
What do you mean by no intercept and strange slope ?
You should get the same results no matter what approach you use to solve your least squares problem.
If you got something different, I'd be interested in knowing more about it.
fitlm by default computes the intercept for you, here is an example:
x = (1:10)'
y = 10+5*x + randn(10,1)
fitlm(x,y)
ans =
Linear regression model:
y ~ 1 + x1
Estimated Coefficients:
Estimate SE tStat pValue
________ _______ ______ __________
(Intercept) 10.164 0.85652 11.866 2.3351e-06
x1 5.0984 0.13804 36.934 3.1669e-10
Number of observations: 10, Error degrees of freedom: 8
Root Mean Squared Error: 1.25
F-statistic vs. constant model: 1.36e+03, p-value = 3.17e-10
star on 28 Jun 2016
these two methods (polyparci and fitlm) find the same trend values. But, the results of the confidence intervals are different in these two methods. Polyparci seems to be more optimistic. For a given set of data, polyparci results in confidence interval with 95% (3 sigma) between CI =
4.8911 7.1256
5.5913 11.4702
So, this means we have a trend value between 4.8911 and 5.5913 in 95% confidence interval. What we found from this result is that 1 sigma is 0.1167.
However, for the same data set fitlm results in SE
Estimate SE tStat pValue
________ _______ ______ __________
(Intercept) 9.2979 1.1682 7.9592 4.5304e-05
x1 5.2412 0.18827 27.838 2.9924e-09
this indicates 0.18827 for one sigma. So, the trend values are same. But, the sigma values of estimated trends are different.
### Categories
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GATE CSE 1999
Subjective
+2
-0
(a) Mr. X claims the following:
If a relation R is both symmetric and transitive, then R is reflexive. For this, Mr. X offers the following proof.
"From xRy, using symmetry we get yRx. Now because R is transitive, xRy and yRx togethrer imply xRx. Therefore, R is reflextive."
Briefly point out the flaw in Mr. X' proof.
(b) Give an example of a relation R which is symmetric and transitive but not reflexive.
2
GATE CSE 1998
+2
-0.6
The binary relation R = {(1, 1)}, (2, 1), (2, 2), (2, 3), (2, 4), (3, 1), (3, 2), (3, 3), (3, 4) } on the set A = { 1, 2, 3, 4} is
A
Reflexive, symmetric and transitive
B
Neither reflexive, nor irreflexive but transitive
C
Irreflexive, symmetric and transitive
D
Irreflexive and antisymmetric
3
GATE CSE 1998
Subjective
+2
-0
Let (A, *) be a semigroup. Furthermore, for every a and b in A, if $$a\, \ne \,b$$, then $$a\,*\,b \ne \,\,b\,*\,a$$.
(a) Show that for every a in A
a * a = a
(b) Show that for every a, b in A
a * b * a = a
(c) Show that for every a, b, c in A
a * b * c = a * c
4
GATE CSE 1998
Subjective
+2
-0
Suppose A = {a, b, c, d} and $${\Pi _1}$$ is the following partition of A
$${\Pi _1}\, = \,\{ \{ a,\,\,b,\,\,c\,\} \,,\,\{ d\} \,\}$$
(a) List the ordered pairs of the equivalence relations induced by $${\Pi _1}$$
(b) Draw the graph of the above equivalence relation.
GATE CSE Subjects
EXAM MAP
Medical
NEET | 544 | 1,403 | {"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} | 3.640625 | 4 | CC-MAIN-2024-30 | latest | en | 0.851663 |
http://www.haskell.org/pipermail/haskell-cafe/2005-October/011776.html | 1,369,512,228,000,000,000 | text/html | crawl-data/CC-MAIN-2013-20/segments/1368706153698/warc/CC-MAIN-20130516120913-00062-ip-10-60-113-184.ec2.internal.warc.gz | 520,615,294 | 2,171 | Ross Paterson ross at soi.city.ac.uk
Wed Oct 19 11:32:08 EDT 2005
```On Wed, Oct 19, 2005 at 03:17:41PM +0100, Conor McBride wrote:
> I was just about to send, when up popped Ross's program, which does give
> me a datatype, including just enough extra stuff to support functoriality.
>
> >>data RegExp tok a
> >> = Zero
> >> | One a
> >> | Check (tok -> a) (tok -> Bool)
> >> | Plus (RegExp tok a) (RegExp tok a)
> >> | forall b. Mult (RegExp tok (b -> a)) (RegExp tok b)
> >> | forall e. Star ([e] -> a) (RegExp tok e)
>
> This combines several dodges rather neatly. You can see the traces of
> of saying forall e. Star (Eq [e] a) (RegExp tok e), Ross has kept just
> the half of the iso he needs in order to extract the parsed value.
The direction I've kept is the one that matters if everything is
covariant, because
forall a. F a -> T (G a)
~=
forall a, b. (G a -> b) -> F a -> T b
if F, G and T are functors. So we can translate
data T :: * -> * where
C :: F a -> T (G a)
to
data T b
= forall a. C (G a -> b) (F a)
data RegExp tok a
= Zero (Empty -> a) Empty
| One (() -> a) ()
| Check (tok -> a) (tok -> Bool) (RegExp tok a)
| forall b c. Plus (Either b c -> a) (RegExp tok b) (RegExp tok c)
| forall b c. Mult ((b, c) -> a) (RegExp tok b) (RegExp tok c)
| forall e. Star ([e] -> a) (RegExp tok e)
A little simplification (ignoring lifted types here and there) yields
the version I gave.
And of course we're no longer assuming that the function is half of an iso.
> Throwing away the other half more-or-less allows him to hide the
> head-glueing functions inside the grammar of the regular expressions. In
> effect, Map has been distributed through the syntax.
``` | 526 | 1,681 | {"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} | 2.71875 | 3 | CC-MAIN-2013-20 | longest | en | 0.835441 |
https://diaridelsestudiants.com/what-is-symbol-in-intersymbol-interference/ | 1,656,152,909,000,000,000 | text/html | crawl-data/CC-MAIN-2022-27/segments/1656103034930.3/warc/CC-MAIN-20220625095705-20220625125705-00182.warc.gz | 255,572,604 | 10,253 | ## What is symbol in intersymbol interference?
In telecommunication, intersymbol interference (ISI) is a form of distortion of a signal in which one symbol interferes with subsequent symbols. This is an unwanted phenomenon as the previous symbols have similar effect as noise, thus making the communication less reliable.
## What is intersymbol interference in optical communication?
Note 1: In fiber optic systems, intersymbol interference can occur when dispersion causes an excessive increase in pulse duration, i.e., spreading in time and space occupied by the pulse as it propagates along the optical fiber resulting in pulse overlap that might be so large that a photo-detector can no longer …
What point can be interpreted from eye diagrams?
As can be seen in Figure 4, an eye diagram can reveal important information. It can indicate the best point for sampling, divulge the SNR (signal-to-noise ratio) at the sampling point, and indicate the amount of jitter and distortion.
How does the eye diagram give information about ISI?
An eye pattern provides the following information about a particular system. Actual eye patterns are used to estimate the bit error rate and the signal-to-noise ratio. The width of the eye opening defines the time interval over which the received wave can be sampled without error from ISI.
### Who was the first to solve the problem of intersymbol interference?
4. Who was the first to solve the problem of ISI? Explanation: Nyquist was the first to solve the problem of ISI. He overcome the problem of ISI while keeping the transmission bandwidth low.
### What is correlative coding?
Correlative coding is also known as partial response signalling schemes which are used to obtain a bit rate of 2W bits per second in a channel of bandwidth W Hertz. ISI is usually an unwanted phenomenon and correlative coding helps in mitigating it.
What’s the remedy to manage the dispersion in the multi mode fiber?
To minimize this, it is desirable to operate at wavelengths where the optical fiber’s chromatic dispersion is small or use a light source, such as laser technology, which consists of only a few wavelengths.
How does light travel through the eye?
Light enters the cornea, the clear “window” of the eye. The cornea bends the light so it passes through the pupil. The iris makes the pupil bigger or smaller, which determines how much light gets to the lens. The lens angles the light through the clear vitreous to focus it on the retina.
#### What is USB eye diagram?
The data eye diagram is a methodology to represent and analyze a high speed digital signal. The eye diagram allows key parameters of the electrical quality of the signal to be quickly visualized and determined.
#### What is the bandwidth of PCM?
In North America and Japan, PCM samples the analog waveform 8000 times per second and converts each sample into an 8-bit number, resulting in a 64 kbps data stream. The sample rate is twice the 4 kHz bandwidth required for a toll-quality voice conversion.
Which is an example of intersymbol interference ( ISI )?
Intersymbol interference (ISI) occurs when a pulse spreads out in such a way that it interferes with adjacent at the sample instant. Example: assume polar NRZ line code.
Why is precoding intersymbol interference a common problem?
Introduction to precoding Intersymbol interference (ISI) is a common problem in telecommunication systems, such as terrestrial television broadcasting, digital data communication systems, and cellular mobile communication systems. Dispersive effects in high-speed data transmission and multipath fading are the main reasons for ISI.
## How to calculate Ber from an eye diagram?
–Eye diagrams help us understand: •BER versus Samples per bit (1/(bit rate)) •Calculating BER from Eye Diagram –By picture in lecture, details in recitation •Noise and Deconvolution –Massaging the Unit Sample response. Block Diagram of the Channel Bits Xmit Rcvr in Bits out Channel Unit Sample Response and Eye Diagrams (35 Samples per bit)
## How many samples per bit in an eye diagram?
Unit Sample Response for a Simple Example Eye Diagram for 3 samples per bit Eye Diagram for 4 Samples per bit Eye Diagram for 5 Samples per bit Eye Diagram for 6 Samples per bit Eye Diagram For 7 Samples per bit BER Versus Samples per Bit (std = 0.1) | 885 | 4,339 | {"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} | 2.515625 | 3 | CC-MAIN-2022-27 | latest | en | 0.937235 |
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In this geometry exercise, children calculate the perimeter of various trapezoids by adding up the lengths of their sides.
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Vocabulary Cards: Real Life Perimeter
Use these vocabulary cards with the EL Support Lesson: Real Life Perimeter. | 628 | 3,011 | {"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} | 3.59375 | 4 | CC-MAIN-2021-21 | latest | en | 0.799111 |
https://physics.stackexchange.com/questions/339282/why-doesnt-e-mc2-contradict-the-conservation-of-mass-principle/339284 | 1,653,148,734,000,000,000 | text/html | crawl-data/CC-MAIN-2022-21/segments/1652662539131.21/warc/CC-MAIN-20220521143241-20220521173241-00601.warc.gz | 525,226,426 | 69,026 | # Why doesn't $E = mc^2$ contradict the conservation of mass principle?
I was watching this very interesting video: The mathematics of weight loss
and at 12:35 the presenter says: "(...) people think that you can turn atoms into energy. It's one of the founding principles of modern chemistry: you cannot turn atoms into pure energy. It's called the conservation of mass."
Einstein's famous equation immediately came to my mind: $$E = mc^2.$$
Isn't that equation saying you can turn mass into energy and vice versa? Doesn't that contradict the conservation of mass principle then?
• E=mc^2 implies that mass and energy are interconvertible. Mass can be converted to energy and vice versa. Therefore, mass is not conserved. Jun 14, 2017 at 8:02
• I think in fact you can't turn atoms into pure energy because of baryon-number conservation.
– user107153
Jun 14, 2017 at 9:14
• @tfb You can actually turn matter into pure energy, it needs to collide with anti matter which are known as antibaryons with number -1 suppose of an antiproton if a proton's baryon number is 1. Thus they can turn to pure energy and baryon number is conserved(1-1=0) Jun 14, 2017 at 9:40
• @TausifHossain Yes, sorry: what I meant is that you can't turn the atoms you're made of into pure energy because of baryon number conservation. You could do this if you were made partly of antimatter, I agree, but you can't just take some of your atoms, do some process not involving more (anti-)atoms and end up with pure energy. I have already patented the 'antimatter diet' which will be in a shop near you soon.
– user107153
Jun 14, 2017 at 9:56
• @TausifHossain: yes, the tfb antimatter diet(TM) must be used according to instructions. Failure to follow instructions may cause side-effects including detonation, destruction of country, planet etc. Do not taunt tfb antimatter diet.
– user107153
Jun 14, 2017 at 10:33
It's true, it does violate the conservation of mass. This conservation of mass principle was established before Einstein showed his famous equation of $E=mc^2$. So today we say that in a closed system mass-energy is conserved. That is the sum of mass and energy in a closed system is constant. ( If you still like to think of the conservation of mass then think that mass and energy are equivalent and hence if you say that mass, which is equivalent to energy is conserved then the principle still holds). And also it's not true that you can't turn atoms into pure energy, you absolutely can. You just collide them with equal mass of antimatter. As almost everything around is matter hence it makes sense that in practice it is very difficult to turn atoms into pure energy.
• Thanks for the reply Tausif Hossain. It's funny because the guy is a physicist so I would imagine he would not make such statement if it wasn't true. Maybe he tried to dumb down the explanation in the video then? Or maybe because it is much more common to turn molecules into other molecules than to turn their atoms into pure energy? Jun 14, 2017 at 8:16
• Yes, you're right, it's the commonality of it not happening might be the reason. Jun 14, 2017 at 8:37
• Please verify the answer if you find it satisfactory. Thanks. Jun 14, 2017 at 8:43
• I'll add that the presentation may have been operating more in the range of classical physics where mass conservation is a pretty safe bet. In this case it's probably safe to assume that in the context, the mass is approximately conserved, and the any change in mass will not be significant. I think that's a valid assumption and is often assumed in chemistry at this level.
– JMac
Jun 14, 2017 at 11:58
There is no conservation of mass principle. Mass is approximately conserved in chemical reactions, the context of the remark.
Actually, a better way of stating the notion that the speaker is trying to get across in chemistry is to state it stoichiometrically: the number of atoms of each and every elemental species making up reactants and reaction products is unchanged by chemical reaction. If you have 20 hydrogen atoms and 10 oxygen atoms (making up ten hydrogen molecules and five oxygen molecules) before their reaction, and they combine to make water, then you still have 20 hydrogens and 10 oxygens after the reaction, only they are in 10 water molecules.
In the hundred years since science thought that mass was conserved, mass has become a less and less important notion in physics. Mass now has only one rigorous use in physics as the notion of rest mass:
1. The rest mass $m_0$ of a system equals the total energy of that system measured from a frame that is at rest relative to the system (in natural units - in SI units we have $E = m_0\,c^2$). "At rest" means that the system's total momentum is nought in this frame;
2. Newton's second law becomes $\mathbf{F} = \frac{\mathrm{d}\mathbf{P}}{\mathrm{d}\,t}= \frac{\mathrm{d}(m_0\,\mathbf{u})}{\mathrm{d}\,t}$, where $\mathbf{F}$ is the four force and $\mathbf{u}$ the four velocity.
But even rest mass is not conserved, and it is not linearly additive for composite systems. For example, two photons, each of energy $E$ moving in opposite directions relative to our frame, each have a rest mass of nought. But the system as a whole, from a frame where the two have equal momentums (which happens to be ours), has a rest mass of $2\,E/c^2$.
For everyday systems undergoing chemical reactions, conservation and linear additivity for composite systems are both good approximate properties of the mass notion.
Nuclear reactions change that idea altogether. Typically products of an exothermic nuclear reaction have a few percent mass deficit compared to the reactants. Even in chemical reactions there are differences between the masses of reactants and products, but the differences are tiny.
Mass only seems to be constant, because if a system only changes its rest mass significantly by releasing / taking on quantities of energy that are far greater than we see in the everyday world. | 1,427 | 5,977 | {"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} | 2.734375 | 3 | CC-MAIN-2022-21 | longest | en | 0.952441 |
http://www.icoachmath.com/math_dictionary/minimum.html | 1,524,468,659,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125945855.61/warc/CC-MAIN-20180423070455-20180423090455-00520.warc.gz | 449,223,670 | 6,134 | Minimum
Definition Of Minimum
Minimum is the smallest or the least value in a given set of data.
Finding the minimum number is easy by arranging the numbers in descending order.
Examples Of Minimum
All the numbers in the above figure are arranged in descending order. The least number is 5 among all the numbers. So, 5 is the minimum value.
A. 106
B. 222
C. 100
D. 230 | 92 | 374 | {"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} | 3.125 | 3 | CC-MAIN-2018-17 | latest | en | 0.835725 |
https://en.wikipedia.org/wiki/Talk:Primitive_recursive_function | 1,505,992,342,000,000,000 | text/html | crawl-data/CC-MAIN-2017-39/segments/1505818687740.4/warc/CC-MAIN-20170921101029-20170921121029-00451.warc.gz | 677,340,541 | 34,292 | # Talk:Primitive recursive function
WikiProject Mathematics (Rated B-class, Mid-priority)
This article is within the scope of WikiProject Mathematics, a collaborative effort to improve the coverage of Mathematics on Wikipedia. If you would like to participate, please visit the project page, where you can join the discussion and see a list of open tasks.
Mathematics rating:
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Field: Foundations, logic, and set theory
1. the initial set of X: they are axioms, not functions or terms. they are statements.
2. successor: you had better not use + in the definition. we haven't defined addition.
3. projection: the s suffix on words makes things plural.
4. p.r. versus primitive recursive: I personally think it was nicer with the abbreviation, but it's not a strong opinion.
I spent a lot of time in crafting this page. Please do me the courtesty of investing a similar degree of effort in your changes. --Wmorgan
Regarding number 2: I was assuming knowledge of the natural numbers and their addition. If you want to assume only Peano's axioms and start everything from there, you should link to the Peano axioms and not to "natural number line". Or do you want to start from a primitive, "geometric" understanding of the natural number line? --AxelBoldt
I think you have a point that "natural number line" does presuppose some ideas which I shouldn't assume are defined at this point. But certainly as addition is defined later on in the page I think it would be safest not to use it explicitly quite yet. Actually I'm a bit unclear as to whether the Peano postulates should be assumed or not. The textbook that I have on this subject (Epstein & Carnelli) uses the phrase "that number which follows n in the natural number series". Thoughts?
(BTW in rereading my comments above I come off as fairly obnoxious. That wasn't my intention, so please accept my apologies.)
And one last comment... I think I will change the definition of the set of p.r. functions to an inductive one rather than using terms like "smallest" and "closed", as upon further study, the latter, taken in the set-theoretic sense, presupposes infinite classes of functions, whereas with the former we can stay safely away from the i- word. --Wmorgan
You need at least the Peano axioms; otherwise you cannot talk about natural numbers in any meaningful way. I would probably not even bother; just mention the natural numbers, link to them, and be done with it. Then later show that the "intuitive addition" of natural numbers can be defined as a p.r. function. Everybody knows the natural numbers (or they think they do).
Also, a nice example of a p.r. function would be f(x,y) = 1 if x < y and 0 if xy. And maybe a typical function that's recursive but not p.r. --AxelBoldt
## Diagonal argument
[about the diagonal argument:] Note that this argument can be applied to any class of functions that can be enumerated in this way. (One might think this implies that any explicit list of the computable functions cannot be complete, but that's false because of the undecidability of the Halting Problem.)
(One might think this implies that any explicit list of the computable functions cannot be complete, but that's false because of the undecidability? of the Halting Problem.)
I changed this back, clarifying that we only talk about total computable functions here. Indeed, an explicit (in the sense of recursively enumerable) list of total computable functions can never be complete, as the diagonal argument shows.
It is possible to have a complete explicit list of partial computable functions though. I guess that's the misunderstanding. 199.17.234.96
I don't understand what the point of this 'diagonal argument' is. To show that there are computable functions that are not Primitive Recursive one just exhibits one -- such as Ackermann (as is written at the end of the article). Does anyone have an the objection to snipping this bit out? --Sam Staton 15:56, 23 May 2006 (UTC)
The 'diagonal argument' is necessary. Merely exhibiting the Ackermann function isn't a proof. You must prove that it grows faster than any primitive recursive function. I suspect that proof is at least as long as the 'diagonal argument' proof. SpectatorRah (talk) 00:14, 3 April 2010 (UTC)
## Gödel's incompleteness theorem
An essential piece of Gödel's theorem uses primitive recursive functions...should that be noted here?
## Sentence structure
Many of the functions normally studied in number theory, and approximations to real-valued functions, are primitive recursive, such as addition, division, factorial, exponential, finding the nth prime, and so on (Brainerd and Landweber, 1974).
It hurts to read this sentence. Fredrik Johansson 00:53, 30 April 2006 (UTC)
Fixed, I think. Adam (talk) 04:02, 23 October 2008 (UTC)
## Zero-based or One-based numbering?
Whoever is in charge of this article should make up his/her mind whether he/she is using zero-based numbering or one-based numbering for lists of functions and for their arguments. JRSpriggs 03:14, 30 July 2006 (UTC)
Since no one else did anything, I converted the article to consistent one-based numbering. Please let us keep it that way. JRSpriggs 03:57, 3 August 2006 (UTC)
## ideas to improve the article
Hi. I made a comment on the math Wikiproject talk page that this article needed some improvement. An editor has asked me to give more precise comments so here goes.
• My main criticism is that the page is not readable enough for the layman. Of course, this is not a really easy subject but still, I think the intro for one should say a bit more. For instance giving a quick definition of a computable function and some basic intuition as to why anyone would consider primitive recursive functions in the first place.
• There's not enough discussion as to why these were considered.
• point 2 of the definition should be restated in a cleaner way.
• again, following the definition, there should be an attempt at conveying some intution, enough so that people would accept the proof that addition is primitive recursive without involving the projections.
• the limitations section begins by saying that primitive recursive correspond to our intuitive notion of computable. In the computer age, I think that's pretty much incorrect.
The article is not that bad, but it could need some help if one wants to rely on it for other articles, notably the Ackermann function. Pascal.Tesson 19:31, 18 September 2006 (UTC)
Since your criticisms are not entirely clear to me, I suggest that you try to fix them yourself. If you mess it up, I will correct you.
About defining computable functions in the introduction, I moved that stuff out of the introduction specifically to make the introduction easier to read. If you use the Turing machine definition, it is completely different from the definition of primitive recursive functions and would only confuse beginners. If you use the definition with mu-recursion, then it is even more complicated than primitive recursion. So it would also confuse people. And I wanted to get the characterization of primitive recursive functions in terms of Turing machines and the Ackermann function out of the introduction because it would look like the definition which it is not.
Use of the projections cannot be avoided without making the other stuff even worse.
Any function which can be calculated by an actual physical computer is primitive recursive on its domain, but there are many primitive recursive functions which cannot be calculated by any physical computer. JRSpriggs 07:04, 19 September 2006 (UTC)
## Nonsense?
I dont know how I landed up here but this doesnt makes sense !
"The primitive recursive functions are defined using primitive recursion and composition as central operations and are a strict subset of the recursive functions (recursive functions are also known as the computable functions)."
What is primitive recursion? the article becomes denser by each word :( 122.169.148.119 (talk) 20:32, 25 November 2007 (UTC)
Sorry, but this is a difficult concept. The definition is in the first section after the lead. However, I could over-simplify it by saying that primitive recursive functions are those which can be calculated within a predetermined number of steps (which depends on inputs). JRSpriggs (talk) 03:35, 26 November 2007 (UTC)
## Critique/Suggestions To Improve the Article
This article lacks concise and comprehensive definitions of what it is trying to describe. Declaring relationships or information that may be relevant to a topic without precisely defining that topic leads to the obfuscation of and abandonment of concise definition. If you feel that the material is a difficult concept, then please abandon the approach of providing strict declarative knowledge, which really says nothing precisely about a topic at all, only relationships relevant to that topic. Since this particular topic is of interest to computer scientists, a strictly mathematical approach is of good use but not sufficient. I look forward to seeing an updated page. 14:39, 9 May 2008 —Preceding unsigned comment added by Org322001 (talkcontribs)
---
The simple one-accumulator register machine might offer a (non-strict) example of the five axioms. In this example the axioms boil down into a few primitive machine operations:
1 Constant function: 0 is primitive recursive: CLEAR r, (abbreviated CLR r) where "r" is any register that the machine has access to, symbolized as 0 --> r.
Suppose we have four registers A, P, Q, R. Then CLR P will cause the contents of register P to be 0 (in other words, P will be empty of counts): 0 --> P. Registers A, Q and R will be unaffected.
2 Successor function: INCREMENT r (abbreviated: INC r)
Example: INC P will add one count to register P, the contents symbolized with brackets around the register (cf. Boolos-Burgess-Jeffrey symbolism): [P]+1 --> P
3 Projection function: i.e. we have access to any register in the machine. We need to distinguish the two types: COPY and MOVE. COPY r1,r2 i.e. copy the contents of r2 into r1. This is easier to see if we restrict our model to a machine with a special "accumulator" register that we call "A", and the instruction "LOAD r" ( LDA r) that does the following: [r] --> A.
Example: LDA P, symbolized [P] --> A
Example: LOAD A,P symbolized [P] --> A
4 Composition: STOREA r (abbreviated: STA r). COPY the contents of A -- the contents may be the result of many operations -- into any register (including itself); the contents of A is left untouched.
5 Primitive recursion: The IF ... EQUALS ... THEN GOTO ... operation. We need any two of the following 3 versions:
• 5.1: IF the contents of register A EQUALS the contents of register r, then JUMP_TO instruction 7 (abbreviated: JE A,r or perhaps, JEA r)
• 5.2: IF the contents of register A is not equal to the contents of register r then GOTO instruction x (abbreviated: JNE A,r,x or perhaps JNEA r,x. 7: Jump if A is Zero to instruction 7)
• 5.3: "Unconditional jump" (JUMP_TO instruction x, appreviated J x ).
Primitive recursion actually involves incrementing too, so really, primitive recursion is an IF-THEN LOOP that counts up until the IF THEN is satisfied, at which point the function either terminates (HALT) or leaps to another instruction.
Example: ADD the contents of register P to Q and deposit the result in R
1 CLEAR A ;register A is a counter to be used in the two recursions
2 CLEAR R :register R is where the result will appear
;First primitive recursive loop -- copies the count in register P into result-register R:
;1st primitive-recursive loop:
3 JEA P,7 ;Is (contents of) A equal to (contents of) P? If so then go to instruction 7 else continue to next instruction.
4 INC R
5 INC A
6 JUMP_TO 3
7 CLEAR A ;A will again be used as a counter to add the counts in Q to the counts in R
;2nd primitive-recursive loop:
8 JEA Q,12 ;Is A equal to Q? If so then go to instruction 12 else continue to next instruction.
9 INC R
10 INC A
11 JUMP_TO 8
12 HALT ; [R]=[P]+[Q]
The above is only one version of ADD -- maybe the reader can suggest a better one -- but it illustrates the point. I don't know whether something like this would help a reader or not. One thing that comes out of it is that we know from Turing equivalence that other "instruction sets" are sufficient. Indeed, there are other sufficient axiom sets besides the "Peano set" given in this article. Who is it ... Laszlo Kalmar (1943) it was ... who originated another set similar to the counter machine (i.e. his set starts with constant 1, has INCREMENT, a subtraction (DECREMENT) and the finite sum and finite product -- these are where recursion appears (cf Kleene 1952/1971:285 and p. 526 citing Kalmar 1943). Bill Wvbailey (talk) 16:56, 9 May 2008 (UTC), slight emendation Wvbailey (talk) 18:31, 31 May 2008 (UTC)
## importance
I noticed the new text on importance in the lede. While being r.e. is a nice property of the primitive recursive functions, I am not sure it is the key reason for their importance. Things that seem more important to me include:
• Most of the effective procedures that arise in elementary proof theory are primitive recursive. For example, the functions in Goedel's incompleteness theorem are all primitive recursive
• Primitive recursive arithmetic (PRA) is widely regarded as an embodiment Hilbert's finitism
• The primitive recursive functions are essy to prove total, unlike computable functions in general. In particular, they are exactly the provably total functions of RCA0.
These things ought to be in the article, actually. Unfortunately, I don't have in mind any sources that explicitly try to explain why the primitive recursive functions are important. — Carl (CBM · talk) 01:33, 23 August 2009 (UTC)
Carl, you list three reasons. I think your first reason is certainly a nice property of PR functions, but does not distinguish them from general recursive functions. I would be interested in seeing references on your second point; perhaps the reason for this regard might be valid as a reason why the primitive recursive functions are notable. Your last point ought to be added to the reasons for notability (and I intend to do so). AshtonBenson (talk) 00:57, 28 August 2009 (UTC)
Hrm, on second thought, I have concerns about your third point. The reason why it's easy to prove that they are total is that they are inductively generated (the totality proof proceeds by induction on the enumeration of all PR functions). So the fact that they can be proven total is important, but the reason why this is the case is because they -- as a class -- are RE. That's the "easy" you mention. AshtonBenson (talk) 00:59, 28 August 2009 (UTC)
The class of all partial recursive functions is also r.e., as is the class of elementary functions, so it is not clear to me that this is really a unique property that makes the primitive recursive functions interesting. Can you say who makes this claim in print? — Carl (CBM · talk) 01:23, 28 August 2009 (UTC)
The article says "subset of the set of all total recursive functions" -- the class of partial recursive functions does not meet this criteria. What makes PR notable is that it it is the strongest "common" system with all the properties mentioned (and this is what distinguishes it from the elementary functions). Now what I'm really curious to know is why, say, the primitive recursive functions plus a symbol for the Ackermann function, and closed under composition, wasn't chosen instead. I have no answer to that question. AshtonBenson (talk) 03:57, 28 August 2009 (UTC)
P.S. The reason that the primitive recursive functions are easy to prove total is that all the induction needed to do so in arithmetic is included in the scheme ${\displaystyle I\Sigma _{1}^{0}}$, which consists of the first-order induction scheme limited to ${\displaystyle \Sigma _{1}^{0}}$ formulas. The collection of all functions primitive recursive in the Ackermann function is also r.e. and contains only total functions, but the Ackermann function itself is not provably total in RCA0. So the mere fact that the primitive recursive functions are r.e. is not the key point. — Carl (CBM · talk) 01:36, 28 August 2009 (UTC)
If there were a name for that class of functions, and if that class had been discovered at the same time as the PR functions (or very shortly thereafter), I bet that class would be notable instead. AshtonBenson (talk) 04:01, 28 August 2009 (UTC)
The elementary functions are also perfectly notable, although we don't appear to have an article on them. As are the partial recursive functions. — Carl (CBM · talk) 10:39, 28 August 2009 (UTC)
See ELEMENTARY. What an awful link. I found this via Laszlo Kalmar. Bill Wvbailey (talk) 16:35, 28 August 2009 (UTC)
Boolos Burgess Jeffrey 2002 say that "Another process, called (primitive) recursion, is what is involved in defining multiplication as repeated addition, exponentiation as repeated multiplication, as so on." (p. 58); we can't get what we need to do arithmetic as we know it with just "zero", "successor", "identity" and "composition". Kleene 1952:217 introduces his Chapter IX "Primitive Recursive Functions" with "To establish the lemma for Goedel's theorm, we shall develop an intuitive theory about a certain class of number-theoretic functions and predicate [etc]...". Minsky implies the machines associated with PR are "not quite so complicated" [as a Turing machine] so explorations of undecidability might be easier (p. 116). That's about all I've got. Bill Wvbailey (talk) 02:02, 23 August 2009 (UTC)
Bill, thanks for the nice citations in which people mention PR functions, but I don't really think any of those speak to their notability (while they certainly do describe the PR functions!) AshtonBenson (talk) 00:59, 28 August 2009 (UTC)
Re Ashton, PRA: the identification of PRA with finitism is a long-running discussion in the philosophy of mathematics. Everyone I have read agrees that PRA is included in "finitism"; the point of contention is whether finitism goes beyond PRA or not, with some on each side. It is trivial to find papers where this is discussed using google. One influential paper is:
• "Remarks on finitism", Wiliam Tait, [1].
Some other works that discuss the issue are:
• "Partial realizations of Hilbert's program", Stephen Simpson, [2]
Er, you know that this paper merely cites the one above and then moves on, right? It doesn't really add anything on this topic. AshtonBenson (talk) 04:23, 28 August 2009 (UTC)
• "Finitistic Properties of High Complexity", Dmytro Taranovsky, [3]
• "Finitism and intuitive knowledge", Charles Parsons [4]
Here is a quote from Simpson on the FOM email list in 1999 [5]:
"Tait in his 1981 paper argued that Hilbert's finitism is formalized by PRA. This conclusion is widely accepted in the f.o.m. literature. I certainly accept it..."
There are many more references than this; the relationship between PRA and finitism has been thoroughly explored in the literature. — Carl (CBM · talk) 01:13, 28 August 2009 (UTC)
This merely cites the same paper you cite above by Tait. There's really no additional content there. And, as a side note, I don't know if I'd count the FOMlist as a reliable source ;) AshtonBenson (talk) 04:09, 28 August 2009 (UTC)
That leaves the actual papers cited above. There are many more authors who discuss the relationship between PRA and finitism, I just included a few references to make the point. — Carl (CBM · talk) 10:39, 28 August 2009 (UTC)
I guess I don't understand Astonbenson's notion of "notable", or "important".
The following is certainly historically important. So I'll offer it up:
Hilbert viewed "recursion" ("primitive", the only kind known at the time he gave his 1928) as the keystone of his formal, axiomatic theory of arithmetic. Hilbert (1926) had conjectured that there might be functions that could not be generated by [primitive] recursion, but Ackermann had not yet presented his (1928) novel "double-recursion", nor had Péter (1935) [reference: Kleene 1952:271]. So, Hilbert, in his 1927 The foundations of mathematics (van Heijenoort pp. 464ff) had only primitive recursion (based on Peano's successor and induction) at his disposal. He says "Finally, we also need explicit definitions, . . . as well as certain recursion axioms, which result from a general recursion schema. . . . For in my theory contentual inference is replaced by manipulation of signs according to rules; in this way the axiomatic method attains that reliability and perfection that it can and must reach if it is to become the basic instrument of all theoretical research."(boldface added, p. 467) He goes on about a page later to define what he means by "recursion" (nothing surprising -- the previous calculation is employed in generating the next calculation see p. 468), and after that, he states "In a corresponding way, the recursion axioms are formula systems that are modeled upon the recursive procedure. ¶ These are the general foundations of my theory. To familiarize you with the way in which it is applied I would like to adduce some examples of particular functions as they are defined by recursion." (p. 469) Here he offers examples of simple recursions starting with ι(0)=0; ι(a')=1, [etc].
I think this strongly supports my point. Had Ackermann's function been known at the time, we probably would have wound up with some class of functions which includes it (and is closed under composition) as our most-notable class of "obviously" terminating functions (termination being obvious because the termination proof can proceed by induction on the recursive procedure for enumerating all the functions in the class). And in fact I bet we'd call them "the primitive recursive functions." Point being, that name and the notability that goes with it was given to the first-to-be-discovered "large" subset of the total recursive functions which was itself RE. AshtonBenson (talk) 04:09, 28 August 2009 (UTC)
That viewpoint is somewhat ahistorical. Gödel introduced the primitive recursive functions, under the name "recursive", before what we now call computable functions had been developed at all. Later the name "recursive function" became a synonym for "general recursive function" and "primitive recursive function" was used to distinguish that class, which is distinguished from the general recursive functions by having a recursion scheme that is limited in a certain way. Monk (Mathematical logic, p. 34) says, "We feel-that it is only an historical accident that elementary functions are not more widely discussed than primitive recursive functions." — Carl (CBM · talk) 12:10, 28 August 2009 (UTC)
To sum up, "primitive" recursion provided "the general foundations" of Hilbert's theory that was to be used, in essence, by Goedel a few years later. "Full" recursion was not the driver, "primitive" recursion was. Kleene notes that the formal system he (Kleene) presents (essentially that used by Goedel 1931) "has function symbols only for the three functions ', +, *. ... This proof [Goedel's "Theorem VII: Every [primitive] recursive relation is arithmetic[al]"] is not essential to our program of formalizing number theory. If it did not succeed, we could have arranged instead that recursion equations for other functions besides + and * should be axioms of the system. ... However, it is of some interest that a finite system suffices, the more so that we can get along with the two chief functions + and * of traditional arithmetic, when taken with the logical constants and the predicate =." (boldface added, Kleene 1952:239). Bill Wvbailey (talk) 02:53, 28 August 2009 (UTC)
Ashton: could you please let everyone know exactly which source you are looking at that explicitly says that the reason the primitive recursive functions is important is that they are r.e.? As I said, I have looked through several books, and what they all say is just that the primitive recursive functions include most of the functions commonly encountered in mathematics. — Carl (CBM · talk) 10:39, 28 August 2009 (UTC)
Also, I agree with Wvbailey that you seem to be misinterpreting the word "notable". According to WP:N, something is notable exactly when it is discussed by secondary sources. — Carl (CBM · talk) 10:40, 28 August 2009 (UTC)
---
Somewhat technical history of the development of the notion of "recursion" (as opposed to primitive recursion): In a paper dated 14 July 1931 (published 1932) Herbrand proposed an expanded notion of "recursion"; van Heijenoort notes that, "The functions [Herbrand proposes] are, in fact, (general) recursive functions, and here is the first appearance of the notion of recursive (as opposed to primitive recursive) function" (van Heijenoort's commentary before Herbrand 1931b On the consistency of arithmetic1965:619). In a note dated 22 January 1931 (published 1932) On Completeness and Consistency Goedel begins with "Let Z be the formal system that we obtain by supplementing the Peano axioms with the schema of definition by recursion (on one variable) and the logical rules of the restricted functional calculus" (boldface added, van Heijenoort 1967:616). Goedel (1931) is thus aware of Ackermann (1928).
Then in spring 1934 at his IAS Princeton lectures (Davis 1965:41-71 + Goedel's 1964 Postscriptum 1965:71-73) Goedel states that "Recursive functions have the important property that, for each given set of values of the arguments, the value of the function can be computed by a finite procedure"; he goes on to postulate, in footnote #3, that the converse is true if we admit "recursions of other forms . . . this cannot be proved, since the notion of finite computation is not defined, but it serves as a heuristic principle." (Davis 1965:44). Goedel then tacks on a sub-lecture "9. General recursive functions" (Davis 1965:69-71), giving an example of a function not recursive in his restricted sense of [primitive] recursion, and noting that he needs to "generalize our β function". (In footnote 34 he mentions that this notion is attributable to a private communtication between him and Herbrand. But later, ca 1960's communications with Davis, he observes problems with Herbrand's shifting definition that are really technical (meaning: I don't understand them, cf curly-braces footnote #34 in Davis 1965:70)). Goedel goes on to discuss Herbrand's notion, restrict it a bit, and then propose this as an expanded definition of "recursion"; thus ends his 1934 lectures.
