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https://keio.pure.elsevier.com/en/publications/dynamical-systems-of-type-mn-and-their-c-algebras | # Dynamical systems of type (m,n) and their C*-algebras
Pere Ara, Ruy Exel, Takeshi Katsura
Research output: Contribution to journalArticle
12 Citations (Scopus)
### Abstract
Given positive integers n and m, we consider dynamical systems in which (the disjoint union of) n copies of a topological space is homeomorphic to m copies of that same space. The universal such system is shown to arise naturally from the study of a C*-algebra denoted by {\cal O}-{m,n}, which in turn is obtained as a quotient of the well-known Leavitt C*-algebra L-{m,n}, a process meant to transform the generating set of partial isometries of L-{m,n} into a tame set. Describing {\cal O}-{m,n} as the crossed product of the universal (m,n)-dynamical system by a partial action of the free group F-m+n, we show that {\cal O}-{m,n} is not exact when n and m are both greater than or equal to 2, but the corresponding reduced crossed product, denoted by {\cal O}-{m,n} r, is shown to be exact and non-nuclear. Still under the assumption that m,n 2, we prove that the partial action of \mathbb F-m+n is topologically free and that O-m,n r satisfies property (SP) (small projections). We also show that {\cal O}-{m,n}^radmits no finite-dimensional representations. The techniques developed to treat this system include several new results pertaining to the theory of Fell bundles over discrete groups.
Original language English 1291-1325 35 Ergodic Theory and Dynamical Systems 33 5 https://doi.org/10.1017/S0143385712000405 Published - 2013 Oct
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Partial Action
Crossed Product
Algebra
C*-algebra
Dynamical systems
Dynamical system
Partial Isometry
Process Mean
Generating Set
Discrete Group
Homeomorphic
Free Group
Topological space
Bundle
Disjoint
Quotient
Union
Projection
Transform
Integer
### ASJC Scopus subject areas
• Mathematics(all)
• Applied Mathematics
### Cite this
Dynamical systems of type (m,n) and their C*-algebras. / Ara, Pere; Exel, Ruy; Katsura, Takeshi.
In: Ergodic Theory and Dynamical Systems, Vol. 33, No. 5, 10.2013, p. 1291-1325.
Research output: Contribution to journalArticle
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https://testbook.com/question-answer/the-ideal-angle-of-banking-provided-on-the-curves--602248957f58a1d5c1097f44 | # The ideal angle of banking provided on the curves of the roads depends on:
This question was previously asked in
JKSSB JE ME 2015 Official Paper
View all JKSSB JE Papers >
1. Weight of the vehicle.
2. Square of the velocity of the vehicle.
3. Nature of the road surface.
4. Co-efficient of friction between the road and vehicle contact point.
Option 2 : Square of the velocity of the vehicle.
Free
ST 1: General Knowledge
2958
20 Questions 20 Marks 20 Mins
## Detailed Solution
Explanation:
Whenever a roadway (or railway) is laid on a curved path, then its outer edge is always made higher than the inner edge, to keep the vehicle in equilibrium while in motion.
The amount by which the outer edge is raised is known as cant or superelevation.
In the case of roadways, the process of providing superelevation is known as banking of the roads. The general practice, to define the superelevation in roadways, is to mention the angle of inclination (also called the angle of banking) of the road surface, such that
$$\tan {\rm{\theta }} = \frac{{{{\rm{v}}^2}}}{{{\rm{gr}}}}$$
Where v = Velocity of the vehicle, r = Radius of the circular path.
In the case of railways, the general practice to define the superelevation is to mention the difference of levels between the two rails. In such a case, superelevation is given by
$${S} = \frac{{{\rm{G}}{{\rm{v}}^2}}}{{{\rm{gr}}}}$$
Where G = gauge of the track.
Note:
(1) When a vehicle is moving on a level circular path, then the maximum velocity of the vehicle, in order to avoid overturning is given by
$${{\rm{v}}_{{\rm{max}}}} = \sqrt {\frac{{gra}}{h}}$$
and in order to avoid skidding
$${{\rm{v}}_{{\rm{max}}}} = \sqrt {μ gr}$$
Where h = Height of center of gravity of the vehicle from the ground level, 2a = Distance between the outer and inner wheel, and μ = coefficient of friction between the wheels of the vehicle and the ground, g = acceleration due to gravity.
(2) When a vehicle moves on a level circular path, the reaction (Rin) at the inner wheel is given by
$${{\rm{R}}_{{\rm{in}}}} = \frac{{mg}}{2}\left( {1 - \frac{{{v^2}h}}{{gra}}} \right)$$
and reaction (Rot) at the outer wheel
$${{\rm{R}}_{{\rm{ot}}}} = \frac{{mg}}{2}\left( {1\; + \;\frac{{{v^2}h}}{{gra}}} \right)$$
Where m = Mass of the vehicle in kg. | 2021-09-17 03:25:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7474056482315063, "perplexity": 975.1423797427826}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780054023.35/warc/CC-MAIN-20210917024943-20210917054943-00651.warc.gz"} |
https://ysharifi.wordpress.com/category/noncommutative-ring-theory-notes/von-neumann-regular-rings/ | ## von Neumann regular rings (3)
Posted: October 31, 2010 in Noncommutative Ring Theory Notes, von Neumann Regular rings
Tags: , , , , ,
We saw in part (2) that von Neumann regular rings live somewhere between semisimple and semiprimitive rings. The goal in this post is to prove a theorem of Armendariz and others which gives a necessary and sufficient condition for a ring to be both regular and reduced. This result extends Kaplansky’s result for commutative rings (see the corollary at the end of this post). We remark that a commutative von Neumann regular ring $R$ is necessarily reduced. That is because if $x^2=0$ for some $x \in R,$ then choosing $y \in R$ with $x=xyx$ we will get $x=yx^2=0.$
Definition . A von Neumann regular ring $R$ is called strongly regular if $R$ is reduced.
Theorem 1. (Armendariz, 1974) A ring $R$ with 1 is strongly regular if and only if $R_M$ is a division ring for all maximal ideals $M$ of $Z(R).$
Proof. Suppose first that $R$ is strongly regular and let $M$ be a maximal ideal of $Z(R).$ Let $0 \neq s^{-1}x \in R_M.$ So $tx \neq 0$ for all $t \in Z(R) \setminus M.$ Since $R$ is regular, there exists some $y \in R$ such that $xyx = x.$ Then $xy=e$ is an idempotent and thus $e \in Z(R)$ because in a reduced ring every idempotent is central. Since $(1-e)x=0$ we have $1-e \in M$ and hence $e \in Z(R) \setminus M.$ Thus $e^{-1}sy$ is a right inverse of $s^{-1}x.$ Similarly $f=yx \in Z(R) \setminus M$ and $f^{-1}sy$ is a left inverse of $s^{-1}x.$ Therefore $s^{-1}x$ is invertible and hence $R_M$ is a division ring. Conversely, suppose that $R_M$ is a division ring for all maximal ideals $M$ of $Z(R).$ If $R$ is not reduced, then there exists $0 \neq x \in R$ such that $x^2=0.$
Let $I=\{s \in Z(R): \ sx = 0 \}.$ Clearly $I$ is a proper ideal of $Z(R)$ and hence $I \subseteq M$ for some maximal ideal $M$ of $Z(R).$ But then $(1^{-1}x)^2=0$ in $R_M,$ which is a division ring. Thus $1^{-1}x=0,$ i.e. there exists some $s \in Z(R) \setminus M$ such that $sx = 0,$ which is absurd. To prove that $R$ is von Neumann regular, we will assume, to the contrary, that $R$ is not regular. So there exists $x \in R$ such that $xzx \neq x$ for all $z \in R.$ Let $J= \{s \in Z(R): \ xzx=sx \ \text{for some} \ z \in R \}.$ Clearly $J$ is a proper ideal of $Z(R)$ and so $J \subseteq M$ for some maximal ideal $M$ of $Z(R).$ It is also clear that if $sx = 0$ for some $s \in Z(R),$ then $s \in J$ because we may choose $z = 0.$ Thus $1^{-1}x \neq 0$ in $R_M$ and hence there exists some $y \in R$ and $t \in Z(R) \setminus M$ such that $1^{-1}x t^{-1}y = 1.$ Therefore $u(xy-t)=0$ for some $u \in Z(R) \setminus M.$ But then $x(uy)x=utx$ and so $ut \in J,$ which is nonsense. This contradiction proves that $R$ must be regular. $\Box$
Corollary. (Kaplansky) A commutative ring $R$ is regular if and only if $R_M$ is a field for all maximal ideals $M$ of $R. \ \Box$
At the end let me mention a nice property of strongly regular rings.