All of this has to do with Hilbert's Entsheidungsproblem and the attempt to arrive at a suitable defintion of computability; by 1936 Church will present "an unsolvable problem of elementary number theory", Turing appears in 1936-7. Indeed, in his commentary before the 1934 lectures Davis notes that Goedel stated (in a letter to him) that "he was, at the time of these lectures, not at all convinced that his concept of recursion comprised all possible recursions" (Davis commentary in Davis 1965:40). Indeed, in both Davis and van Heijenoort, we observe that by 1963-4 Goedel had abandoned recursion altogether and proposed Turing's "general notion of formal system" in its place (Davis 1965:71-73, van Heijenoort 1967:616); Goedel's take on lambda-calculus was that it was "much less suitable for our purpose" (footnote * in Davis 1965:72). Bill Wvbailey (talk) 16:25, 28 August 2009 (UTC)
The historical reason why primitive recursive functions came to preeminence is that for a while (in the 1920s) they were believed to be sufficient to express computation. Ackermann's function was actually developed as a counterexample of that. At least Scott Aaronson says so. Of course, they were believed to be sufficient for computation purposes precisely because all/most functions used in math were/are of that kind. Pcap ping 12:29, 18 September 2009 (UTC)
Aaronson doesn’t say who those mathematicians were who “thought that ‘computable’ coincided with a technical notion called ‘primitive recursive’”, so we cannot determine if this is a true statement. Here are two prominent counterexamples. As noted above, for purposes of his 1931 Goedel “invented” what we think of nowadays as “the primitive recursion schema”, and Goedel admitted he didn’t think they were sufficient (cf Davis’s commentary in Davis 1965:40). Hilbert also included “recursion” in his formalism. But was it sufficient? As is discussed in Kleene 1952: "Are there recursions which are not reducible to primitive recursion, and in particular can recursion be used to define a function which is not primitive recursive? This question arose from a conjecture of Hilbert 1926 on the continuum problem, and was answered by Ackermann 1928". For alot of historical detail after Ackermann's discovery see Kleene's §55. General recursive functions in Kleene 1952:270-276. Kleene considers his primitive recursive schema of his §43 (it’s the one you find in Rogers 1987 on page 6) nothing but definition by mathematical induction (cf top of page 274). Bill Wvbailey (talk) 14:34, 18 September 2009 (UTC)
## Kronecker?
Didn't Kronecker invent these? People keep saying it's Godel.Likebox (talk) 16:01, 31 December 2009 (UTC)
WP:CS 71.139.12.24 (talk) 16:37, 31 December 2009 (UTC)
It's not clear who exactly first invented/discovered/described "recursion" as in: using a previous calculation in a subsequent calculation in the manner of mathematical induction. It appears in the late 1800's in Peano's axiom-based, "recursive" definitions of addition and multiplication. So maybe Kronecker had something to do with this "reuse" notion (as in: formal inductive proof), but I suspect this goes back to the ancient Greeks. I believe Goedel was the first to adopt/describe (primitive) recursion formally in his "incompleteness" proofs, but the general notion can be found in Hilbert's lectures of a few years before. Subsequently (after the problem of the Ackermann function appeared), Goedel was responsible for describing "general" or "full recursion" in his Princeton lectures, but this came from a suggestion by Herbrand who was working with Hilbert. With respect to a theory that would allow calculating anything calculable, throughout his life Goedel had no use for lambda calculus and remained suspicious of recursion in any form ("primitive" or "general" i.e. with the added mu-operator) and eventually rejected the idea in favor of Turing-like mechanical processes. BillWvbailey (talk) 16:58, 31 December 2009 (UTC)
Thanks--- I understand. But I think there was a precise moment at which primitive recursion first appears in the literature, and I think it is in a work of Kroneker in the late 1890s. I might be wrong--- I vaguely recall this from years ago. It might have been Peano, or some other of the early logicians. I think that Godel does not attribute his formal definitions of primitive recursion in his 1931 paper because it is common knowledge, not because it is new. I don't want to screw up the priority.Likebox (talk) 17:15, 31 December 2009 (UTC)
I did some research by querying both my cc's derived from googlebooks (I've OCR-converted them to searchable text), and then querying googlebooks directly. Dedekind in his (1903) Essays on the Theory of Numbers uses the word p. 33 in a 1901 translation: ". . .definition by induction (or recursion)"; Peano cited Dedekind but also a host of logicians. I did not find it in my OCR'd cc's of Jevons, Pierce/Ladd-Franklin, Boole, Cantor or Couturat. But via the query with googlebooks I did find it in (i) J. L. Raabe's (1857) Mathematische Mittheilungen, (ii) Adam Rittern von Burg's (1851, 1836?) Compendium der hoeheren Mathematick, and in (iii) Kaiserl's 1848 Stizungsberichte der Mathematish-Naturwissenscheaftliche Classe. I can't read German but the context where the word is used is clearly one of iteration of formulas. There's a Latin usage in an 1899 edition of Pope Sylvester II's (972-1003) Opera Mathematica where the word "recursione" appears to be used in the context of the repeating seasons of the year: " . . . qualiter naturali alternatione et annus recursione nunc jovianis orbem aspirat temperametis . . .". So at least we know where that word came from originally.
The word "primitive" was tacked on after Goedel and Herbrand came up with their more-general recursion; Goedel in his incompleteness proofs used the word "recursiv". If I can trace the usage back further than Kaiserl 1848 and von Burg 1851/1836? I'll add it here(is von Burg a 2nd edition? Unclear since I can't read the introductions as to what is going on here). [Leopold Kronecker (December 7, 1823 – December 29, 1891)]. Bill Wvbailey (talk) 23:26, 31 December 2009 (UTC)
The word is also spelled (in German) "rekursion", and it has the usage "rekursiv". But google books doesn't produce any earlier results than those listed above. I noticed that the word was used in reference to integration (e.g. as in accumulating finite elements) and this makes me wonder if something could be traced back to e.g. Newton. Bill Wvbailey (talk) 16:56, 1 January 2010 (UTC)
From the book: Charles Davies, William Guy Peck, 1859, Mathematical dictionary and cyclopedia of mathematical science, A. S. BARNES & BURR, 51 & 53 JOHN STREET, NEW YORK
"There is a mathematical process of demonstration which possesses somewhat the character of induction, inasmuch as a general truth is gathered from the examination of particular cases, but it differs from it inasmuch as each successive case is made to depend upon the preceding one. This process has been called the process of successive induction. (p. 310)
Bill Wvbailey (talk) 17:54, 1 January 2010 (UTC)
from: Florian Cajori (1893, 1919) ‘’A History of Mathematics’’, The Macmillan Company, London. Note the use of the word "recurrent" that I have boldfaced [the following was derived from OCR'd text and has not been doublechecked for italics etc]:
“To Maurolycus has been ascribed also the discovery of the inference by mathematical induction. It occurs in his introduction to his Opuscula mathematica, Venice, 1575. Later, mathematical induction was used by Pascal in his Traite du triangle arithmetique (1662). Processes akin to mathematical induction, some of which would yield the modem mathematical induction by introducing some slight change in the mode of presentation or in the point of view, were given before Maurolycus. Giovanni Campana (latinized form, Campanus) of Novara in Italy, in his edition of Euclid (1260), proves the irrationality of the golden section by a recurrent mode of inference resulting in a reductio ad absurdum. But he does not descend by a regular progression from n to n- 1, n- 2, etc., but leaps irregularly over, perhaps, several integers. Campano's process was used later by Fermat. A recurrent mode of inference is found in Bhliskara's "cyclic method" of solving indeterminate equations, in Theon of Smyrna (about 130 A. D.) and in Proclus's process for finding numbers representing the sides and diagonals of squares; it is found in Euclid's proof (Elements IX, 20) that the number of primes is infinite.” (p. 142)
"In [De Morgan’s] article "Induction (Mathematics)," first printed in 1838, occurs, apparently for the first time, the name "mathematical induction"; it was adopted and popularized by I. Todhunter, in his Algebra. The term "induction" had been used by John Wallis in 1656, in his Arithmetica infinitorum; he used the "induction" known to natural science. In 1686 Jacob Bernoulli criticLed him for using a process which was not binding logically and then advanced in place of it the proof from n to n+1. This is one of the several origins of the process of mathematical induction. From Wallis to De Morgan, the term "induction" was used occasionally in mathematics, and in a double sense, (I) to indicate incomplete inductions of the kind known in natural science, (2) for the proof from n to n+ 1. De Morgan's "mathematical induction" assigns a distinct name for the latter process. The Germans employ more commonly the name "vollstandige Induktion," which became current among them after the use of it by R. Dedekind in his Was sind und was solten die ZaJUen, 1887.” (p. 331)
I think this should do it, from the historical perspective. Bill Wvbailey (talk) 18:23, 1 January 2010 (UTC)
## Primitive recursive, recursive, and computable
The term "recursive function" is defined as "total computable function", so the class of recursive functions is not identical to the class of computable functions (the class of [μ-recursive functions is, however). Furthermore, there is nothing surprising about the fact that the primitive recursive functions are a strict subset of the computable functions, since all p.r. functions are total and the class of computable functions contains at least one function which is not total. That is the reason why I changed the introduction to express more clearly that the class of p.r. functions does not constitute all recursive functions.
Also, please don't revert a complete edit if you only disagree with a small part of it. Thanks. – Adrianwn (talk) 05:05, 13 July 2010 (UTC)
Reversion is proper protocol. It forces the discussion to the talk page. Until this is hammered out here, I will revert your edit. BillWvbailey (talk) 15:19, 13 July 2010 (UTC)
My objection was not against a revert in general. You reverted an edit of mine which contained more than just the part which you disagree with; accordingly you should have only reverted that part of it, not everything. Let me put emphasis on my sentence above: please don't revert a complete edit if you only disagree with a small part of it. (edit in question) – Adrianwn (talk) 16:20, 13 July 2010 (UTC)
As I pointed out on a different talk page, "recursive function" and "computable function" are complete synonyms in computability theory. There is no difference in meaning. — Carl (CBM · talk) 10:51, 13 July 2010 (UTC)
Carl, do you agree with the edit? I don't. I agree with what you wrote above: "(u)-recursive function" is identical to "computable function". This is my understanding of the words:
• "5.8 Theorem. All recursive functions are abacus computable (and hence Turing computable)" (Boolos-Burgess-Jeffrey 2002:61).
The adjective "Total" restricts the class of computable (aka recursive) functions to those that terminate for all integers in their defined domain; if they are to terminate, partial functions require restricted domains (cf B-B-J:7), e.g. for termination the (general, or u-)recursive function "division" disallows "division by 0", over the integers unrestricted subtraction p - q fails when q > p cf B-B-J:69 problem 7. So to make "subtraction" total, and coincidentally primitive recursive, it must be modified to become "proper" subtraction, etc.
• Primitive recursive functions lack the u-operator. They are a "subclass" of recursive functions (B-B-J:63).
• "The class of recursive functions is identical to the class of partial recursive functions" (cf Hopcrof-Ulmann 1979:175 problem 7.6.)
• "Every primitive recursive function is a total recursive function" (cf Hopcroft-Ulmann 1979:175 problem 7.7 a).
• "Adding the minimization operator [to the primitive recursion operators]. . . yields all partial recursive functions." (cf Hopcrof-Ulmann 1979:175 problem 7.6.)(cf Hopcrof-Ulmann 1979:175 problem 7.7.c)
BillWvbailey (talk) 15:19, 13 July 2010 (UTC)
They did not give the word "computable" a definite meaning in my schooling, so I would prefer that we restrict ourselves to "partial recursive", "total recursive", and "primitive recursive". "Recursive" alone is subject to confusion as to which of these it means.
To Adrianwn: If you do not want your whole edit reverted (and there are some good things in it), then I suggest that you break it down into parts, putting the non-controversial changes in one edit and the ones likely to be reverted into another. JRSpriggs (talk) 16:50, 13 July 2010 (UTC)
There is a similar discussion on the talk page of Ackermann function. It turns out that "recursive" is not a universally defined term. I never disputed that "computable" is identical to "µ-recursive"; whether "recursive" is identical to "computable" or to "total computable" is a matter of taste and depends on the author (I can give you several citations). For this reason, I agree with JRSpriggs that it should be unambiguated, for example: "total µ-recursive function".
As I explained above, the interesting thing about primitive recursive functions is not that they are a strict subset of all computable functions (which is trivial since these include non-total functions), but that they are a strict subset of the total computable functions, which I wanted to express with my edit.
JRSpriggs, although I agree with you regarding the size of edits in general, I don't like it when the history is cluttered with a myriad of small changes, and at the time I did not think my edits would be that controversial. – Adrianwn (talk) 19:54, 13 July 2010 (UTC)
Am confused. At least since Kleene 1952 and then later in his 1967 the word has been well-defined. Kleene 1967 starts here:
"Similarly, if there is a computation procedure for a function, we call the function computable" (p. 228)
where he has previously defined "computation procedure" as follows:
"...just as we may have a decision procedure or algorithm for a countably infinite class of questions each calling for a "yes" or "no" answer, we may have a computation procedure or algorithm for a countably infinite class of questions which require as answer the exhibiting of some object" (p. 226)
Kleene admits that this "intuitive notion of computation procedure . . . is vague" (p. 231) but then he asserts that the notion has been presented in "exact terms" -- "Most mathematical logicians agree that it was found in 1935 (and published in 1936), as we shall see in the next section [§41. Turing machines, Church's Thesis]" (p. 231-232).
Over the years, a number of authors have shown the equivalence of (general or u-)recursion to Turing machines (and Post-Turing machines and Register machines and abacus machines (aka counter machines). My favorite is B-B-J 2002:
"In the preceding several chapters we have introduced the intuitive notion of effective computability, and studied three reigorously defined technical notions of computability: Turing computabilitym, abacus computability, and recursive computability, noting along the way that any funtion that is computable in any of these technical senses is computable in the intuitive sense. We have also proved that all recursive functions are abacus computable and that all abacus computable functions are Turing computable. In this chapter we show that all Turing-computable functions are recursive, so that all three notions of computability are equivalent" (p. 88, introduction to Equivalent Defintions of Computability")
Minsky 1967 does something similar. Kleene did it way back in 1952. My engineering-grad text by Stone uses the Turing machine as the fundamental model of computation. In the Index of Enderton 2nd edition 2002 "Computable Functions, ..., see also Recursive functions" (cf pages 208-209 in particular where he formally defines "recursive"). Etc. BillWvbailey (talk) 20:24, 13 July 2010 (UTC)
I only knew "recursive functions" as "total µ-recursive functions"; it is only now that I learned that others might use a different definition. See also recursive set, which has a total computable characteristic function. – Adrianwn (talk) 21:41, 13 July 2010 (UTC)
[unindent] What do you think about the following version of the first paragraph:
"The primitive recursive functions are defined using primitive recursion and composition as central operations and are a strict subset of the total µ-recursive functions (µ-recursive functions are also called partial recursive). The term was coined by Rózsa Péter."
This way,
• there is no confusion over whether "recursive" implies "partial" or "total" (the exact meaning depends on the author)
• it is emphasized that the p.r. functions do not comprise all total (computable) functions
• the close relationship between p.r. and µ-recursive is stressed
Adrianwn (talk) 15:55, 19 July 2010 (UTC)
If no one objects, I will make those changes in a couple of days. – Adrianwn (talk) 07:13, 22 July 2010 (UTC)
## Definition
This article suffers from the same exasperating flaw just about every mathematics wikipedia article has. The authors seem incapable of understanding what a definition is! For Pete's sake, give a definition! These articles are incomprehensible unless you already know the material. Our most eminent physicist, Richard Feynman, once famously said that "if you can't explain something such that a freshman can understand it, it's because you don't understand it yourself." It appears that most of our wikipedia mathematics contributors are really clever crunching numbers, but they don't really understand the fundamental meaning of what they are doing. If they did, they could explain it! — Preceding unsigned comment added by 98.170.193.226 (talk) 02:33, 25 June 2012 (UTC)
There is a definition given. If you have a problem with it, then say what the problem is! Non-specific complaints are not helpful. JRSpriggs (talk) 05:34, 25 June 2012 (UTC)
The problem is that the article is laid out in a very confusing way, and uses unnecessarily complex language (perhaps in an attempt to be both precise and concise at the same time, but it ends up being very confusing for the uninitiated). I have a few suggestions:
The opening paragraph provides a definition whose meaning is unclear because it relies on terms that are seemingly circular (i.e. that a primitive recursive function is defined using primitive recursion is probably something that I could have guessed to start with, but given that at this point I have no idea what exactly primitive recursion is, it isn't exactly helpful). I would combine the first two paragraphs as follows:
In computability theory, the primitive recursive functions are a class of function (a strict subset of the total µ-recursive functions or partial recursive functions) that form an important building block on the way to a full formalization of computability and are important in proof theory. They are defined using a short list of ways of composing functions and a particular form of recursion known as primitive recursion. The term was coined by Rózsa Péter.
• Follows WP:MOS by introducing the field before defining the concept.
• Provides a simple idea of the kind of thing they are before going on to provide more detail
• Use of bold indicates that primitive recursion will be defined in the article (rather than just mentioning it which might make a reader assume they are expected to know what it is already)
Next, I would change the definition section. The use of the term n-ary function can be confusing, particularly where n is replaced with a complex expression; I would drop it and replace it with the phrase a function accepting n arguments. I would also drop some of the more esoteric language that is not necessary to understanding the definition and use common explanations (perhaps introducing the phrase in brackets afterwards, if it is a particularly important one or will be used again in the rest of the article), so something like:
The primitive recursive functions are functions which take some number (potentially zero) of natural numbers (nonnegative integers) {0, 1, 2, ...} as arguments and produce natural numbers as their results.
The basic primitive recursive functions are given by these axioms:
1. Constant function: The constant function 0 is primitive recursive.
2. Successor function: The single-argument successor function S, which returns the successor of its argument (see Peano postulates), is primitive recursive. That is, S(k) = k + 1.
3. Projection function: For every n≥1 and each i with 1≤in, the projection function Pin, which takes n arguments and returns its i-th argument, is primitive recursive.
and so on. I'm not sure if the reference to the Peano postulates should stay or not -- it is not essential to understanding the subject, but is not particularly harmful, either. I hope you see that this is a clearer way of phrasing the definition, which while not as brief as the original avoids the use of notations or terminology the reader may be unfamiliar with and is therefore easier for a novice to read. JulesH (talk) 09:13, 2 September 2013 (UTC)
I agree that your suggestion is much better than the existing article. But, in my opinion, the first sentence is yet too technical. I would suggest:
"In computability theory, the primitive recursive functions are, roughly speaking, the functions that may be defined and computed by a computer program made up from the arithmetic operations, the if then else control statement and the for i = 1 to n loop (excluding the while loop with a number of iterations that are is not known when entering in the loop). The primitive recursive functions form an important building block on the way to a full formalization of computability and are important in proof theory. Historically, and for allowing simpler proofs, they are formally defined using a short list of ways of composing functions and a particular form of recursion known as primitive recursion. The term was coined by Rózsa Péter."
As almost everybody knows the bases of computer programming this would make the first paragraph understandable for a much wider audience. This characterization of the primitive recursive functions has also the advantage to allow a non specialist to recognize primitive recursive functions by himself. D.Lazard (talk) 17:02, 2 September 2013 (UTC)
If either of you make any changes to the article, please make them incrementally: make a small (localized) change, wait a few days to see what the reaction is, make another small change, wait a few more days, etc.. This way I or others can correct any errors you introduce instead of having to revert you wholesale. JRSpriggs (talk) 02:46, 3 September 2013 (UTC)
## symbol for proper subtraction (#Some common primitive recursive functions )
I'm no expert here, but shouldn't the symbol for proper subtraction be ⊥ (U+22A5, 'Up tack') or ⟂ (U+27C2, 'perpendicular'), not ┴ (U+2534, 'Box drawing light up and horizontal', currently used)? I don't expect box drawings be used as a mathematical expression... -- あるうぃんす (talk) 14:45, 14 September 2013 (UTC) (sorry about my username!)
Actually the symbol I have seen is similar to ${\displaystyle 3\div 5=0\,}$ except that the dot below the line is removed. JRSpriggs (talk) 09:26, 15 September 2013 (UTC)
---
Yes, this symbol ∸ , derived from Arial Unicode MS symbol code: 2238 Unicode (Hex). Bill Wvbailey (talk) 20:54, 15 September 2013 (UTC)
Thanks to Wvbailey for the character. I put it into the article. JRSpriggs (talk) 09:16, 16 September 2013 (UTC)
## More intuitive definition ?
I found the following on [wolfram](http://mathworld.wolfram.com/PrimitiveRecursiveFunction.html): "As first shown by Meyer and Ritchie (1967), do-loops (which have a fixed iteration limit) are a special case of while-loops. A function that can be implemented using only do-loops is called primitive recursive. (In contrast, a computable function can be coded using a combination of for- and while-loops, or while-loops only.) Examples of primitive recursive functions include power, greatest common divisor, and p_n(the function giving the nth prime). "
This definition might just be a name clash, but if it is equivalent, it does get a point across much more quickly and more layman-friendly. But I am reluctant to edit the article as I do not have the expertise. What is your opinion JSpriggs? I don't think we should remove information, but if this 'primitive recursive function' is the same as that 'primitive recursive function' then we should mention that early on. Also, if this definition is added, we should elaborate what we mean by fixed iteration limit more precisely. JimCrayne (talk) 02:58, 2 February 2015 (UTC)
This is not a name clash, and the two definitions are equivalent, a soon as one has proved that the programming language which is used computes primitive functions (Church thesis). More precisely, if, for each loop of the program, there is a primitive function which can upper bound the number of iterations before entering the loop, then the function computed by the program is primitive. There is a related theorem, which is also rather intuitive, and may help to understand complexity theory: A recursive function is primitive if and only if its computation time is upperbounded by a primitive function of the size of the input. The relationship is the following: Starting for a program, compute first a bound B of the execution time; then transform all while loops into do loops of the form "for i = 1 to B do". The practical consequence is that, as soon as you have computed the worst-case complexity of an algorithm, you know that it computes a primitive function. IMO, the article should insist on these results, as, except for specialists of recursive functions, there are the main properties of primitive recursive functions that deserve to be known by mathematicians and computer scientists. I have learn this a long time ago in a book, the name of which I do not remember. Therefore editing the article accordingly would take too much time for me. Note also that I have suggested before (#Definition) a modification of the lead that is similar to this. D.Lazard (talk) 10:10, 2 February 2015 (UTC)
Yes, I think you two have the right idea of what a primitive recursive function is. However, I would rather that you make the change than that I make it because I am happy with the present version. You can change it to make it clear to yourselves and then I will make sure that it is still technically correct. JRSpriggs (talk) 04:24, 3 February 2015 (UTC)
## List of p.r. functions
The numbered list of functions from Addition to Logarithm had several inconsistencies and typos and unnecessary elements; I fixed several of them as a minor edit. This last one I left as a major edit because I'm not at all sure if I've preserved the original intent -- the original text
"b divides a" [ a | b ]: If the remainder ( a, b )=0 then [ a | b ] else b does not divide a "evenly"
isn't even grammatically sensible, and seems to be confused about which of a and b is the potential divisor. I rewrote it to
a | b: (a divides b): If b=k×a for some k then 0 else 1
under the assumption that it was intended to be the (t=0,f=1) representation function for the usual "a divides b" predicate.
There are two (evidently different) functions both written as a×b in this list. Perhaps this needs addressing.
I left the final item
lo(x, y): logarithm of x to the base y
untouched, but since "logarithm" is understood by default to be real-valued, this needs a clarification of what it means. My best guess would be that lo(576, 2) = 6, which makes it similar to, but not identical to, the (a)i function earlier in the list. Joule36e5 (talk) 06:43, 6 April 2015 (UTC) | 13,026 | 55,221 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 3, "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} | 2.84375 | 3 | CC-MAIN-2017-39 | latest | en | 0.937461 |
https://nicefreedatingall.com/how-to-calculate-compound-interest-on-hp-10bii.php | 1,624,350,001,000,000,000 | text/html | crawl-data/CC-MAIN-2021-25/segments/1623488512243.88/warc/CC-MAIN-20210622063335-20210622093335-00408.warc.gz | 367,267,207 | 11,104 | ## How to calculate compound interest on hp 10bii
HP 10bII Financial Calculator - Solving for Loan Payments
The interest rate per period is computed by taking the nominal annual rate and dividing by the number of periods per year. Compound interest problems can be directly solved using the time value of money application. The nominal annual interest rate is entered and the HP 10bII automatically uses the value for the number of periods per year to compute the interest rate per period. HP 10bII Financial Calculator - Solving for Loan Payments. The time value of money application. Loan payments. Practice solving for loan payments. In a compound interest problem, for example, if a positive value is input for the, then a computed will be displayed as a negative number. In an annuity problem, of the three monetary variables.
Are you a student? Did you know that Amazon is offering 6 months of Amazon Prime - free two-day shipping, free movies, and other benefits - to students?
Click here to learn more. Many, perhaps most, time value of money problems in the real world involve other than annual time periods. For example, most consumer loans e. All of the examples in the previous pages have used annual time periods for simplicity. On this page, I'll show you how to make green tea at home in tamil easy it is to deal with non-annual problems.
The first thing to understand is that all of the principles that you have learned to apply for annual problems still apply for non-annual problems. In truth, nothing has changed at all. If you try to think in terms of "periods" rather than years, you will be ahead of the game.
A period can be any amount of time. Most common would be daily, monthly, quarterly, semiannually, or annually. However, a time period could be any imaginable amount of time e.
The first, and most important, thing to think about when dealing with non-annual periods is the number of periods in a year. The reason that this is so important is because you must be what are symptoms of brain infection when entering data into the HP 10BII.
Very often in a problem, you are given annual numbers but then told that "payments are made on a monthly basis," or that "interest is compounded daily.
Let's look at an example:. So, you how to get rid of a corn on little toe be forgiven for expecting that a period is one year. However, on further reading you see that the payments must be made every month. Therefore, the length of a period is one month, and you must convert the variables to a monthly basis in order to get the correct answer. Since there are 12 months in a year, we calculate the total number of periods by multiplying 30 years by 12 months per year.
So, N is months, not 30 years. The same logic would apply if there was an FV in this problem. When you solve for the payment, the calculator will automatically give you the monthly per period to be exact payment amount. In this problem, then, we would solve for the payment amount by entering in N0. One thing to be careful about is rounding. Do not do the calculation and then write down the answer for later entry.
If you do, you will be truncating the interest rate to the number of decimal places that are shown on the screen, and your answer will suffer from the rounding. The difference may not be more than a few pennies, but every penny matters. Try sending your lender a payment that is consistently three cents less than required and see what happens. It probably won't be long before you get a nasty letter.
You might be tempted to think that you could treat the problem as an annual one, and then adjust your answer to be monthly. Don't do that! The math simply doesn't work that way.
To prove it, let's input annual numbers, and then convert the annual payment to monthly by dividing by Do you see the problem? So, when you make the adjustments matters. Always adjust your variables before solving the problem. The reason for the difference is the compounding of interest. If you have read through my tutorial on the Mathematics of Time Value of Moneythen you know that the more frequently interest is compounded, the smaller the payment has to be in order to grow to a particular future value.
I strongly recommend that you avoid this feature because I think it causes more problems than it solves. The reason is that this setting is hidden away, and if you forget to change it you will probably get a wrong answer. It can be difficult to spot problems caused by this setting. Regardless of my feelings about this setting, I'm going to tell you how to use it. However, and this is very important, it will not adjust the number of periods or the payment amount!
That makes this feature virtually worthless. Let's do the problem again, but using this "feature. Now, we can enter the data. The answer is correct, but what did you save by using that "shortcut? In fact, it takes an extra keystroke or two to use this feature. Furthermore, if you forget to change the setting when you do the next problem, you will get the wrong answer unless that problem also happens to use monthly compounding.
I hope that you have found this tutorial to be helpful. If you have any questions or comments, please feel free to contact me. HP 10BII.
Simple and compound interest
i HP 10bII+ Financial Calculator User’s Guide HP Part Number: NW Edition 1, May File Size: 2MB. Product: HP 10BII Hello, I bought an HP BII Financial calculator and experienced problems in calculation of continuously compound interest. I can't find either ln nor e button. Jan 19, · The HP 10BII financial calculator has a built in settings for payments per year that attempts to auto-adjust the interest rate based on how many periods there are in a year. However, this does not auto-adjust the N and PMT components (you still have to do this manually), which makes this function cause more problems than it’s worth.
Click here. Sign out. Select registration option. Email address. Error: Javascript is disabled in this browser. This page requires Javascript. Modify your browser's settings to allow Javascript to execute. See your browser's documentation for specific instructions. HP Customer Support. Select your model. How does HP install software and gather data? The time value of money application. The time value of money application The time value of money application built into the HP 10bII is used to solve annuities that involve regular, uniform payments.
Annuity problems require the input of 4 of these 5 values:. Once these values have been entered in any order, the unknown value can be computed by pressing the key for the unknown value. The time value of money application operates on the convention that money invested is considered positive and money withdrawn is considered negative.
In a compound interest problem, for example, if a positive value is input for the , then a computed will be displayed as a negative number. In an annuity problem, of the three monetary variables, at least one must be of a different sign than the other two. For example, if the and are positive, then the will be negative. If the and are both negative, then the must be positive.
An analysis of the monetary situation should indicate which values are being invested and which values are being withdrawn. This will determine which are entered as positive values and which are entered as negative values. Interest rates are always entered as the number is written in front of the percent sign, i.
The number of periods per year is set using the yellow-shifted function. Problems involving annual compounding or annual payments should be solved with this value set to 1. Problems involving monthly compounding or monthly payments should be solved with this value set to Additional information can be found in the learning module covering time value of money basics. Loan payments Nearly everyone makes loan payments at one time or another, since few of us are able to always pay cash for houses and cars.
Loan payments are computed so that part of the payment made pays for interest that has accrued on the loan since the last payment and part goes toward reducing the outstanding loan balance. Over the life of the loan, the portion of each payment that goes toward interest and the outstanding loan balance or principal changes, with the portion of each payment going toward principal increasing throughout the lifetime of the loan.
This aspect of a loan is explained in greater detail in the learning module on loan amortizations. Cash flow diagrams and sign conventions The sign conventions for cash flows in the HP 10bII follow this simple rule: money received is positive arrow pointing up , money paid out is negative arrow pointing down.
The key is keeping the same viewpoint through each complete calculation. The regular use of cash flow diagrams allows a faster approach to solve most TVM-related problems. The cash flow diagram below represents the borrower viewpoint of the most problems and their relationship to the TVM variables.
The terms she has been offered are a month loan at 4. What would be the size of her monthly car payment? Sarah might want to see if there are less strenuous alternatives. Since she felt the car payment in Example 2 was a little high each month, she shopped around and found a bank that would finance the car for 72 months at 2.
What is the size of their monthly payment? Select a location. Europe, Middle East, Africa. Asia Pacific and Oceania. Select a language. Confirm Back. Search all support. Search help. Tips for better search results Ensure correct spelling and spacing - Examples: "paper jam" Use product model name: - Examples: laserjet pro p, DeskJet For HP products a product number. Loading Results. The Virtual Agent is currently unavailable.
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## 5 thoughts on “How to calculate compound interest on hp 10bii”
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Kaivian Hines no | 2,133 | 10,210 | {"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} | 3.34375 | 3 | CC-MAIN-2021-25 | latest | en | 0.947652 |
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Latest Threads log log n Interpretation Forum: Exam 1 Last Post: sammaryland 1 hour ago » Replies: 1 » Views: 7 MRT Question Forum: Exam 1 Last Post: sammaryland 9 hours ago » Replies: 2 » Views: 37 freeing strings and token... Forum: Project 1 Last Post: NiceHam Yesterday, 03:57 PM » Replies: 2 » Views: 107 Review Session Forum: Study Groups Last Post: kamadson Yesterday, 03:19 AM » Replies: 0 » Views: 12 Tokens or quoted strings Forum: Project 1 Last Post: sbcarp 02-17-2018, 05:26 PM » Replies: 2 » Views: 83 extractHEAP Forum: Project 1 Last Post: chibbluffy 02-17-2018, 05:50 AM » Replies: 2 » Views: 103 What was it I said I woul... Forum: Miscellany Last Post: sammaryland 02-16-2018, 08:07 PM » Replies: 1 » Views: 46 Is root node a leaf node? Forum: Project 1 Last Post: lusth 02-16-2018, 03:36 PM » Replies: 2 » Views: 109 Max or min heap Forum: Project 1 Last Post: chibbluffy 02-16-2018, 08:01 AM » Replies: 1 » Views: 121 Heap test Forum: Project 1 Last Post: chibbluffy 02-16-2018, 03:50 AM » Replies: 4 » Views: 144
insertHEAP and extractHEAP
Posted by: grayson - 02-09-2018, 03:11 AM - Forum: Project 1 - Replies (5)
What kinds of properties are our heaps supposed to maintain? The logarithmic runtime extractHEAP function is supposed to rebuild the heap somehow, but assuming buildHEAP runs in linear time, it must do this without calling buildHEAP. In this case, what kind of ordering is expected? Is the heap supposed to be rebuilt maintaining the order of insertion? Since insertHEAP doesn't do any fixing up on insert according to the spec, there are no guaranteed properties (like min or max) about our heap other than its completeness. I'm not understanding from where extractHEAP's logarithmic runtime arises.
Websites to checkout
Posted by: ccatwater - 02-08-2018, 06:29 PM - Forum: Self Balancing Search Trees - No Replies
Here are a few good videos I found on self balancing trees: Rotations and Red black trees, provides really good and quick summary of the basics - https://www.youtube.com/watch?v=95s3ndZRGbk Short video on rbt insertion rules - https://www.youtube.com/watch?v=tJ7niBAhDQI Avl trees - https://www.youtube.com/watch?v=5C8bLQBjcDI Also this site is a great interactive tool for almost every data structure in 201- https://www.cs.usfca.edu/~galles/visuali...ithms.html
displayHEAPdebug
Posted by: sammaryland - 02-08-2018, 04:28 PM - Forum: Project 1 - Replies (3)
For the displayHEAPdebug function, the spec says to call the display debug method of the underlying data structure, but without a parameter of a file pointer, should we just pass stdout to displayBSTdebug?
Recursive implementations?
Posted by: magarwal - 02-08-2018, 05:51 AM - Forum: Project 1 - Replies (1)
After looking at the project spec, it is my understanding that the insert, find, delete and display functions are not to be implemented recursively because they don't have a BSTNODE *root parameter. Am I correctly understanding this? I'm just confused about the entire BST spec because the BSTNODE and BST are separate entities here, and there appear to be no subtrees. Shouldn't every node be its own subtree?
Posted by: mcoram - 02-08-2018, 03:48 AM - Forum: Project 0 - Replies (2)
After submitting to the Dropbox, I get the following errors with my makefile. I'm confused (especially with the response "no makefile found") because everything in my makefile works fine in my terminal window. Running your tests -------------------------------------- make: *** No rule to make target 'clean'. Stop. make: *** No targets specified and no makefile found. Stop. You are alloted 10 seconds for testing make: *** No rule to make target 'test'. Stop. --------------------------------------
Resubmission #2
Posted by: sammaryland - 02-08-2018, 02:55 AM - Forum: Project 0 - Replies (1)
When will resubmission 2 be graded?
Notes from class
Posted by: meganw - 02-08-2018, 12:04 AM - Forum: Notes - No Replies
Here is a google drive folder of my notes. Please let me know if I should update anything or have copied something down incorrectly. https://drive.google.com/drive/folders/1...sp=sharing
Valgrind on Cygwin
Posted by: Nathaniel Wade - 02-07-2018, 08:32 PM - Forum: Project 0 - Replies (1)
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## Math Riddle (Answer reveal included)Posted: Wed Feb 03, 2016 5:09 pm
XeX_Troy
• Challenger
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An athlete is able to jump FOREVER. However, every time that she jumps she gets a bit more tired, and every jump goes 1/2 as far as her prior jump. Now, for her very first jump, she goes 1/2 of a foot.
On her second jump, she goes 1/4 of a foot, and so on and so forth.
How many jumps does it take for her to travel 1 foot?
She will never get to the 1 foot mark because you keep adding smaller and smaller amounts!
#2. Posted:
Nick
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Motto: We're stacking up We're piling high We've gone too far to recognise salvation This is civil isolation
Got one for you, but I won't be as nice as you and won't reveal the answer. Did this one in my AP stats class.
How can you add eight 8's to get the number 1,000? (only use addition)
#3. Posted:
DeluxeHazard
• Christmas!
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I am giving my word that I did not look at the answer before because I have heard of similar riddles like this. The answer is never. When the person has "x" distance left to jump, she jumps half of that distance. So when she need to jump half a foot she jumps a fourth of a foot, when she needs to jump a fourth of a foot she jump an eight of a foot, and this continues infinitely since every time she jumps half of the necessary distance to finish a whole foot. I remember that Vsauce posted a great video explaining. Here is the link to it: [ Register or Signin to view external links. ]
#4. Posted:
Pint | 494 | 1,818 | {"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} | 3.5625 | 4 | CC-MAIN-2019-51 | longest | en | 0.95941 |
https://www.hackmath.net/en/problem/61 | 1,566,132,848,000,000,000 | text/html | crawl-data/CC-MAIN-2019-35/segments/1566027313889.29/warc/CC-MAIN-20190818124516-20190818150516-00513.warc.gz | 830,565,174 | 6,646 | # Rectangle
Area of rectangle is 3002. Its length is 41 larger than the width. What are the dimensions of the rectangle?
Result
length: 79
width: 38
#### Solution:
Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):
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#### To solve this verbal math problem are needed these knowledge from mathematics:
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Find g(1) if g(x) = 3x - x2 Find f(5) if f(x) = x + 1/2 | 583 | 2,345 | {"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} | 3.578125 | 4 | CC-MAIN-2019-35 | latest | en | 0.906502 |
https://ch.mathworks.com/matlabcentral/cody/players/3174313/solved | 1,606,204,112,000,000,000 | text/html | crawl-data/CC-MAIN-2020-50/segments/1606141171126.6/warc/CC-MAIN-20201124053841-20201124083841-00547.warc.gz | 241,076,382 | 21,163 | Cody
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Depdendent Variable
Number of equations to solve: 23456789
Equ. #1:
Equ. #2:
Equ. #3:
Equ. #4:
Equ. #5:
Equ. #6:
Equ. #7:
Equ. #8:
Equ. #9:
Solve for:
Dependent Variable
Number of inequalities to solve: 23456789
Ineq. #1:
Ineq. #2:
Ineq. #3:
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mer än 2 år ago | 0 | 1,500 | 5,887 | {"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} | 2.796875 | 3 | CC-MAIN-2024-22 | latest | en | 0.784604 |
https://www.sweatlodgeradio.com/what-is-not-a-whole-number/ | 1,675,943,591,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764499966.43/warc/CC-MAIN-20230209112510-20230209142510-00765.warc.gz | 1,008,260,513 | 41,770 | # What is not a whole number?
## What is not a whole number?
The whole numbers are the numbers 0, 1, 2, 3, 4, and so on (the natural numbers and zero). Negative numbers are not considered “whole numbers.” All natural numbers are whole numbers, but not all whole numbers are natural numbers since zero is a whole number but not a natural number.
## Is 9 3 a whole number?
Numerator. This is the number above the fraction line. For 9/3, the numerator is 9. It’s an integer (whole number) and a proper fraction.
Can you simplify 9 3?
The simplest form of 93 is 31.
### What is meant by one half?
One half is the irreducible fraction resulting from dividing one by two (2) or the fraction resulting from dividing any number by its double. One half appears often in mathematical equations, recipes, measurements, etc. Half can also be said to be one part of something divided into two equal parts.
### What is the smallest whole number?
The smallest whole number is “0” (ZERO).
What is 1/3 in a whole number?
0./div>
#### How do you write 2.5 years?
To summarize for simplicity: two half years = 1 year; two and a half years = 2.5 years. The confusion comes from the fact the latter phrase is generally accepted as “two and a half years” rather than “two and half years.”
#### What is 5/8 in a whole number?
The fraction 5/8 can never be a whole number because it represents part of a whole. The whole is divided into 8 pieces, and the fraction 5/8…
What is 25% as a whole number?
Example
Problem Write 25% as a simplified fraction and as a decimal.
Simplify the fraction by dividing the numerator and denominator by the common factor 25.
Write as a decimal. 25% = = 0.25 You can also just move the decimal point in the whole number 25 two places to the left to get 0.25.
## Is 88 a whole number?
79, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89,90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100.
## What is 9 4 as a whole number?
The third step in the process of converting a fraction to a mixed number is the easiest step. Remember that we still need a denominator for our mixed number. The denominator is the exact same number as the denominator in the original improper fraction; in this case, 4. So 9/4 equals 2 1/4.
What is 3/4 as a whole number?
1 Expert Answer 3/4 isn’t a whole number. You can write it as a decimal: 0.75.
### What is a 3rd of 100%?
Percentage Calculator: What is . 3 percent of 100.? = 0.3.
### Is 3 a whole number?
In mathematics, whole numbers are the basic counting numbers 0, 1, 2, 3, 4, 5, 6, … and so on. 17, 99, 267, 8107 and are examples of whole numbers. Whole numbers include natural numbers that begin from 1 onwards.
What is 1/2 in a whole number?
2 Answers By Expert Tutors In the same way, 1/2 is never equal to a whole number. It is equal to 0.5, which has a decimal but not a fraction. You could multiply by 0.5 the same way you multiply by 5, except that you might have at least one extra decimal place in the answer.
#### How do you classify numbers?
The classifications of numbers are: real number, imaginary numbers, irrational number, integers, whole numbers, and natural numbers. Real numbers are numbers that land somewhere on a number line. Imaginary numbers are numbers that involve the number i, which represents \sqrt{-1}.
#### What do you mean by 1%?
1 eV is defined as the energy gained by an electron when it has been accelerated by a potential difference of 1 volt, hence 1 eV = 1.60210-19J. The work function of platinum is highest (Θ0=5.65 eV) and caesium is the lowest (Θ0=2.14 eV). …
What is 3 as a fraction?
Decimal to fraction conversion table
Decimal Fraction
0.3 3/10
0./td>
1/3
0.375 3/8
0.4 2/5
## How is half written?
So “1/2” should always be written out as one-half. (Unless it’s in a sentence like “one half of a perfect pair,” in which case it’s not a fraction.) One half need not be hyphenated when used as a noun; however, it must be hyphenated when used as an adjective: 1. | 1,097 | 3,972 | {"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} | 4.46875 | 4 | CC-MAIN-2023-06 | longest | en | 0.917813 |
http://mathhelpforum.com/pre-calculus/107178-identifying-vertex-quadratic-function.html | 1,480,796,327,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541134.5/warc/CC-MAIN-20161202170901-00103-ip-10-31-129-80.ec2.internal.warc.gz | 178,771,795 | 10,584 | 1. ## Identifying the vertex of a Quadratic Function
I really don't mean to be a nusance, I am new here and hope to be more of a contributer of this site rather that bothering people, so I apologize. I seem to have a hard time with a specific step in taking a quadratic trinomial that cannot be factored and and converting it into a vertex formula [f(x)=(x-h)²+k].
In this case:
f(x)= 2x² + 8x + 7
I know that the first step is to group the x terms leaving the leading coefficient out of the parenthesis such as:
f(x)= 2(x² + 4x) + 7
Next step is to take the middle term and square half the coefficient: (4/2)² and then add and subtract by that number.
f(x)= 2(x² + 4x+4-4) + 7
Now here is where it gets fuzzy for me, I read this online and here is the further step according to what I read:
Now, move the second -4 to the outside of the parenthesis, only now we have to consider that the outside coefficient isn't just a simple positive one. There's a 2 out there.
f(x) = 2(x² + 4x + 4) - 2(4) + 7
Question, is that -2 that is underlined the -4 that was outside the parentesis? And if so where did that four to the right of it come from? I'm stumped as to how it got there because if the -2 was the -4 inside the parenthesis and we have the +4 inside the parenthesis, that (4) that is next to the -2 seems to have crashed the party. I just can't figure out how it got there according to there steps and there seems to be no sufficient information as to how it got there, please explain.
2. Alright, given: $f(x)=2x^2+8x+7$
You want it in the form $f(x)=a(x-h)^2+k$, which can also be written as $y-k=a(x-h)^2$
So, subtract over 7 and factor out a 2: $y-7=2(x^2+4x)$
You understand the step of completing the square. Divide 4 by 2, square, and add: $2(x^2+4x+4)$ Because we added 8 (you have to multiple $a$ through the quadratic) to one side, we add it to the other:
$y+1=2(x+2)^2$, or
$f(x)=2(x+2)^2-1$
Vertex = $(h,k)$, or $(-2, -1)$ | 588 | 1,952 | {"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} | 4.53125 | 5 | CC-MAIN-2016-50 | longest | en | 0.95005 |
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Course Number: ACCOUNTING 2, Fall 2009
College/University: Santa Monica
Word Count: 1241
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# the tree. Assume a = 56, b = 26 c = 210 ft. (Round your answer to the nearest whole number.) A water tower 30 m tall is located at the top of a hill. From a distance of D = 110 m down the hill, it is observed that the angle formed between the top and base of the tower is 8. Find the angle of inclination of the hill. Round your answer to the nearest tenth degree. Use the Law of Cosines to determine the indicated...
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tree. the Assume a = 56, b = 26 c = 210 ft. (Round your answer to the nearest whole number.) A water tower 30 m tall is located at the top of a hill. From a distance of D = 110 m down the hill, it is observed that the angle formed between the top and base of the tower is 8. Find the angle of inclination of the hill. Round your answer to the nearest tenth the degree. Use Law of Cosines to determine the indicated side x. = 82 Use the Law of Cosines to determine the angle : x = 120.4 Use the Law of Cosines to determine the angle . (Round your answer to one decimal place.) a = 12, b = 13, c = 23 Solve triangle ABC. (If there is no such triangle enter NONE for each answer. Round your answers to 1 decim
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Math 53 - Multivariable CalculusQuiz # 5August 1st, 2012Exercise 1. Let and be any two surfaces with equivalent boundaries = C = . Is it true that F dS =3 F dS for any vector eld F which is dierentiable on R ? Justify your answer.Exercise 2. Let F
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Northwestern - MATH - 290-1 | 3,765 | 13,778 | {"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} | 3.734375 | 4 | CC-MAIN-2014-15 | latest | en | 0.912149 |
https://robot.sia.cn/cn/article/id/167 | 1,708,636,612,000,000,000 | text/html | crawl-data/CC-MAIN-2024-10/segments/1707947473824.45/warc/CC-MAIN-20240222193722-20240222223722-00046.warc.gz | 500,441,956 | 38,421 | 引用本文: 代小林, 黄其涛, 韩俊伟, 李洪人. 基于运动学正解的三转动并联机构迭代补偿控制[J]. 机器人, 2009, 31(6): 518-522,528.
DAI Xiaolin, HUANG Qitao, HAN Junwei, LI Hongren. Iterative Compensation Control of 3-DOF Rotational Parallel Mechanism Based on Forward Kinematics[J]. ROBOT, 2009, 31(6): 518-522,528.
Citation: DAI Xiaolin, HUANG Qitao, HAN Junwei, LI Hongren. Iterative Compensation Control of 3-DOF Rotational Parallel Mechanism Based on Forward Kinematics[J]. ROBOT, 2009, 31(6): 518-522,528.
## Iterative Compensation Control of 3-DOF Rotational Parallel Mechanism Based on Forward Kinematics
• 摘要: 首先建立三转动并联机构的运动学方程，研究该并联机构的运动学反解和运动学正解，然后建立该机构的动力学方程并分析其动力学特性．基于该机构研制了能复现自行武器行进时的车体姿态变化过程的动态模拟器试验台．该试验台利用运动学反解算法进行闭环控制，并采用基于运动学正解的开环迭代补偿控制算法修正姿态驱动信号，使试验台的响应逐渐逼近期望的姿态指令．测试表明该系统时域波形复现精度优于95%，验证了迭代补偿控制的有效性．
Abstract: The kinematics equation of a 3-DOF(degree of freedom) rotational parallel mechanism is established,and the solutions of the inverse and forward kinematics are investigated. Then the dynamics equation of the robot is built,and the dynamics characteristics are analyzed. A dynamic simulator based on this mechanism is developed to simulate the vehicle posture changes of self-propelled weapons during moving. A closed loop controller based on inverse kinematics is used to control the simulator,and an open loop iterative compensation controller based on forward kinematics is developed at the same time to correct the posture driving signal and make simulator's response approximate the posture command gradually. Experiments show that the system precision is better than 95%,which validates the effectiveness of the iterative compensation control strategy.
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分享至好友和朋友圈 | 564 | 1,674 | {"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} | 2.515625 | 3 | CC-MAIN-2024-10 | latest | en | 0.646369 |
http://upscfever.com/upsc-fever/en/maths/en-math-chp4.html | 1,555,791,285,000,000,000 | text/html | crawl-data/CC-MAIN-2019-18/segments/1555578530040.33/warc/CC-MAIN-20190420200802-20190420222802-00462.warc.gz | 181,802,333 | 6,598 | 1. Rational numbers can be represented in the form p/q where q ≠ 0. Irrational numbers cannot be represented in the form p/q where q ≠ 0. The decimal number expansion of a number is either terminating or non terminating recurring.
2. The decimal expansion of an irrational number is non terminating, non recurring.
3. The sum or difference of a rational number and an irrational number is irrational
4. The product or quotient of a non-zero rational number with an irrational number is irrational.
5. add, subtract, multiply or divide two irrationals, the result may be rational or irrational.
6. √(ab) = √a*√b
7. √a/√b = √(a/b)
8. (√a+√b)(√a-√b) = a-b
9. (a+√b)(a-√b) = a2-b
10. (√a+√b)(√c+√d) = (√ac + √ad + √bc + √bd)
11. (√a+√b)2= a + 2 √ab + b
Q. Show that 0.3333... = 03. can be expressed in the form p/q are such p,q are integers and q ≠ 0
Ans.let x = 0.333. Therefore 10 x = 3.333...
So we have 10x = 3 + 0.3333...
which is 10x=3+x and so x=1/3
Q.Show that 1.272727... can be expressed in the form p/q and p,q are integers and q ≠ 0.
1. so let x=1.27272...
2. we have 100x=127.2727...
3. 100x=126+1.2727..
4. 100x=126+x which gives x=126/99
Ans.x=14/11
Q.Show that 0.2353535.. can be expressed in the form p/q and p,q are integers and q ≠ 0.
1. so let x=0.2353535...
2. we have 100x=23.5353535...
3. 100x=23.3+0.2353535..
4. 100x=23.3+x which gives x=233/990
Ans.x=233/990
1. Divide p(x) by g(x), where p(x) = x + 3x2 – 1 and g(x) = 1 + x.
2. Write the dividend x + 3x2 – 1 and the divisor 1 + x in the standard form, i.e., after arranging the terms in the descending order of their degrees. So, the + x –1 and divisor is x + 1. dividend is 3x2
3. We divide the first term of the dividend by the first term of the divisor, i.e., we divide 3x 2 by x, and get 3x. This gives us the first term of the quotient. i.e. 3x
4. We multiply the divisor by the first term of the quotient, and subtract this product from the dividend, i.e., we multiply x + 1 by 3x and subtract the product 3x2 + 3x from the dividend 3x2 + x – 1. This gives us the remainder as –2x – 1.
5. We treat the remainder –2x – 1 as the new dividend. The divisor remains the same. We repeat Step 2 to get the next term of the quotient, i.e., we divide the first term – 2x of the (new) dividend by the first term x of the divisor and obtain – 2. Thus, – 2 is the second term in the quotient.
6. We multiply the divisor by the second term of the quotient and subtract the product from the dividend. That is, we multiply x + 1 by – 2 and subtract the product – 2x – 2 from the dividend – 2x – 1. This gives us 1 as the remainder.
7. This process continues till the remainder is 0 or the degree of the new dividend is less than the degree of the divisor. At this stage, this new dividend becomes the remainder and the sum of the quotients gives us the whole quotient.
8. Thus, the quotient in full is 3x – 2 and the remainder is 1.
1. Let p(x) be any polynomial of degree greater than or equal to one and let a be any real number. If p(x) is divided by the linear polynomial x – a, then the remainder is p(a).
2. If p(x) is a polynomial of degree n > 1 and a is any real number, then (i) x – a is a factor of p(x), if p(a) = 0, and (ii) p(a) = 0, if x – a is a factor of p(x).
3. (x + y + z)2 = x2 + y2 + z2 + 2xy + 2yz + 2zx
4. (x + y)3 = x3 + y3 + 3 xy (x + y)
5. (x - y)3 = x3 - y3 - 3 xy (x - y)
6. x3 + y3 + z3 – 3xyz = (x + y + z) (x2 + y2 + z2 – xy – yz – zx)
7. Every linear equation in one variable has a unique solution. A linear equation in two variables has infinitely many solutions.
8. Fahrenheit = (9/5) * Celsius + 32
9. The graph of every linear equation in two variables is a straight line.
10. x = 0 is the equation of the y-axis and y = 0 is the equation of the x-axis. The graph of x = a is a straight line parallel to the y-axis. The graph of y = a is a straight line parallel to the x-axis.
11. An equation of the type y = mx represents a line passing through the origin.
Q.Find the remainder when x4 + x3 – 2x2 + x + 1 is divided by x – 1.
1. p(1) = (1)4 + (1)3 – 2(1)2 + 1 + 1 = 2
2. p(1) = 2
Ans.remainder = 2
Q.Examine whether x + 2 is a factor of x3 + 3x2 + 5x + 6 and of 2x+4.
1. x+2 gives a=-2. and so we can calculate P(-2)
2. P(-2) = 0
Ans.
1. A straight line may be drawn from any one point to any other point.
2. Given two distinct points, there is a unique line that passes through them
3. A terminated line can be produced indefinitely.
4. A circle can be drawn with any centre and any radius
5. All right angles are equal to one another.
6. If a straight line falling on two straight lines makes the interior angles on the same side of it taken together less than two right angles, then the two straight lines, if produced indefinitely, meet on that side on which the sum of angles is less than two right angles.
7. For example, the line PQ in Fig. below falls on lines AB and CD such that the sum of the interior angles 1 and 2 is less than 180° on the left side of PQ. Therefore, the lines AB and CD will eventually intersect on the left side of PQ.
1. Two figures are congruent, if they are of the same shape and of the same size.
2. Two circles of the same radii are congruent.
3. Two squares of the same sides are congruent.
4. If two sides and the included angle of one triangle are equal to two sides and the included angle of the other triangle, then the two triangles are congruent (SAS Congruence Rule).
5. If two angles and the included side of one triangle are equal to two angles and the included side of the other triangle, then the two triangles are congruent (ASA Congruence Rule).
6. If two angles and one side of one triangle are equal to two angles and the corresponding side of the other triangle, then the two triangles are congruent (AAS Congruence Rule).
7. Angles opposite to equal sides of a triangle are equal.
8. Sides opposite to equal angles of a triangle are equal.
9. Each angle of an equilateral triangle is of 60°.
10. If three sides of one triangle are equal to three sides of the other triangle, then the two triangles are congruent (SSS Congruence Rule).
11. If in two right triangles, hypotenuse and one side of a triangle are equal to the hypotenuse and one side of other triangle, then the two triangles are congruent (RHS Congruence Rule).
12. In a triangle, angle opposite to the longer side is larger (greater).
13. In a triangle, side opposite to the larger (greater) angle is longer.
14. Sum of any two sides of a triangle is greater than the third side.
15. A line through the mid-point of a side of a triangle parallel to another side bisects the third side.
16. The quadrilateral formed by joining the mid-points of the sides of a quadrilateral, in order, is a parallelogram
17. The line-segment joining the mid-points of any two sides of a triangle is parallel to the third side and is half of it
18. Diagonals of a square bisect each other at right angles and are equal, and vice-versa.
19. Diagonals of a rhombus bisect each other at right angles and vice-versa.
20. Diagonals of a rectangle bisect each other and are equal and vice-versa.
21. A diagonal of a parallelogram divides it into two congruent triangles.
22. A quadrilateral is a parallelogram, if (i) opposite sides are equal or (ii) opposite angles are equal or (iii) diagonals bisect each other or (iv)a pair of opposite sides is equal and parallel
1. Two congruent figures have equal areas but the converse need not be true.
2. Area of a parallelogram is the product of its base and the corresponding altitude.
3. If a parallelogram and a triangle are on the same base and between the same parallels, then area of the triangle is half the area of the parallelogram.
4. Triangles on the same base (or equal bases) and between the same parallels are equal in area.
5. Area of a triangle is half the product of its base and the corresponding altitude.
6. A median of a triangle divides it into two triangles of equal areas | 2,323 | 8,021 | {"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} | 4 | 4 | CC-MAIN-2019-18 | latest | en | 0.836207 |
https://socratic.org/questions/a-circle-has-a-chord-that-goes-from-pi-2-to-11-pi-6-radians-on-the-circle-if-the-1 | 1,620,307,349,000,000,000 | text/html | crawl-data/CC-MAIN-2021-21/segments/1620243988753.97/warc/CC-MAIN-20210506114045-20210506144045-00024.warc.gz | 561,656,805 | 5,913 | # A circle has a chord that goes from ( pi)/2 to (11 pi) / 6 radians on the circle. If the area of the circle is 5 pi , what is the length of the chord?
##### 1 Answer
Aug 8, 2016
$= 9.4$
#### Explanation:
A chord that goes from $\frac{\pi}{2}$to $11 \frac{\pi}{6}$
so it travels the distance $11 \frac{\pi}{6} - \frac{\pi}{2} = 4 \frac{\pi}{3}$;
or
$4 \frac{\pi}{3} \div 2 \pi = \frac{2}{3}$ of the Circumference of the Circle
Area of the Circle$= \pi {r}^{2} = 5 \pi$
or
${r}^{2} = 5$
or
$r = \sqrt{5}$
or
$r = 2.24$
Circumference of the circle$= 2 \pi r = 2 \left(\pi\right) \left(2.24\right) = 14.07$
Therefore Length of the chord$= 14.07 \left(\frac{2}{3}\right) = 9.4$ | 279 | 680 | {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 11, "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} | 4.53125 | 5 | CC-MAIN-2021-21 | latest | en | 0.652038 |
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# New Book
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### Author Topic: ENERGY AMPLIFICATION (Read 2269495 times)
#### that_prophet
• Sr. Member
• Posts: 491
##### Re: ENERGY AMPLIFICATION
« Reply #7980 on: August 26, 2017, 05:13:08 PM »
PROOF OF CREATION + A YOUNG EARTH = (space dust) has mass + billions of years of dust would add up eventually + mess up the orbits of all planets + moons. We could measure the amount of dust on the moon, and divide the total by the amount of dust that is deposited every year, coming up with an age for the moon, and thereby finding out the age of our earth. Most of us have seen pictures of the moon landing, and realize that there is only a few centimeters, meaning that by the deposit of space dust, the moon has only been orbiting us for a few thousand years. Less than 10,000 year
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COME ON,,, ALL OF YOU BACK YARD MECHANICS,,, Get some AC + DC motors together of the same voltage, and start building these GEM free energy power supplies,, + not only for 1.5, 3, 6, 9 + 12 volt batteries, but household 120 volt, + 12 volt, to powering these new electric cars. Let's throw the oil companies out of work, producing toxic smoke + maybe even make money with them, by throwing any excess power from these perpetually running energy generators that we have the time, + small amount of money to purchase parts to build. Think of it as not only keeping money in your pocket, but you are keeping money from the countries that either fund terrorist, or which are unknowingly funding them. This is not to mention the experimenting that we could be doing with the anti-gravity + speeds approaching light speed. Now I know that there are many out there like me, which would enjoy knowing how one type of this motor was powering a UFO in the Bible, in Ezekiel 1:16. http://aliensandghosts.yolasite.com/
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Most people have heard that the "day + hour knoweth no man"-(Mat 24:36), but why does nobody mention the soon arriving doors that we are not only allowed to know, but in the original Greek, it is worded like a command = “know that it is near, even at the doors”,,, + that 1st Door will close on 2019.04 + the last Door will close on 2025.94. So we are guaranteed that Jesus will set His foot on the Mount of Olives before the year 2026.
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Did you ever wonder how you could know that it’s near, if we can’t know the day. Near to what then, maybe it’s near to the door/deadline = "know that it is near, even at the doors" Mat 24:33. Doors are plural, because of the two appearances of Jesus, the first is in the clouds,(Rapture) http://rapturequestion.yolasite.com/ before the 7 year peace treaty is signed + then His second arrival is as His Foot touches earth, on the Mount of Olives. DOOR = (this is not the date of His Arrival, which we are warned that nobody can know, but this is the date that Christ must return before) A day that the Tribulation Saints will not only know, but they will probably being counting down the days until. = (He Returns when the 7 year peace treaty ends)
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EVil-sOLUTION = isn’t it amazing what Truth can be revealed, when the “il-s” of life are included. http://decimationofthisevolutionfairytale.yolasite.com/
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I can give you a free to run, perpetual power supply = http://free-energy.yolasite.com/ This GEM mechanism can do this because of how AC electricity is created by rotations. as in the more rotations the greater amount of AC electricity, and pulleys can be used to multiply rotations. So, you are using pulley mechanics to multiply your total amount of AC electricity, by trading one rotation of a large 100 cm circumference pulley, into 100 rotations of as many 1 cm circumference pulleys as you choose to add to the same belt. If you add AC generators to these mini-pulleys then you could be multiplying AC electricity. If you added 4 of these mini-pulleys with AC generators attached, you would gain 400 cycles of AC electricity, and all for the single burst of DC current, the minute amount of current that a DC motor takes to rotate one single time.
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These mini-pulleys would be easy to rotate, as the only resistance that they would generate, would be caused by any power that they were generating. These mini-pulleys would only be winding up massive voltages, because the only current needed to rotate your large 100 cm pulley on a DC motor, is one simple spark, or short burst, the amount to rotate your large pulley only one single time. Torque is only caused when you are generating power, and power is generated by current multiplied by voltage. Since we only need one single spark of current, (practically zero) the total amount of power being generated would still be practically zero, costing practically zero torque.
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This was given to mankind before the first door closes = http://my2020vision.yolasite.com/
Especially for the soon coming Tribulation Saints http://doorschristmustpassthrough.yolasite.com/
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Sorry if it offends you, that I add a little bit of Biblical stuff in my explanations, but when I came up with this super simple idea, it was just after asking God for a way to help the Tribulation Saints. Just think about how super simple this AC electricity multiplier truly is, and how the voices in your head tell you that it cannot work. When how much more simple can it be, then to only pay for the one rotation of a large 100 cm pulley, when you can get a return of 100 cycle of AC electricity, for every 1 cm mini-pulley that you attach to the same belt, (with AC generators attached). Yes that’s an input of one single spark of DC current, returning you 100 cycles of AC electricity for every mini-pulley that you attach to the same belt. If you only added 4 mini-pulleys, you would get a return of 40 cycles of AC electricity. Please remember, that there is a most powerful spiritual warfare going on over this GEM technology.
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There is a most powerful spiritual warfare going on over this GEM technology. Can you believe the problems that I have had, getting this super simple way of using pulleys to multiply the total amount of AC cycles of electricity? I think that it’s totally ridiculous, when you truly take a close look at it. Pulleys can be used to multiply the # of rotations, and AC electricity is made of rotations of a coil through a magnetic field. It should be dirt simple, as you are using pulleys to multiply your total # of rotations, and AC electricity is made of rotations, so you are effectively multiplying AC electricity. .
#### Free Energy | searching for free energy and discussing free energy
##### Re: ENERGY AMPLIFICATION
« Reply #7980 on: August 26, 2017, 05:13:08 PM »
#### pulp
• Jr. Member
• Posts: 62
##### Re: ENERGY AMPLIFICATION
« Reply #7981 on: August 26, 2017, 05:14:42 PM »
Bs.
#### that_prophet
• Sr. Member
• Posts: 491
##### Re: ENERGY AMPLIFICATION
« Reply #7982 on: August 26, 2017, 05:48:00 PM »
TIME IS SHORT = the Pre-Trib Rapture + the infamous 7 year Peace Treaty with Israel MUST START before this 1ST DOOR closes on 2019.04 = Jan 14th http://my2020vision.yolasite.com/ - “know that it is near, even at the doors”,(Mat 24:33) http://doorschristmustpassthrough.yolasite.com/.
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Free Energy + perpetual motion can be easily produced using pulleys, costing only the minuscule bit of power that it takes to rotate a DC motor with a large 100 cm circumference pulley one single time. You can gain or multiply massive amounts of AC electricity using mini-pulleys with AC generators. You are capable of doing this by running this long length of belt, (off the circumference of large pulley) past a few 1 cm circumference mini-pulleys, with AC generators attached. This GEM-(Geometrical Electricity Multiplier) device is gaining you 100 cycles of AC electricity, for every mini-pulley that you choose to attach to this sane belt. So, if you added 10 mini-pulleys, you could get a return of 1000=10X100 cycles of AC electricity, and all costing you only one mere spark of DC current. How could you not be multiplying AC electricity, when you are using simple pulley mechanics to trade one spark of DC current, for 100-1000 cycles of AC electricity-(duel sparks).
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This super simple free energy technology: http://free-energy.yolasite.com/ works on the ability of combinations of pulleys being able to easily + freely multiply your total # of rotations. You can do this because of the fact that you don’t have to expend 100 times more electricity to rotate a large 100 cm circumference pulley, than it takes to rotate a 1 cm circumference mini-pulley. Yet if you run the 100 cm of moving belt, that comes off the one rotation of a large 100 cm pulley, past any # of mini-pulleys of 1 cm, then you could gain a return of 100 rotations for every mini-pulley that you choose to attach to the same belt. (As for torque, it only comes from generating power, and power is voltage multiplied by current) + We only need to produce one single spark of DC current to make this a self-powering mechanism. So one spark of DC current, (which is practically nothing) multiplied by even massive voltage, would still equal practically zero power, which takes practically zero torque to rotate.
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This multiplication of rotations could be extremely helpful, if you only added AC generators to these mini-pulleys, you could be multiplying the total cycles of AC electricity. This AC generator takes no torque to rotate, because although it would be winding up massive voltage, it does not need to be winding up practically any current-(1 mere spark) which is practically zero. Torque is only caused when you are generating power, and you are generating practically zero power, as power is equal to voltage times current. So, no matter how massive of voltage you are generating, it is multiplied by practically zero current, as we only need one spark of current, or practically zero. This works because zero times anything is still equal to zero, and practically zero works the same way.
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What is AC electricity, + how is it made = it is made out of the easy rotations of coils of wire through a magnetic field of two oppositely positioned magnets right. Using pulley technology, we can easily + freely convert one rotation of a large 100 cm circumference pulley, into 100 rotations of as many 1 cm circumference mini-pulleys that we choose to attach to the same belt that comes off of your large pulley. So, if you added 10 mini-pulleys to this same belt, and added AC generators to each mini-pulley, you could gain you 1000 = 100X10 cycles of AC electricity.
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All these cycles of AC electricity are from the single burst of DC electricity, which is the small amount of current that a DC motor takes to rotate one single time =(one mere spark). These cycles of AC electricity would cost practically zero torque to rotate, as torque is only caused when you are generating power, and you are not generating practically any power in this system. This is because although you may be winding up massive voltage,(electrical pressure) to keep this GEM mechanism running, you only need to generate one single spark of DC current, and P=IV, or power equals current multiplied by voltage.
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So your total power output would be practically zero current multiplied by any amount of voltage, which would still be equal to practically zero power, taking practically zero torque. So, you could be easily + freely generating massive amounts of rotations of these mini-pulleys, which are generating you massive voltage, or the ability/potential to gain plenty of current, which will allow you to produce plenty of power. This is because the greater the voltage/pressure, the greater the ease that there is to generate more current. PLEASE,,, let me show you how ridiculous this mythical torque problem really is. Do you think that the 100 cycles of AC electricity would have a hard time producing the single spark of DC current, which is all that you need to crank over your DC motor once, with your 100 cm circumference pulley attached?
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Mankind was given the best Gift from God, (other than Jesus) http://free-energy.yolasite.com/ right here in Atlantic Canada + just before the infamous 7 years Peace Treaty. This seven years of time, which the 2nd half of is the Great Tribulation, is when this GEM tech will be needed most. This will be the worst time for earth, where not only is there constant war, but most all of the evil fallen angels, and the Nephilum , will be sent to the earth. Nephilum are the offspring of fallen angels + human women, as angels are all male, because God only wanted there to be a set # of angels. This is not only the ones that are still alive, but also the spirits of all that have died. This could be massive amounts of evil spirits, considering that this includes the ones from before the flood. (How can we be billions of years old, when the moon will leave orbit within 10,000 years) + all orbiting bodies will have messed up orbits, because of this yearly amount of space debris adding mass.
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This is free energy technology, which we all will need and love, as it has practically no cost to run, and there is no need for any fuel to be purchased. Nor would there be any exhaust to cause environmental or noise pollution. So,,, why haven’t we figured this simple little bit of technology out long ago? Evil spirits are, and have been hiding this simple technology from mankind. These AC generators are extremely easy to rotate, because the only resistance torque,(other than the viscosity of the lubricant in the bearings) would come from a great need for current, which would practically never happen, especially when you are dealing with such small amounts of power as the example that I describe here.
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I confirmed that this free energy technology, discovered in the early 2000’s, was from God + not from evil forces, by finding it in a UFO motor description in Ezekiel 1:16. Thankfully, there are many ways that we can freely multiply the total # of rotations, like a set of varied sized pulleys, can be easily used to multiply the total # of rotations. Then, by simply adding an AC generator to your mini-pulley, you can convert your rotations into cycles of AC electricity.
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This is one super simple GEM of an idea, and it is made from pre-school technology, so why was this not out long ago. Can you believe the power that evil spirits have, to be able to dumb down a whole population of humans + for so long. I still have problems getting people to believe that there is no torque problem. Think that this may actually be a good enough reason for you to find out if GOD IS REAL = http://beliefstoliveby.yolasite.com/ + if HE IS RETURNING SOON = http://my2020vision.yolasite.com/
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Do you want to hear how truly super simple this technology is, Where you only pay to crank over the DC motor one time, with a 100 cm circumference pulley, Then you use the 100 cm of moving belt off this large pulley circumference, + run it past one or more mini-pulleys of only one centimeter circumferences, All that you have to do is add an AC generator to these mini-pulleys, giving you a free return of 100’s of cycles of AC electricity. That’s one small pulse of DC current as an input, returning you 100 cycles of AC electricity output, How can you not multiply your AC electricity, with this rotation multiplication technology
-
IT IS TRULLY THAT SIMPLE
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Come on Nova Scotia,,,
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This is where this GEM-(Geometrical Electricity Multiplier) technology of free energy for the End Times was 1st started, (early 2000’s when He first shared this with me). Let's get out there and start taking advantage of it, by not only building GEM units to power all of our electric tools, toys + gadgets, but we could be starting companies that have electric appliances, utensils, devices, tools, toys, + gadgets with these GEM perpetual power supplies built into them, (let’s start letting electricity generate itself) + on our labels we could even proudly say "FIGHTING TERRORISM + FIGHTING POLLUTION"
#### Free Energy | searching for free energy and discussing free energy
##### Re: ENERGY AMPLIFICATION
« Reply #7982 on: August 26, 2017, 05:48:00 PM »
#### that_prophet
• Sr. Member
• Posts: 491
##### Re: ENERGY AMPLIFICATION
« Reply #7983 on: August 26, 2017, 05:49:27 PM »
PROOF OF CREATION + A YOUNG EARTH = (space dust) has mass + billions of years of dust would add up eventually + mess up the orbits of all planets + moons. We could measure the amount of dust on the moon, and divide the total by the amount of dust that is deposited every year, coming up with an age for the moon, and thereby finding out the age of our earth. Most of us have seen pictures of the moon landing, and realize that there is only a few centimeters, meaning that by the deposit of space dust, the moon has only been orbiting us for a few thousand years. Less than 10,000 year
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COME ON,,, ALL OF YOU BACK YARD MECHANICS,,, Get some AC + DC motors together of the same voltage, and start building these GEM free energy power supplies,, + not only for 1.5, 3, 6, 9 + 12 volt batteries, but household 120 volt, + 12 volt, to powering these new electric cars. Let's throw the oil companies out of work, producing toxic smoke + maybe even make money with them, by throwing any excess power from these perpetually running energy generators that we have the time, + small amount of money to purchase parts to build. Think of it as not only keeping money in your pocket, but you are keeping money from the countries that either fund terrorist, or which are unknowingly funding them. This is not to mention the experimenting that we could be doing with the anti-gravity + speeds approaching light speed. Now I know that there are many out there like me, which would enjoy knowing how one type of this motor was powering a UFO in the Bible, in Ezekiel 1:16. http://aliensandghosts.yolasite.com/
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Most people have heard that the "day + hour knoweth no man"-(Mat 24:36), but why does nobody mention the soon arriving doors that we are not only allowed to know, but in the original Greek, it is worded like a command = “know that it is near, even at the doors”,,, + that 1st Door will close on 2019.04 + the last Door will close on 2025.94. So we are guaranteed that Jesus will set His foot on the Mount of Olives before the year 2026.
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Did you ever wonder how you could know that it’s near, if we can’t know the day. Near to what then, maybe it’s near to the door/deadline = "know that it is near, even at the doors" Mat 24:33. Doors are plural, because of the two appearances of Jesus, the first is in the clouds,(Rapture) http://rapturequestion.yolasite.com/ before the 7 year peace treaty is signed + then His second arrival is as His Foot touches earth, on the Mount of Olives. DOOR = (this is not the date of His Arrival, which we are warned that nobody can know, but this is the date that Christ must return before) A day that the Tribulation Saints will not only know, but they will probably being counting down the days until. = (He Returns when the 7 year peace treaty ends)
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EVil-sOLUTION = isn’t it amazing what Truth can be revealed, when the “il-s” of life are included. http://decimationofthisevolutionfairytale.yolasite.com/
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I can give you a free to run, perpetual power supply = http://free-energy.yolasite.com/ This GEM mechanism can do this because of how AC electricity is created by rotations. as in the more rotations the greater amount of AC electricity, and pulleys can be used to multiply rotations. So, you are using pulley mechanics to multiply your total amount of AC electricity, by trading one rotation of a large 100 cm circumference pulley, into 100 rotations of as many 1 cm circumference pulleys as you choose to add to the same belt. If you add AC generators to these mini-pulleys then you could be multiplying AC electricity. If you added 4 of these mini-pulleys with AC generators attached, you would gain 400 cycles of AC electricity, and all for the single burst of DC current, the minute amount of current that a DC motor takes to rotate one single time.
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These mini-pulleys would be easy to rotate, as the only resistance that they would generate, would be caused by any power that they were generating. These mini-pulleys would only be winding up massive voltages, because the only current needed to rotate your large 100 cm pulley on a DC motor, is one simple spark, or short burst, the amount to rotate your large pulley only one single time. Torque is only caused when you are generating power, and power is generated by current multiplied by voltage. Since we only need one single spark of current, (practically zero) the total amount of power being generated would still be practically zero, costing practically zero torque.
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This was given to mankind before the first door closes = http://my2020vision.yolasite.com/
Especially for the soon coming Tribulation Saints http://doorschristmustpassthrough.yolasite.com/
-
Sorry if it offends you, that I add a little bit of Biblical stuff in my explanations, but when I came up with this super simple idea, it was just after asking God for a way to help the Tribulation Saints. Just think about how super simple this AC electricity multiplier truly is, and how the voices in your head tell you that it cannot work. When how much more simple can it be, then to only pay for the one rotation of a large 100 cm pulley, when you can get a return of 100 cycle of AC electricity, for every 1 cm mini-pulley that you attach to the same belt, (with AC generators attached). Yes that’s an input of one single spark of DC current, returning you 100 cycles of AC electricity for every mini-pulley that you attach to the same belt. If you only added 4 mini-pulleys, you would get a return of 40 cycles of AC electricity. Please remember, that there is a most powerful spiritual warfare going on over this GEM technology.
-
There is a most powerful spiritual warfare going on over this GEM technology. Can you believe the problems that I have had, getting this super simple way of using pulleys to multiply the total amount of AC cycles of electricity? I think that it’s totally ridiculous, when you truly take a close look at it. Pulleys can be used to multiply the # of rotations, and AC electricity is made of rotations of a coil through a magnetic field. It should be dirt simple, as you are using pulleys to multiply your total # of rotations, and AC electricity is made of rotations, so you are effectively multiplying AC electricity. .
#### luc2010
• Jr. Member
• Posts: 92
##### Re: ENERGY AMPLIFICATION
« Reply #7984 on: September 25, 2017, 04:27:25 AM »
First, the cap is charged (by the supply) when the controller is open. The current charging the capacitor moves through a circuit which includes the motor windings, and primary of the transformer......Doh! The cap discharge (at switch closure) is NOT the only current exciting the transformer!!!!!
....
Regards
'' is NOT the only current exciting the transformer!!!!! ''
assuming that we have two currents exciting the transformer?
very puzzling for me!! and fascinating stuff dont you think?
thanks and regards
luc2010
#### Free Energy | searching for free energy and discussing free energy
##### Re: ENERGY AMPLIFICATION
« Reply #7984 on: September 25, 2017, 04:27:25 AM »
#### that_prophet
• Sr. Member
• Posts: 491
##### Re: ENERGY AMPLIFICATION
« Reply #7985 on: September 25, 2017, 09:01:06 AM »
Free Energy is so simple that it can be generate with a large pulley attached to a DC motor, at least one mini-pulley connected to an AC generator of the same voltage, 4 diodes, some wire to connect your electrical components together, and a belt to connect the two pulleys together.
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The way this works, is that you are using the 100 cm of moving belt off of one rotation of your large 100 cm circumference, which does not cost 100 times more power to rotate, yet if you run this 100 cm of moving belt past a 1 cm circumference pulley, you would get 100 cycles of AC electricity.
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The best part about this is, you can get a return of 100 cycles of AC electricity for as many mini-pulleys that choose to attach to the same belt. These mini-pulleys + AC generators would run freely, because although you are winding up massive voltage, you only need to generate the one spark of DC current. Torque is caused when generating power, and power is calculated by multiplying voltage times current, so even though you are winding up massive voltage, it is multiplied by practically zero current, so in the end you are generating practically zero power, costing practically zero torque.
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You are seemingly cheating the laws of thermodynamics by using pulley mechanics to multiply the # of rotations, and then by adding an AC generator, you are actually multiplying AC cycles of electricity. The AC generator is running very free, as it is only winding up massive voltage, as it only needs to generate one mere spark of DC current, just enough to rotate your DC motor + large 100 cm pulley the one single time.
« Last Edit: September 25, 2017, 11:44:43 AM by that_prophet »
#### forest
• Hero Member
• Posts: 3852
##### Re: ENERGY AMPLIFICATION
« Reply #7986 on: September 25, 2017, 10:26:03 AM »
Watch Ismael Aviso videos
#### Free Energy | searching for free energy and discussing free energy
##### Re: ENERGY AMPLIFICATION
« Reply #7986 on: September 25, 2017, 10:26:03 AM »
#### forest
• Hero Member
• Posts: 3852
##### Re: ENERGY AMPLIFICATION
« Reply #7987 on: September 25, 2017, 10:28:53 AM »
Actually what Erfinder said may be also another effect but not described clearly by Tesla. Sorry, I can't tell you any details. Tesla worked like 3 to 5 years before he was able to step up to the Colorado Springs tests.
#### endlessoceans
• Jr. Member
• Posts: 98
##### Re: ENERGY AMPLIFICATION
« Reply #7988 on: September 25, 2017, 01:03:00 PM »
Watch Ismael Aviso videos
Yeh sure Tito!! LOL Why would anyone waste time watching that. Poor old Ismael has soo much free energy he has to spend time selling cancer healing bogus water to make money. Oh wait....its all those men in black that scared him away from his project!!! hahaha
Such ridiculous Nonsense
#### Free Energy | searching for free energy and discussing free energy
##### Re: ENERGY AMPLIFICATION
« Reply #7988 on: September 25, 2017, 01:03:00 PM »
#### endlessoceans
• Jr. Member
• Posts: 98
##### Re: ENERGY AMPLIFICATION
« Reply #7989 on: September 25, 2017, 01:06:43 PM »
I came up with this super simple idea, it was just after asking God for a way to help the Tribulation Saints. Just think about how super simple this AC electricity multiplier truly is, and how the voices in your head tell you that it cannot work. When how much more simple can it be, then to only pay for the one rotation of a large 100 cm pulley, when you can get a return of 100 cycle of AC electricity, for every 1 cm mini-pulley that you attach to the same belt, (with AC generators attached). Yes that’s an input of one single spark of DC current, returning you 100 cycles of AC electricity for every mini-pulley that you attach to the same belt. If you only added 4 mini-pulleys, you would get a return of 40 cycles of AC electricity. Please remember, that there is a most powerful spiritual warfare going on over this GEM technology.
-
There is a most powerful spiritual warfare going on over this GEM technology. Can you believe the problems that I have had, getting this super simple way o .
#### luc2010
• Jr. Member
• Posts: 92
##### Re: ENERGY AMPLIFICATION
« Reply #7990 on: September 25, 2017, 06:47:52 PM »
Dear Sir,
Since we have at least two current exciting the transformer,
one current is produced from capacitor discharge, then where did the other current came from?
Thanks and Regards
luc2010
#### Free Energy | searching for free energy and discussing free energy
##### Re: ENERGY AMPLIFICATION
« Reply #7990 on: September 25, 2017, 06:47:52 PM »
#### luc2010
• Jr. Member
• Posts: 92
##### Re: ENERGY AMPLIFICATION
« Reply #7991 on: September 25, 2017, 07:23:54 PM »
Hello Again,
i find that patent:
N Tesla
'' ELECTRICAL CIRCUIT CONTROLLER '' US patent n 609 245
its the same circuit!!!!!!!!!!!!!!!! why its used for the circuit controller?
where the cap is charged in LC series circuit and may be discharged in parallel LC?
But i cant see the other current exciting the transformer???
very puzzling....
Thanks and Regards
luc2010
#### forest
• Hero Member
• Posts: 3852
##### Re: ENERGY AMPLIFICATION
« Reply #7992 on: September 25, 2017, 07:46:27 PM »
Hello Again,
i find that patent:
N Tesla
'' ELECTRICAL CIRCUIT CONTROLLER '' US patent n 609 245
its the same circuit!!!!!!!!!!!!!!!! why its used for the circuit controller?
where the cap is charged in LC series circuit and may be discharged in parallel LC?
But i cant see the other current exciting the transformer???
very puzzling....
Thanks and Regards
luc2010
The same circuit ? Compared to what ?
#### luc2010
• Jr. Member
• Posts: 92
##### Re: ENERGY AMPLIFICATION
« Reply #7993 on: September 25, 2017, 11:17:57 PM »
The same circuit ? Compared to what ?
Hello My Friend Forest,
I think, Its the same circuit compared to ozone patent? .. why?
very puzzling!!