Theorem 2. (Pere Ara, 1996) If $R$ is strongly regular and $Ra+Rb=R,$ for some $a, b \in R,$ then $a+rb$ is a unit for some $r \in R.$
## von Neumann regular rings (2)
Posted: October 22, 2010 in Noncommutative Ring Theory Notes, von Neumann Regular rings
Tags: , ,
Theorem 1. (von Neumann, 1936) The center of a regular ring $R$ is regular.
Proof. Let $a$ be a central element of $R$ and let $x \in R$ be such that $a=axa=a^2x.$ So $a^2x$ is central. Let $z \in R.$ Then $a^2xz=za^2x$ and hence $xa^2z=a^2zx,$ i.e. $a^2z$ commutes with $x$ and so it commutes with $x^3.$ Therefore $a^2x^3z=za^2x^3,$ i.e. $y=a^2x^3$ is central. But, since $a^2x^2=ax,$ we have $y=ax^2$ and clearly $aya=a^2x^2a=axa=a.$ $\Box$
Remark. In a commutative regular ring $R$ every prime ideal $P$ is maximal. To see this, let $a \in R \setminus P$ and $r \in R$ be such that $a=ara.$ Then $a(1-ra)=0 \in P$ and so $1-ra \in P.$ Therefore $P+Ra=R$ and hence $P$ is maximal.
Notation. Let $M$ be a maximal ideal of $Z(R),$ the center of $R.$ The localization of $R$ at $M$ is denoted by $R_M.$
Lemma. If $R$ is a commutative regular ring and $M$ is a maximal ideal of $R,$ then $R_M$ is a field.
Proof. The unique maximal ideal of $R_M$ is $M_M.$ So, to prove that $R_M$ is a field, we only need to show that $M_M=\{0\},$ i.e. for every $a \in M,$ there exists some $s \notin M$ such that $sa=0.$ This is easy to see: we have $a=xa^2,$ for some $x \in R,$ because $R$ is a commutative regular ring, and thus $(1-xa)a=0$ and clearly $s=1-xa \notin M$ because $a \in M. \ \Box$
The converse of the lemma is also true and we will prove it in a more general setting in part (3). This result that a commutative ring $R$ is regular if and only if $R_M$ is a field for any maximal ideal $M$ of $R$ is due to Kaplansky.
Theorem 2. (Armendariz, 1974) Let $R$ be a ring with the center $Z(R).$ If $Z(R)$ is regular, then $R/MR \cong R_M$ for any maximal ideal $M$ of $Z(R).$
Proof. Let $f: R \longrightarrow R_M$ be the natural homomorphism defined by $f(x)=1^{-1}x,$ for all $x \in R.$ Let $S=Z(R) \setminus M.$
1) $f$ is surjective. To see this, let $s^{-1}x \in R_M.$ Since $Z(R)$ is regular, there exists some $c \in Z(R)$ such that $s=cs^2.$ Hence $s(1-cs)=0$ and therefore $f(cx)=1^{-1}cx = s^{-1}x.$
2) $\ker f = MR.$ To see this, let $f(x)=1^{-1}x=0.$ That means $sx = 0$ for some $s \in S.$ Since $Z(R)$ is regular, there exists some $c \in Z(R)$ such that $s(1-cs)=0 \in M.$ Thus $1-cs \in M$ because $s \notin M.$ Therefore $x=(1-cs)x \in MR.$ This proves $\ker f \subseteq MR.$ For the other side of the inclusion, we first apply the above lemma to $Z(R)$ to get $1^{-1}a=0$ for all $a \in M.$ Thus for every $a \in M$ and $x \in R$ we have $f(ax)=1^{-1}ax = 1^{-1}a 1^{-1}x = 0.$ So $ax \in \ker f$ and therefore $MR \subseteq \ker f. \ \Box$
## von Neumann Regular rings (1)
Posted: October 22, 2010 in Noncommutative Ring Theory Notes, von Neumann Regular rings
Tags: , , , ,
Definition. A ring $R$ is called von Nemann regular, or just regular, if for every $a \in R$ there exists $x \in R$ such that $a=axa.$
Remark 1. Regular rings are semiprimitive. To see this, let $R$ be a regular ring. Let $a \in J(R),$ the Jacobson radical of $R,$ and choose $x \in R$ such that $a=axa.$ Then $a(1-xa)=0$ and, since $1-xa$ is invertible because $a$ is in the Jacobson radical of $R,$ we get $a=0.$
Examples 1. Every division ring is obviously regular because if $a = 0,$ then $a=axa$ for all $x$ and if $a \neq 0,$ then $a=axa$ for $x = a^{-1}.$
Example 2. Every direct product of regular rings is clearly a regular ring.
Example 3. If $V$ is a vector space over a division ring $D,$ then ${\rm End}_D V$ is regular.
Proof. Let $R={\rm End}_D V$ and $f \in R.$ There exist vector subspaces $V_1, V_2$ of $V$ such that $\ker f \oplus V_1 = {\rm im}(f) \oplus V_2 = V.$ So if $u \in V,$ then $u=u_1+u_2$ for some unique elements $u_1 \in {\rm im}(f)$ and $u_2 \in V_2.$ We also have $u_1 = v_1 + v$ for some unique elements $v_1 \in \ker f$ and $v \in V_1.$ Now define $g: V \longrightarrow V$ by $g(u)=v.$ It is obvious that $g$ is well-defined and easy to see that $g \in R$ and $fgf=f. \ \Box$
Example 4. Every semisimple ring is regular.
Proof. For a division ring $D$ the ring $M_n(D) \cong End_D D^n$ is regular by Example 3. Now apply Example 2 and the Wedderburn-Artin theorem.
Theorem. A ring $R$ is regular if and only if every finitely generated left ideal of $R$ is generated by an idempotent.
Proof. Suppose first that every finitely generated left ideal of $R$ can be generated by an idempotent. Let $x \in R.$ Then $I=Rx = Re$ for some idempotent $e.$ That is $x = re$ and $e=sx$ for some $r,s \in R.$ But then $xsx=xe=re^2=re=x.$ Conversely, suppose that $R$ is regular. We first show that every cyclic left ideal $I=Rx$ can be generated by an idempotent. This is quite easy to see: let $y \in R$ be such that $xyx=x$ and let $yx=e.$ Clearly $e$ is an idempotent and $xe=x.$ Thus $x \in Re$ and so $I \subseteq Re.$ Also $e=yx \in I$ and hence $Re \subseteq I.$ So $I=Re$ and we’re done for this part. To complete the proof of the theorem we only need to show that if $J=Rx_1 + Rx_2,$ then there exists some idempotent $e \in R$ such that $J=Re.$ To see this, choose an idempotent $e_1$ such that $Rx_1=Re_1.$ Thus $J=Re_1 + Rx_2(1-e_1).$ Now choose an idempotent $e_2$ such that $Rx_2(1-e_1)=Re_2$ and put $e_3=(1-e_1)e_2.$ See that $e_3$ is an idempotent, $e_1e_3=e_3e_1=0$ and $Re_2=Re_3.$ Thus $J=Re_1 + Re_3.$ Let $e=e_1+e_3.$ Then $e$ is an idempotent and $J=Re. \Box$
Corollary. If the number of idempotents of a regular ring $R$ is finite, then $R$ is semisimple.
Proof. By the theorem, $R$ has only a finite number of left principal ideals. Since every left ideal is a sum of left principal ideals, it follows that $R$ has only a finite number of left ideals and hence it is left Artinian. Thus $R$ is semisimple because $R$ is semiprimitive by Remark 1. $\Box$
Remark 2. The theorem is also true for finitely generated right ideals. The proof is similar.