Thanks and Regards
luc2010
#### luc2010
• Jr. Member
• Posts: 92
##### Re: ENERGY AMPLIFICATION
« Reply #7994 on: September 26, 2017, 03:46:02 AM » | 7,281 | 30,661 | {"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} | 2.671875 | 3 | CC-MAIN-2019-22 | latest | en | 0.876704 |
http://www.cliffsnotes.com/literature/e/ethics/summary-and-analysis/book-v-chapter-v | 1,464,738,433,000,000,000 | text/html | crawl-data/CC-MAIN-2016-22/segments/1464053252010.41/warc/CC-MAIN-20160524012732-00243-ip-10-185-217-139.ec2.internal.warc.gz | 430,347,466 | 26,101 | ## Summary and Analysis Book V: Chapter V - Reciprocal Justice and the Function of Money
Summary
The Pythagoreans define absolute justice as reciprocity, saying that justice in the unqualified sense is having done to one what one has done to another (i.e., an eye for an eye). The principle of reciprocity as they state it is oversimplified and does not agree with the ideas of distributive and remedial justice as we have explained them above. There are many situations in which reciprocity and justice are not the same (e.g., if a magistrate strikes a man, he should not be struck in return, but if an ordinary citizen strikes a magistrate, he should not only be struck in return but punished).
In certain kinds of dealings between men, however (e.g., economic activities and associations based on mutual exchange), the principle of reciprocity does apply, if it is defined as proportional reciprocity rather than reciprocity on the basis of absolute equality.
A state or community is bound together by relations between its members based on exchange of goods and services. Since people are not willing to exchange unless they get as good as they give, a principle or proportional reciprocity is necessary for guiding such relations. Proportional reciprocity takes into account the comparative skill of both parties and the comparative worth of their products, and is determined by a diagonal combination of terms. Here is an example:
A is a builder, B is a shoemaker, C is a house, D is a shoe. The builder takes the shoemaker's product (a shoe) from the shoemaker and gives his own product (a house) in return. A fair reciprocal exchange takes place if equality has been established between the goods.
Simple reciprocity as shown in the above example will not usually work since the exchanging parties and the value of the things they offer for exchange must always be taken into consideration. Many cases are complicated because A may want B's product while B does not want A's product in return. Before any fair exchange can take place, it is necessary to find a standard of value by which all goods and services can be measured.
This is the function of money, which has been developed and put into use as a kind of common denominator for expressing the value of goods and services. It acts as a sort of middle term in the proportion, telling us, for example, how many shoes are equal to a house or to a given amount of food. Money acts as a representative of demand. Money exists by current convention rather than by nature, and it is within human power to change or destroy its value.
Money is subject to fluctuations in value, just like all other commodities, but it is more stable than goods whose value is specifically related to the particular demands of individuals at any given moment. By using money as a measure to establish proportional value, it is possible to make goods equal, and this standard, arbitrarily accepted, makes exchange and community possible. All things, however different, can be measured in terms of money.
Exchange only takes place when equality between goods can be established. There can be no real equality without an idea of proportion.
While it is impossible for different things really to be equal, money allows the establishment of an equality adequate for the needs of daily intercourse. Here is an illustration:
A is a house, B is \$10.00, C is a bed. The value of the house is \$5.00 (A=B/2), the value of the bed is \$1.00 (C=B/l0). This makes it clear how many beds are equal in value to one house (5) and makes it possible for a fair exchange to take place.
Prior to the development of money, exchange may have existed on just this basis as a form of barter, for it makes little real difference (aside from the convenience) whether one pays five beds or the value of five beds for one house. The convenience, however, is a very important factor, since it makes possible all kinds of transactions, with the nature and conditions of these transactions not dependent on the type of goods or service one happens to produce or the type of goods or service required by the other party.
In regard to the whole discussion of justice in its different forms, it can be said that just behavior is a mean between doing injustice and suffering it. To do injustice is to have more than one's share and to suffer injustice is to have less.
Justice can be viewed as a mean, but it is unlike the other virtues. They are all relative things determined in regard to certain extremes. Justice is a permanent attitude of the soul toward the mean (i.e., a disposition by virtue of which a man always deliberately chooses that which is just). Injustice is related to vice in the same way. We may conclude that justice is the objective observation of proportion in all areas of life based on a subjective perception of what is proportional. | 993 | 4,880 | {"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} | 2.65625 | 3 | CC-MAIN-2016-22 | latest | en | 0.971959 |
http://www.numbersaplenty.com/6578 | 1,597,445,357,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439740343.48/warc/CC-MAIN-20200814215931-20200815005931-00387.warc.gz | 152,191,006 | 3,337 | Search a number
6578 = 2111323
BaseRepresentation
bin1100110110010
3100000122
41212302
5202303
650242
725115
oct14662
910018
106578
114a40
123982
132cc0
14257c
151e38
hex19b2
6578 has 16 divisors (see below), whose sum is σ = 12096. Its totient is φ = 2640.
The previous prime is 6577. The next prime is 6581. The reversal of 6578 is 8756.
6578 divided by its sum of digits (26) gives a triangular number (253 = T22).
It is a Harshad number since it is a multiple of its sum of digits (26).
It is a plaindrome in base 14.
It is not an unprimeable number, because it can be changed into a prime (6571) by changing a digit.
It is a pernicious number, because its binary representation contains a prime number (7) of ones.
It is a polite number, since it can be written in 7 ways as a sum of consecutive naturals, for example, 275 + ... + 297.
It is an arithmetic number, because the mean of its divisors is an integer number (756).
26578 is an apocalyptic number.
6578 is a deficient number, since it is larger than the sum of its proper divisors (5518).
6578 is a wasteful number, since it uses less digits than its factorization.
6578 is an odious number, because the sum of its binary digits is odd.
The sum of its prime factors is 49.
The product of its digits is 1680, while the sum is 26.
The square root of 6578 is about 81.1048703840. The cubic root of 6578 is about 18.7369093812.
The spelling of 6578 in words is "six thousand, five hundred seventy-eight". | 433 | 1,481 | {"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} | 3.265625 | 3 | CC-MAIN-2020-34 | latest | en | 0.904027 |
http://factscenter.gq/win-online-roulette/how-do-you-guess-numbers-on-roulette-are-online-roulette-games-rigged-ballyhoo/ | 1,611,613,766,000,000,000 | text/html | crawl-data/CC-MAIN-2021-04/segments/1610704792131.69/warc/CC-MAIN-20210125220722-20210126010722-00337.warc.gz | 37,844,054 | 9,423 | ### How do you guess numbers on roulette? – Are Online Roulette Games Rigged Ballyhoo
No… I don’t have any particular technique. I just look at what numbers have been played so far and try to predict the next hand that we would see. I’m always curious to see what the number of bets on the roulette wheel is. I usually do just the number of bets that I saw on the wheel so far.
I think that most of us can do that. The number of bets you see… if you see a few more then you can guess. But if you see 10, or 10, let’s call that number, I might think it’s too low (because it’s less than the number of bets I saw this hand before) or too much, or too high. So the next hand is what do I do then? I can see it and tell that I have enough knowledge to guess. I am confident we have that amount of knowledge, but I don’t know all the numbers.
I guess you will notice that the number of bets that you see on the roulette wheel is not just a fixed number. You see so many different hands on the wheel that your number of bets might be too limited. You will see 1,2,4,6, 8, and then 12,20,28,38, … How do you get this number to change? This is one of the questions that people often ask me.
I have done research on it. It might be the best question. All the studies I do look at one thing: can I guess for at least 2, 3… four? In other words, I can make a guess if this is a good hand. And if you see 9, then you can also guess that you would see 11, or 12,or 13… maybe even 18. But you’d have to know the numbers that you saw before for two, three, or four. Or you could not guess and you would end up with a bad hand.
So, I have studied this. And what I have found is that most people can’t always guess. One question that’s a common question is can I guess at least 1, 2… 4? It can vary, depending on the number of bets that they saw on the wheel. One study I did, we put out these tables where you could choose and what number of bets would you want to see (I guess maybe 6?). The number of bets that I chose, I could have seen 1, and 1 is just guessing, and I could see anything, and there
online roulette real money free, online roulette wheel layout diagram of substation, are online roulette games rigged fishing, best online roulette strategies \$3000, largest online wheels | 575 | 2,281 | {"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} | 4.03125 | 4 | CC-MAIN-2021-04 | latest | en | 0.970669 |
https://www.riddlesandanswers.com/puzzles-brain-teasers/how-many-presents-can-santa-fit-in-an-empty-sack-riddles/ | 1,675,923,020,000,000,000 | text/html | crawl-data/CC-MAIN-2023-06/segments/1674764501407.6/warc/CC-MAIN-20230209045525-20230209075525-00337.warc.gz | 967,992,882 | 27,509 | # HOW MANY PRESENTS CAN SANTA FIT IN AN EMPTY SACK RIDDLES WITH ANSWERS TO SOLVE - PUZZLES & BRAIN TEASERS
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## Solving How Many Presents Can Santa Fit In An Empty Sack Riddles
Here we've provide a compiled a list of the best how many presents can santa fit in an empty sack puzzles and riddles to solve we could find.
Our team works hard to help you piece fun ideas together to develop riddles based on different topics. Whether it's a class activity for school, event, scavenger hunt, puzzle assignment, your personal project or just fun in general our database serve as a tool to help you get started.
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## The Secret Santa Exchange
Hint: It's not as difficult as it seems. It's the number of ways the friends can form a circle divided by the number of ways the names can be drawn out of the hat.
1/10
For a group of n friends, there are n! (n factorial) ways to draw the names out of the hat. Since a circle does not have a beginning and end, choose one person as the beginning and end of the circle. There are now (n-1)! ways to distribute the remaining people around the circle. Thus the probability of forming a single circle is
(n-1)! / n!
Since n! = (n-1)! * n (for n > 1), this can be rewritten as
(n-1)! / (n*(n-1)!)
Factoring out the (n-1)! from the numerator and denominator leaves
1/n
as the probability.
Did you answer this riddle correctly?
YES NO
## An Empty Stomach Riddle
Hint:
One bite. After that, the stomach isnt empty.
Did you answer this riddle correctly?
YES NO
## Santa And A Space Ship
Hint:
A u-f-ho-ho-ho!
Did you answer this riddle correctly?
YES NO
## Santa's Helpers Riddle
Hint:
Subordinate Clauses.
Did you answer this riddle correctly?
YES NO
Solved: 36%
## Santa's Coal Riddle
Hint:
Global warming!
Did you answer this riddle correctly?
YES NO
Solved: 54%
## The Fitness Center Riddle
Hint:
They were at the fitness center the whole time. They ran and cycled on exercise equipment.
Did you answer this riddle correctly?
YES NO
Solved: 81%
## Standstill Santa Riddle
Hint:
Santa Pause!
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YES NO
Solved: 46%
## Santa's Slay Riddle
Hint:
Nothing, it was on the house!
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YES NO
Solved: 46%
## Santa's Gardens Riddle
Hint:
So he can go HOE HOE HOE.
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YES NO
Solved: 47%
## Deep Fried Santa Riddle
Hint:
Crisp Kringle.
Did you answer this riddle correctly?
YES NO
Solved: 51%
## Emptying A Backpack
Hint:
One! After that it's not empty.
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YES NO
## Easter Bunny Fitness Riddle
Hint:
Egg-xercise!
Did you answer this riddle correctly?
YES NO
Solved: 56%
## Detective Santa Riddle
Hint:
Santa Clues!
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YES NO
## The Ghost And Santa Riddle
Hint:
Ill have a boo Christmas without you.
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YES NO
## Santa's Birthday Riddle
Hint:
Freeze a jolly good fellow
Did you answer this riddle correctly?
YES NO
Solved: 48% | 915 | 3,456 | {"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} | 4.09375 | 4 | CC-MAIN-2023-06 | latest | en | 0.886873 |
https://wwrenderer.libretexts.org/render-api?sourceFilePath=Library/Rochester/setIntegrals0Theory/csuf_in_0_1_mo.pg&problemSeed=1234567&courseID=anonymous&userID=anonymous&course_password=anonymous&answersSubmitted=0&showSummary=1&displayMode=MathJax&language=en&outputFormat=nosubmit | 1,716,476,856,000,000,000 | text/html | crawl-data/CC-MAIN-2024-22/segments/1715971058642.50/warc/CC-MAIN-20240523142446-20240523172446-00571.warc.gz | 553,801,089 | 2,857 | The interval $[0,5]$ is partitioned into $n$ equal subintervals, and a number $x_i$ is arbitrarily chosen in the $i^{th}$ subinterval for each $i$. Then:
$\displaystyle \lim_{n\to \infty} \sum_{i=1}^{n}\frac{2 x_i - 6}{n} =$ | 82 | 225 | {"found_math": true, "script_math_tex": 6, "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} | 2.71875 | 3 | CC-MAIN-2024-22 | latest | en | 0.47348 |
http://stackoverflow.com/questions/10361869/compilation-error-for-an-array-of-rational-polynomials | 1,441,449,120,000,000,000 | text/html | crawl-data/CC-MAIN-2015-35/segments/1440646242843.97/warc/CC-MAIN-20150827033042-00251-ip-10-171-96-226.ec2.internal.warc.gz | 221,107,476 | 18,794 | # Compilation Error for an array of rational polynomials
I am coding a matrix, whose entries are polynomials with rational coefficients. Any help would be greatly appreciated.
I have rational number and rational polynomial declared:
rational_number.h
``````struct long_rational{
long p;
long q;
};
typedef struct long_rational rational;
``````
polynomial.h
``````#define MAX_DEGREE 200
struct rational_polynomial{
long degree;
rational coef[MAX_DEGREE]; //rational coefficients in increase power.
};
typedef struct rational_polynomial polynomial;
``````
poly_mat.c in its entirety
``````#include "poly_mat.h"
#define NR_END 1
#define FREE_ARG char*
polynomial **poly_matrix( long nrl, long nrh, long ncl, long nch )
/* allocates a matrix with polynomial entries in the range m[nrl..nrh][ncl..nch] */
{
long i, nrow=nrh-nrl+1,ncol=nch-ncl+1;
polynomial **m;
/* allocate pointers to rows */
m=( polynomial ** ) malloc( ( size_t )( ( nrow+NR_END )*sizeof( polynomial* ) ) );
if ( !m ) nrerror( "allocation failure 1 in matrix()" );
m += NR_END;
m -= nrl;
/* allocate rows and set pointers to them */
m[nrl]=( polynomial * ) malloc( ( size_t )( ( nrow*ncol+NR_END )*sizeof( polynomial ) ) );
if ( !m[nrl] ) nrerror( "allocation failure 2 in matrix()" );
m[nrl] += NR_END;
m[nrl] -= ncl;
for ( i=nrl+1; i<=nrh; i++ ) m[i]=m[i-1]+ncol;
/* return pointer to array of pointers to rows */
return m;
}
void **free_poly_matrix( polynomial **m, long nrl, long nrh, long ncl, long nch )
/* free a polynomial matrix allocated by poly_matrix() */
{
free( ( FREE_ARG ) ( m[nrl]+ncl-NR_END ) );
free( ( FREE_ARG ) ( m+nrl-NR_END ) );
}
void init_random_poly_matrix( int **m, long nrl, long nrh, long ncl, long nch )
/* initialize a random polynomial matrix with coefficient <=100*/
{
long i,j;
long iseed = ( long )time( NULL );
srand ( iseed );
for ( i=nrl; i<=nrh; i++ )
{
for ( j=ncl; j<=nch; j++ )
{
m[i][j].degree=( rand()%MAX_DEGREE );
for ( k=0;k<=MAX_DEGREE;k++ )
{
m[i][j].coef[k].p = (rand()%100 );
m[i][j].coef[k].q = (1+rand()%100 );
}
}
}
}
``````
Here is the enigmatic error message:
```gcc -Wall -c -o poly_mat.o poly_mat.c
poly_mat.c: In function ‘init_random_poly_matrix’:
poly_mat.c:6: error: expected declaration specifiers before ‘(’ token
poly_mat.c:28: error: expected ‘=’, ‘,’, ‘;’, ‘asm’ or ‘__attribute__’ before ‘{’ token
poly_mat.c:35: error: expected ‘=’, ‘,’, ‘;’, ‘asm’ or ‘__attribute__’ before ‘{’ token
poly_mat.h:14: error: old-style parameter declarations in prototyped function definition
poly_mat.c:51: error: expected ‘{’ at end of input
make: *** [poly_mat.o] Error 1
```
poly_mat.h with missing semicolon filled.
``````#ifndef POLY_MAT_H
#define POLY_MAT_H
#include <math.h>
#include <stdio.h>
#include <stdlib.h>
#include <time.h>
#include "nrutil.h"
#include "rational_number.h"
#include "polynomial.h"
/* matrix with polynomial entries */
polynomial **poly_matrix( long nrl, long nrh, long ncl, long nch );
void init_random_poly_matrix( int **m, long nrl, long nrh, long ncl, long nch );
void **free_poly_matrix( polynomial **m, long nrl, long nrh, long ncl, long nch );
#endif
``````
Now I can not access member of polynomials in the array with dot operator.
New Error Message:
```gcc -Wall -c -o poly_mat.o poly_mat.c
poly_mat.c: In function ‘init_random_poly_matrix’:
poly_mat.c:43: error: request for member ‘degree’ in something not a structure or union
poly_mat.c:46: error: request for member ‘coef’ in something not a structure or union
poly_mat.c:47: error: request for member ‘coef’ in something not a structure or union
make: *** [poly_mat.o] Error 1
```
Edit 2: Found the mistake. declare it as int** instead of polynomial**.
-
What's in poly_mat.h? – Joachim Isaksson Apr 28 '12 at 8:28
Are you sure that `polynomial` is visible in the .cpp file? And that it actually is the typedef at that point? – Bo Persson Apr 28 '12 at 8:48
plz show us poly_mat.h – Peter Miehle Apr 28 '12 at 9:43
There seem to be a lot of small errors in this code that would prevent compilation (or at least give compiler warnings), which suggests that you designed the code and typed it all in without testing any of it. Start small, build up, test at every stage, never add to code that doesn't work. – Beta Apr 28 '12 at 14:03 | 1,265 | 4,275 | {"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} | 2.765625 | 3 | CC-MAIN-2015-35 | latest | en | 0.531806 |
https://oeis.org/A229040 | 1,547,695,020,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583658681.7/warc/CC-MAIN-20190117020806-20190117042806-00459.warc.gz | 599,765,442 | 3,822 | This site is supported by donations to The OEIS Foundation.
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A229040 Fibonacci numbers in which parity of the decimal digits alternates. 0
0, 1, 2, 3, 5, 8, 21, 34, 89, 610, 987, 4181, 6765 (list; graph; refs; listen; history; text; internal format)
OFFSET 1,3 COMMENTS No more values through F(12000). LINKS FORMULA A000045 INTERSECTION A030141. MAPLE isA030141 := proc(n) dgs := convert(n, base, 10) ; for i from 2 to nops(dgs) do if modp(op(i, dgs), 2) = modp(op(i-1, dgs), 2) then return false; end if; end do: true ; end proc: for i from 0 do f := combinat[fibonacci](i) ; if isA030141(f) then print(f) ; end if; end do: # R. J. Mathar, Mar 13 2015 CROSSREFS Cf. A000045, A030141, A030152, A030144. Sequence in context: A002363 A041457 A161468 * A143873 A273046 A117774 Adjacent sequences: A229037 A229038 A229039 * A229041 A229042 A229043 KEYWORD nonn,base AUTHOR Jonathan Vos Post, Sep 12 2013 STATUS approved
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Last modified January 16 21:37 EST 2019. Contains 319206 sequences. (Running on oeis4.) | 489 | 1,536 | {"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} | 2.703125 | 3 | CC-MAIN-2019-04 | latest | en | 0.552197 |
https://www.lido.app/tutorials/minifs-google-sheets | 1,721,211,442,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514759.39/warc/CC-MAIN-20240717090242-20240717120242-00146.warc.gz | 732,625,620 | 18,192 | # MINIFS in Google Sheets (Easiest Way to Use It in 2024)
May 8, 2024
MINIFS is a function in Google Sheets that calculates the minimum value among cells specified by a given set of conditions or criteria. This function is particularly useful for analyzing data sets where you need to find the lowest value that meets certain conditions.
## Syntax
The syntax of the MINIFS function is as follows:
MINIFS(range, criteria_range1, criterion1, [criteria_range2, criterion2, ...])
• range: The range of cells from which the minimum value will be calculated.
• criteria_range1: The range of cells to evaluate with the first criterion.
• criterion1: The criterion that must be met in the criteria_range1. It can be a number, expression, cell reference, or text that defines which cells will be considered for the minimum calculation.
• criteria_range2, criterion2, ... (optional): Additional ranges and their corresponding criteria to test.
## How to Use MINIFS in Google Sheets
Here is a practical example to illustrate how to use the MINIFS function in Google Sheets where we have sales data for various salespeople across different regions. Simply follow the steps below.
### 1. Select the Column with Values to Analyze as Data Range
Determine the column that contains the values you want to analyze. For our example, you want to analyze sales figures, so your range is column C.
### 2. Identify the Column with Criteria for Filtering as Criteria Range
Identify the column with the criteria for filtering your analysis. In this case, since you want to filter by region, your criteria range is column B, which lists the regions.
### 3. Choose the Specific Condition for Data Filtering as Criterion
Decide on the specific condition the data must meet. For the example, if you're interested in finding the lowest sales figure for the "East" region, your criterion is "East".
### 4. Input the MINIFS Formula with Specific Data Range and Criteria
In an empty cell, type in the MINIFS formula with your specific details. Following our example, you would enter: =MINIFS(C2:C9, B2:B9, "East"). This formula looks for the minimum sales figure in the East region.
### 5. Extend the Formula with Additional Criteria (Optional)
If you need to apply more conditions, such as finding sales above a certain amount, extend your formula with additional criteria ranges and criteria. However, for simplicity, our current example sticks to one condition.
### 6. Execute the Formula by Pressing Enter and Review the Result
After pressing Enter, Google Sheets will display the lowest sales figure for the East region based on the dataset provided. This shows you the effectiveness of the MINIFS function in filtering and analyzing data.
### 7. Review and Adjust the Formula as Necessary for Accurate Results
If the result is not what you expected, check your formula for any potential mistakes in the range or criteria specified. Adjust as necessary to ensure accuracy in your analysis.
We hope that you now have a better understanding of how to use MINIFS in Google Sheets. If you enjoyed this article, you might also like our article on how to find correlation coefficients in Google Sheets or our article on the Google Sheets loan payment formula.
Get Google Sheets productivity and automation tips delivered straight to your inbox | 689 | 3,333 | {"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} | 3 | 3 | CC-MAIN-2024-30 | latest | en | 0.838787 |
https://knowm.org/signal-prediction/ | 1,548,116,291,000,000,000 | text/html | crawl-data/CC-MAIN-2019-04/segments/1547583822341.72/warc/CC-MAIN-20190121233709-20190122015709-00098.warc.gz | 567,599,365 | 15,776 | ## Signal Prediction
Consider the following scenario: A researcher at a wealth management fund has gathered data concerning the movement of its security interests over the previous ten years. For each year over that period, the fundamental and technical data information concerning the price movement of that security has been recorded and they would like to assess the value of each instrument at some time in the future.
Stock Prices
If these researchers decided to use their historical information to build a predictive model from this data, they would be applying a technique from Signal Prediction.
Signal prediction is not limited to finance however, it is broadly described as any prediction which involves using the prior history of a signal or group of signals to determine the future state of the signal. In the case above, the signal of interest is the price of the asset.
Signals can be any kind of order-dependent information, including price indices, global temperatures, resource supplies, or object positions. Signals like these, in particular, are important to understand and accurate predictive models are highly sought after. Widely in use are those for financial & insurance purposes, telecommunications, resource planning, healthcare diagnostics, and robotic actuation. Predictive climate models specifically, have the potential to effect, on a large scale, the actions of government and people during this century.
Climate Prediction
## Methods
Current prediction approaches and algorithms are diverse but can be broadly be grouped into statistical, regression, and Machine Learning techniques.
### Regression
Regression models attempt to find a predictive equation based on the response of our signal to a set of independent predictor variables. Linear Regression, for instance, finds linear combinations of these predictor variables which fit a number of data points. Other regression types, such as discrete, non-linear apply different functions to the independent variables. In all cases, the objective of a regression method is to select the parameters of the model which minimize the error function between the model and the data.
Once a regression model has been found, predictions are made by extrapolating the interest signal at some later date.
Simple Linear Regression
### Time Series Models
Time series models account for the fact that data points taken over time may have an internal structure (such as autocorrelation, trend or seasonal variation) that should be accounted for. Statistical methods are used to extract these features from a signal and commonly decomposed into the trend, seasonal, and cyclical component of the series. Future values are then assumed to follow these trend components.
Trend analysis in noisy temperature data
## Machine Learned Models
Machine Learning models employ techniques to enable computers to learn a model through a set of examples. These include Artificial Neural Networks, Support Vector Machines, K-Nearest neighbors and Decision Trees. The learned model is then applied to unseen data for prediction.
Predicting Apple Stock with Machine Learning
If you’re interested in using one of these Machine Learning techniques, we built a comprehensive list of Statistical and Machine Learning libraries in this article.
## Signal Prediction with kT-RAM
Signal Prediction on kT-RAM is most similar to another Machine Learning technique because no explicit equation is formed (as in regression), nor are signals explicitly decomposed into components (as done by time series models). Instead, a model of that signal is both learned and represented by synaptic connections on kT-RAM.
In one approach, we pose the future state of our series as a multi-label classification problem. In this way, the complex signals can be learned and predicted using the AHaH classifier.
As a simplified proof of concept to demonstrate this, a complex temporal signal prediction experiment can be designed. For each moment of time, the real-valued signal F(S(t)) is converted into a sparse spike encoding representation. These features are buffered to form a feature set:
$\{ F(S(t - N)), F(S(t - N+1)), F(S(t - N+2)), \ldots , F(S(t-1)) \}$
This feature set is then used to make predictions of the current feature F(S(t)), and the spikes of the current feature are used as supervised labels. After learning, the output prediction may be used in lieu of the actual input and run forward recursively in time. In this way, extended predictions about the future are possible.
In the next article, we demonstrate this machine learning method through an example. We use a complex sine wave as the signal and a kT-RAM classifier to make predictions.
Previous: Clustering KNN Encodings
Next: Complex Sine Wave Prediction | 900 | 4,789 | {"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": 1, "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} | 2.921875 | 3 | CC-MAIN-2019-04 | latest | en | 0.931718 |
http://us.metamath.org/ilegif/nfnfc.html | 1,642,804,944,000,000,000 | text/html | crawl-data/CC-MAIN-2022-05/segments/1642320303717.35/warc/CC-MAIN-20220121222643-20220122012643-00182.warc.gz | 66,464,280 | 3,514 | Intuitionistic Logic Explorer < Previous Next > Nearby theorems Mirrors > Home > ILE Home > Th. List > nfnfc Unicode version
Theorem nfnfc 2200
Description: Hypothesis builder for . (Contributed by Mario Carneiro, 11-Aug-2016.)
Hypothesis
Ref Expression
nfnfc.1
Assertion
Ref Expression
nfnfc
Proof of Theorem nfnfc
Dummy variable is distinct from all other variables.
StepHypRef Expression
1 df-nfc 2183 . 2
2 nfnfc.1 . . . . 5
32nfcri 2188 . . . 4
43nfnf 1485 . . 3
54nfal 1484 . 2
61, 5nfxfr 1379 1
Colors of variables: wff set class Syntax hints: wal 1257 wnf 1365 wcel 1409 wnfc 2181 This theorem was proved from axioms: ax-1 5 ax-2 6 ax-mp 7 ax-ia1 103 ax-ia2 104 ax-ia3 105 ax-io 640 ax-5 1352 ax-7 1353 ax-gen 1354 ax-ie1 1398 ax-ie2 1399 ax-8 1411 ax-10 1412 ax-11 1413 ax-i12 1414 ax-bndl 1415 ax-4 1416 ax-17 1435 ax-i9 1439 ax-ial 1443 ax-i5r 1444 ax-ext 2038 This theorem depends on definitions: df-bi 114 df-nf 1366 df-sb 1662 df-cleq 2049 df-clel 2052 df-nfc 2183 This theorem is referenced by: (None)
Copyright terms: Public domain W3C validator | 490 | 1,110 | {"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} | 2.53125 | 3 | CC-MAIN-2022-05 | latest | en | 0.229934 |
https://earthscience.stackexchange.com/questions/26065/whats-wrong-with-my-penman-monteith-model | 1,721,268,686,000,000,000 | text/html | crawl-data/CC-MAIN-2024-30/segments/1720763514816.43/warc/CC-MAIN-20240718003641-20240718033641-00757.warc.gz | 185,083,840 | 40,546 | # What's wrong with my Penman-Monteith model?
UPDATE: I believe I have found the mistake. I had missed that the project instructions stated that conductance of sensible heat flux should be equal to aerodynamic conductance. The model behaves as expected now that I've made that adjustment. Thank you to everyone who chimed in!
Original question:
I am trying to model Penman-Monteith reference evapotranspiration in MATLAB using Ameriflux data (https://ameriflux.lbl.gov/sites/siteinfo/US-Ro4, data from June 17, 2021). The task is to calibrate the model to the evapotranspiration data (the latter calculated using latent heat flux) by adjusting the value for canopy conductance. The canopy conductance was expected to lie somewhere between 0.002 and 0.03 m/s. I was asked to plot an overestimate, an underestimate, and a best fit model on the same plot as the ET data.
Unfortunately, it seems that the model is off. Regardless of the choice of G_c, the plot oscillates in unexpected places, and contains negative values. Also, the G_c value that minimizes error--as far as I've found with the current approach of manual adjustment--lies outside the recommended range.
I will owe a life debt to anyone who can point me toward my mistake(s). Apologies for the needlessly bothersome aspects of the code, the large images, and any breaches I may have made of forum etiquette: I'm a newbie to both MATLAB and StackExchange.
clear
dates = datevec(FluxData.TIMESTAMP_START);
selector = dates(:, 1) == 2021 & dates(:, 2) == 6 & dates(:, 3) == 17;
Flux_6_17_21 = FluxData(selector, :);
% Calculate evapotranspiration from LE data
Lv = 2257000; % Latent heat of vaporization [J/kg]
E = Flux_6_17_21.LE/Lv; % Evapotranspiration rate from LE data [kg/(s·m^2)]
% Account for other terms in the Penman-Monteith equation
% Temperature
TA_K = Flux_6_17_21.TA + 273.15; % Air temperature [K] at measurement height z
TS_all = [Flux_6_17_21.TS_1_1_1, Flux_6_17_21.TS_1_2_1, Flux_6_17_21.TS_1_3_1, Flux_6_17_21.TS_1_4_1];
TS_C = mean(TS_all, 2); % Mean of different sensors' surface temperature readings [deg C]
TS_K = TS_C + 273.15; % Mean surface temperature [K]
% Vapor pressure
PA = 1000 * Flux_6_17_21.PA; % Atmospheric pressure [Pa]
a = 611; % Clausius-Clapeyron fitting parameter [Pa]
b = 17.27; % C-C parameter [-]
c = 237.3; % C-C parameter [deg C]
e_ss = a * exp(b * TS_C ./ (TS_C + c)); % Saturated water vapor
% pressure [Pa] at surface, from Clausius-Clapeyron
e_sz = a * exp(b * Flux_6_17_21.TA ./ (Flux_6_17_21.TA + c)); % Sat
% water vapor pressure [Pa] at z
e_az = e_sz .* Flux_6_17_21.RH ./ 100; % Actual water vapor pressure [Pa] at z
D = Flux_6_17_21.VPD_PI .* 100; % Vapor pressure deficit [Pa]
% Delta [Pa/K]
delt = a * b * c ./ (Flux_6_17_21.TA + c).^2 .* exp(b * Flux_6_17_21.TA ./ (Flux_6_17_21.TA + c));
% Slope of C-C eqn
% Air density
R = 8.314; % Universal gas constant [J/(K·mol)]
c_pd = 1005; % Specific heat capacity of dry air [J/(kg·K)]
c_pw = 1930; % Specific heat capacity of water vapor [J/(kg·K)]
mol_fract = e_az ./ PA; % Mol fraction [-] of water vapor at z
c_p = (1-mol_fract) .* c_pd + mol_fract .* c_pw; % Specific heat capacity
% of moist air [J/(kg·K)]
p_d = PA - e_az; % Partial pressure of dry air [Pa] at z
M_a = 0.02897; % Molar mass of dry air [kg/mol]
M_w = 0.018; % Molar mass of water [kg/mol]
rho_a = (M_w * e_az + M_a * p_d) ./ (R * TA_K); % Mass density of air [kg/m^3]
% Aerodynamic conductance
kappa = 0.41; % von Karman constant [-]
z = 10; % Measurement height [m]
h = 0.5; % Height of vegetation canopy [m]
d = 0.667 * h; % Zero plane displacement [m]
zm = 0.123 * h; % Roughness length for momentum transfer [m]
zh = 0.1 * zm; % Roughness length for heat & water vapor [m]
G_a = kappa^2 * Flux_6_17_21.WS ./ (log((z - d)/zm) * log((z - d)/zh)); % Aerodynamic
% conductance [m/s]
% Other conductances (all [m/s])
G_c = 0.12; % Canopy conductance, used interchangeably with surface conductance. Vary this to find best fit
G_L = G_c .* G_a ./ (G_c + G_a); % Total conductance of latent heat flux
G_H = Flux_6_17_21.H ./ (rho_a .* c_p .* (TS_K - TA_K)); % Conductance of sensible heat flux
% Psychrometric constant [Pa·K]
gamma = c_p .* PA / (Lv * M_w / M_a);
% Recalculate ET with Penman-Monteith equation
E_PM = (delt .* (Flux_6_17_21.NETRAD - Flux_6_17_21.G) + rho_a .* c_p .* G_H .* D) ./ (Lv ...
* (delt + gamma .* G_H ./ G_L)); % [kg/(s·m^2)]
Error = mean(rmse(E, E_PM, 2)) % Look for value of G_c that minimizes error between E and E_PM
% Variation #1
G_c_1 = 0.03; % [m/s]
G_L_ov = G_c_1 .* G_a ./ (G_c_1 + G_a); % [m/s]
E_PM_ov = (delt .* (Flux_6_17_21.NETRAD - Flux_6_17_21.G) + rho_a .* c_p .* G_H .* D) ./ (Lv ...
* (delt + gamma .* G_H ./ G_L_ov)); % [kg/(s·m^2)]
% Variation #2
G_c_2 = 0.002; % [m/s]
G_L_und = G_c_2 .* G_a ./ (G_c_2 + G_a); % [m/s]
E_PM_und = (delt .* (Flux_6_17_21.NETRAD - Flux_6_17_21.G) + rho_a .* c_p .* G_H .* D) ./ (Lv ...
* (delt + gamma .* G_H ./ G_L_und)); % [kg/(s·m^2)]
figure(1)
plot (Flux_6_17_21.TIMESTAMP_START, E, '-b')
hold on
plot (Flux_6_17_21.TIMESTAMP_START, E_PM, '--g')
plot (Flux_6_17_21.TIMESTAMP_START, E_PM_ov, '-.k')
plot (Flux_6_17_21.TIMESTAMP_START, E_PM_und, ':r')
datetick('x', 'HHPM')
xlabel('Hour')
ylabel('Evapotranspiration rate [kg/(s·m^{2})]')
legend ('Data', ['Penman-Monteith equation with G_c = ', num2str(G_c), ...
' m/s'], ['Penman-Monteith equation with G_c = ', num2str(G_c_1), ...
' m/s'], ['Penman-Monteith equation with G_c = ', num2str(G_c_2), ' m/s'])
legend('Location', 'northoutside')
hold off
• Hi,pls ask on other stack exchange Pages (e.g. stack overflow) I Think you will finde there faster an answer :) Commented Mar 13 at 8:15
• Oh, thank you for the tip! I wasn't aware of stack overflow. I don't know if I've messed up due to a misunderstanding of MATLAB commands or of the Penman-Monteith equation, or both. If it's the former, hopefully the other site can help! Commented Mar 13 at 8:42
• OK, I might keep the question here instead because I don't see a hydrology tag in stack overflow. Commented Mar 13 at 9:18
• I'd say: begin by double and triple checking your units. You do a lot of conversions, for °C to K, from hPa or kPa to Pa... From my experience, when writing MATLAB script like this, 95% of the time errors will come from a unit conversion issue. Commented Mar 13 at 9:21
• Generally it's not suggested to bounce a question around and try a lot of places. I agree that the limited community here will probably(?) take a while to respond if at all. Then again, not sure SO will have the knowledge base to help. An answer from someone like Jean-Marie is probably your best hope :) Commented Mar 13 at 9:29 | 2,200 | 6,670 | {"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} | 2.53125 | 3 | CC-MAIN-2024-30 | latest | en | 0.88728 |
https://www.lawyersgunsmoneyblog.com/2010/04/silvers-model-on-the-british-election | 1,726,766,779,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700652055.62/warc/CC-MAIN-20240919162032-20240919192032-00868.warc.gz | 753,748,845 | 24,971 | Home / 2010 British Election / Silver’s Model on the British Election
# Silver’s Model on the British Election
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Following five days in Chicago “working” at my day job, and then a couple days on the Oregon coast celebrating my birthday with my fiancée, it’s time to get back to serious business. Barring that, I’ll write a general post on the British election. This was meant to be an omnibus post addressing several topics only tenuously related as having something to do with the British election, but the more I dug into the first topic, the more I had to say. I’ll leave the rest for a post hopefully later today.
Nate Silver, Renard Sexton, and Daniel Berman have developed a sophisticated, nuanced predictive model. It has many strengths, so I’ll concentrate instead on a few critiques.[1] I’ll preface this by saying that I only just read the post on this model, so these are off-the-cuff thoughts.[2] First, he presents the “uniform national swing” as a bit of a straw argument. Silver is correct to suggest that its value lies in its simplicity, and that it does on occasion fail miserably — but then too have the very probability sampling based opinion polls in the British context (e.g. 1992) upon which such vote -> seat translations are based. When it tends to work, even in its lack of precision, it does so because it is assumed that the error for any given deviation in swing is randomly distributed across the entire sample. In other words, across the 650 constituencies, deviation from a uniform swing average out. Furthermore, there are sophisticated models, such as that used by the Elections Centre at the University of Plymouth, do factor in a number of additional variables in making seat projections. Indeed, and somewhat ironically, in the introduction to “Step 2”, he is simply proposing a uniform national swing based on their sophisticated matrix rather than simple polling data: “Originally, this step had been simple: we assumed that the proportion of voters changing hands from one party to the next was the same in each constituency.” They didn’t reject this approach because it was a uniform swing, but rather because using their matrix, it produced some illogical results.
Usually, the limitations of the uniform swing model are largely irrelevant as it usually does predict who will form the government, and that’s all that really matters. Much like while we’ve known all along that vote counting is simply another statistical routine infected with concomitant error, that error is usually a hell of a lot smaller than the margin between the 1st and 2nd placed candidates. Only in extraordinarily close elections does error become salient, the best known example of which was Florida 2000. In the 2010 British election, the limitations of the uniform swing model are likewise laid bare, as Silver argues.
Second, while Silver believes that this model “embodies what I believe to be sound logic about voter behavior”, he does undersell the notion of the tactical voter, which is a central concept to what we as political scientists understand about voter behavior from both theoretical (e.g. Downs, Duverger, Rae, Lijphart, et al. ad nauseum) and empirical perspectives. There is quite a bit of empirical literature on tactical (aka strategic) voting to suggest that it does happen, often, and when it does happen, those voters who employ it damn well understand it. My British students, admittedly while taking political science classes at a university from a prof who does voting behavior , understand the concept of tactical voting intuitively — much better than my American students ever did, or presumably the students at the university in the Netherlands where I used to work. It is part of the political culture in the United Kingdom in ways not approached in the United States (due to the lack of a strong national third party or strong regional parties) or the Netherlands (due to their use of a single national constituency and list proportional representation, which largely eviscerates the incentives to vote tactically). Indeed, while Silver suggests that “my impression is also that the phrase “tactical voting” has somewhat too much currency is often used as a band-aid to cover up flaws with the uniform swing model”, that has not been my impression at all, either in conversation or from reading the empirical literature.