Remark 3. Since, by the Wedderburn-Artin theorem, a commutative ring is semisimple if and only if it is a finite direct product of fields, it follows from the Corollary that if the number of idempotents of a commutative von Neumann regular ring $R$ is finite, then $R$ is a finite direct product of fields. | 2018-07-23 02:05:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 264, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9682149291038513, "perplexity": 91.29597424624643}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-30/segments/1531676594790.48/warc/CC-MAIN-20180723012644-20180723032644-00492.warc.gz"} |
https://www.physicsforums.com/threads/rov-stability-analysis.397174/ | ROV stability analysis
1. Apr 21, 2010
andesam
Hi.
Im designing an ROV and need to know it will be stabile during "flight".
I am considering the (imaginary) line between the center of flotation, CF, and center of mass, CM, as a pendulum. Where the tourqe around CF = -mgl*sin(theta). Theta being the angle between the pendulum and the direction of g (the ground).
Alsow, the pendulum is dampend. Tourqe = (ohmega^2)*konstant. Ohmega = rad/s, konstant is calculatet using computer CAD software. (Edit: im not shure if ohmega skould be squared or not here. By definition, the damping ratio is not squared (Ff=-c*v), but for drag force, velocity is squared (Fd=K*v^2).
Now, how can i calculate the time needed for the system to settle (thetha = 0), given a initial angel and angular velocity? Anyting else i should calculate to determine system stability?
- Thanks
Last edited: Apr 21, 2010
2. May 4, 2010
andesam
OK. so i have found a formula wich describes a damped pendulum:
I*Theta''(t)+m*g*L*Theta(t)+Gamma*L^2*Theta'(t)=0
Assuming small variations in theta (-10 - 10 degrees) and that damping force is propotional to gamma.
I being the inertia (m*L^2) and Gamma the damping coff.
Now, i am wondering if its possible to determine Gamma. From the solidworks model i can calculate a formula for drag force (with respect to the water velocity), perpendiculary on to the vessle. Is it possible to calculate Gamma from this information? | 2017-08-19 12:43:37 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8955348134040833, "perplexity": 2811.1804134746567}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-34/segments/1502886105341.69/warc/CC-MAIN-20170819105009-20170819125009-00168.warc.gz"} |
https://www.zbmath.org/?q=an%3A0997.76032 | # zbMATH — the first resource for mathematics
Evidence of longitudinal vortices evolved from distorted wakes in a turbine passage. (English) Zbl 0997.76032
Summary: Two types of longitudinal vortices are found to arise from distorted, migrating wakes convecting through a low-pressure turbine stator passage. The primary vortices emerge within the free stream as the wake is subjected to irrotational strains. Their axes align approximately with the local mean wake velocity. They are dragged over the surface and induce secondary vortices near the wall, which have the sense of rotation opposite to the primary vortices. Although they form on the concave side, these secondary vortices are neither produced nor sustained by Görtler instability; rather, they are a consequence of severely straining the passing wakes. Evidence is drawn from a numerical simulation of the unsteady, incompressible flow through a turbine stator passage with and without upstream turbulent wakes. The computations were performed with 2.5 and $$5.7 \times 10^7$$ grid points on a parallel computer.
##### MSC:
76F25 Turbulent transport, mixing 76F65 Direct numerical and large eddy simulation of turbulence 76D25 Wakes and jets 76U05 General theory of rotating fluids
Full Text: | 2021-05-17 16:44:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6103638410568237, "perplexity": 4468.857570057313}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991258.68/warc/CC-MAIN-20210517150020-20210517180020-00102.warc.gz"} |
http://webermarkovchains.blogspot.com/2012/10/lecture-5.html | ## Thursday, October 18, 2012
### Lecture 5
Today's lecture was on recurrence and transience. Let me make a few comments and emphasise some points:
1. We make the definition that state i is recurrent if $P_i(V_i = \infty)=1$. It is defined to be transient otherwise, i.e if $P_i(V_i = \infty) < 1$. Later (in Theorem 5.3) we show that if $i$ is transient then actually $P_i(V_i = \infty)=0$ (but this is a consequence, not part of our starting definition of transience).