Third, regarding retiring incumbents, I’d need to see his regression data before commenting with any depth, but here I’ll offer an impression of my own. Incumbency simply doesn’t matter anywhere near the way it does in the American context. Granted, Silver allows for this, so I’m intrigued by the finding, and also by the deviance between the estimate of 1.5% for Labour and the Tories, and 3% for the Lib Dems and others. What accounts for the effect to begin with? What explains the deviance between the two sets of parties? I don’t doubt the finding, but I’d like to better understand the causal mechanism behind it. I suspect that there is an effect similar to retirements in House (and Senate) elections: members of the party expected to lose seats, especially those in marginal seats to begin with, are far more likely to opt out, so we’d see a lot of Labour retirements in 1979, Tory retirements in 1997, Labour in 2010. What they take away with retirement from the electoral arena isn’t name recognition the way it’s understood in the US, but rather, I suspect, their mobilizing organizations.
I have one minor and one major point remaining. The former is that Northern Ireland should be taken out of the equation entirely, and indeed in every “swingometer” and every matrix that translates vote % into seats, this is done. The three “national” parties in British politics simply do not exist in Northern Ireland, thus the concept of swing to / away from any of the three major parties is irrelevant. Northern Ireland will elect its 18 MPs from Sinn Fèin, the SDLP, the UUP, and the DUP. There is an outside chance that there will be a new unionist party in the mix (the TUV), and likewise a chance that the UUP will be electorally eliminated — but this is partially due to the controversy surrounding their “alliance” with the British Conservative Party. However, it’s as illogical to discuss Labour, Conservative, or Liberal Democrat for these 18 seats as it is for the SNP to gain vote share in Watford.
I assume that the major point is factored into their model, but I’d like to know how — with 2010, constituency boundaries are changed, in some cases quite radically. In US parlance, it’s redistricting. Therefore, without precise data on how the new constituencies map onto the old, any model of swing based on 2005 constituencies is open to considerable error. These data do exist, indeed the media guide on the new constituencies (and how they map onto the old) was produced by my colleagues in my department.
Finally, I would like to highlight one strength in the model: that of regional adjustments. Yes, Scotland is different than the Southeast, and yes, any variation in swing away from Labour matters where it is located. This is, to my knowledge, already accounted for by the more sophisticated academic vote% -> seats matrices (I can’t speak for the various media outlets), but it’s good to see this acknowledged.
Regular readers of LGM know I have admired Silver’s work going back to his BP days, and this is no different. In all, its an impressive, nuanced model, and honestly, I would like to see it succeed as the limitations of assuming a uniform national swing are plain. However, the uniform swing is not as dire as suggested, some if not a lot of this work has been done, and there are several points, both in the narrative and in the functionality of the model itself that need to be addressed in future iterations of this model.
[1] Because that’s what I do for a living. In fact, what I should be doing right now is reviewing a manuscript for Electoral Studies, which is two weeks late and slipping later. Hopefully the editor of ES doesn’t read LGM, and thankfully, for a change, this is the only manuscript I have ‘on my desk’. (Which means of course once I publish this post and check my work email . . . )
[2] When I review a manuscript, I like to read it, set it aside, and read it again before submitting my review. The above represents my take on a first read only, and are thus limited in nature, possibly erroneous in places, so consume and dispense with appropriately. | 1,885 | 8,556 | {"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} | 2.578125 | 3 | CC-MAIN-2024-38 | latest | en | 0.954582 |
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A loopy exploration of z^2+1=0 (z squared plus one) with an eye on winding numbers. Try not to get dizzy! | 291 | 1,253 | {"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} | 2.65625 | 3 | CC-MAIN-2017-47 | latest | en | 0.765444 |
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The linearized longitudinal Equations of motion of a typical
equation: (8u 8w 89 80) = (-0.00643 -0.0991 -0.000222 0
0.0263 -0.629 -0.00153 0 0 820 -0.668 1 -32.2 0 0 0) (8u 8w
89 80) Use MATLAB to find the eigenvalues and
eigenvectors of the system matrix A above. A wind gust
causes a perturbation of delta theta = 1 degree in steady
level flight. Find the response of the airplane to this
perturbation using a modal analysis.
Solution
### Unformatted Attachment Preview
The linearized longitudinal Equations of motion of a typical Business jet in steady level flight is given by the following equation: (8u 8w 89 80) = (-0.00643 -0.0991 -0.000222 0 0.0263 -0.629 -0.00153 0 0 820 -0.668 1 -32.2 0 0 0) (8u 8w 89 80) Use MATLAB to find the eigenvalues and eigenvectors of the system matrix A above. A wind gust causes a perturbation of delta theta = 1 degree in steady level flight. Find the response of the airplane to this perturbation using a modal analysis. Solution Name: Description: ...
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4.4 | 377 | 1,204 | {"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} | 2.71875 | 3 | CC-MAIN-2022-21 | latest | en | 0.788712 |
http://mathhelpforum.com/algebra/207892-average-speed.html | 1,553,538,112,000,000,000 | text/html | crawl-data/CC-MAIN-2019-13/segments/1552912204086.87/warc/CC-MAIN-20190325174034-20190325200034-00395.warc.gz | 132,070,158 | 11,097 | 1. ## average speed
Tom drove for 3 hours at 30 km/hr and another 2 hrs at 70km/h. What was his average speed for the journey?
attempt:
using S = d/t
Given: 2 hrs at 70km/h and 3 hrs at 30km/h
Solve: 30/3 + 70/2 = (10 + 35 ) /2 = 45/2 = 22.5 km/h
please correct me if im wrong.
because im not so sure with my solution.
thanks
2. ## Re: average speed
Yes, you are wrong.
How far does he travel in the first 3 hours ?
How far does he travel in the next 2 hours ?
What is his total distance travelled ?
What is the total time taken ?
What is his average speed ?
3. ## Re: average speed
Originally Posted by BobP
Yes, you are wrong.
How far does he travel in the first 3 hours ?
How far does he travel in the next 2 hours ?
What is his total distance travelled ?
What is the total time taken ?
What is his average speed ?
What was his average speed for the journey?
is only ask... but may i know how it is solved ...
thanks
5. ## Re: average speed
3(30) + 2(70) = 90 + 140 = 230 km total
5 hrs also in total
230/5 = 46
so it is 46 km/hr is the answer..
can anyone check my solution because im so sure with my answer
thanks
6. ## Re: average speed
Originally Posted by rcs
What was his average speed for the journey?
is only ask... but may i know how it is solved ...
thanks
By using the formula you wrote in your first post- average speed is the distance traveled divided by the time. And those are given by answering the questions in the first response.
7. ## Re: average speed
how come and how it is really done?
8. ## Re: average speed
Originally Posted by rcs
how come and how it is really done?
The equation for average speed is based on the total distance over the total time. So $\displaystyle v_{ave} = \frac{\text{total distance}}{\text{total time}} = \frac{d}{t}$
-Dan
9. ## Re: average speed
Originally Posted by rcs
3(30) + 2(70) = 90 + 140 = 230 km total
5 hrs also in total
230/5 = 46
so it is 46 km/hr is the answer..
can anyone check my solution because im so sure with my answer
thanks
This is correct. | 576 | 2,048 | {"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} | 4.375 | 4 | CC-MAIN-2019-13 | latest | en | 0.968746 |
http://www.cfd-online.com/Forums/openfoam-solving/79930-calculation-friction-velocity-yplus-laminar-flow.html | 1,480,879,293,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541361.65/warc/CC-MAIN-20161202170901-00223-ip-10-31-129-80.ec2.internal.warc.gz | 384,693,587 | 14,941 | # Calculation of friction velocity and yPlus for laminar flow
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September 8, 2010, 13:34 Calculation of friction velocity and yPlus for laminar flow #1 Senior Member Join Date: Mar 2009 Posts: 248 Rep Power: 10 Dear Forum Users Good Evening I am calculating the friction velocity and yPlus like this: volScalarField U_tau ( IOobject ( "U_tau", runTime.timeName(), mesh, IOobject::NO_READ, IOobject::AUTO_WRITE ), mesh, dimensionedScalar ( "U_tau", U.dimensions(), scalar(0.0) ) ); forAll(U_tau.boundaryField(), patchi) { U_tau.boundaryField()[patchi] = Foam::sqrt( nu.value() * mag(-U.boundaryField()[patchi].snGrad()) ); } volScalarField yPlus ( IOobject ( "yPlus", runTime.timeName(), mesh, IOobject::NO_READ, IOobject::NO_WRITE ), mesh, dimensionedScalar("yPlus", dimless, 0.0) ); const fvPatchList& patches = U.mesh().boundary(); volScalarField::GeometricBoundaryField d = nearWallDist(mesh).y(); forAll(patches, patchi) { const fvPatch& currPatch = patches[patchi]; if (isA(currPatch)) { yPlus.boundaryField()[patchi] = ( (d[patchi] * mag(U_tau.boundaryField()[patchi])) / (nu.value() )); } } Info<< "Writing yPlus to field " << yPlus.name() << nl << endl; yPlus.write(); It would be very helpful if users could cross check and point out the mistakes. Best Regards jaswi
September 13, 2010, 08:41 #2 Senior Member Join Date: Mar 2009 Posts: 248 Rep Power: 10 Dear Forum Users Can somebody please cross check the formulation. After corrections , we all can use this as I have seen some similar posts. Hope some body with experience will find some time to comment . Best Regards jaswi
October 7, 2010, 07:19 #3 Senior Member Francois Join Date: Jun 2010 Posts: 107 Rep Power: 9 Hi there! I'm also programming a function to determine u_tau and yPlus, but for turbulent flows. What type of geometry are you working on? Regards, Francois
March 6, 2014, 18:38 #4 Member CHARLES Join Date: May 2013 Posts: 46 Rep Power: 5 I found a useful solution here: y+ and u+ values with low-Re RANS turbulence models: utility + testcase
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# Cambridge checkpoint maths p2 specimen 2012
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### Cambridge checkpoint maths p2 specimen 2012
1. 1. UNIVERSITY OF CAMBRIDGE INTERNATIONAL EXAMINATIONS Cambridge CheckpointMATHEMATICS 1112/02Paper 2 For Examination from 2012SPECIMEN PAPER 1 hourCandidates answer on the Question Paper.Additional Materials: Geometrical Instruments Calculator Tracing PaperREAD THESE INSTRUCTIONS FIRSTWrite your Centre number, candidate number and name on the work you hand in. For Examiners UseWrite in dark blue or black pen. 1You may use a pencil for any diagrams, graphs or rough working. 2Do not use staples, paper clips, highlighters, glue or correction fluid. 3Answer all questions. 4 5You should show all your working in the booklet.The number of marks is given in brackets [ ] at the end of each question or part 6question. 7The total number of marks for this paper is 50. 8 9 10 11 12 13 Total This document consists of 13 printed pages and 1 blank page.© UCLES 2011 [Turn over
2. 2. 21 Here are the ages of a group of office workers. 45 18 27 26 32 28 47 30 35 Work out (a) the median age [1] (b) the mean age. [2]© UCLES 2011 1112/02/SP/12
3. 3. 32 (a) Ken makes a fruit drink. For Examiners He mixes apple juice : mango juice in the ratio 3 : 1 Use Work out (i) how much apple juice he mixes with 3 litres of mango juice litres [1] (ii) how much mango juice he mixes with 1.5 litres of apple juice. litres [1] (b) Ivana uses 1.5 kg carrots, 500 g potatoes and 1 kg onions to make vegetable soup. Write the ratio carrots : potatoes : onions in its simplest form. : : [2] (c) In a school the student ratio of girls : boys is 3 : 5 There are 450 boys. Work out the total number of students in the school. [2]© UCLES 2011 1112/02/SP/12 [Turn over
4. 4. 43 (a) The cost of a computer repair is worked out using the formula C = 35 + 15h where C is the cost in dollars and h is the time taken in hours. Use the formula to find (i) the cost of a repair that takes 3 hours \$ [1] (ii) the time taken for a repair that costs \$110 hours [2] (b) Rearrange the formula k = 3m – 2 to make m the subject. m= [2]© UCLES 2011 1112/02/SP/12
5. 5. 54 Here is part of a bus timetable. For Examiners All of the buses are on time. Use Business Park 14 03 14 33 15 03 15 33 South Hill 14 18 14 48 15 18 15 48 Hospital 14 28 14 58 15 28 15 58 Clock Tower 14 42 15 12 15 42 16 12 Bus Station 14 47 15 17 15 47 16 17 (a) Nihal gets to the bus stop at South Hill at 14 50 (i) At what time does the next bus arrive? [1] (ii) Write your answer to part (i) using the 12-hour clock. [1] (b) Meera catches the 14 58 bus from the Hospital. Work out how long it takes to get to the Bus Station. minutes [1] (c) The distance from the Business Park to South Hill is 10 kilometres. Work out the average speed of a bus from the Business Park to South Hill. Give your answer in kilometres per hour. km/hour [2]© UCLES 2011 1112/02/SP/12 [Turn over
6. 6. 65 The diagram shows triangles A and B and point P and R on a grid. y 5 P 4 3 R 2 A 1 x –6 –5 –4 –3 –2 –1 0 1 2 3 4 5 6 –1 B –2 –3 –4 –5 (a) Mark the point (3, 2). Label it Q. [1] (b) Point M is the midpoint of the line PR. Write down the coordinates of M. ( , ) [1] (c) Reflect triangle A in the y-axis. Label the image C. [1] (d) Describe in full the rotation that maps triangle A onto triangle B. [2]© UCLES 2011 1112/02/SP/12
7. 7. 76 Ameera makes a sequence of patterns using counters. For Examiners The first three patterns are shown. Use Pattern 1 Pattern 2 Pattern 3 Pattern number (p) 1 2 3 4 5 Number of counters (c) 5 8 11 (a) Complete the table. [1] (b) Work out the number of counters in Pattern 10. [1] (c) Find the formula for the number of counters, c, in pattern p. c= [2] (d) Ameera thinks that she can make one of these patterns with exactly 60 counters. Explain why she is wrong. [1]© UCLES 2011 1112/02/SP/12 [Turn over
8. 8. 8 7 (a) Calculate the area of this triangle. 4.8 cm 6.5 cm cm2 [1] (b) The diagram shows the full-size net of a cuboid drawn on a cm2 grid. Work out the volume of the cuboid in cm3. Show your measurements and working clearly. cm3 [2]© UCLES 2011 1112/02/SP/12
9. 9. 9 (c) Calculate the area of the semicircle with radius 5 cm. For Examiners Use cm2 [2]© UCLES 2011 1112/02/SP/12 [Turn over
10. 10. 108 (a) Lola buys a new car on credit. The total cost of the car is \$6900 She pays a 20% deposit. How much is the deposit? \$ [1] (b) Lola wins \$240 She spends \$48 on a dress. What percentage of the \$240 has she spent? % [2] (c) Lola puts \$150 into a bank account. The account pays 4% per annum simple interest. Work out the total amount of money in her account at the end of the year. \$ [2]© UCLES 2011 1112/02/SP/12
11. 11. 119 The diagram shows a triangular plot of land drawn to a scale of 1 cm to 10 m. For Examiners Use B Scale: 1 cm to 10 m Scale: 1 cm to 10 m A C A tree is planted in the plot at point T such that • T is 70 metres from point A • T is 20 metres from side AB Using a ruler and compasses mark the point T. Leave all your construction lines. [3]© UCLES 2011 1112/02/SP/12 [Turn over
12. 12. 1210 Jamal uses two fair five-sided spinners in a game. His score is the total of the two numbers shown on the spinners. (a) Complete the table to show all his possible scores. 1 2 3 4 5 1 2 3 4 5 6 2 4 5 6 7 3 6 7 8 4 8 9 5 10 [1] (b) Find the probability that Jamal gets (i) a score of 10 [1] (ii) a score of 1 [1] (c) Find the probability that Jamal gets a score less than 6. Give your answer as a fraction in its lowest terms. [2]© UCLES 2011 1112/02/SP/12
13. 13. 1311 The diagram shows a rectangular field ABCD. For AB = 40 m, BC = 25 m. Examiners Use 40 m A B 25 m D C A path crosses the field from A to C. Use Pythagoras’ theorem to work out the length of the path. m [3]© UCLES 2011 1112/02/SP/12
14. 14. 14 BLANK PAGEPermission to reproduce items where third-party owned material protected by copyright is included has been sought and cleared where possible. Every reasonable effort hasbeen made by the publisher (UCLES) to trace copyright holders but, if any items requiring clearance have unwittingly been included, the publisher will be pleased to makeamends at the earliest possible opportunity.University of Cambridge International Examinations is part of the Cambridge Assessment Group. Cambridge Assessment is the brand name of University of Cambridge LocalExaminations Syndicate (UCLES), which is itself a department of the University of Cambridge.© UCLES 2011 1112/02/SP/12 | 2,191 | 6,981 | {"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} | 3.078125 | 3 | CC-MAIN-2017-51 | latest | en | 0.772754 |
http://iqnes.com/how-to-solve-a-system-of-two-equations/?amp=1 | 1,723,105,177,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640723918.41/warc/CC-MAIN-20240808062406-20240808092406-00820.warc.gz | 14,990,648 | 25,173 | August 8, 2024
How To Solve A System Of Two Equations
A system of two equations typically refers to a pair of equations involving two variables. The general form of a system of two equations can be represented as:
ax + by = c \\ dx + ey = f \end{cases} \] Where $$a$$, $$b$$, $$c$$, $$d$$, $$e$$, and $$f$$ are constants, and $$x$$ and $$y$$ are variables. The solutions to a system of two equations represent the values of the variables $$x$$ and $$y$$ that satisfy both equations simultaneously. These solutions can be: 1. **Unique Solution**: The system has one unique solution, which means there is one specific point that satisfies both equations. Geometrically, this corresponds to the point of intersection of the two lines represented by the equations. 2. **No Solution**: The system has no solution, meaning there are no values of $$x$$ and $$y$$ that satisfy both equations simultaneously. Geometrically, this corresponds to two parallel lines that do not intersect. 3. **Infinite Solutions**: The system has infinitely many solutions, indicating that all points on one line are solutions to both equations. Geometrically, this corresponds to two overlapping lines, meaning they coincide with each other. The methods to solve a system of two equations include substitution, elimination, graphical representation, matrix methods, and computational techniques. Depending on the specific equations and the desired approach, one method may be more suitable than others. The choice of method depends on factors such as the complexity of the equations, available tools, and personal preference.
How To Solve A System Of Two Equations
To solve a system of two equations, you can use various methods, including:
1. Substitution Method:
• Solve one of the equations for one variable in terms of the other.
• Substitute this expression into the other equation.
• Solve the resulting equation for the remaining variable.
• Substitute the value found back into one of the original equations to find the value of the other variable.
2. Elimination Method:
• Manipulate one or both equations so that when you add or subtract them, one of the variables is eliminated.
• Solve the resulting equation for one variable.
• Substitute the value found back into one of the original equations to find the value of the other variable.
3. Graphical Method:
• Graph each equation on the same coordinate plane.
• The solution to the system is the point(s) where the graphs intersect.
4. Matrix Method (Gaussian Elimination or Cramer’s Rule):
• Write the system of equations in matrix form.
• Use techniques like Gaussian elimination to transform the matrix into row-echelon or reduced row-echelon form.
• Solve for the variables using back-substitution or by applying Cramer’s Rule.
5. Technology:
• You can also use computational tools like calculators or software (such as MATLAB, Mathematica, or Python with libraries like NumPy) to solve the system of equations numerically.
Choose the method that suits you best based on the specific equations you’re dealing with and your preferences. Each method has its advantages and is applicable in different scenarios. | 658 | 3,154 | {"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} | 4.6875 | 5 | CC-MAIN-2024-33 | latest | en | 0.917423 |
https://www.nagwa.com/en/videos/595127892640/ | 1,568,814,150,000,000,000 | text/html | crawl-data/CC-MAIN-2019-39/segments/1568514573289.83/warc/CC-MAIN-20190918131429-20190918153429-00291.warc.gz | 935,675,394 | 5,672 | # Video: Decomposing Teen Numbers into Ten Ones and Some More Ones
Decompose this number to complete the number bond.
00:44
### Video Transcript
Decompose this number to complete the number bond. 16 is 10 and the missing number.
Here we have a tens block to represent the 10 in the number. We need to make number 16. So we’ll need some ones blocks. So we already have 10, 11, 12, 13, 14, 15, 16. Now we have 16 blocks altogether. We have a tens block and six ones. So the missing number is six. | 136 | 499 | {"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} | 3.5 | 4 | CC-MAIN-2019-39 | longest | en | 0.874719 |
http://linas.org/art-gallery/mderive/mderive.html | 1,679,989,319,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296948817.15/warc/CC-MAIN-20230328073515-20230328103515-00654.warc.gz | 34,241,618 | 3,330 | M-Set Derivatives
One way of coloring the inside of the M-set is to work with the the various derivatives that describe the 'flow' of Zn. These images are all based on the computation of the derivative of Zn with respect to c. The expression for this is simple: Z'n+1 = dZn+1/dc = 2 * Zn * Z'n + 1, which must be iterated. Note that this derivative can be though of as a vector: it has a real component and an imaginary component. Thus, we can take its curl or divergence as well as it's absolute value.
Because Z'n has a high 'rotation', it is handier to deal with the normalized vector Pn = Z'n/Zn Here we graph the phase phi=arctan (Re Pn / Im Pn). Note that not all buds are alike: the interior of some buds see a full rotation of the phase by 360 degrees; others do not.
Very curiously, this seems to depend on the factorization of the loop termination count. When the loop termination count is prime, none of the buds rotate; when it is a product of many small (repeated) factors, most buds rotate. For example, in this image, most buds rotate because iteration was stopped at 1260=4*9*5*7,
whereas this image stopped at 1259 (which is a prime number) and none of the buds rotate.
The phase of the second normalized derivative Qn = Z''n/Zn where Z''n+1 = 2 * (Zn * Z''n + Z'2n)
Modulus of second derivative.
Iterated to a high order (N=4153) before stopping.
Same image as above, but iterated to only N=19. Note the presence of 'zeros' (black dots) on the interior, which are missing from the high-iteration image.
As above, but iterated to N=18. Note that this image contains one less black dot on the belt.
Iterated to N=17. Notice how the images generated with prime N are subtly different than those with composite iteration counts.
Iterated to N=16. Note that 18 is divisible by 3, while 16 is not: thus the large bud has a green dot in the middle, but the next-smaller one doesn't (unlike the N=18 case).
The second derivative is handy for exhibiting another phenomenon that is hinted at elsewhere in this page, but otherwise difficult to exhibit. This image is created quite artificially: the interior color is recorded only if the modulus of Qn = Z''n/Zn is less than one for some n. In other words, we record the color only if Qn is near a zero. Thus we see a simultaneous depiction of the zero's of the various Qn for various n. These seem to go to a hyperbolic-like limit-circle.
In this image, black is zero, moving through blue, green, yellow to a red of 1.0.
Note the Moire patterning make it difficult to discern where the actual limit is. To eliminate this, this image was iterated only to N=50, and so we can see the limit-circle at 50 dots.
The 'distance estimator' is the inverse infinitesimal flow of the iteration number. It gets this name because it provides a rough estimate of how far away an exterior point is from the boundary of the M-Set. The smooth (real-valued) iteration count is given by mu = n+1-log(log(|z|))/log2, as demonstrated in the Escape Theory Room (which is, in turn, the logarithm of the Douady-Hubbard potential). Taking the derivative of mu w.r.t. c we get dmu/dc = d|z|/dc / (|zl log |z| log 2). The 'distance estimator' is one over this quantity.
This first picture shows the iteration to n=9. (We've dropped the factor of log 2).
Iterate to n=19.
Iterate to n=49.
Iterate to n=2520=8*9*5*7 a product of small primes. Oddly, the n=2 bulb is unlit, but n=3 and so on light up.
Iterate to n=2519 which is a prime number. Oddly, the n=2 bud lights up, the none of the other buds do. Thus, the counting rules here seem to be a bit different than one might expect ...
Don't confuse the absolute value of the derivative with the derivative of the absolute value.
This image shows |z| / |z'|.
This image shows |z| / |z|'.
Copyright (c) 1997, 2000 Linas Vepstas | 999 | 3,831 | {"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} | 3.53125 | 4 | CC-MAIN-2023-14 | latest | en | 0.941137 |
http://spotidoc.com/doc/1506915/file---ms.-struthers--classroom | 1,582,322,161,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875145538.32/warc/CC-MAIN-20200221203000-20200221233000-00286.warc.gz | 138,949,821 | 7,153 | # File - Ms. Struthers` Classroom
```AP Statistics
Name: _____________________
Lesson 9-2 Conducting Significance Tests
Recap:
Tests of Significance
Stating a Hypothesis
Null Hypothesis:
Alternative Hypothesis:
Ex. #1 In the past, the mean score of the seniors at XYZ Secondary on the Euclid contest has been 50. This
year a special preparation course is offered and all 53 seniors planning to take the contest enrol in the
course. The mean of their 53 contest scores is 54.1. The principal believes that the new course has
improved the students’ contest scores. Assume that the contest scores for seniors at XYZ secondary
vary normally with a standard deviation of 8.
a)
Identify the population and parameter of interest.
b)
State the hypothesis that you would use to test the principals’ claim. Use both words and
symbols.
Test Statistic and Conditions:
-
A test statistic is used for calculating the x-score for the sample mean
Conditions for using a significance test:
SRS, normality, and independence
These three conditions must be verified before performing a significance test about a population
mean/proportion
-
If these three conditions are met then the distribution of x is normal with a standard deviation of
Test statistic =
estimate( x) − hypothesised value
σ
n
σ
n
AP Statistics
This is a z-score!
Name: _____________________
** note for today’s class we are assuming we know the standard deviation of the
population, that is not always the case!
P-value
Probability against the null hypothesis, if it was true.
Small p-value, the null hypothesis (Ho) is unlikely, the results from the sample did not occur by chance
or sampling variability, change did occur
2-Tailed test P-value = P ( z < −α ) + P ( z > α )
1-Tailed test Ha: µ < k
P-value P ( z < −α )
P-value P ( z > α )
Ha: µ > k
Ex. #1 A hospital monitors paramedic response times. Last year the average response time was 6.7 minutes
( σ = 2 min ). This year a sample of 400 responses had an average of 6.48 minutes. The hospital wants
evidence that response time have decreased?
a) State the null and alternative hypothesis
b) Calculate the test statistic and the p-value. Is there evidence that the response time has decreased at
a 5% level of significance?
AP Statistics
Name: _____________________
Ex. #2 In the past, the mean score of the seniors at XYZ Secondary on the Euclid contest has been 50. This
year a special preparation course is offered and all 53 seniors planning to take the contest enrol in the
course. The mean of their 53 contest scores is 54.1. The principal believes that the new course has
improved the students’ contest scores. Assume that the contest scores for seniors at XYZ secondary
vary normally with a standard deviation of 8. (Lesson 11.2 – note change to value of standard
deviation)
Use our Four Steps Process to find evidence that the contest scores have/have not increased.
AP Statistics
Ex. #3
Name: _____________________
Bottles of cola are supposed to contain 300 ml of cola. There is some variation from bottle to
bottle. The distribution of the volume of cola is normal with a standard deviation of 3 ml. An
inspector suspects that the bottles are under filled and randomly selects six bottles form the same
day to check. Given the results of his check, is there convincing evidence that the mean amount
of cola in all the bottles filled that day is less than 300 ml? Use a significance level of α = 0.05 .
Results: 295.4, 296.7, 300.9, 297.9, 299.2, 297.0
Homework:
b)
Would your conclusion be any different if the significance level was α = 0.01?
c)
If you were the cola manufacturer, which significance level would you be likely to use?
pg. 546 #1-25 odd and 27-30 (M/C)
``` | 899 | 3,692 | {"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} | 4.5625 | 5 | CC-MAIN-2020-10 | latest | en | 0.905219 |
https://quantumfrontiers.com/2023/02/19/a-quantum-complex-legacy-part-deux/comment-page-1/ | 1,679,313,796,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296943483.86/warc/CC-MAIN-20230320114206-20230320144206-00573.warc.gz | 548,604,823 | 32,863 | # A (quantum) complex legacy: Part deux
I didn’t fancy the research suggestion emailed by my PhD advisor.
A 2016 email from John Preskill led to my publishing a paper about quantum complexity in 2022, as I explained in last month’s blog post. But I didn’t explain what I thought of his email upon receiving it.
It didn’t float my boat. (Hence my not publishing on it until 2022.)
The suggestion contained ingredients that ordinarily would have caulked any cruise ship of mine: thermodynamics, black-hole-inspired quantum information, and the concept of resources. John had forwarded a paper drafted by Stanford physicists Adam Brown and Lenny Susskind. They act as grand dukes of the community sussing out what happens to information swallowed by black holes.
We’re not sure how black holes work. However, physicists often model a black hole with a clump of particles squeezed close together and so forced to interact with each other strongly. The interactions entangle the particles. The clump’s quantum state—let’s call it $| \psi(t) \rangle$—grows not only complicated with time ($t$), but also complex in a technical sense: Imagine taking a fresh clump of particles and preparing it in the state $| \psi(t) \rangle$ via a sequence of basic operations, such as quantum gates performable with a quantum computer. The number of basic operations needed is called the complexity of $| \psi(t) \rangle$. A black hole’s state has a complexity believed to grow in time—and grow and grow and grow—until plateauing.
This growth echoes the second law of thermodynamics, which helps us understand why time flows in only one direction. According to the second law, every closed, isolated system’s entropy grows until plateauing.1 Adam and Lenny drew parallels between the second law and complexity’s growth.
The less complex a quantum state is, the better it can serve as a resource in quantum computations. Recall, as we did last month, performing calculations in math class. You needed clean scratch paper on which to write the calculations. So does a quantum computer. “Scratch paper,” to a quantum computer, consists of qubits—basic units of quantum information, realized in, for example, atoms or ions. The scratch paper is “clean” if the qubits are in a simple, unentangled quantum state—a low-complexity state. A state’s greatest possible complexity, minus the actual complexity, we can call the state’s uncomplexity. Uncomplexity—a quantum state’s blankness—serves as a resource in quantum computation.
Manny Knill and Ray Laflamme realized this point in 1998, while quantifying the “power of one clean qubit.” Lenny arrived at a similar conclusion while reasoning about black holes and firewalls. For an introduction to firewalls, see this blog post by John. Suppose that someone—let’s call her Audrey—falls into a black hole. If it contains a firewall, she’ll burn up. But suppose that someone tosses a qubit into the black hole before Audrey falls. The qubit kicks the firewall farther away from the event horizon, so Audrey will remain safe for longer. Also, the qubit increases the uncomplexity of the black hole’s quantum state. Uncomplexity serves as a resource also to Audrey.
A resource is something that’s scarce, valuable, and useful for accomplishing tasks. Different things qualify as resources in different settings. For instance, imagine wanting to communicate quantum information to a friend securely. Entanglement will serve as a resource. How can we quantify and manipulate entanglement? How much entanglement do we need to perform a given communicational or computational task? Quantum scientists answer such questions with a resource theory, a simple information-theoretic model. Theorists have defined resource theories for entanglement, randomness, and more. In many a blog post, I’ve eulogized resource theories for thermodynamic settings. Can anyone define, Adam and Lenny asked, a resource theory for quantum uncomplexity?
By late 2016, I was a quantum thermodynamicist, I was a resource theorist, and I’d just debuted my first black-hole–inspired quantum information theory. Moreover, I’d coauthored a review about the already-extant resource theory that looked closest to what Adam and Lenny sought. Hence John’s email, I expect. Yet that debut had uncovered reams of questions—questions that, as a budding physicist heady with the discovery of discovery, I could own. Why would I answer a question of someone else’s instead?
So I thanked John, read the paper draft, and pondered it for a few days. Then, I built a research program around my questions and waited for someone else to answer Adam and Lenny.
Three and a half years later, I was still waiting. The notion of uncomplexity as a resource had enchanted the black-hole-information community, so I was preparing a resource-theory talk for a quantum-complexity workshop. The preparations set wheels churning in my mind, and inspiration struck during a long walk.2
After watching my workshop talk, Philippe Faist reached out about collaborating. Philippe is a coauthor, a friend, and a fellow quantum thermodynamicist and resource theorist. Caltech’s influence had sucked him, too, into the black-hole community. We Zoomed throughout the pandemic’s first spring, widening our circle to include Teja Kothakonda, Jonas Haferkamp, and Jens Eisert of Freie University Berlin. Then, Anthony Munson joined from my nascent group in Maryland. Physical Review A published our paper, “Resource theory of quantum uncomplexity,” in January.
The next four paragraphs, I’ve geared toward experts. An agent in the resource theory manipulates a set of $n$ qubits. The agent can attempt to perform any gate $U$ on any two qubits. Noise corrupts every real-world gate implementation, though. Hence the agent effects a gate chosen randomly from near $U$. Such fuzzy gates are free. The agent can’t append or discard any system for free: Appending even a maximally mixed qubit increases the state’s uncomplexity, as Knill and Laflamme showed.
Fuzzy gates’ randomness prevents the agent from mapping complex states to uncomplex states for free (with any considerable probability). Complexity only grows or remains constant under fuzzy operations, under appropriate conditions. This growth echoes the second law of thermodynamics.
We also defined operational tasks—uncomplexity extraction and expenditure analogous to work extraction and expenditure. Then, we bounded the efficiencies with which the agent can perform these tasks. The efficiencies depend on a complexity entropy that we defined—and that’ll star in part trois of this blog-post series.
Now, I want to know what purposes the resource theory of uncomplexity can serve. Can we recast black-hole problems in terms of the resource theory, then leverage resource-theory results to solve the black-hole problem? What about problems in condensed matter? Can our resource theory, which quantifies the difficulty of preparing quantum states, merge with the resource theory of magic, which quantifies that difficulty differently?
I don’t regret having declined my PhD advisor’s recommendation six years ago. Doing so led me to explore probability theory and measurement theory, collaborate with two experimental labs, and write ten papers with 21 coauthors whom I esteem. But I take my hat off to Adam and Lenny for their question. And I remain grateful to the advisor who kept my goals and interests in mind while checking his email. I hope to serve Anthony and his fellow advisees as well.
1…en route to obtaining a marriage license. My husband and I married four months after the pandemic throttled government activities. Hours before the relevant office’s calendar filled up, I scored an appointment to obtain our license. Regarding the metro as off-limits, my then-fiancé and I walked from Cambridge, Massachusetts to downtown Boston for our appointment. I thank him for enduring my requests to stop so that I could write notes.
2At least, in the thermodynamic limit—if the system is infinitely large. If the system is finite-size, its entropy grows on average.
This entry was posted in News, Real science, Reflections, Theoretical highlights by Nicole Yunger Halpern. Bookmark the permalink.
## About Nicole Yunger Halpern
I’m a theoretical physicist at the Joint Center for Quantum Information and Computer Science in Maryland. My research group re-envisions 19th-century thermodynamics for the 21st century, using the mathematical toolkit of quantum information theory. We then apply quantum thermodynamics as a lens through which to view the rest of science. I call this research “quantum steampunk,” after the steampunk genre of art and literature that juxtaposes Victorian settings (à la thermodynamics) with futuristic technologies (à la quantum information). For more information, check out my upcoming book Quantum Steampunk: The Physics of Yesterday’s Tomorrow. I earned my PhD at Caltech under John Preskill’s auspices; one of my life goals is to be the subject of one of his famous (if not Pullitzer-worthy) poems. Follow me on Twitter @nicoleyh11.
## 4 thoughts on “A (quantum) complex legacy: Part deux”
1. Reading this reminded me of two fanciful notions I’ve encountered, and I wondered if I might ask your expert opinion on them:
Firstly, is it possible that in the (hopefully eventual) marriage of QM and GR that unitarity is NOT true in all situations? Specifically, is it possible that information is truly lost in black holes (and perhaps other extreme situations)? If so, it would eliminate the paradox. I know unitarity is considered bedrock among many physicists, but Roger Penrose apparently suspects otherwise.
Secondly, I frequently hear how entropy is time’s “ratchet” — that time runs forward because of entropy (the laws of physics supposedly working when time is reversed). What about the notion that time is fundamental and axiomatic, and entropy is the result of the laws of physics plus time?
Are there good reasons to definitely rule out these notions?
• (Apologies if my questions were unworthy or too far off topic.)
2. Some physicists have favored nonunitarity at various points, but I’m not sure precisely what the current status is. I see entropy as a quantifier; whether its behavior is a cause or an effect might be a matter of philosophy.
• Thanks for the reply!
FWIW, I have a hard time seeing entropy as a cause (in the sense of it being a force or fundamental) given its statistical nature and that it can, if momentarily, reverse. I suspect there’s more than philosophy there but something fundamental about how reality works. But I’m very much in the metaphorical position of someone who doesn’t know much about art but knows what he likes. | 2,261 | 10,739 | {"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": 7, "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} | 2.546875 | 3 | CC-MAIN-2023-14 | latest | en | 0.93814 |
https://short-facts.com/how-the-born-oppenheimer-approximation-is-used/ | 1,680,188,253,000,000,000 | text/html | crawl-data/CC-MAIN-2023-14/segments/1679296949331.26/warc/CC-MAIN-20230330132508-20230330162508-00385.warc.gz | 564,317,531 | 41,673 | # How the Born-Oppenheimer approximation is used?
## How the Born-Oppenheimer approximation is used?
The Born-Oppenheimer Approximation is the assumption that the electronic motion and the nuclear motion in molecules can be separated. It leads to a molecular wave function in terms of electron positions and nuclear positions. The proton, itself, is approximately 2000 times more massive than an electron.
## Why do we need Born-Oppenheimer approximation?
The Born-Oppenheimer approximation is one of the basic concepts underlying the description of the quantum states of molecules. This approximation makes it possible to separate the motion of the nuclei and the motion of the electrons.
Are there instances where the Born-Oppenheimer approximation breaks down for some molecules?
In fact, the BO approximation breaks down in some cases when non-adiabatic effects are not negligible (e.g. loss or gain of energy due to changes in electronic orbits).
### What are the limitations of Born-Oppenheimer approximation?
The original BO approach had certain limitations: • They considered only stationary states, i.e., the time-independent SE. They considered only stable molecules (those having a configuration in which the forces on the nuclei vanish) and relatively small displace- ments of the nuclei from equilibrium.
### What is the Schrödinger equation for the electron when the Born Oppenheimer approximation is used?
The Schrödinger equation, which must be solved to obtain the energy levels and wavefunction of this molecule, is a partial differential eigenvalue equation in the three-dimensional coordinates of the nuclei and electrons, giving 3 × 12 + 3 × 42 = 36 nuclear + 126 electronic = 162 variables for the wave function.
What is Hamiltonian operator in chemistry?
The Hamiltonian operator is the sum of the kinetic energy operator and potential energy operator. The kinetic energy operator is the same for all models but the potential energy changes and is the defining parameter.
#### When Born Oppenheimer approximation breaks down?
We reiterate that when two or more potential energy surfaces approach each other, or even cross, the Born–Oppenheimer approximation breaks down, and one must fall back on the coupled equations.
How can you calculate total energy of molecule with the help of Born Oppenheimer approximation method?
The Born–Oppenheimer approximation assumes that the molecular wavefunction can be written in the form ψtotal=ψelectronicψvibrationψrotation and therefore that the energies due to each type of motion are additive Etotal=Eelectronic+Evibrational+Erotational.
## What is the starting point in density functional theory calculations?
Usually one starts with an initial guess for n(r), then calculates the corresponding Vs and solves the Kohn–Sham equations for the φi. From these one calculates a new density and starts again. This procedure is then repeated until convergence is reached.
## How are Hamiltonian operators calculated?
The Hamiltonian operator, H ^ ψ = E ψ , extracts eigenvalue E from eigenfunction ψ, in which ψ represents the state of a system and E its energy. The expression H ^ ψ = E ψ is Schrödinger’s time-independent equation. | 649 | 3,212 | {"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} | 2.671875 | 3 | CC-MAIN-2023-14 | longest | en | 0.882982 |
http://www.matrixlab-examples.com/ohms-law-calculator.html | 1,571,708,675,000,000,000 | text/html | crawl-data/CC-MAIN-2019-43/segments/1570987795403.76/warc/CC-MAIN-20191022004128-20191022031628-00440.warc.gz | 288,257,682 | 6,791 | # Ohm’s law Calculator
You can find the calculator at the bottom of this article. We’ll start with an introduction to this topic.
The Ohm’s law (after Georg Ohm) defines the relationship between voltage (V), current (I) and resistance (R). Power (P) relationships appear as a logic consequence of the others. One ohm is the resistance value through which one volt will produce a current of one ampere. The Ohm’s formula is V = IR.
Voltage (V) is the difference in electrical potential between two points in an electronic circuit, and it is measured in volts (V).
Current (I) is a flow of electrons on a conductor, and it is measured in amperes (A).
Resistance (R) determines how much current will flow through an electrical device. Resistors are used to control or limit voltage and current levels. A high resistance will allow a small current to flow. A low resistance will allow a larger current to flow. Resistors are measured in ohms.
Power (P) is the voltage multiplied by the current, and it’s measured in watts (W).
Ohm’s law Pie Chart
### Electrical Calculations
Let’s say that a 12V car battery is connected to a 3 ohm light bulb. What is the voltage measured at the light bulb?
We can use our calculator and enter
V = 12.0 V
R = 3.0 ohms
We get
I = 4.0 A
### Parallel Resistors
Our calculator can also be used to find out the equivalent resistor of up to three resistors in parallel. For example, three 20-ohm parallel resistors are connected across a 120 V power source. What is the current of this circuit?
We use the section on parallel resistors and enter
R1 = 20 ohms
R2 = 20 ohms
R3 = 20 ohms
we learn that the equivalent resistor is Req = 6.7 ohms.
Now, we use the formula I = V/R and enter the known values of voltage and resistance
V = 120 V
R = 6.7 ohms
and we discover that the total current flowing is I = 17.91 amperes.
Please enable JavaScript codes on this page. The calculator uses them.
Parallel Resistors R1 = ohms R2 = ohms R3 = ohms Req = ohms V = I R I = A R = ohms V = V V = P/I P = W I = A V = V V = sqrt( PR ) P = W R = ohms V = V I = V/R V = V R = ohms I = A I = P/V P = W V = V I = A I = sqrt( P/R ) P = W R = ohms I = A R = V/I V = V I = A R = ohms R = V2/P V = V P = W R = ohms R = P/I2 P = W I = A R = ohms P = VI V = V I = A P = W P = V2/R V = V R = ohms P = W P = I2R I = A R = ohms P = W
From 'Ohms Law Calculator' to home
From 'Ohms Law Calculator' to Free Online Calculators
Top Creative Electronic Projects Electronic Experiments Electrical Calculations | 717 | 2,534 | {"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} | 4.3125 | 4 | CC-MAIN-2019-43 | latest | en | 0.931503 |
https://answers.yahoo.com/question/index?qid=20120112035535AASw2aq | 1,580,116,069,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579251696046.73/warc/CC-MAIN-20200127081933-20200127111933-00022.warc.gz | 319,338,989 | 23,900 | Anonymous
Anonymous asked in Science & MathematicsEngineering · 8 years ago
# Can someone help me solve this? tan s is over 1+cos s + sin s is over 1-cos s = cot s + sec s csc S?
Its about Verifying Trigonometric functions & that's the last # I need to. But I just can't get the right solution.. :/
Relevance
• 8 years ago
tried doing it fancy by typing it on word first but it didn't work :( oh well, you're just gonna have a hard time deciphering it ;P
tan s/(1+cos s )+ sin s/(1-cos s )=cot s+(sec s x csc s)
LHS = tan s/(1+cos s )+ sin s/(1-cos s )
(tan s(1-cos s)+sin s(1+cos s) )/(1- cos^2 s )
(tan s - sin s + sin s + (cos s x sin s) )/sin^2 s
(tan s + (cos s x sin s) )/sin^2 s
1/(sin s x cos s) + cos s/sin s
(sec s x csc s) + cot s
QED | 336 | 790 | {"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} | 3.421875 | 3 | CC-MAIN-2020-05 | latest | en | 0.813152 |
https://lua-users.org/lists/lua-l/2008-04/msg00194.html | 1,638,493,401,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964362571.17/warc/CC-MAIN-20211203000401-20211203030401-00194.warc.gz | 437,714,817 | 3,028 | • Subject: table.insert and negative numbers
• From: Matthew Paul Del Buono <delbu9c1@...>
• Date: Tue, 8 Apr 2008 19:09:46 -0400 (EDT)
```In my testing I encountered an issue where the following line would cause the system to go into (what seemed to be, at the time) an infinite loop:
t = {};
table.insert(t, 2^31, 1);
After researching, however, it appears that this is due to the fact that 2^31 becomes a negative number. I expanded my search and found that tinsert() attempts to copy every value up one index until it reaches the pos value (2^31, or approx. -2 billion), which is an extremely expensive operation if the index doesn't presently exist (especially if the table is empty). Even numbers as low as -1000000 take a long time on an empty table (tested on an AMD64 x2 4400+).
While it's conceivable to say that Lua doesn't support negative numbers in table.insert, or that the value -1000000 will likely never be reached, is there any particular reason that the negative case is going completely unchecked? A simple test can speed up the operation significantly for those rare cases where such a table structure might be desired. The price to pay for such a check would is practically zero when compared to the expense of the table.insert operation itself. Patched test cases and patch follows. If anyone has any recommendations or comments here I'd love to hear them.
Regards,
-- Matthew P. Del Buono
P.S. I had several iterations of this patch, including one which just plain didn't support negative numbers and gave an error, but I figured that for backwards compatibility reasons, functionality should remain in-tact. I don't particularly like this solution due to the double-traversal on negative positions, but I couldn't think of a better solution to acquiesce to everyone. Perhaps someone else has another idea.
Lua 5.1.3 Copyright (C) 1994-2008 Lua.org, PUC-Rio
> t = {1,2,3};
> table.insert(t, 2, 0)
> for k,v in pairs(t) do print(k,v) end
1 1
2 0
3 2
4 3
> t = {[-1]=-1,[-2]=-2,[-3]=-3};
> for k,v in pairs(t) do print(k,v) end
-2 -2
-1 -1
-3 -3
> table.insert(t, -2, 0)
> for k,v in pairs(t) do print(k,v) end
-2 0
0 -1
-1 -2
-3 -3
> t = {};
> table.insert(t, 2^31, 1)
> for k,v in pairs(t) do print(k,v) end
-2147483648 1
----- Patch follows
101c101,119
< if (pos > e) e = pos; /* `grow' array if necessary */
---
> if (pos < 0) /* Determine how much we need to move */
> {
> i = pos;
> lua_rawgeti(L, 1, i);
> while (!lua_isnil(L, -1))
> {
> lua_pop(L, 1);
> lua_rawgeti(L, 1, ++i);
> };
> lua_pop(L, 1);
> /* Now i is the first nil index greater than pos */
> for (; i > pos; i--) { /* Move them up */
> lua_rawgeti(L, 1, i-1);
> lua_rawseti(L, 1, i); /* t[i] = t[i-1] */
> }
> break;
> }
> /* Non-negative, just move backwards */
> if (pos > e) e = pos; /* `grow' array if necessary */
``` | 876 | 3,197 | {"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} | 2.71875 | 3 | CC-MAIN-2021-49 | latest | en | 0.930805 |
https://gmatclub.com/forum/which-gmat-course-is-the-best-132541.html?sort_by_oldest=true | 1,490,294,375,000,000,000 | text/html | crawl-data/CC-MAIN-2017-13/segments/1490218187193.40/warc/CC-MAIN-20170322212947-00140-ip-10-233-31-227.ec2.internal.warc.gz | 806,932,538 | 57,549 | Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack
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# Which GMAT course is the best.
Author Message
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Joined: 01 Apr 2012
Posts: 26
Location: United States
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Kudos [?]: 13 [0], given: 18
Which GMAT course is the best. [#permalink]
### Show Tags
14 May 2012, 01:11
Hi All,
I am planning to buy a GMAT course but not sure which one is the best ( Cost effective as well as good learning wise). I searched and have found the following one
1. Manhattan
2. Knewton
3. Magoosh
4. e Gmat
5. Veritas
although option (1,2 and 5) are quite expensive.....i am willing to shell out that much if they help..
Regards,
Ankit
Magoosh Discount Codes Jamboree Discount Codes e-GMAT Discount Codes
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Re: Which GMAT course is the best. [#permalink]
### Show Tags
14 May 2012, 03:39
1
KUDOS
Have you seen our review page and thread:
http://gmatclub.com/reviews/
gmat-prep-course-reviews-discount-codes-78451.html
There are some discounts listed on 2nd link.
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Intern
Joined: 01 Apr 2012
Posts: 26
Location: United States
Concentration: Technology, Economics
GMAT Date: 05-13-2012
WE: Consulting (Computer Software)
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Kudos [?]: 13 [0], given: 18
Re: Which GMAT course is the best. [#permalink]
### Show Tags
14 May 2012, 03:57
Hey...thanks a lot buddy.........i also wanted some lastest reviews..thats why asked it here...but thanks a lot for pointing me to the correct thing.... (+1 Kudos to you)
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Re: Which GMAT course is the best. [#permalink]
### Show Tags
31 Dec 2013, 12:39
hi,ankitbansal85
Did you sign up for any of those tests? If yes what do you suggest,based on your experience?
I am also looking for taking some online course.
Thanks.
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Re: Which GMAT course is the best. [#permalink]
### Show Tags
09 Jan 2014, 14:00
Hi all,
Perhaps you should take a few weeks to "test out" the courses. Most probably offer some sort of free content. Economist GMAT Tutor offers a free 7-day trial. The free trial comes with a 1:1 strategy session with a tutor, so it's really worth checking out. If you're interested, check it out here: http://gmat.economist.com. You'll be able to get a solid feel for what the course can offer you.
Regards,
Elizabeth
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Re: Which GMAT course is the best. [#permalink]
### Show Tags
14 Jan 2014, 22:08
One nice thing about the GMAT is that, if the test makers are to be fair, the concepts they test become very predictable. Once you've developed a comfort with the foundational ideas, and completed some practice with a workable approach, the test becomes far less daunting.
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Re: Which GMAT course is the best. [#permalink]
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23 Nov 2014, 02:11
Optimus Prep has several great products for GMAT test takers and is the best rated company on gmatclub!
Our rates are always lower than the rates of competitors and we offer free online trial hours where you can meet your 99th percentile tutor for free to discuss details!
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# Which GMAT course is the best.
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Powered by phpBB © phpBB Group and phpBB SEO 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®. | 1,620 | 5,707 | {"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} | 2.640625 | 3 | CC-MAIN-2017-13 | longest | en | 0.853679 |
http://www.computerforums.org/forums/hardware/download-time-estimator-146745.html | 1,527,388,195,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794867977.85/warc/CC-MAIN-20180527004958-20180527024958-00094.warc.gz | 363,716,750 | 15,478 | 06-29-2006, 08:02 PM #2 Daemon Poster Join Date: Feb 2005 Posts: 1,099 Re: Download time estimator.. Most torrent clients have an Estimated Time Remaining... With math: 1,024 Kilobyte (KB) = 1 Megabyte (MB) You're getting 0.00390625MB/S so 0.00390625x=600 x=600/0.00390625 x=153600 seconds = 2560 minutes = 42.66 hours So in the end, Time Remaining Formula = ((B) / (A/1024)) / (3600) Where A is Kb/s and B is total MB remaining __________________ __________________ traffic in the skyy
06-29-2006, 08:05 PM #3 Golden Master Join Date: Oct 2005 Posts: 7,846 Re: Download time estimator.. I can tell you passed your exams! Thanks mate. The program does have an estimator, I have two hours left? Stupid thing, it's wrong for all of them, kinda sucks. Thanks again! __________________
06-29-2006, 08:11 PM #4 Daemon Poster Join Date: Feb 2005 Posts: 1,099 Re: Download time estimator.. Hahahah dangit, I got a C+ on my final in math this year :P If only they had asked for Filesize conversions and torrent ETR... Noooo instead we had to get trig. Silly school __________________ traffic in the skyy
06-29-2006, 08:28 PM #5 Golden Master Join Date: Oct 2005 Posts: 7,846 Re: Download time estimator.. Haha! Yeah, I just took my GCSE exam, awaiting my results - not getting my hopes up.. __________________ | 389 | 1,320 | {"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} | 2.609375 | 3 | CC-MAIN-2018-22 | latest | en | 0.785316 |
http://mathhelpforum.com/algebra/219810-vectors-print.html | 1,498,604,236,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128321938.75/warc/CC-MAIN-20170627221726-20170628001726-00381.warc.gz | 253,276,902 | 2,840 | # Vectors
Printable View
• Jun 12th 2013, 09:49 PM
Fratricide
Vectors
ORST is a parallelogram. U is the midpoint of RS and V is the midpoint of ST. Relative to
the origin O, r, s, t, u and v are the position vectors of R, S, T, U and V respectively.
(a) Express s in terms of r and t.
(b) Express v in terms of s and t.
(c) Hence or otherwise show that 4 (u + v) = 3 (r + s + t)
I got (a) alright, but (b) and (c) are perplexing. I know that the answer for (b) is v = (1/2)(s + t), but I'm struggling to figure out how to get there.
Thanks in advance.
• Jun 12th 2013, 10:18 PM
Prove It
Re: Vectors
Let's say \displaystyle \begin{align*} S = (S_x , S_y ) \end{align*} and \displaystyle \begin{align*} T = (T_x , T_y ) \end{align*}. Since V is the midpoint, that means
\displaystyle \begin{align*} V &= \left( \frac{ S_x + T_x }{ 2 } , \frac{ S_y + T_y }{ 2 } \right) \\ &= \frac{1}{2} \left( S_x + T_x , S_y + T_y \right) \\ &= \frac{1}{2} \left[ \left( S_x , S_y \right) + \left( T_x , T_y \right) \right] \\ &= \frac{1}{2} \left( S + T \right) \end{align*} | 404 | 1,063 | {"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": 3, "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} | 4.09375 | 4 | CC-MAIN-2017-26 | longest | en | 0.756687 |
http://sportdocbox.com/Olympics/76344733-Australian-teams-over-time.html | 1,544,858,780,000,000,000 | text/html | crawl-data/CC-MAIN-2018-51/segments/1544376826800.31/warc/CC-MAIN-20181215061532-20181215083532-00270.warc.gz | 282,670,704 | 25,791 | # AUSTRALIAN TEAMS OVER TIME
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1 LEVEL Upper primary AUSTRALIAN TEAMS OVER TIME DESCRIPTION In these activities, students learn about the number of athletes who have represented Australia in the Olympics, with a focus on the previous London games in 1908 and They analyse data from a table, compare the number of athletes over the years, discuss the use of charts and graphs as a way to represent data and transfer data from a table to a graph. These cross-curriculum activities contribute to the achievement of the following: Studies of society and environment Identifies the types of data and sources required by the task and decides how they will be used to gain information Translates information from text to graphical form English Interprets and discusses some relationships between ideas, information and events in visual texts for general viewing. Mathematics Interprets tables of data in a table, asking and answering questions about the information. SUGGESTED TIME approximately minutes for each activity (this may be customised accordingly) WHAT YOU NEED class copies of Student handout examples of charts and graphs from newspapers etc Internet access to Australian Olympic Team website w ww.olympics.com.au (locate photos of Australian Olympians) Internet access to John Treloar s interview at
2 ACTIVITIES The following activities may be completed independently or combined as part of a more comprehensive learning sequence, lesson or educational program. Please refer to your own state or territory syllabus for more explicit guidelines. Australian Olympic Team 1. Ask the class to guess how many people go to your school. Expand the discussion to estimate the number of student who are part of sub-groups within the school, such as the number of students who play handball or the number of students who represent the school in competition with other schools. 2. Discuss previous Olympic games and ask students to guess how many athletes were sent to represent Australia. Explain that the size of the Australian Olympic Team has increased over the years. Mention the two previous London games in 1908 and 1948 when 27 and 77 Olympians represented Australia (respectively). 3. Watch John Treloar s interview Explain that John Treloar was a member of the Australian Olympic Team in London in Discuss the sports and events in which he competed as well as his life achievements. 4. Explain that in Sydney 2000, the size of the Australian Olympic Team was over 600 athletes. Brainstorm guesses related to the size of the Australian Olympic Team in London 2012 as outlined in the following sample: Twenty five Three hundred seven size of the Australian Olympic Team London 2012 Thirty five
3 Distribute student handout. Discuss the data in the graph with students and ask them to complete the questions. Graphing data 1. Review the size of the Australian Olympic Team from the previous activity (if needed), pointing out the numbers in the table. Ask the class to think about numbers, data and information they might have seen in their everyday life. Introduce the basic idea of using a chart or a graph to represent numbers and data. Expand the discussion by using an example from a newspaper or television news report featuring populations or other large numbers. Brainstorm the features of a chart or graph as outlined in the following sample: little pictures squares grid horizontal axis title Graph features labels numbers at the side years scale numbers Distribute student handout. Discuss each of the features of the graph, explaining the importance of each. Work with the class to finish labelling the graph by adding numbers to the horizontal axis (year) and vertical axis (number of athletes) of the graph. Analyse the data in the table. Work with the class to translate the data to the graph, using a small cross for each point. Join the points together with a line and discuss. Use art materials to add colour to the graph.
4 REFLECT ON a.s.p.i.r.e. VALUES Discuss how the a.s.p.i.r.e. values relate to other contexts and situations, such as various Olympic sporting situations. How and why do you think the Australian Olympic Team might have come up with this particular list of values? What are some emotions felt by the Australian Olympic Team when they see the final list of the London 2012 team? EXPLORE A LITTLE FURTHER Draw some pictures of the Australian Olympic Team over the years and display on the classroom wall. Write a short play where the characters travel back through time as members of the Australian Olympic Team in Athens Explore the values that might be the same and those that might be different. Collect photos and illustrations of people involved in Olympic games over the years. Research the methods used to collect data in Australia and in other parts of the world. Explore more about previous Olympic games at
5 STUDENT HANDOUT Australian Olympic Team - table Games Australian Team Size Athens Paris St Louis London Stockholm Antwerp Paris Amsterdam Los Angeles Berlin London Helsinki Melbourne Rome Tokyo Mexico City Munich Montreal Moscow Los Angeles Seoul Barcelona Atlanta Sydney Athens Beijing 2008 London 2012 Questions 1. What was the size of the Australian team at London 1948? 2. What was the size of the Australian team at Beijing 2008? 3. What was the size of the Australian team at Sydney 2000? 4. In which year was the Australian team the largest? 5. In which year was the Australian team the smallest?
6 STUDENT HANDOUT Australian Olympic Team - graph London 2012 Athens Year Number in team
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A table was measure 16 times. The average of these measurements was 12.6 feet, with a standard deviation of 3. We can figure that there is a 95% chance that the length of the table is between... 12' and 13' 10.6' and 14' 11.6' and 13.6' 11.1' and14.1' 10.9' and 14'
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Subtract from both sides of the equation.
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Divide each term in by .
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Move the negative in front of the fraction.
Factor out of .
Factor out of .
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# Responding to the publics fascination with-and sometimes
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Director
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Responding to the publics fascination with-and sometimes [#permalink]
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28 Apr 2008, 12:41
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Responding to the public’s fascination with-and sometimes
undue alarm over-possible threats from asteroids, a scale
developed by astronomers rates the likelihood that a particular
asteroid or comet may
collide with Earth.
A. a scale developed by astronomers rates the likelihood
that a particular asteroid or comet may
B. a scale that astronomers have developed rates how
likely it is for a particular asteroid or comet to
C. astronomers have developed a scale to rate how likely
a particular asteroid or comet will be to
D. astronomers have developed a scale for rating the
likelihood that a particular asteroid or comet will
E. astronomers have developed a scale that rates the
likelihood of a particular asteroid or comet that may.
If you have any questions
New!
Manager
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### Show Tags
28 Apr 2008, 13:52
E
==>> "Responding to the public’s fascination with-and sometimes
undue alarm over-possible threats from asteroids" is modifier so next word after "," should be astronomer.
==> final clause has to say "may" and not "will" as the comet strike is only a possibity not a guarentee.
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### Show Tags
28 Apr 2008, 15:03
Sentence has modifier, passive voice and certain/uncertain change issues
A. a scale developed by astronomers rates the likelihood that a particular asteroid or comet may [Modifier issue – need to have the astronomers – eliminate it]
B. a scale that astronomers have developed rates how likely it is for a particular asteroid or comet to [Modifier issue – need to have the astronomers – eliminate it]
C. astronomers have developed a scale to rate how likely a particular asteroid or comet will be to [changes the sentence tone from uncertain to certain – may/will – eliminate it]
D. astronomers have developed a scale for rating the likelihood that a particular asteroid or comet will [changes the sentence tone from uncertain to certain – may/will – may/will – eliminate it]
E. astronomers have developed a scale that rates the likelihood of a particular asteroid or comet that may. [Hold it]
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28 Apr 2008, 15:12
I was originally going to answer D but after reading hanumayamma's explaination E makes sense now.
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28 Apr 2008, 16:09
Modifier question - It is the astronomers that are responding so A and B can be eliminated.
C & D use 'will' which means its guranteed to happen, it may or may not happen. So answer is 'E'
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### Show Tags
28 Apr 2008, 16:09
1
KUDOS
Straight D.
AB have modifier issues, CE change the meaning of the original sentence.
saravalli wrote:
Responding to the public’s fascination with-and sometimes undue alarm over-possible threats from asteroids, a scale developed by astronomers rates the likelihood that a particular asteroid or comet may collide with Earth.
A. a scale developed by astronomers rates the likelihood that a particular asteroid or comet may
B. a scale that astronomers have developed rates how likely it is for a particular asteroid or comet to
C. astronomers have developed a scale to rate how likely a particular asteroid or comet will be to
D. astronomers have developed a scale for rating the likelihood that a particular asteroid or comet will
E. astronomers have developed a scale that rates the likelihood of a particular asteroid or comet that may.
Last edited by bsd_lover on 28 Apr 2008, 16:13, edited 1 time in total.
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### Show Tags
28 Apr 2008, 16:13
D.
A and B - wrong modifier
C - "will be to" is not correct usage
E - "likelihood of" requires something on the lines of colliding but the question has collide. So eliminate E as well.
That leaves D.
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28 Apr 2008, 17:33
guys lets discuss more. Please eliminate C with concrete reasons.
likelihood and may are a little redundant in E. But whats wrong in saying
likelihood of comet will hit me is very less ? (..something along those lines).
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28 Apr 2008, 19:19
saravalli wrote:
Responding to the public’s fascination with-and sometimes
undue alarm over-possible threats from asteroids, a scale
developed by astronomers rates the likelihood that a particular
asteroid or comet may
collide with Earth.
A. a scale developed by astronomers rates the likelihood
that a particular asteroid or comet may
B. a scale that astronomers have developed rates how
likely it is for a particular asteroid or comet to
C. astronomers have developed a scale to rate how likely
a particular asteroid or comet will be to
D. astronomers have developed a scale for rating the
likelihood that a particular asteroid or comet will
E. astronomers have developed a scale that rates the
likelihood of a particular asteroid or comet that may.
I'm with the D boys...
A and B are obvious elimination because "a scale" cannot "response to public fascination". It is the astronomers. Incorrect comparison in both A and B.
In C, "will be to" is super awkward.
Between D and E, hanumayamma mentioned that D changes the meaning of the sentence from uncertain to certain, and I disagree. From many GMAT problems I did, I feel that the intended meaning wins over change in meaning (someone please and I mean please confirm this!!!).
This problem, however, is about the usage of "likelihood". You determine that the likelihood of something "will", not "may".
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28 Apr 2008, 19:24
I think it should be E : The idiom is likelihood of . Likelihood that sounds incorrect. Whats the OA
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30 Apr 2008, 05:34
The use of "may" in E is preferable to the use of "will" (which connotes certainty). Hence E.
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30 Apr 2008, 10:28
guys OA says C.
Can anyone prove / disprove ?
Thanks
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30 Apr 2008, 13:04
Wow, I would have said E, but not C at all....
Where is this question from?
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30 Apr 2008, 13:16
E for me. Seriously cannot take C , it is way too ugly..
astronomers have developed a scale to rate how likely
a particular asteroid or comet will be to -> Will be to is awkward.
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30 Apr 2008, 14:20
i actually picked C. In D , I didnt like the use of the phrase 'for rating the likelihood' ... cant quite explain it, it just didnt sound right
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02 May 2008, 19:38
I Picked D over E for the same reason that Likelihood and may are redundant...
you always cannot eliminate a sentence because it has will...
you don't say - what is the likelihood that you may go to school
I still dont see how C can be the answer.
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Re: Responding to the publics fascination with-and sometimes [#permalink]
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Analog and digital clocks are also of similar meaning. Your clock hung on a wall of the room or in your wrist watch with Hour hand, Minute hand, and Second hand fall in continuous variables and are the analog clocks. While the time in your mobile phone generally used or some blink watches which gives time in the form of 12:00:00 fall under digital type.
Basic Structure of a Digital Computer
The von Neumann architecture, which is also known as the von Neumann model and Princeton architecture, is a computer architecture based on that described in 1945 by the mathematician and physicist John von Neumann. This describes a design architecture for an electronic digital computer with parts consisting of a processing unit containing an arithmetic logic unit and processor registers; a control unit containing an instruction register and program counter; a memory to store both data and instructions; external mass storage; and input and output mechanisms. The key idea of the Von Neumann architecture is the stored program concept. A stored-program digital computer is one that keeps its program instructions, as well as its data, in read-write, random-access memory (RAM). Stored-program computers were an advancement over the program-controlled computers of the 1940s.
Figure: Block Diagram of Computer
The main components of a computer are Input unit (IU), Central Processing unit (CPU) and Output unit (OU). The information like data, programs etc. are passed to the computer through input devices. The keyboard, mouse, floppy disk, CD, DVD, joystick etc. are certain input devices. The output device is to get information from a computer after processing. VDU (Visual Display Unit), Printer, Floppy disk, CD etc are output devices. The brain of a computer is the CPU. It has three components- Memory unit, Control unit and Arithmetic and Logical unit (ALU).
The memory unit also called as the storage device is to store information. Two types of memory are there on a computer. They are RAM (random access memory) and ROM (read-only memory). When a program is called, it is loaded and processed in RAM. When the computer is switched off, whatever stored in RAM will be deleted. So it is a temporary memory. Whereas ROM is a permanent memory, where data, program etc are stored for future use. Inside a computer, there is a storage device called Hard disk, where data are stored and can be accessed at any time.
The control unit is for controlling the execution and interpreting of instructions stored in the memory. ALU is the unit where the arithmetic and logical operations are performed. The information to a computer is transformed into groups of binary digits, called bit. The length of bit varies from computer to computer, from 8 to 64. A group of 8 bits is called a Byte and a byte generally represents one alphanumeric ( Alphabets and Numerals) character. The physical components of a computer are called hardware. But for the machine to work it requires certain programs ( A set of instructions is called a program ). They are called software. There are two types of software, System software, and Application software. System software includes Operating systems, Utility programs, and Language processors.
Operating System:
The set of instructions which resides in the computer and governs the system are called operating systems, without which the machine will never function. They are the medium of communication between a computer and the user. DOS, Windows, Linux, Unix, android system etc are Operating Systems.
Utility Programs:
These programs are developed by the manufacturer for the users to do various tasks. Word, Excel, Photoshop, Paint etc are some of them.
Programming Language:
1. Low-level Language:
Low-level languages are machine level and assembly level language. In machine level language computer only understand digital numbers i.e. in the form of 0 and 1. So, the instruction given to the computer is in the form binary digit, which is difficult to implement instruction in binary code. This type of program is not portable, difficult to maintain and also error-prone.
The assembly language is, on the other hand, a modified version of machine level language. Where instructions are given in English like the word as ADD, SUM, MOV etc. It is easy to write and understand but it is hard for the computer to understand. So the translator used here is assembler to translate into machine level. Although language is bit easier, the programmer has to know low-level details related to low-level language. In the assembly level language, the data are stored in the computer register, which varies for a different computer. Hence it is not portable.
2. High-level Language
These languages are machine independent, means it is portable. The language in this category is Pascal, Cobol, Fortran etc. High-level languages are not understood by the machine. So it needs to translate by the translator into machine level. A translator is a software which is used to translate high-level language as well as low-level language into machine level language. | 1,287 | 6,388 | {"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} | 2.515625 | 3 | CC-MAIN-2023-06 | latest | en | 0.932132 |
https://discuss.leetcode.com/topic/111701/reverse-integer-soln-in-python3 | 1,526,866,620,000,000,000 | text/html | crawl-data/CC-MAIN-2018-22/segments/1526794863901.24/warc/CC-MAIN-20180521004325-20180521024325-00005.warc.gz | 547,715,646 | 8,097 | # Reverse Integer Soln in Python3
• ``````class Solution:
def reverse(self, x):
"""
:type x: int
:rtype: int
"""
returned_val = 0
if x >= 0:
digits = [int(d) for d in str(x)]
reverse = list(reversed(digits))
returned_val = int(''.join(str(alpha) for alpha in reverse))
if returned_val > 2147483647:
return 0
else:
return returned_val
else:
unassigned = abs(x)
digits = [int(d) for d in str(unassigned)]
reverse = list(reversed(digits))
returned_val = -1*(int(''.join(str(alpha) for alpha in reverse)))
if returned_val < -2147483647:
return 0
else:
return returned_val
``````
Looks like your connection to LeetCode Discuss was lost, please wait while we try to reconnect. | 190 | 672 | {"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} | 2.9375 | 3 | CC-MAIN-2018-22 | latest | en | 0.59776 |
https://stacks.math.columbia.edu/tag/0H2Q | 1,713,506,513,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817289.27/warc/CC-MAIN-20240419043820-20240419073820-00646.warc.gz | 482,649,129 | 6,069 | Lemma 37.81.2. Let $X$ be a scheme. If the canonical morphism $X \to \mathop{\mathrm{Spec}}(\Gamma (X, \mathcal{O}_ X))$ of Schemes, Lemma 26.6.4 has a retraction, then $X$ is an affine scheme.
Proof. Write $S = \mathop{\mathrm{Spec}}(\Gamma (X, \mathcal{O}_ X))$ and $f : X \to S$ the morphism given in the lemma. Let $s : S \to X$ be a retraction; so $\text{id}_ X = sf$. Then $f s f = \text{id}_ S f$. Since $f$ induces an isomorphism $\Gamma (S, \mathcal{O}_ S) \to \Gamma (X, \mathcal{O}_ X)$ this means that $fs$ and $\text{id}_ S$ induce the same map on $\Gamma (S, \mathcal{O}_ S)$. Whence $f s = \text{id}_ S$ as $S$ is affine. Hence $f$ is an isomorphism and $X$ is an affine scheme, as was to be shown. $\square$
In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the toolbar). | 313 | 921 | {"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": 2, "x-ck12": 0, "texerror": 0} | 2.84375 | 3 | CC-MAIN-2024-18 | latest | en | 0.744191 |
https://math.stackexchange.com/questions/2715908/laplace-transform-of-heat-equation-in-spherical-coordinates | 1,558,806,481,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232258147.95/warc/CC-MAIN-20190525164959-20190525190959-00193.warc.gz | 540,858,406 | 30,977 | # Laplace transform of heat equation in spherical coordinates
Consider the PDE $$\frac{\partial u}{\partial t}=\frac{D}{r}\frac{\partial ^2}{\partial r^2}(ru),$$ where $D>0$ and we have the auxiliary conditions \begin{align*} u(r,0)&=0, \\ u(a,0)&=u_0.\end{align*}
I want to solve this problem using Laplace transforms. Defining the Laplace transform of a function $f:(0,\infty) \to \mathbb{R}$ as $$F(p)=\int_0^{\infty} e^{-pt}f(t) \, dt,$$ it follows that the PDE becomes $$pU(r,p)=\frac{D}{r}\frac{\partial ^2}{\partial r^2}(rU(r,p)).$$
After applying the boundary condition and requiring that the Laplace transform be bounded, I find that $$U(r,p)=\frac{au_0}{pr}e^{(a-r)\sqrt{p/D}}.$$
However, I'm told that the correct answer should be $$U(r,p)=\frac{au_0}{pr}\frac{\sinh\left(r\sqrt{\frac{p}{D}}\right)}{\sinh\left(a\sqrt{\frac{p}{D}}\right)}.$$
• Where does $k$ come from? – Kyle Mar 31 '18 at 15:57
• @Kyle Sorry, it was supposed to be $D$, not $k$. I've changed this now. – Si.0788 Mar 31 '18 at 16:29 | 363 | 1,016 | {"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} | 3.234375 | 3 | CC-MAIN-2019-22 | longest | en | 0.798454 |
https://www.lotterypost.com/thread/249588/143 | 1,480,939,234,000,000,000 | text/html | crawl-data/CC-MAIN-2016-50/segments/1480698541692.55/warc/CC-MAIN-20161202170901-00042-ip-10-31-129-80.ec2.internal.warc.gz | 963,385,859 | 16,388 | Welcome Guest
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# Sherita Breaking Down Ga Cash3!
Topic closed. 2516 replies. Last post 3 years ago by Sherita.
Page 143 of 168
Vtracs is My Game!
Georgia
United States
Member #3617
February 6, 2004
7416 Posts
Offline
Posted: November 2, 2013, 7:43 pm - IP Logged
How did you find those? You did a search in the Ga Lottery?
No, my workout for the past few draws...
Congrats To All Winners and Posters!
We are all in it to win! My Pet numbers 103,724,152,397,189,118,205.
Ga Lottery Player!
Hot-Due-Cold. Short Sums/Last Digit Sum. Pairs. Vtracs. Vtrac Pairs. SUM OF VTRACS CHART.
Don't forget to FLIP 6/9 in all WORKOUTS! 66=99=69. Vtracs Code sheets available....
gay,ga
United States
Member #68810
December 30, 2008
5942 Posts
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Posted: November 2, 2013, 7:46 pm - IP Logged
I just did mine for tomorrow mid and the single digits the way I do it, show a 3,9,0.........bring that 301 Deb.........
Does it show in yours?
Vtracs is My Game!
Georgia
United States
Member #3617
February 6, 2004
7416 Posts
Offline
Posted: November 2, 2013, 7:47 pm - IP Logged
I just did mine for tomorrow mid and the single digits the way I do it, show a 3,9,0.........bring that 301 Deb.........
Does it show in yours?
Yes...
Congrats To All Winners and Posters!
We are all in it to win! My Pet numbers 103,724,152,397,189,118,205.
Ga Lottery Player!
Hot-Due-Cold. Short Sums/Last Digit Sum. Pairs. Vtracs. Vtrac Pairs. SUM OF VTRACS CHART.
Don't forget to FLIP 6/9 in all WORKOUTS! 66=99=69. Vtracs Code sheets available....
gay,ga
United States
Member #68810
December 30, 2008
5942 Posts
Offline
Posted: November 2, 2013, 7:48 pm - IP Logged
Coule be we do the same method, I use that Laverne Maloney one
Vtracs is My Game!
Georgia
United States
Member #3617
February 6, 2004
7416 Posts
Offline
Posted: November 2, 2013, 7:50 pm - IP Logged
Coule be we do the same method, I use that Laverne Maloney one
Not familiar with that one...I use Vtracs...
Congrats To All Winners and Posters!
We are all in it to win! My Pet numbers 103,724,152,397,189,118,205.
Ga Lottery Player!
Hot-Due-Cold. Short Sums/Last Digit Sum. Pairs. Vtracs. Vtrac Pairs. SUM OF VTRACS CHART.
Don't forget to FLIP 6/9 in all WORKOUTS! 66=99=69. Vtracs Code sheets available....
Vtracs is My Game!
Georgia
United States
Member #3617
February 6, 2004
7416 Posts
Offline
Posted: November 2, 2013, 7:52 pm - IP Logged
910
912,917,913,918
902,907,903,908
102,107,103,108
462,467,463,468
452,457,453,458
652,657,653,658
991,911,990,900,110,100
446,466,445,455,566,556
Congrats To All Winners and Posters!
We are all in it to win! My Pet numbers 103,724,152,397,189,118,205.
Ga Lottery Player!
Hot-Due-Cold. Short Sums/Last Digit Sum. Pairs. Vtracs. Vtrac Pairs. SUM OF VTRACS CHART.
Don't forget to FLIP 6/9 in all WORKOUTS! 66=99=69. Vtracs Code sheets available....
gay,ga
United States
Member #68810
December 30, 2008
5942 Posts
Offline
Posted: November 2, 2013, 7:53 pm - IP Logged
I just can't grasp how they work.....LOL
No need to explain, I will just view what you post.......
Vtracs is My Game!
Georgia
United States
Member #3617
February 6, 2004
7416 Posts
Offline
Posted: November 2, 2013, 7:54 pm - IP Logged
Mirror
279,271,270
274,276,275
389,381,380
384,386,385
Congrats To All Winners and Posters!
We are all in it to win! My Pet numbers 103,724,152,397,189,118,205.
Ga Lottery Player!
Hot-Due-Cold. Short Sums/Last Digit Sum. Pairs. Vtracs. Vtrac Pairs. SUM OF VTRACS CHART.
Don't forget to FLIP 6/9 in all WORKOUTS! 66=99=69. Vtracs Code sheets available....
Vtracs is My Game!
Georgia
United States
Member #3617
February 6, 2004
7416 Posts
Offline
Posted: November 2, 2013, 7:56 pm - IP Logged
Vtracs..
v534,v532,v531,v542,v541,v234,v231,v241,v134
v553,v533,v554,v544,v223,v233,v224,v244,v113,v133,v114,v144
Congrats To All Winners and Posters!
We are all in it to win! My Pet numbers 103,724,152,397,189,118,205.
Ga Lottery Player!
Hot-Due-Cold. Short Sums/Last Digit Sum. Pairs. Vtracs. Vtrac Pairs. SUM OF VTRACS CHART.
Don't forget to FLIP 6/9 in all WORKOUTS! 66=99=69. Vtracs Code sheets available....
Vtracs is My Game!
Georgia
United States
Member #3617
February 6, 2004
7416 Posts
Offline
Posted: November 2, 2013, 7:59 pm - IP Logged
Watch out for 197 Combo Ga!
Congrats To All Winners and Posters!
We are all in it to win! My Pet numbers 103,724,152,397,189,118,205.
Ga Lottery Player!
Hot-Due-Cold. Short Sums/Last Digit Sum. Pairs. Vtracs. Vtrac Pairs. SUM OF VTRACS CHART.
Don't forget to FLIP 6/9 in all WORKOUTS! 66=99=69. Vtracs Code sheets available....
gay,ga
United States
Member #68810
December 30, 2008
5942 Posts
Offline
Posted: November 2, 2013, 8:01 pm - IP Logged
Watch out for 197 Combo Ga!
Thats for eve and mid?
Vtracs is My Game!
Georgia
United States
Member #3617
February 6, 2004
7416 Posts
Offline
Posted: November 2, 2013, 8:04 pm - IP Logged
Thats for eve and mid?
Yes and it is a Combo not Str!
Congrats To All Winners and Posters!
We are all in it to win! My Pet numbers 103,724,152,397,189,118,205.
Ga Lottery Player!
Hot-Due-Cold. Short Sums/Last Digit Sum. Pairs. Vtracs. Vtrac Pairs. SUM OF VTRACS CHART.
Don't forget to FLIP 6/9 in all WORKOUTS! 66=99=69. Vtracs Code sheets available....
gay,ga
United States
Member #68810
December 30, 2008
5942 Posts
Offline
Posted: November 2, 2013, 8:05 pm - IP Logged
Yes and it is a Combo not Str!
Ok, thanks, will box it tomorrow
BEVERELY HILLS
United States
Member #88631
March 20, 2010
3369 Posts
Offline
Posted: November 3, 2013, 2:16 am - IP Logged
Watch out for 197 Combo Ga!
Thanks for the tip.. I got 397 as a qp for the eve draw!!!
Scared money don't make no money.
Vtracs is My Game!
Georgia
United States
Member #3617
February 6, 2004
7416 Posts
Offline
Posted: November 3, 2013, 10:34 am - IP Logged
Thanks for the tip.. I got 397 as a qp for the eve draw!!!
My Pet#...I am on it!
Congrats To All Winners and Posters!
We are all in it to win! My Pet numbers 103,724,152,397,189,118,205.
Ga Lottery Player!
Hot-Due-Cold. Short Sums/Last Digit Sum. Pairs. Vtracs. Vtrac Pairs. SUM OF VTRACS CHART.
Don't forget to FLIP 6/9 in all WORKOUTS! 66=99=69. Vtracs Code sheets available....
Page 143 of 168 | 2,246 | 6,387 | {"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} | 2.578125 | 3 | CC-MAIN-2016-50 | latest | en | 0.78893 |
white579.sibnoghre.com | 1,627,365,069,000,000,000 | text/html | crawl-data/CC-MAIN-2021-31/segments/1627046152236.64/warc/CC-MAIN-20210727041254-20210727071254-00061.warc.gz | 621,479,235 | 24,397 | ## Roulette Table: Learning the Game
Posted on July 16, 2021
# Roulette Table: Learning the Game
A Roulette table includes the Roulette wheel (often called a 인터넷 바카라 ‘tenne’ in British English), numerous roulette balls, a place for the playing ball to spin around on, and finally a thin circular playing area between your balls. The Roulette table is generally an arrangement of seven roulette wheels placed in a square circular shape on a solid wooden table with a central hole. On every roulette wheel there are two red balls and a metal revolving plate that rotate on a vertical axis on the table. If you place your money in the playing area, you can spin the wheel to get the ball and spin it round the circular playing area, hoping that you’ll get five or more red balls in the round. If you do, then you win the overall game!
In the earlier days, a Roulette table had little else than those three things mentioned previously. The only other furniture piece included was a wheel and a little counter that counting the amount of red balls in the spin. That is clearly a large amount of obstacles to overcome if you are attempting to win the game! Just how did this innovative approach to gambling become popular? And why has it fallen out of favour?
In 1811, an Englishman by the name of Benjamin Franklin invented the machine of laying out the roulette wheels. Franklin found that by placing a bet on lots, rather than on the specific wheel he could improve his likelihood of winning. Thus, instead of laying out seven separate coins for every spin, he put the bet on whether the number was a prime number or a double zero. The odds of picking prime numbers were great, but Franklin’s system gave him the extra advantage of having the ability to select a low-odds bet.
Roulette began in England, where a game called fox racing was in fact invented from the efforts of an individual zero wheel. This game was based around the same idea because the roulette table: by betting on the number or a double zero, a new player could then hope to win by selecting a single number out of a hat. While it was a slow game, it became hugely popular in Europe, and soon after, in the us. A speedier version originated by the Italians, which were referred to as the ‘hot wheel’, and the word ‘wheels’ itself originated in the overall game of horse racing.
When it first began in the Americas, the overall game took on a single names as its European counterparts: these were called simply ‘racing’, and the wheel itself was called a ‘pilot’. Because the popularity of this new gambling took off in the early 1800s, however, it was quickly replaced with the more familiarized term ‘wagering’. The reason for this is clear to see: in the us, gambling was closely tied to the economic revolution sweeping the nation. Gambling, therefore, became connected with prosperity, and the wheel was often used as symbolic of luck – at least until the First World War.
So as to set the odds in the game, the casino would make use of the basic setup of the roulette table, and just how that it worked. Generally in most casinos nowadays, the wheel may be the central focus of the betting layout. It sits directly under a long counter, where players can place bets. That is also where in fact the money for the bets will undoubtedly be placed, and the names of the bettors and the ones who are placing them is seen on printed slips under the counters. Across the the surface of the wheel is the name of the home, and the quantity of each bet shown addititionally there is printed.
On some Roulette tables, the names of the players are written across the top of the wheel, while on others there exists a small board above the wheel, with numbers on it. By flipping of these small pieces, you will get a closer consider the numbers on the wheel – and since it is now easier to browse the layout, the odds are usually better. The more numbers that are turned over on the wheel, the higher the chances of winning, since there is a specific number of spins that is guaranteed to come up. However, in a few casinos, this is simply not done, because they believe it distracts players from the true count – which can actually work in the house’s favor.
When playing Roulette, it is necessary that you understand the various ways that the wheel is used. The first method is known as the traditional wheel. This involves setting up the numbers on the wheel – from one to twenty-two, inclusive. This is where you make the bets and win money if they come up. The downside to the method is that because you have no idea which number the wheel will turn, you may end up choosing a number that does not really have any benefits for you personally – hence losing money. The second type of Roulette table used in casinos is called the croupier wheel – which is very different than the traditional wheel, where you lay down the numbers.
## A Look at ONE OF THE MOST Popular Table Games
Posted on July 16, 2021
# A Look at ONE OF THE MOST Popular Table Games
Table games will always be a part of casino entertainment. They are an important section of gambling, whether in a offline casino, or online. They are also more popular at card table games.
Blackjack is probably the hottest card game played at a casino. It has been the game of preference at the high limit tables for years, where in fact the “buy-in” is higher. Although it may not be as exciting as other games like craps or roulette, there is absolutely no doubt that it’s rather a very lucrative activity for the right player. Blackjack is played at more than two-thirds of all U.S. casinos.
Another type of game that is popular for the most part U.S. casinos are the games of the wheel. They’re called variants because players use several set of numbers and place their bets in different ways. For example, you can find four suits of cards, the full total number of cards (not counting the King) will always follow exactly the same pattern, irrespective of which card is raised or lowered. Raising and lowering bets on the four-suit deck is done differently, depending on the placement of the bets. Most casinos have added blackjack and keno to the varieties offered; they’re extremely popular games.
점보 카지노 There are three other styles of games that are regularly played. The first of the is stud Hi. This is another variant of the overall game of the wheel, but rather of using the numbers on the card, the players rotate them around on a chalkboard. Before the game will start, each player chooses one card to be the starting card. Then, the dealer draws five cards and places them face down on the board. Players take turns rotating the cards, until a winner is available.
Another popular variant is poker games. Poker is really a form of gambling, but its main goal is to win at the casino table. Therefore many players use variations of poker as a way to win. For example, one player may choose a suit, say spades, and the rest of the table may rotate that suit around the table.
One particular version of poker is stud Hi, where players place bets in line with the position of the card faces up for grabs. That means, a stud could be either low or high, making the decision of bet difficult. If stud Hi is played right, it is possible to increase one’s winnings by winning many of these bets. On the other hand, if one misses a bet, the result is normally negative.
Another type of table game is pai gow poker, played on a table with four marked chairs. Four cards are placed face up at the table, and the ball player who marks the cards first reaches take off three of his own cards – a high card and two low cards. Whoever gets all the high cards first, wins. This is one of the oldest forms of gambling, and it is very popular in Thailand. A similar type of game, pai gow ree, is used two decks of fifty cards, and the dealer sits at a table with five marked chairs facing one another.
Among the best known table games, and possibly the most popular, are craps. Craps is played on a table with three chairs and three small piles of cards, one for every person. When all the players have already been dealt their cards, and when the time for betting is here, the group collectively decides what they want to do, which is to pass a bet. Whoever gets the highest total points once the time for the pass bet has ended wins. However, this type of craps is usually only used in casino-style board games, since it is difficult to hold a large number of people’s hands at once.
## Do I have to Stop Gambling?
Posted on July 16, 2021
# Do I have to Stop Gambling?
What’s gambling? Simply put, it is the act of placing a bet on an unpredictable event with the intention of winning something valuable. Gambling is frequently misunderstood because it is often confused with sports betting or even computer gambling. Gambling as it relates to online gambling, though, is completely different from all other types of gambling.
Many things can be considered gambling, however, none are as unfortunate as compulsive gambling. Compulsive gambling is whenever a gambler feels he/she must gamble so as to cope with symptoms such as anxiety, stress, depression, frustration, or even loss of money. Gambling can be characterized by over-the-top betting amounts and repeated gambling activities regardless of having little to stake in the overall game. Many gamblers will repeatedly gamble despite feeling they are not in control of their gambling actions. Gambling addicts are not only physically addicted, they are also dependent on having a thrill with compulsive gambling.
The initial step for gamblers to take when confronted with gambling problems is to admit that they have a problem. Many gamblers try to hide their addiction by pretending to have little to no involvement with the overall game. This is not a productive way to cope with a problem. A true statement that is honest and truthful is very important in helping to stop gambling problems.
After admitting you have gambling problems, the next step is to seek specialized help through anther approach to treatment such as counseling. If you don’t have to gamble for financial purposes, you may wish to avoid joining card rooms. Even though actual betting may not be as “hands on” as may be the case generally in most card rooms, the psychological aspect of gambling continues to be very powerful. Gamblers that leave the comfort of these homes to partake in legal gambling activities are more likely to become hooked than individuals who usually do not place themselves at such risk.
There are several things to consider when it comes to legally betting on any type of legal gambling activity. The vital thing is location. Yes, there are casinos all over the United States, in states which range from Hawaii to Tennessee. However, nearly all card rooms and internet gaming sites can be found in New York, New Jersey, Florida, or Illinois. Therefore, in the event that you live in one of these brilliant “Gambling Capital” states, it can be difficult to start gambling without breaking regulations. Legally, gambling in the United States is strictly prohibited in any state where gambling is prohibited by state law.
Another essential aspect to consider may be the choice. Do you enjoy playing blackjack or roulette? Do you want to try your luck at slot machines? If you enjoy playing one particular type of gambling game, you should not be concerned about whether it is legal in your unique state. All you need to accomplish is find a site where one can choose to gamble and choose where and how often to gamble.
However, there are several other things that are illegal in every fifty states, whether or not they’re considered legalized gambling. For example, gambling through lottery tickets and instant lotteries is against most state and county laws. Although a local ordinance might permit lottery tickets for certain designated purposes, doing so via an online site may be against local laws as well. In this case, you’ll still need a valid license to use the lottery in your town.
In conclusion, while there are many examples of why many gamblers elect to gamble, it’s important to remember that gambling is really a game of chance. So that you can win, a gambler must depend on their very own skill and knowledge more than anything else. Although there are a lot of examples of people winning large sums of money through online gambling, the reality is that just a few lucky gamblers win consistently. Much like many problem gamblers, it is almost always best not to take a gamble of any kind unless you have the means to afford to lose any longer than a little.
## Slots With Progressive Machines – Are They Really WORTHWHILE?
Posted on July 16, 2021
# Slots With Progressive Machines – Are They Really WORTHWHILE?
A slot machine, called also variously, the plug-in slot, puffer fish, slots, fruit machines, slots or poker machines, is a mechanical gambling device that generates a casino game of luck because of its users. A slot machine is a mechanism that generates random results when a lever is pulled. Slots are mechanical devices that imitate other objects such as for example coin drops or balls dropped from above. The player pushes a lever and pulls it again in succession to “ray” a slot. If the ball player wins, the machine pays out and deducts the amount from the participant’s winnings.
You can find three basic types of slot machines: progressive, direct and straight slots. All three types of slot machines operate on exactly the same principles but differ on the number of lever pulls necessary for a win. Some machines offer combinations, others offer “matching” and progressive machines, but still others feature “looping” slots. In addition, some machines offer simultaneous play, in which a player can play both slots simultaneously.
Progressive slots are operated with the aid of levers. When the lever is pulled, the machine will rotate and hit a jackpot. The chances of winning increase with each pull of the lever. For a progressive machine, the jackpot increases each time the lever is pulled. A jackpot that a single player will hit with a single pull is called the “par” jackpot.
Jackpot email address details are not only dependent on the lever pulling by way of a player, but also be determined by the number of bets placed on the machine. Machines with progressive features adjust their results based on just how much the players have bet. It also depends on how much is left on the bet slot. The device will either pay out a big amount or will decrease it over a period. For progressive machines, the odds may be easy to read, but this is the case with almost all of the machines.
Slots with progressive features provide a better opportunity for casino goers to win. This is because these machines are programmed going to progressive results more often than those that are non-progressive. These machines have a distinctive and interesting method of calculating winnings. The way that this works is that if you put money on the machine and then stop paying it, the device will continue to payout for you. But when you retain playing and keep paying, the machine will eventually hit a progressive result and can eventually payout a much bigger amount.
However, you should remember that a few of the progressive slot machines aren’t really that progressive. Additionally, there are those that have only a fixed amount that can be won from the device. Though these machines might seem to be the identical to progressive machines because of their fixed payout, they have their own advantages. Because they can’t be resized to accommodate the amount that was bet, you’re more likely to hit an excellent bet here.
Alternatively, there are also the non-progressive machines that not have the feature of progressive results. Many of these machines can 우리 카지노 40 프로 총판 모집 only be utilized if the player has coins in his pockets. This feature makes it less likely that you will hit a progressive machine since the chance of using coins is almost zero. As such, you are still more likely to hit a non-progressive machine. However the payouts listed below are not that big when compared to progressive machines.
When you wish to play slot games, you need to know your limitations. You ought not get too carried away with the possibility of hitting something huge just because you saw a streak of good numbers using one of the machines. Be realistic and set your limit. Understand that playing slots is fun and there is a big chance that you might hit something. Just do not expect that you will get thousands of dollars immediately.
## Choosing Online Slots WHICH ARE Right For You
Posted on July 15, 2021
# Choosing Online Slots WHICH ARE Right For You
Online Slots may be the latest craze in online gambling. It wasn’t way back when that slots were considered strictly a gambling device reserved for the young and inexperienced. The truth has been changed; today there are plenty of reputable sites offering genuine slots for everyone, irrespective of experience or age. Here we look at some of the factors that have led to the recent surge in popularity.
Good odds: Finding the right online casinos for playing slots is a combination of factors, like the type of payout and odds offered. No complicated skills necessary: The likelihood of winning on slot machines relies solely on luck. Higher payout percentages: slots regularly pay out much more compared to the minimum line option. Numerous sites pay out around ten thousand the actual line price.
Good graphics: Many people are attracted to the flashy graphics that many websites use. Whilst this can be enticing, the vast majority of slot machines work in simply the same way as any other casino machine. It’s simply a matter of picking the jackpot option. While flashy, good graphics can be informative and provide a fun way to explore the particular slot games, they have no real bearing on whether a slot machine will pay big.
MasterCard logos: All online casinos must have a merchant license and must prominently display a MasterCard logo. This ensures that your customers know that you’re an authentic casino. In addition, it works as a deterrent against fraudulent transactions. Any other business, which is providing the very same products or services that you are, is at a severe disadvantage.
Good customer support: While all casinos need to provide a certain level of service to their customers, especially those that gamble online, none way more than the ones who play slot games. Top quality slots sites should offer both direct and indirect slots players support. You have to be able to contact them by phone with any problem, query or issue, and should be able to obtain satisfactory answers to each one of these concerns in a timely manner.
Widespread slots play: To be able to win, you’ve got to play slots! Some online casino sites only provide a select few bonus symbols, rendering it difficult for all however the most dedicated players to participate. On the other hand, the best casinos will offer you a wide variety of slots games, a lot of which are played together in a single casino site. This is important because it gives new players a chance to find out about each game without worrying about whether they’ll have enough money to play it. This also helps prevent players from losing out on generous welcome bonuses, which are generally given to new players as a means of encouraging them to play more.
Decent customer support: While it’s true that one could sometimes get lucky and land a jackpot when playing slots, it is critical to remember that you’re just one single person out of hundreds, if not thousands, of other slot players. You have to look for a casino site with a reputed customer service team who can assist you to resolve any issues that may arise during your session. It also pays to opt for sites that have been in operation for some time, as this ensures that they’ve got a decent reputation in terms of serving their customers. You don’t want to gamble with a site it doesn’t provide adequate support because of its players, in the end.
Betting limits: Most casino slots allow players to choose between “standard” or “tournament” slots, and winning requires skill in beating the reels. If you choose tournament slots, you must be ready to wager a set amount, no matter how large, before your turn begins. In standard slots, however, winning is a matter of chance – you merely need to match the red or black reel with the corresponding number in the spinning reel (yes, there are different numbers, and the patterns are different, too). Either way, though, you have to be able to tell when the reels have been spun just right to help make the big score. Choosing a limit that’s too low will mean that you won’t get the payout that you 카지노 쿠폰 would like, but choosing a limit that’s too high may imply that you’ll pay more than you really need to.
## Win Baccarat Online
Posted on July 14, 2021
# Win Baccarat Online
Baccarat or just baccarat is really a popular card game usually played at online casinos. It really is basically a compounding card game usually played between two competing banks, the ball player and the banker. Each baccarat coup contains three possible outcomes: the “win”, “loss”, and “ties”. Baccarat can be played with one, two, or three decks. Generally, baccarat is played with a standard deck of 52, but this is not set standard and can vary from casino to casino.
In a baccarat game, each player receives three cards face down and two cards face up in front of them. They are called the playing cards and so are used for betting and paying down. The player is also dealt three cards face down and two 실시간 카지노 cards face through to the table in the opposite corner of the area from where in fact the players will sit. In a few casinos, these positions are alternated.
When players place bets, it is customary that they do so on a straight bet or perhaps a spread bet. In the baccarat game, however, you can find no restrictions on which kind of bets one can make, aside from the third card that is dealt to the banker. Players may either bet or fold, or take a third card and stick it in the middle of the table in front of them. Thereafter, all other players take turns picking out cards and placing them to their hands based on the first card that’s dealt to them.
At the end of the baccarat game, if a player gets the winning edge, that player wins the game. This edge is measured by the full total of all winning bets minus the amount of the losses. The higher the sum of the the losses, the lower the player’s edge is. In a few casinos, if the player is not satisfied with his edge, he may attempt a “punto banco” (betting minus the casino’s knowledge). Therefore the ball player could place a bet with the casino, but that bet will be hidden from the dealer who’ll then count it against him when the player reveals his bet.
Placing bets in the baccarat game can be carried out through different means. It could be done in person at the baccarat tables, through live dealers at online casinos, or via an automated system that functions like an electronic online roulette system. Players can play baccarat online through software packages that allow them to put wagers through a computer. There are even softwares that enable players to take part in real-time baccarat gambling via a personal computer or a television. You can find even websites offering players a chance to play baccarat free of charge; though, players ought to be wary about how they would manage their money while playing this game online.
Players who would like to try their luck in online casinos may go for the “baccarat game played in person” or the “online baccarat game.” Both ways, players place bets on special cards and can also try their luck while playing this casino game. With regards to the online version of baccarat game, players make use of banks to facilitate the management of their money; thus, winning bets can be transferred to their account as the funds for bets are added, withdrawn, and updated.
Players should therefore learn to read the reactions of those around them. In case a player feels that someone else in the casino table is bluffing, a new player win baccarat immediately. A new player should therefore not hesitate of turning down high bids. He also needs to not be afraid to stand up at the bank and make what is called a “bad shot” if you have no bet on the table for the round. When a player loses his game, he shouldn’t lose hope because baccarat is really a game that may be won; however, it isn’t possible for a new player to win each time he plays.
Players should use all their skills and strategies as well to win baccarat. The baccarat game is played under normal casino conditions with the dealer placing the cards face down. Although it is not advisable to put bets with eyes closed, it is still possible to determine the value of a card by observing how the dealer is dealing the cards. However, players who have mastered the art of reading faces and reading indicators might use an edge over the dealer by making educated guesses concerning the cards placed on the table. This will create a slight edge and could result in the possibility of winning the casino game.
## Enjoying the Free Slots Online Casino Slots
Posted on July 14, 2021
# Enjoying the Free Slots Online Casino Slots
Make reference to free slots as virtual online slots you can actually play and win without investing any cash. The same virtual slot machines which offer this sort of service are also exactly the same ones you will discover in online casinos but rather will be access with a free mode or demo. However, with a lot more risks involved since you really do not know if you will actually win or not. In fact, it’s even more fun than gambling in a casino because you still have all your money in a virtual account and you don’t have to cope with coping with high markups.
Every free slots online has three reels arranged in a pattern which spins counter-clockwise. This pattern is named the ‘reel’, where each reel completes three steps before coming into contact with the next one. The first two have been completely started and so are running on the clockwise rotation. When you start to see the symbols on the reels of the device, you will see lots sequence that represents the value you will get when the ball lands on any of those symbols. If you get a red symbol, the ball will land on the 3rd reel, and that means you have won.
Now, there are various websites that offer you the very best free slots games on the net. Among the best free slots games designed for download on the internet can be an Android version of the overall game. Since many people use their mobiles to play slots games, it only is practical to have an option where you could use the same application to play slots games from your smartphone. This allows one to save well on your mobile phone’s battery together with space in addition to time and permits you to keep playing so long as you want.
As you would expect, the free slots offered on these sites are entirely virtual and so are in line with the same logic as those used in the land-based casinos. They still need a strategy to win plus some luck, but the it’s likely that heavily stacked contrary to the casino’s visitors. On the other hand, you will be able to utilize your smart phone’s accelerometer to regulate the direction in which you’re spinning your reels. This may seem like cheating, but if you’re really thinking about winning big amounts of real money, then this is definitely the ideal solution.
Some people may doubt whether they can actually win real cash while playing free online slots. Well, if you use a casino slot machine that has not yet accumulated a jackpot, you then have every potential for winning something. However, you have to remember that regardless of how lucky you are together with your reels, you cannot be prepared to get anything more than what is called the maximum amount. This amount is around 400 times the specific jackpot prize that the casino offers at that particular time. Of course, you would be surprised using what kind of results you can get if you increase your bets just a little higher.
When you play free slots casinos, it is best to remember that luck is really a major component with regards to winning real cash from these games. Naturally, you will have better luck if you stick with the machine that has a lower maximum jackpot prize. In fact, there’s one casino slot game that has a maximum jackpot that is higher than the rest of them – and you would need to play almost 1 million spins to even stand a chance of winning this huge prize. You may well be able to imagine which kind of reaction this might inspire!
Also, in the event that you actually want to win big, then it really is highly advisable that you avoid free slots online casino games that have bonus rounds. Bonus rounds are usually announced shortly before the machines are about to spin their random numbers. With bonus rounds, the jackpots become significantly larger because they are continuously put into the machine’s collection. Unfortunately, because of this they do not have any limit on how big the jackpots could be, so beware of trying to take advantage of this by playing games with one of these forms of bonus rounds.
Lastly, when you play free Vegas slots online, it’s best if you don’t play very many times per day. If you play more than five times per day, you are almost guaranteed to feel just like you are working for the casino. For the reason that there is a constant reduction in your bankroll and there is a greater threat of you hitting a hot streak and betting more than you can afford to reduce. So, whenever you can, 인터넷 바카라 limit yourself to play no more than five times per day to be able to feel like you are doing work for the free slot games. In the end, it takes care of to play more often, but not to play forever.
## Great things about Playing Free Slots
Posted on July 14, 2021
# Great things about Playing Free Slots
In order to get free slots for testing purposes, then read this. You’ll discover how you can find free slots and how exactly to use them. The reason for doing this is indeed you could determine if these slots are what you are looking for and if you want to try playing these online games then there are particular rules that need to be followed.
To start with, free slots are described online casino slots which you can actually play but still enjoy without actually wagering any cash in it. The free slots which provide this type of functionality are the identical ones that you will find in real casinos but will most likely be accessible through a trial offer or demo mode. There are various of these online casino slots which provide players with free spins and they are usually known as scratter games. For more info on these free slots, then continue reading.
When looking for free slots, you can find two ways in which you can do it. One is by using online casino software and another is by using a software development kit. Both these methods have their own benefits and drawbacks. In the case of the software development kit, it’s likely you’ll find the game very quick since there are a great deal of features integrated into this kind of software. On the other hand, when looking for real money games, then it is very important that you ensure that the online casino has a good inventory so that you will do not lose out on any bargains.
You can find two forms of free slots and these are progressive jackpots and bonus slots. With progressive jackpots, players receive a chance to raise the amount of money that they can eventually win when they hit a certain pattern on the machine. The more patterns that you hit, the bigger your chances are of winning big. When you have hit at the very least five patterns, then your likelihood of winning big are pretty high.
Bonus slots may also be known as leader boards and so are basically used for the objective of gaming and gaining tips from others. You could find free slots with this feature without downloading anything. This sort of slot games are very easy to set up and play, even for a newcomer player. After you have registered, then all you need to do is wait for the game to start. Generally, you will get the outcomes instantly through email. Without downloading anything, you’ll just have to click on the results and gain tips and tricks without much effort.
In free slots, you can be given a variety of choices when you select a game. These options depends on the pay line which you have selected. In real money games, there are various options that you can pick from. But in online slots, you will usually get the machine you have chosen if 엠 카지노 쿠폰 you bet a certain amount of money.
For gamblers, free slots offer a lot of convenience since it makes playing convenient and straight forward. Most free online slots offer instant payment and instant winnings. Most of all, many of these websites give incentives to gamers by allowing them to register without paying anything.
## Tips on Winning Online Slots With REAL CASH
Posted on July 13, 2021
# Tips on Winning Online Slots With REAL CASH
Online slots for 88 카지노 cash are enormously popular in the United States online gambling industry. Spinning the reels in slot machines makes up approximately 70% of most bets placed. Here you’ll find all the top internet casinos with free online slots for playing, to novices and pros alike. To ensure your success, take heed of the tips.
Avoid Online Slots for Cash Games With REAL CASH – Most of us, when we hear what “online slots” often associate them with internet poker, or casino games with actual money, such as for example Blackjack. While online slots do play money, they are generally played using coins, with no monetary value assigned to them in the game. Thus while it is true that you may win true to life money from online slots, those promotions that promise to give you “play cash” soon aren’t telling the reality. They’re basically lying for you. For best results, avoid any online slots which promise you “play cash” because they most likely are online casino games which are not intended for serious gaming.
Aim For the Best Rigs – The slots that seem the easiest to beat will be the ones with the cheapest payouts. This means that players should set a budget and stick to it. In addition, the newer web sites, the better, since players have a tendency to study from the site’s mistakes. A reliable online slots website will undoubtedly be constantly improving their system and making the games more fair and consistent, so players won’t need to worry about getting cheated out of their winnings.
## An Introduction to Casino Baccarat
Posted on July 13, 2021
# An Introduction to Casino Baccarat
Baccarat or just baccarat is a card game usually played in casino settings. It’s a popular card game usually played between two players, often among whom is the banker and the other player is the player. Each baccarat bet has three possible outcomes: win, tie, and lose. In some instances, both players have an equal chance of winning the baccarat game. In terms of playing online baccarat, you can find two methods to play.
The initial way to play baccarat is called the ‘pool play’ where one player is in the pool and two more players are put up for grabs in ‘blind’. The banker sits on the seat facing the players that are in the pool and contains a deck containing seven cards. Those in the pool are referred to as ‘lay outs’ while those in the table with the blinds face towards the dealer are referred to as the ‘lay outs’. Players can call the dealer if they want to bet and never have to show their cards. However, this action results in having the banker lose face.
The next way to play baccarat is named the ‘tally’, where each player contributes his own card and has their hand including the cards in the dealer’s hand and the ones in the pockets. The bets are made with the highest bidder getting the right to call. In case a player calls and bets, all of the bets of this player come under one group. If a player bets and folds, all the bets of this player come under another group.
The baccarat system differs from the original betting methods in that instead of picking a winner, players determine how much they are ready to loose. They can win by paying the lowest sm 카지노 amount or by paying the most. In addition, regarding baccarat, unlike in live baccarat where there is always someone to pay, in online baccarat the player is responsible for paying the banker, not the home. The banker, however, must still have a card that represents that he has gone out of money.
When placing your bets, players may place the fixed, pre-determined wager or perhaps a single, pre-determined amount of bets. The fixed wager may be the player’s constant wager. If he wins, then he gets his winnings in addition to the interest accumulated on his deposit. Likewise, if he loses, he then gets to replace his lost wager. It seems sensible to play high stakes baccarat with a fixed wager so as to reduce the impact of random chance on the outcome.
Online baccarat is played with a third card banker that adds another layer of complexity to the overall game. The player has to remember the banker’s tendencies and preferences and also determine which card the banker is holding at any given moment. Also, the ball player has to be skillful enough to know when to bet and when to fold, since baccarat depends on timing more than luck. Since the banker’s card may occasionally overlap with other cards in the deck, you should memorize the layout of the baccarat deck, both in front of and after the game is over.
Another variant of casino table game that borrows from baccarat may be the two cards baccarat. For players who usually do not desire to play with three cards, this is an ideal casino game. Two cards baccarat includes a lot of strategic possibilities. For instance, a new player can play with two cards and try to remove one of them (the prior owner of the card should hide it), and hope that his opponent will fold their own card. That is called “cute” as the player gets to win the pot and never have to cope with the action of removing a card. The two cards baccarat also have a short range of decisions that depend on the folding pattern of the two cards: if the first card is hidden, the second one can be easily accessed and vice versa.
Online casino baccarat supplies a variety of real money games. Although these are not as exciting because the ones played in brick and mortar casinos, they are just as fun. Many online casinos allow players to use “virtual money” to play baccarat. Online casino software will not require the player to use real money so there is no risk involved. Players can enjoy all the excitement of the game without putting your financial status on the line. | 8,075 | 39,137 | {"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} | 2.515625 | 3 | CC-MAIN-2021-31 | latest | en | 0.961977 |
https://stats.stackexchange.com/questions/77557/how-are-partial-regression-slopes-calculated-in-multiple-regression | 1,723,025,810,000,000,000 | text/html | crawl-data/CC-MAIN-2024-33/segments/1722640690787.34/warc/CC-MAIN-20240807080717-20240807110717-00828.warc.gz | 423,053,305 | 43,823 | # How are partial regression slopes calculated in multiple regression?
I'm trying to understand how multiple regression statistically controls for the effects of other predictor variables when calculating partial regression slopes. In a multiple regression of Y~X1+X2, would the partial regression slope of X1 be given by [Y]~[residuals of X1~X2], or by [residuals of Y~X2] ~ [residuals of X1~X2]? Different pages on the internet tell me different things.
I've done some simulations to try and figure this out (see below), and it seems that both methods give the same estimates of slopes as multiple regression, but only the latter method has similar standard errors around those estimates. This makes me think the latter method is the one that multiple regression uses, but it would be nice to know for sure.
Similarly, if I wanted to plot Y against X1 so that I could visualise how strongly the two were related while also controlling for any confounding with X2, would I plot [Y]~[residuals of X1~X2], or [residuals of Y~X2] ~ [residuals of X1~X2]? These two plots in the code below look very different in terms of the strength of the relationship.
Jay
#1. simulate data, where x1 and x2 are correlated due to lurking variable,
#...and y is explained by both.
lurker <- rnorm(n=100)
x1 <- rnorm(n=100, mean=lurker*2, sd=1)
x2 <- rnorm(n=100, mean=lurker*5, sd=1)
y <- rnorm(n=100, mean=x1*2 + x2*5, sd=1)
#2. multiple regn model to estimate partial slopes:
summary(lm(y~x1+x2)) #partial slopes pretty close to simulated values
#3. calculate partial slopes manually, using either
#....(1) Y~[resids of X1~X2] OR (2) [resids of Y~X2]~[resids of X1~X2]
#3.a. based on (1) Y~[resids of X1~X2]
m.x1x2 <- lm(x1~x2)
resids.x1x2 <- m.x1x2$residuals summary(lm(y ~resids.x1x2)) #slope pretty close to true value, but conf intervals MUCH larger than those for MR estimate #3.b. based on (2) [resids of Y ~ X2]~[resids of X1~X2] m.y1x2 <- lm(y~x2) resids.y1x2 <- m.y1x2$residuals
summary(lm(resids.y1x2 ~resids.x1x2)) #also very close to true value, but conf intervals now similar scale to those from MR.
# plot the relationship between y and x1 after controlling for x2, based on the different methods:
op <- par(mfrow=c(2,1))
plot(y ~resids.x1x2)
plot(resids.y1x2 ~resids.x1x2)
par(op)
if I wanted to plot Y against X1 so that I could visualise how strongly the two were related while also controlling for any confounding with X2, would I plot [Y]~[residuals of X1~X2], or [residuals of Y~X2] ~ [residuals of X1~X2]?
The second one. You want to plot $e(Y|X_2) \sim e(X_1|X_2)$ to obtain the added variable plot for $X_1$ for the model already containing $X_2$. Intuitively think of it this way: the presence of $X_2$ in the model you already have is reducing the variance of the residuals (which is relative to the response). You want to determine if adding $X_1$ will reduce this variance further, so you want to consider $e(Y|X_2)$, which contains the variance remaining in the residuals after taking the predictor $X_2$ into consideration.
As you put it: you want to "partial out" the effects of the predictor(s) currently in your model on both the predictor(s) you are considering adding as wells as the response.
To avoid blackening the place, I will not use bold symbols -but the answer will be carried out in matrix form. Vectors are column vectors, a prime will denote the transpose.
Let a linear regression model
$$y = X_1b_1 + X_2b_2 + u_A \qquad [A]$$
The normal equations for the OLS estimator are
\begin{align} \left(X_1'X_1\right)b_1+\left(X_1'X_2\right)b_2=& X_1'y \qquad [1]\\ \\ \left(X_2'X_1\right)b_1+\left(X_2'X_2\right)b_2=& X_2'y \qquad [2]\\ \end{align} Solving $[2]$ for $b_2$ we have $$[2]\rightarrow b_2= \left(X_2'X_2\right)^{-1}X_2'y-\left(X_2'X_2\right)^{-1}\left(X_2'X_1\right)b_1$$
Inserting this into $[1]$ we obtain $$\left(X_1'X_1\right)b_1+\left(X_1'X_2\right)\left(X_2'X_2\right)^{-1}X_2'y-\left(X_1'X_2\right)\left(X_2'X_2\right)^{-1}\left(X_2'X_1\right)b_1= X_1'y$$
Collecting terms w.r.t $b_1$ and $y$, $$X_1'\left[I-X_2\left(X_2'X_2\right)^{-1}X_2'\right]X_1b_1= X_1'\left[I-X_2\left(X_2'X_2\right)^{-1}X_2'\right]y$$ $$\Rightarrow X_1'M_2X_1b_1 = X_1'M_2y \qquad [3]$$
where $M_2$ is the "annihilator" or "residual maker"matrix related to $X_2$, namely the matrix that produces the residuals when a variable is regressed on $X_2$, by pre-multiplying this variable. This matrix is symmetric and idempotent, $M_2=M_2',\; M_2= M_2M_2$. So we can write
$$(M_2X_1)'(M_2X_1)b_1 = (M_2X_1)'y$$ $$\Rightarrow R_{1\sim2}'R_{1\sim2}b_1=R_{1\sim2}'y \Rightarrow \hat b_1 = \left(R_{1\sim2}'R_{1\sim2}\right)^{-1}R_{1\sim2}'y\qquad [4]$$
where $R_{1\sim2}$ denotes the residual vector from regressing $X_1$ on $X_2$.
This last formula is exactly the OLS formula from the regression model $$y= R_{1\sim2}d_1+u_B \qquad [B]$$
So eq. $[4]$ tells us that the coefficient estimate for $X_1$ that we will obtain in a multiple regression setting, will be exactly the same with what we will obtain if we regress the dependent variable on the residuals from the regression of $X_1$ on $X_2$.
Now consider the second case, regressing the residuals on the residuals. This is the model
$$R_{y\sim2} = R_{1\sim2}c_1+u_C \Rightarrow (M_2y)= (M_2X_1)c_1 +u_C \qquad [C]$$
The OLS estimator of $c$ is $$\hat c_1 = \left[(M_2X_1)'(M_2X_1)\right]^{-1}(M_2X_1)'(M_2y) \qquad [5]$$
By the properties of $M_2$ we have $$(M_2X_1)'(M_2y) = X_1'M_2'M_2y=X_1'M_2M_2y=X_1'M_2y=X_1'M_2'y=(M_2X_1)'y$$ Noting that $M_2X_1 = R_{1\sim2}$ eq. $[5]$ becomes
$$\hat c_1= \left(R_{1\sim2}'R_{1\sim2}\right)^{-1}R_{1\sim2}'y \qquad [6]$$
which is identical to eq. $[4]$, and so $\hat c_1 = \hat d_1 =\hat b_1$. In other words the three models give mathematically identical results.
Let's now consider the issue of the estimator variance. Models $[B]$ and $[C]$ have the same regressor matrix so the question is what happens with the estimated error variances, $\sigma^2_B$ and $\sigma^2_C$. We will denote $M(r)_{1\sim2}$ the annihilator matrix of the regressor $R_{1\sim2}$. It has analogous properties as $M_2$ For model $[B]$ we have
$$u'_Bu_B = \left(M(r)_{1\sim2}y\right)'\left(M(r)_{1\sim2}y\right) = y'M(r)_{1\sim2}y \qquad [7]$$
while for model $[C]$ we have
$$u'_Cu_C = \left(M(r)_{1\sim2}(M_2y)\right)'\left(M(r)_{1\sim2}(M_2y)\right) = y'M_2M(r)_{1\sim2}M_2y \qquad [8]$$
Are the RHS of eq. $[7]$ and $[8]$ equal? I 'll leave that to the reader.
• Thanks for that in depth answer...which unfortunately has gone way over my head! At this stage I'm after a more conceptual cf mathematical understanding - ie is the partial slope of X1 in a model also containing X2 found by partialling out effects of X2 on X1 AND partialling out the effects of X2 on Y, or just by partialling out the effects of X2 on X1? Cheers
– jay
Commented Nov 25, 2013 at 3:38
• "The three models give mathematically identical results" means that either way you will obtain the exact same result. Can you get the intuition as to why? Commented Nov 25, 2013 at 8:42
• I've read through it multiple times and I'm afraid no, don't get the intuition. I appreciate you taking the time to write out such a detailed explanation...it's just not in a language that I understand.
– jay
Commented Nov 28, 2013 at 7:14
• No problem Jay... try this: informally, residuals are "what is left unexplained". The X2~X1 residuals is what of X1 is not explained by X2. Now consider the Y~X2 residuals. These reflect what part of Y is not explained by X2 (and therefore is explained by X1 and by the error term). So even if you regress the original Y on the X2~X1 residuals, these will only explain that part of Y that is left unexplained by X2. So by using Y~X2 as the dependent variable, you "remove" only that part of Y that is explained by X2- leaving unaffected that part of Y that is explained by the residuals X2~X1. Commented Nov 28, 2013 at 14:57
• Yes that makes sense thanks. We got there in the end!
– jay
Commented Dec 1, 2013 at 5:09 | 2,718 | 8,039 | {"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": 1, "equation": 0, "x-ck12": 0, "texerror": 0} | 3.53125 | 4 | CC-MAIN-2024-33 | latest | en | 0.877603 |
https://biodatamining.biomedcentral.com/articles/10.1186/1756-0381-4-4/tables/1 | 1,660,204,902,000,000,000 | text/html | crawl-data/CC-MAIN-2022-33/segments/1659882571246.56/warc/CC-MAIN-20220811073058-20220811103058-00339.warc.gz | 148,342,789 | 43,489 | # Table 1 Case-Control Models
Model A Model B Model C
Rule1: Rule1: Rule1:
If rs5 = AA and rs10 = AB then Case If rs5 = BB and rs10 = AA then Case If random number > "threshold" then Case
Rule2: Rule2: Rule 2:
If rs5 = AB and rs10 = AA then Case If rs15 = AA and AUC >105 then Case Else Control
Rule3: Rule3:
If rs5 = AB and rs10 = BB then Case Else Control
Rule4:
If rs5 = BB and rs10 = AB then Case
Rule 5:
Else Control | 139 | 422 | {"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} | 2.796875 | 3 | CC-MAIN-2022-33 | latest | en | 0.577705 |
https://philosophy.stackexchange.com/questions/44947/how-do-we-learn-math-and-science | 1,725,704,540,000,000,000 | text/html | crawl-data/CC-MAIN-2024-38/segments/1725700650826.4/warc/CC-MAIN-20240907095856-20240907125856-00759.warc.gz | 445,025,776 | 42,722 | # How do we learn math and science?
I was wondering how we actually learn math and science (physics). Some people say that it is important to "understand" the formulas/equations. However, if anyone were asked what 5 divided by 5 is, they would immediately respond 1. Most people probably aren't picturing a group of 5 apples (for instance), making groups of 5 out of those apples, and counting how many groups they have. This suggests to me that we do not really understand math/physics -- it seems to me like it is memorization or pattern recognition.
Yet, if I asked someone how many groups of 5 apples they could make from 5 apples, they would know to do 5 divided by 5 and end up with 1. Here, it seems like the person has a true understanding of the concept of division.
Do we understand math/physics or just memorize it? How are we able to seemingly do both? Of course, the example I gave was very simplistic, but I can find many more. For example, I could ask someone with basic physics knowledge to calculate the power in a circuit given that there is 5 volts across it and 1 amp running through it. Most people will quickly calculate that there is 5 watts consumed without even thinking about the "meaning" of the equation they are using (power = voltage × current). Yet, if I asked them to explain to me why they used this formula, it would not be too hard for them to prove that it is correct. In other words, they have an understanding of the formula, but did not apply this understanding when asked to solve a simple problem.
I was wondering if this has a logical explanation. Is our knowledge understanding or memorization? Is one form of knowledge more advantageous than the other? Why do it look like we have both forms? Thank you!
• If people only memorized math equations then they would not be able to solve equations that they didn't already know the answer to. Imagine Alice who has never added 238492893482893 and 2308498234902903 together before. If she only had "memorized" the certain addition problems she's done before, she wouldn't know how to add those two numbers, but clearly we know that anyone who has learned addition can add them together. We know the rules work because we are shown proofs of them; when kids learn math teachers use tangible examples like apples because it helps the kids visualize the proofs. Commented Jul 28, 2017 at 14:50
• But I am genuinely confused as to why you think the first example only shows that people memorize something and don't understand it. If you ask someone to divide two numbers they have never divided before and they do it perfectly, how could they have memorized the answer? Why does them not picturing groups of apples and instead just using a long division algorithm mean that they only memorized the problem and not truly understood the problem? Commented Jul 28, 2017 at 14:52
• Chomsky's poverty of the stimulus argument is slightly related and might interest you. He argued against Skinner's behaviorism idea that language is developed by responding to external stimuli; Chomsky argues that if that were true people would not be able to understand novel sentences said to them that they had never encountered before. We understand patterns and how they work (patterns in language and math) and then we use those patterns when we solve problems. If it was just memorization we couldn't do anything new. Commented Jul 28, 2017 at 14:55
• By "learn" vs. "memorize," are you asking whether physics explains or merely describes? Commented Jul 28, 2017 at 18:24
• It seems that everyone has a philosophical period during which they ask great questions. After that everything becomes familiar and is taken for granted, then no more question is raised. Commented Aug 28, 2017 at 19:38
Math and philosophy was in the acient Greece very connected and many times studied simultaneously as they where (and in some parts of the world still is) thought to coincide.
This is because math describes the fundamentals of nature, it models the world around us to a degree that we, as humans, find satisfying. In the same manner philosophy concerns answers that cannot be mathematically measured, because the subject being studied is a question of emotion, lack of it, reason and sow on.
Just because we are satisfied does not mean that math is completely true, math and philosophy are the only two non-empirical subjects in modern academia, which from a natural science perspective also means that it cant be proven and not to a full extend understood.
Within math it is easy to make proves that is limited by a "false math" the bunny and the turtle is a classic. The bunny can never pass the turtle because thenever the bunny reaches the point the turtle has just left, the turtle has moved on to a new point and sow on. In this limited math, this is true, even though we know it to be false because our math includes time.
We have accepted math to be true because it describes the world in a sensibly way, and it continues to do sow because math constantly develops. Matrices, Fourier transforms and quantum mechanics are examples of this. But we do not know, if all we know, is that the bunny cant pass the turtle.
To answer the question, we don't understand math or fore that matter anything, but we can model it daim well, and this is "proof" enough fore us to believe in it.
• "Not everything that counts can be counted, and not everything that can be counted counts." Commented Sep 20, 2022 at 10:32
Yes, arithmetic rules are memorized just like the rules of board games are memorized. The most important evidence is that everyone calculates in his native language ( or language of instruction) no matter how fluent they are in a foreign language.
Our understanding of the rules of chess is demonstrated by our ability to play chess; our understanding of arithmetic rules is demonstrated by our ability to solve math problems we've never seen before.
There are other sets of arithmetic rules that require a lot more memorization but offer the benefit of greater speed of calculation.
Arithmetic is sometimes applicable to practical problems, sometimes not. For most of us who learned arithmetic from school, where arithmetic applies is also memorized.
Our savage ancestors learned arithmetic by exactly the opposite means.
First, they conceived the number of things. E.g. two pebble, three pebbles, four pebbles, etc. Notice that there were always things or measure words following a numeral.
Then, through experiences, they noticed that two pebbles and two pebbles together are four pebbles.
Then some wise persons used such rules of thumbs as "two pebbles and two pebbles are four pebbles" to predict the outcome instead of putting two pebbles next to two other pebbles and count the total.
At this point, measure words or things following the numeral became too cumbersome and people sometimes dropped them for brevity's sake. Then they got such rules of thumbs as "two and two equals to four." The ancient Chinese mathematics book Nine Chapters was a rule-of-thumb era math book; it demonstrated this transition from number of things to number: every problem is a practical problem about land, length or weight, but the solutions simply dropped measure words where a reader would have no problem in understanding that two in this problem meant two dou (bushels), two in that problem meant two mu (acres).
As the number of rules of thumbs grew, someone figured out that some rules of thumbs can be deduced from other rules of thumbs and the number of rules of thumbs needed to memorize began to shrink. Finally, we got the arithmetic rule we have today.
I think, in order for children to have a deeper understanding of arithmetic, this part of our ancestor’s savage life might be worth reliving.
• A sort of Apprenticeship to math. Yes. Commented Sep 20, 2022 at 10:34
Maths in my opinion and in the opinion of others such as Plato and Pythagoras, is a very important part of Philosophy. It defines what is fact, it defines what is rational, and it defines what is true, and Philosophy is all about truth. For example, 1+1=2 is an absolute truth, which we usually learn and understand as a child.
When it comes to memory ... this is a different argument, there are many opinions on our memory. Some like Plato say we knew everything already before birth, but had forgotten it when born. If you're talking about the behavioural side, I would say it is more about understanding. For example, I don't remember algebra from my maths lessons because I simply didn't care or really understand it. My memory therefore thinks it's useless so I now know nothing about algebra.
Whereas in religious education from high school, I remember the 10 commandments, because I understood they were important and the idea appealed to me because I found it interesting, therefore I have remembered it — because I understood the absolute moral code — e.g. do not kill.
• I didn't care much for math either. Not needed as a computer programmer. Psychology, on the other hand... Commented Sep 20, 2022 at 13:14 | 1,956 | 9,091 | {"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} | 3.546875 | 4 | CC-MAIN-2024-38 | latest | en | 0.980991 |
http://scienceline.ucsb.edu/getkey.php?key=1849 | 1,596,625,727,000,000,000 | text/html | crawl-data/CC-MAIN-2020-34/segments/1596439735939.26/warc/CC-MAIN-20200805094821-20200805124821-00155.warc.gz | 96,523,563 | 3,621 | UCSB Science Line
Hi! I have a question regarding the magnetic levitation formula. I calculated than the answer for (mu_0*p*g/x)in the formula b2/z=mu_0*p*g/x. It is 726.49 T2/m. I was wondering, that means that b2/z also has to equal 726.49 T2/m. Does that insure that the bismuth will levitate? In other words, if I calculate that (b2/z) is less than 726.49 T2/m, then the bismuth will not levitate? It has to be perfectly 726.49 T2/m... or more? Thanks for your help. Question Date: 2008-09-11 Answer 1:Yes, that means that B2/z will also have to equal 726.49 T2/m. Anything greater than that should be when the Bismuth will levitate (keeping in mind that this equation is a simplification, and won't be exactly right).Click Here to return to the search form. | 223 | 763 | {"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} | 2.859375 | 3 | CC-MAIN-2020-34 | latest | en | 0.943581 |
http://mathonline.wikidot.com/the-conjugate-transpose-of-a-matrix | 1,618,335,047,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038073437.35/warc/CC-MAIN-20210413152520-20210413182520-00313.warc.gz | 63,527,960 | 4,921 | The Conjugate Transpose of a Matrix
We are about to look at an important theorem which will give us a relationship between a matrix that represents the linear transformation $T$ and a matrix that represents the adjoint of $T$, $T^*$. Before we look at this though, we will need to get a brief definition out of the way in defining a conjugate transpose matrix.
Definition: If $A$ is an $m \times n$ matrix with entries from the field $\mathbb{F}$, then the Conjugate Transpose of $A$ is obtained by taking the complex conjugate of each entry in $A$ and then transposing $A$.
For example, consider the following $3 \times 2$ matrix $A = \begin{bmatrix} 2 & i \\ 1 - 2i & 3 \\ -3i & 2 + i \end{bmatrix}$. Then the conjugate transpose of $A$ is obtained by first taking the complex conjugate of each entry to get $\begin{bmatrix} 2 & -i \\ 1 + 2i & 3 \\ 3i & 2 - i \end{bmatrix}$, and then transposing this matrix to get: | 264 | 919 | {"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} | 3.75 | 4 | CC-MAIN-2021-17 | longest | en | 0.8504 |
http://sigmatechpathshala.com/2018/08/07/capacitive-voltage-divider/ | 1,603,155,619,000,000,000 | text/html | crawl-data/CC-MAIN-2020-45/segments/1603107867463.6/warc/CC-MAIN-20201019232613-20201020022613-00312.warc.gz | 106,065,815 | 17,720 | Voltage divider circuits may be constructed from reactive components just as easily as they may be constructed from fixed value resistors.
But just like resistive circuits, a capacitive voltage divider network is not affected by changes in the supply frequency even though they use capacitors, which are reactive elements, as each capacitor in the series chain is affected equally by changes in supply frequency.
But before we can look at a capacitive voltage divider circuit in more detail, we need to understand a little more about capacitive reactance and how it affects capacitors at different frequencies.
In our first tutorial about Capacitors, we saw that a capacitor consists of two parallel conductive plates separated by an insulator, and has a positive (+) charge on one plate, and an opposite negative () charge on the other. We also saw that when connected to a DC (direct current) supply, once the capacitor is fully charged, the insulator (called the dielectric) blocks the flow of current through it.
Typical Capacitor
A capacitor opposes current flow just like a resistor, but unlike a resistor which dissipates its unwanted energy in the form of heat, a capacitor stores energy on its plates when it charges and releases or gives back the energy into the connected circuit when it discharges.
This ability of a capacitor to oppose or “react” against current flow by storing charge on its plates is called “reactance”, and as this reactance relates to a capacitor it is therefore called Capacitive Reactance ( Xc ), and like resistance, reactance is also measured in Ohm’s.
When a fully discharged capacitor is connected across a DC supply such as a battery or power supply, the reactance of the capacitor is initially extremely low and maximum circuit current flows through the capacitor for a very short period time as the capacitors plates charge up exponentially.
After a period of time equal to about “5RC” or 5 time constants, the plates of the capacitor are fully charged equalling the supply voltage and no further current flows. At this point the reactance of the capacitor to DC current flow is at its maximum in the mega-ohms region, almost an open-circuit, and this is why capacitors block DC.
Now if we connect the capacitor to an AC (alternating current) supply which is continually reversing polarity, the effect on the capacitor is that its plates are continuously charging and discharging in relationship to the applied alternating supply voltage. This means that a charging and discharging current is always flowing in and out of the capacitors plates, and if we have a current flow we must also have a value of reactance to oppose it. But what value would it be and what factors determine the value of capacitive reactance.
In the tutorial about Capacitance and Charge, we saw that the amount of charge, ( Q ) present on a capacitors plates is proportional to the applied voltage and capacitance value of the capacitor. As the applied alternating supply voltage, ( Vs ) is constantly changing in value the charge on the plates must also be changing in value.
If the capacitor has a larger capacitance value, then for a given resistance, R it takes longer to charge the capacitor as τ = RC, which means that the charging current is flowing for a longer period of time. A higher capacitance results in a small value of reactance, Xc for a given frequency.
Likewise, if the capacitor has a small capacitance value, then a shorter RC time constant is required to charge the capacitor which means that the current will flow for a shorter period of time. A smaller capacitance results in a higher value of reactance, Xc. Then we can see that larger currents mean smaller reactance, and smaller currents mean larger reactance. Therefore, capacitive reactance is inversely proportional to the capacitance value of the capacitor, XC ∝-1 C.
Capacitance, however is not the only factor that determines capacitive reactance. If the applied alternating current is at a low frequency, the reactance has more time to build-up for a given RC time constant and oppose the current indicating a large value of reactance. Likewise, if the applied frequency is high, there is little time between the charging and discharging cycles for the reactance to build-up and oppose the current resulting in a larger current flow, indicating a smaller reactance.
Then we can see that a capacitor is an impedance and the magnitude of this impedance is frequency dependent. So larger frequencies mean smaller reactance, and smaller frequencies mean larger reactance. Therefore, Capacitive Reactance, Xc (its complex impedance) is inversely proportional to both capacitance and frequency and the standard equation for capacitive reactance is given as:
### Capacitive Reactance Formula
• Where:
• Xc = Capacitive Reactance in Ohms, (Ω)
• π (pi) = a numeric constant of 3.142
• ƒ = Frequency in Hertz, (Hz)
• C = Capacitance in Farads, (F)
## Voltage Distribution in Series Capacitors
Now that we have seen how the opposition to the charging and discharging currents of a capacitor are determined not only by its capacitance value but also by the frequency of the supply, lets look at how this affects two capacitors connected in series forming a capacitive voltage divider circuit.
### Capacitive Voltage Divider
Consider the two capacitors, C1 and C2connected in series across an alternating supply of 10 volts. As the two capacitors are in series, the charge Q on them is the same, but the voltage across them will be different and related to their capacitance values, as V = Q/C.
Voltage divider circuits may be constructed from reactive components just as easily as they may be constructed from resistors as they both follow the voltage divider rule. Take this capacitive voltage divider circuit, for instance.
The voltage across each capacitor can be calculated in a number of ways. One such way is to find the capacitive reactance value of each capacitor, the total circuit impedance, the circuit current and then use them to calculate the voltage drop, for example:
### Capacitive Voltage Divider Example No1
Using the two capacitors of 10uF and 22uF in the series circuit above, calculate the rms voltage drops across each capacitor when subjected to a sinusoidal voltage of 10 volts rms at 80Hz.
Capacitive Reactance of 10uF capacitor
Capacitive Reactance of 22uF capacitor
Total capacitive reactance of series circuit – Note that reactance’s in series are added together just like resistors in series.
or:
Circuit current
Then the voltage drop across each capacitor in series capacitive voltage divider will be:
When the capacitor values are different, the smaller value capacitor will charge itself to a higher voltage than the larger value capacitor, and in our example above this was 6.9 and 3.1 volts respectively. Since Kirchhoff’s voltage law applies to this and every series connected circuit, the total sum of the individual voltage drops will be equal in value to the supply voltage, VS and 6.9 + 3.1 does indeed equal 10 volts.
Note that the ratios of the voltage drops across the two capacitors connected in a series capacitive voltage divider circuit will always remain the same regardless of the supply frequency. Then the two voltage drops of 6.9 volts and 3.1 volts above in our simple example will remain the same even if the supply frequency is increased from 80Hz to 8000Hz as shown.
## Capacitive Voltage Divider Example No2
Using the same two capacitors, calculate the capacitive voltage drop at 8,000Hz (8kHz).
While the voltage ratios across the two capacitors may stay the same, as the supply frequency increases, the combined capacitive reactance decreases, and therefore so too does the total circuit impedance. This reduction in impedance causes more current to flow. For example, at 80Hz we calculated the circuit current above to be about 34.5mA, but at 8kHz, the supply current increased to 3.45A, 100 times more. Therefore, the current flowing through a capacitive voltage divider is proportional to frequency or I ∝ ƒ.
We have seen here that a capacitor divider is a network of series connected capacitors, each having a AC voltage drop across it. As capacitive voltage dividers use the capacitive reactance value of a capacitor to determine the actual voltage drop, they can only be used on frequency driven supplies and as such do not work as DC voltage dividers. This is mainly due to the fact that capacitors block DC and therefore no current flows.
Capacitive voltage divider circuits are used in a variety of electronics applications ranging from Colpitts Oscillators, to capacitive touch sensitive screens that change their output voltage when touched by a persons finger, to being used as a cheap substitute for mains transformers in dropping high voltages such as in mains connected circuits that use low voltage electronics or IC’s etc.
Because as we now know, the reactance of both capacitors changes with frequency (at the same rate), so the voltage division across a capacitive voltage divider circuit will always remain the same keeping a steady voltage divider. | 1,931 | 9,168 | {"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} | 3.03125 | 3 | CC-MAIN-2020-45 | latest | en | 0.954936 |
https://www.geeksforgeeks.org/numpy-diagflat-python/?ref=lbp | 1,638,685,549,000,000,000 | text/html | crawl-data/CC-MAIN-2021-49/segments/1637964363135.71/warc/CC-MAIN-20211205035505-20211205065505-00612.warc.gz | 829,273,721 | 23,052 | # numpy.diagflat() in Python
• Last Updated : 04 Aug, 2021
numpy.diagflat (a, k = 0): Create a two-dimensional array with the array_like input as a diagonal to the new output array.
Parameters :
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```a : array_like input data with diagonal elements
strong>k : [int, optional, 0 by default]
Diagonal we require; k>0 means diagonal above main diagonal or vice versa.```
Returns :
`array with the array_like input as a diagonal to the new output array.`
## Python
`# Python Program illustrating``# numpy.diagflat method` `import` `numpy as geek` `print``(``"diagflat use on main diagonal : \n"``, geek.diagflat([``1``, ``7``]), ``"\n"``)` `print``(``"diagflat use on main diagonal : \n"``, geek.diagflat([``1``, ``7``, ``6``]), ``"\n"``)` `# Diagonal above main diagonal``print``(``"diagflat above main diagonal : \n"``, geek.diagflat([``1``, ``7``, ``6``], ``1``), ``"\n"``)`
Output :
```diagflat use on main diagonal :
[[1 0]
[0 7]]
diagflat use on main diagonal :
[[1 0 0]
[0 7 0]
[0 0 6]]
diagflat above main diagonal :
[[0 1 0 0]
[0 0 7 0]
[0 0 0 6]
[0 0 0 0]] ```
Note :
These NumPy-Python programs won’t run on onlineID, so run them on your systems to explore them.
This article is contributed by Mohit Gupta_OMG 😀. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks. | 516 | 1,810 | {"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} | 2.890625 | 3 | CC-MAIN-2021-49 | latest | en | 0.660384 |
https://www.metric-conversions.org/energy-and-power/foot-pounds-to-ergs.htm | 1,713,495,019,000,000,000 | text/html | crawl-data/CC-MAIN-2024-18/segments/1712296817253.5/warc/CC-MAIN-20240419013002-20240419043002-00140.warc.gz | 805,031,682 | 12,537 | # Foot-pounds to Ergs (ft-lb to erg)
Ergs to Foot-pounds (Swap Units)
Format
Accuracy
Note: Fractional results are rounded to the nearest 1/64. For a more accurate answer please select 'decimal' from the options above the result.
Note: You can increase or decrease the accuracy of this answer by selecting the number of significant figures required from the options above the result.
Note: For a pure decimal result please select 'decimal' from the options above the result.
Show formula
## Foot-pounds to Ergs formula
erg =
ft-lb
______________
0.000000073756
Show working
Show result in exponential format
## Foot-pounds
One foot pound is the work done by a force of one pounl acting through a distance of one foot, in the direction of the force. It equates to 1.355 817 948 331 4004 joules
erg =
ft-lb
______________
0.000000073756
## Ergs
One erg is equal to the work done by a force of one dyne, when its point of application moves 1cm in the direction of action
## Foot-pounds to Ergs table
Start
Increments
Accuracy
Format
Print table
< Smaller Values Larger Values >
Foot-pounds Ergs
0ft-lb 0.00erg
1ft-lb 13558179.47erg
2ft-lb 27116358.94erg
3ft-lb 40674538.41erg
4ft-lb 54232717.88erg
5ft-lb 67790897.35erg
6ft-lb 81349076.82erg
7ft-lb 94907256.29erg
8ft-lb 108465435.76erg
9ft-lb 122023615.23erg
10ft-lb 135581794.70erg
11ft-lb 149139974.17erg
12ft-lb 162698153.64erg
13ft-lb 176256333.11erg
14ft-lb 189814512.58erg
15ft-lb 203372692.05erg
16ft-lb 216930871.52erg
17ft-lb 230489050.99erg
18ft-lb 244047230.46erg
19ft-lb 257605409.93erg
Foot-pounds Ergs
20ft-lb 271163589.40erg
21ft-lb 284721768.87erg
22ft-lb 298279948.34erg
23ft-lb 311838127.81erg
24ft-lb 325396307.28erg
25ft-lb 338954486.75erg
26ft-lb 352512666.22erg
27ft-lb 366070845.69erg
28ft-lb 379629025.16erg
29ft-lb 393187204.63erg
30ft-lb 406745384.10erg
31ft-lb 420303563.57erg
32ft-lb 433861743.04erg
33ft-lb 447419922.51erg
34ft-lb 460978101.98erg
35ft-lb 474536281.45erg
36ft-lb 488094460.92erg
37ft-lb 501652640.39erg
38ft-lb 515210819.86erg
39ft-lb 528768999.33erg
Foot-pounds Ergs
40ft-lb 542327178.80erg
41ft-lb 555885358.27erg
42ft-lb 569443537.74erg
43ft-lb 583001717.21erg
44ft-lb 596559896.68erg
45ft-lb 610118076.15erg
46ft-lb 623676255.62erg
47ft-lb 637234435.09erg
48ft-lb 650792614.56erg
49ft-lb 664350794.03erg
50ft-lb 677908973.50erg
51ft-lb 691467152.97erg
52ft-lb 705025332.44erg
53ft-lb 718583511.91erg
54ft-lb 732141691.38erg
55ft-lb 745699870.85erg
56ft-lb 759258050.32erg
57ft-lb 772816229.79erg
58ft-lb 786374409.26erg
59ft-lb 799932588.73erg | 1,012 | 2,559 | {"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} | 3.078125 | 3 | CC-MAIN-2024-18 | latest | en | 0.474037 |
https://www.hackmath.net/en/example/1737?tag_id=46 | 1,558,699,560,000,000,000 | text/html | crawl-data/CC-MAIN-2019-22/segments/1558232257605.76/warc/CC-MAIN-20190524104501-20190524130501-00069.warc.gz | 797,704,810 | 7,085 | # Pennies
800 pennies have the same value as 100 ducats. 100 pennies have the same value as 250 tolars. How many ducats has the same value as 100 tolars?
Result
x = 5
#### Solution:
Leave us a comment of example and its solution (i.e. if it is still somewhat unclear...):
Be the first to comment!
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17. Copper plate
Calculate the thickness of the copper plate with a density 8.7 g/cm³ measuring 1.5 meters and 80 cm and its weight is 3.65 kg | 940 | 3,541 | {"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} | 3.75 | 4 | CC-MAIN-2019-22 | latest | en | 0.930642 |
https://learnandlearn.com/python-programming/python-reference/python-copysign-function | 1,524,740,608,000,000,000 | text/html | crawl-data/CC-MAIN-2018-17/segments/1524125948126.97/warc/CC-MAIN-20180426105552-20180426125552-00555.warc.gz | 630,218,258 | 16,853 | # Python copysign() Function
Python `copysign(x,y)` function exists in Standard math Library of Python Programming Language. This function returns a float value consisting of magnitude from parameter` x `and the sign (+ve or -ve) from parameter `y`. This means the sign (+ve or -ve) of parameter `y` is attached to the magnitude of parameter` x`. For example if:
For example if:
Parameter x = 3
Parameter y = -2
The return value will be: -3.0
Here 3 is taken from parameter x and –ve sign is taken from parameter` y`. In return, a float -3.0 is returned. In this reference, `copysign()` function will further be elaborated from a programming perspective.
## Python `copysign()` Function Syntax:
The syntax of `copysign(x,y)` function in Python is:
`math.copysign( x , y )`
## Python `copysign()` Function Parameters:
`x` is any valid Python number. This parameter is required.
`y` any valid Python number. This parameter is required.
Note: In `copysign()` function, both of the parameters are required.
Python 2.x – Yes
Python 3.x – Yes
## Python `copysign()` Function Return Value:
This function will return a float value which is consist of the absolute value or the magnitude of the parameter` x `and the sign of parameter `y`.
## Python `copysign()` Function Example:
Output of Python copysign() function:
` 4.0 -4.0 ` | 343 | 1,336 | {"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} | 2.578125 | 3 | CC-MAIN-2018-17 | longest | en | 0.405545 |
https://www.reference.com/web?q=Isaac+Newton+Laws&qo=contentPageRelatedSearch&o=600605&l=dir&gc=1 | 1,531,954,169,000,000,000 | text/html | crawl-data/CC-MAIN-2018-30/segments/1531676590329.62/warc/CC-MAIN-20180718213135-20180718233135-00403.warc.gz | 946,324,993 | 13,670 | articles
Newton's Third Law of Motion is that all forces operate in equal pairs that move in opposite directions. This is often summarized as "for every action, there is an equal and opposite reaction." More »
www.reference.com Science Physics Motion & Mechanics
Isaac Newton was a physicist, an astronomer, a mathematician and a natural philosopher who lived in England during the 17th and 18th centuries. Today, many scientists consider him to be one of the most influential scient... More »
www.reference.com History Modern History Renaissance & Reformation
Newton's first law of movement is the definition of inertia. The second law is known as the law of momentum: force equals mass times acceleration (F=M*A). The third law is that for every action, there is an equal and opp... More »
www.reference.com Science Physics Motion & Mechanics
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Newton’s Third Law of Motion states that for any action, there is an equal and opposite reaction. In terms of force, the Third Law of Motion states that for every force, there is a reaction force that is equal in size an... More »
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A common example of Newton's Third Law of Motion is found in swimming. As force is exerted against the water with the movement of an arm or leg, it creates an equal, opposite reaction against the swimmer by the water pro... More »
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Some examples of Newton's Third Law are a person pushing against a wall, fish swimming in water, birds flying in the air and the automobile´s propulsion. Newton's Third Law explains the interaction between objects and st... More »
www.reference.com Science Physics Motion & Mechanics | 407 | 2,011 | {"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} | 2.859375 | 3 | CC-MAIN-2018-30 | latest | en | 0.903209 |
https://talkfreethought.org/showthread.php?20002-quot-Line-numbers-quot-finding-a-number-for-any-symbol&s=85cc5d50b6d5a4c9d5cfd8dec5c0dfd8&p=743069 | 1,575,569,775,000,000,000 | text/html | crawl-data/CC-MAIN-2019-51/segments/1575540481281.1/warc/CC-MAIN-20191205164243-20191205192243-00257.warc.gz | 572,791,695 | 11,987 | # Thread: "Line numbers" finding a number for any symbol
1. ## "Line numbers" finding a number for any symbol
edit: the title is incorrect - it is only about line-based 2D graphical symbols...
Hi I was wondering if anyone has heard of this before.... (not from me)
I think just about any line-based 2D graphical symbol can have the "line number" determined...
e.g.
The following symbols involve the following numbers based on how many lines are involved:
3, 4, 2, 1...
Perhaps a 0 could be represented using a dot (0 lines) - the problem with that is that any number of dots would still be a 0.
The infinity symbol is a 1, a cross is a 2 (duality) but I'm not sure about the yin-yang symbol (depends if the inner "S" is joined to the outer circle). The pentagram is 5 and David's star is 6. On a related note, I was told that a 5 pointed star is a feminine star while the 6 pointed star is masculine.
This "heartagram" is a 3.
2. Here the "line numbers" are used to represent numbers:
https://www.digmandarin.com/chinese-tally-mark.html
3. Finding a system is easy . . .
It gets difficult with larger numbers . . .
Pops
4. Well I've been working on the website:
The LineNum Source
5. This video I'm using happened to have a guy with a plain triangle symbol on his arm.... what are the odds!?
6. In addition to the Circle, Cross, Triangle, Square, Star (1 2 3 4 5 lines) I've made the "5 line number energies":
I think they're way better that the 4 elements...
#### Posting Permissions
• You may not post new threads
• You may not post replies
• You may not post attachments
• You may not edit your posts
• | 421 | 1,627 | {"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} | 3.109375 | 3 | CC-MAIN-2019-51 | latest | en | 0.945801 |
https://www.esaral.com/q/the-wavelength-of-an-x-ray-beam-is-10-a-14786 | 1,718,768,883,000,000,000 | text/html | crawl-data/CC-MAIN-2024-26/segments/1718198861797.58/warc/CC-MAIN-20240619025415-20240619055415-00520.warc.gz | 659,937,691 | 11,388 | # The wavelength of an X-ray beam is 10 A.
Question:
The wavelength of an X-ray beam is $10 \AA$. The mass of a fictitious particle having the same energy as that of the $X$ - ray photons is $\frac{x}{3} h \mathrm{~kg}$. The value of $x$ is
Solution:
(10)
Given wavelength of an $x$-ray beam =10 A
$\because E=\frac{h c}{\lambda}=m c^{2}$\
$m=\frac{h}{c \lambda}$
The mass of a fictitious particle having the same energy as that of the $x$-ray photons $=\frac{x}{3}$ hkg
$\frac{x}{3} h=\frac{h}{c \lambda}$
$x=\frac{3}{c \lambda}$
$=\frac{3}{3 \times 10^{8} \times 10 \times 10^{-10}}$
$x=10$
Leave a comment
Click here to get exam-ready with eSaral | 226 | 663 | {"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} | 4.03125 | 4 | CC-MAIN-2024-26 | latest | en | 0.726435 |
https://xbuzznet.com/qa/what-is-an-equation-of-a-horizontal-line.html | 1,618,155,421,000,000,000 | text/html | crawl-data/CC-MAIN-2021-17/segments/1618038064520.8/warc/CC-MAIN-20210411144457-20210411174457-00062.warc.gz | 1,209,866,643 | 5,576 | # What Is An Equation Of A Horizontal Line?
## What is the equation of a horizontal line through (- 4 6?
In a horizontal line the y value remains the same.
In the point ( -4.
-6 ) the y value is -6.
the point notation is always written as ( x, y)..
## What is an equation of the horizontal line that passes through 5 − 7?
The point (a,b) is (5,7) . Therefore, the equation of the line is y=7 .
## What is an example of a horizontal line?
An equation that only crosses the y-axis is a horizontal line. … For example: y=5 is a horizontal line that crosses the y-axis at (0,5).
## What is the slope of any horizontal line?
Slope of a horizontal line. When two points have the same y-value, it means they lie on a horizontal line. The slope of such a line is 0, and you will also find this by using the slope formula. | 213 | 824 | {"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} | 4.1875 | 4 | CC-MAIN-2021-17 | latest | en | 0.890699 |
https://en.scratch-wiki.info/wiki/Boolean | 1,581,947,068,000,000,000 | text/html | crawl-data/CC-MAIN-2020-10/segments/1581875142323.84/warc/CC-MAIN-20200217115308-20200217145308-00420.warc.gz | 374,648,061 | 10,739 | (Redirected from Boolean)
The general shape of a Boolean block.
A Boolean block is an elongated hexagonal block that reports boolean values. When the block is used, it acts as a reporter block, reporting "true" or "false" string values or the numbers "1" and "0" depending on their usage in a script.
There are 13 Boolean blocks, and they can be found in the Sensing, Operators and Variables categories. Custom blocks can have Boolean inputs that may be present in a block definition.
## Blocks
There are 13 Boolean blocks in Scratch 3.0. Click on a block for more information.
## Shape
Boolean blocks are conditions that can either be true or false. They have a hexagonal shape and fit in the corresponding hexagonal slot on other blocks.
The condition gap can be filled with any Boolean block:
```if <key (space v) pressed?> then
end
```
Despite their shapes, Boolean blocks also fit in string and number inputs:
```when gf clicked
forever
say <touching (Sprite1 v)?>
```
In general, Booleans return string values of "true" or "false", but when inserted into a reporter input, the Boolean instead will return "1" or "0", allowing mathematical operations to be performed. For example, consider the script below:
```when gf clicked
forever
say ((3) + <touching (Sprite1 v)?>)
end
```
If the Boolean condition is true, the sprite will say the number "4". A true condition is an equivalent to "1". If the Boolean condition is false, the sprite will say the number "3". A false condition is equivalent to "0". Whether the numbers "1" and "0" are strings or numbers is not important in Scratch since the specification of variables types is unnecessary, unlike some other programming languages.
If the () + () block is ommitted entirely, the Boolean will then return "true" or "false" since the Boolean block would lie in a string input instead of a reporter input.
## Types
Scratch has two types of booleans: booleans that check a specific condition and comparative Booleans.
Conditional booleans check a specific condition. Examples include the () Contains () and Touching ()? blocks.
Comparative booleans compare values. These include () = (), () and (), and Not (). For some of these, a truth table will predict their return values.
## Uses
As Boolean blocks are conditions (and report if they are true or false), they are used whenever a condition is needed. Conditions are used with some C blocks and some Control Stack blocks. A common use for conditions is the If () Then block — if the condition is true, the blocks held inside the C block will activate.
There are a variety of different conditions that can be checked, from checking if the mouse is touching a sprite to checking if a value is equal to another value. An example is below:
```when flag clicked
wait until <touching (edge v)?>
say [Done!] for (2) secs
stop [this script v]
```
The Wait Until () block pauses the script until the Boolean value, here `<touching (edge v)?>`, is true. While the sprite is not touching the edge, `<touching (edge v)?>` is false, and the block waits for it to become true. When the sprite touches the edge, `<touching (edge v)?>` becomes true, and the script below it is run.
## Other Uses
A Boolean block can be used in a string input. If a Boolean in a String input is true, it reports "true". If the Boolean is false, it returns "false". For example, `say <touching (mouse-pointer v)?>` makes the sprite say "true" if the sprite is touching the mouse pointer, and "false" otherwise.
### Direct Comparison
Boolean variables can be compared to non-Boolean variables. For example, the following script, two Booleans are compared to each other directly, and the if statement will execute the code inside if both have the same value (i.e. both true or both false).
```if <<mouse down> = <touching color (#00A)>> then
...
end
```
### Reporting Booleans
Sensor ()? is the only Boolean that can be displayed as a Stage monitor. However, it can be plugged into a Say () block to report the value.
```when gf clicked
forever
say <touching (mouse-pointer v)?>
```
### Storage in Variables
Booleans can be stored in variables as well. The following script stores the current mouse state in the variable "bool".
```set [bool v] to <mouse down?>
```
Later, the variable can be compared to another Boolean with the stored variable:
```if <<mouse down?> = (bool)> then
...
end
```
In this case, the script will check whether the mouse currently has the same state as it did when the variable was stored. | 1,041 | 4,524 | {"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} | 2.75 | 3 | CC-MAIN-2020-10 | latest | en | 0.839171 |
https://fr.mathworks.com/matlabcentral/cody/problems/2533-find-out-sum-of-principal-diagonal-element-of-given-matrix/solutions/769302 | 1,601,311,346,000,000,000 | text/html | crawl-data/CC-MAIN-2020-40/segments/1600401601278.97/warc/CC-MAIN-20200928135709-20200928165709-00415.warc.gz | 371,087,713 | 16,649 | Cody
# Problem 2533. Find Out sum of principal diagonal element of given matrix
Solution 769302
Submitted on 31 Oct 2015 by Peng Liu
This solution is locked. To view this solution, you need to provide a solution of the same size or smaller.
### Test Suite
Test Status Code Input and Output
1 Pass
%% x = 1; y_correct = 1; assert(isequal(sum_diag(x),y_correct))
2 Pass
%% x = eye(3); y_correct = 3; assert(isequal(sum_diag(x),y_correct))
3 Pass
%% x = magic(3); y_correct = 15; assert(isequal(sum_diag(x),y_correct)) | 155 | 528 | {"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} | 2.53125 | 3 | CC-MAIN-2020-40 | latest | en | 0.60986 |
http://senseis.xmp.net/?ChineseCounting | 1,498,349,835,000,000,000 | text/html | crawl-data/CC-MAIN-2017-26/segments/1498128320368.57/warc/CC-MAIN-20170624235551-20170625015551-00413.warc.gz | 345,355,741 | 5,429 | # Chinese Counting
Difficulty: Intermediate Keywords: Rules
Chinese counting can be used for rules that define scoring by area. As a reminder, in area scoring, your score is:
• the number of your stones on the board and
• the number of empty points your stones surround
## Preparing for counting
1. Determine which stones are dead,[1] according to the rule set used.
2. Note your territories: They are the empty points surrounded entirely by your living stones.
3. Remove all dead stones from your territories. These can be placed back in your opponent's bowl.
1. Now you want to make the empty territories you surround be multiples of ten points. To this end you can simply remove stones of your color from the board and return them to your bowl. You can also take stones from your bowl and add them to the board.
This step often distresses people. Remember that with area scoring, you get one point for each empty point you surround, and one point for each stone on the board. So if you take a stone off the board, but leave an empty point it doesn't change your score. Similarly, if you fill one of your empty points with a stone of your own color, it also doesn't change your score.
2. Make a note of the number of empty points. This should be a nice round number, a multiple of ten.
Some people place one stone for every ten points on the table, up against the board, as a reminder.
3. Now count your stones. At this point you can destroy arrangement of stones on the board and simply clump the stones into piles of ten.
If both players are counting their score this way, then you need to make sure that you both have completed counting your empty areas before either of you start this part. Once you start this part, the empty areas on the board will be destroyed. However, see half counting, below.
4. Add the number of stones counted in step 3 to the number of empty points noted in step 2. This is your score.
5a. If there is komi, add it to White's score.
5b. If it is a handicap game, add the number of handicap stones to White's score. (Subtract it from Black's score if counting Black)
## Half counting
In practice, only Black's score needs to be counted. This is because in area scoring, after the dead stones are removed, every point on the board is either:
• White stone (counts for white's score)
• Empty point surrounded by White (counts for white's score) [2]
• Black stone (counts for black's score)
• Empty point surrounded by Black (counts for black's score) [2]
• Empty point that doesn't score [3]
So, if you know:
• The number points on the board (for example, 19x19 = 361)
• Minus the number of points that don't score (usually 0)
• This equals the number of points shared between White and Black
Divide this last number by two, and all you need to know is if Black's score is more or less than this 'half count'. If Black has more, then White has less, and Black wins. If Black has less, then White has more, and White wins.
For every point the winner has over this half count, the Loser is a point below. So the difference between the two scores is twice the difference between the Black's score and the half count.
To deal with komi, subtract the komi from Black's score.
## Example
There is a Chinese counting example with step-by-step diagrams.
## Further techniques
• When performing step 3 above, it is often desirable to create large rectangular shaped empty territories. One can swap equal numbers of Black stones and White stones as and where convenient, to make it easier to clear the stones to create the large rectangular shaped empty territories. See example below.
Example
We can interchange the and stones to create a 5 x 4 = 20 point empty space for White on the upper left corner.
• When using half counting and dealing with points that don't score [3], one can simply fill in equal numbers of Black and White stones in those points. Thus, the number of such points is reduced to either zero or one, simplifying the calculation.
[1] Under area scoring, dead stones are usually determined by agreement, and otherwise by playing it out, but details on this vary between rule sets. The word dead may not always be the most appropriate word to describe the stones to be removed, see discussion.
[2] Includes eyes in seki.
[3] For example, shared liberties in seki. | 968 | 4,339 | {"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} | 2.796875 | 3 | CC-MAIN-2017-26 | latest | en | 0.933293 |
https://www.jobilize.com/online/course/0-5-1-6-vectors-scalars-and-coordinate-systems-by-openstax | 1,579,492,762,000,000,000 | text/html | crawl-data/CC-MAIN-2020-05/segments/1579250597230.18/warc/CC-MAIN-20200120023523-20200120051523-00548.warc.gz | 954,308,858 | 19,767 | # 0.5 1.6 vectors, scalars, and coordinate systems
Page 1 / 3
• Define and distinguish between scalar and vector quantities.
• Assign a coordinate system for a scenario involving one-dimensional motion.
What is the difference between distance and displacement? Whereas displacement is defined by both direction and magnitude, distance is defined only by magnitude. Displacement is an example of a vector quantity. Distance is an example of a scalar quantity. A vector is any quantity with both magnitude and direction . Other examples of vectors include a velocity of 90 km/h east and a force of 500 newtons straight down.
The direction of a vector in one-dimensional motion is given simply by a plus $\left(+\right)$ or minus $\left(-\right)$ sign. Vectors are represented graphically by arrows. An arrow used to represent a vector has a length proportional to the vector’s magnitude (e.g., the larger the magnitude, the longer the length of the vector) and points in the same direction as the vector.
Some physical quantities, like distance, either have no direction or none is specified. A scalar is any quantity that has a magnitude, but no direction. For example, a $\text{20ºC}$ temperature, the 250 kilocalories (250 Calories) of energy in a candy bar, a 90 km/h speed limit, a person’s 1.8 m height, and a distance of 2.0 m are all scalars—quantities with no specified direction. Note, however, that a scalar can be negative, such as a $-\text{20ºC}$ temperature. In this case, the minus sign indicates a point on a scale rather than a direction. Scalars are never represented by arrows.
## Section summary
• A vector is any quantity that has magnitude and direction.
• A scalar is any quantity that has magnitude but no direction.
• Displacement and velocity are vectors, whereas distance and speed are scalars.
what is the stm
How we are making nano material?
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What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
How can I make nanorobot?
Lily
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
how can I make nanorobot?
Lily
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
Difference between extinct and extici spicies
in a comparison of the stages of meiosis to the stage of mitosis, which stages are unique to meiosis and which stages have the same event in botg meiosis and mitosis
Researchers demonstrated that the hippocampus functions in memory processing by creating lesions in the hippocampi of rats, which resulted in ________.
The formulation of new memories is sometimes called ________, and the process of bringing up old memories is called ________.
Got questions? Join the online conversation and get instant answers! | 1,139 | 5,041 | {"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} | 4.15625 | 4 | CC-MAIN-2020-05 | longest | en | 0.911055 |
https://brainmass.com/physics/equilibrium/pg3 | 1,519,234,005,000,000,000 | text/html | crawl-data/CC-MAIN-2018-09/segments/1518891813691.14/warc/CC-MAIN-20180221163021-20180221183021-00215.warc.gz | 613,425,336 | 21,085 | Explore BrainMass
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