2. In the proof of Theorem 5.4 we use the fact that $p_{ii}^{(n+m+r)} \geq p_{ij}^{(n)} p_{jj}^{(r)} p_{ji}^{(m)}$. Please don't think that we are using any summation notation! (We never use summation convention in this course.) This inequality is a simply product of three terms on the right hand side and is a simple consequence of the fact that one way to go $i\to i$ in $n+m+r$ steps is to first take $n$ steps to go $i\to j$, then $r$ steps to go $j\to j$, and finally $m$ steps to go $j\to i$. There is a $\geq$ because there are other ways to go $i\to i$ in $n+m+r$ steps.
3. The proof of Theorem 5.3 can be presented in one line:
\begin{align*}
\sum_{n=0}^\infty p_{ii}^{(n)}&=
\sum_{n=0}^\infty E_i\left(1_{\{X_n=i\}}\right)
=E_i\left(\sum_{n=0}^\infty 1_{\{X_n=i\}}\right)=E_i(V_i)\12pt] &=\sum_{r=0}^\infty P_i(V_i> r) =\sum_{r=0}^\infty f_i^r= \left\{\begin{array}{cc} \infty, & f_i=1\\[6pt] \frac{1}{1-f_i}, & f_i<1 \end{array}\right. \end{align*} Remember that if A is an event then P(A)=E(1_{\{A\}}), where 1_{\{A\}} is the indicator random variable that =1 or =0 as A does or does not occur. 4. In Theorem 5.5 we gave an important way to check if a state is recurrent or transient, in terms of the summability of the p_{ii}^{(n)}. This criterion will be used in Lecture 6. There are other ways to check for transience. One other way is explained in Theorem 5.9. This is to solve the RHE for the minimal solution to \[ y_j = \sum_k p_{jk} y_k,\quad j \neq i,\quad \text{and } y_i=1.So $y_j =P_j(\text{return to }i)$. Now check the value of $\sum_k p_{ik} y_k$. If it is $< 1$ then $i$ is transient. This is essentially the content of Theorem 5.9, which I have put in my published notes (in blue type) but am not going to discuss in lectures. However, you may find it helpful to read the Theorem. It's proof is simple. | 2019-01-22 05:59:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8720523715019226, "perplexity": 355.2274394333544}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-04/segments/1547583829665.84/warc/CC-MAIN-20190122054634-20190122080634-00019.warc.gz"} |
http://cpr-mathph.blogspot.com/2013/01/13010659-guy-biyogmam.html | ## Leibniz Homology of the Affine Indefinite Orthogonal Lie Algebra [PDF]
Guy Biyogmam
In this paper, we compute the Leibniz (co)homology of the affine indefinite orthogonal Lie algebra. This calculation generalizes a result \cite[corollary 4.5]{JL} obtained by Jerry Lodder. We construct several indefinite orthogonal invariants in terms of balanced tensors and provide the Leibniz homology in terms of these invariants.
View original: http://arxiv.org/abs/1301.0659 | 2019-10-23 05:04:57 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8994500637054443, "perplexity": 2218.459649841415}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570987829458.93/warc/CC-MAIN-20191023043257-20191023070757-00362.warc.gz"} |
https://includestdio.com/6341.html | # Node.js version on the command line? (not the REPL)
## The Question :
598 people think this question is useful
I want to get the version of Node.js on the command line. I’m expecting to run a command like:
node -version
but that doesn’t work. Does anybody know what the command line would be? (i.e. not the REPL)
The Question Comments :
• The different answers suggest completely different questions.
• Yes, the runtime question works for the Node command line, not the shell. Of course, “command line” could refer to either thing.
• Check node --help. But, in short, you need 2 dashes for full-name options: node --version. A single dash starts a group of aliases, so -version combines -v, -e, -r, etc — though only 3 of the 7 are recognized by Node.
• @JonathanLonowski: Good to know about node --help (node -h works too). However, node does not support grouping of options the way you describe; e.g., node -p -i works (syntactically – as of 0.12, no combination of short options makes sense semantically), but node -pi results in an unrecognized flag / bad option (0.12) error.
• This may help somebody!
## The Answer 1
1069 people think this answer is useful
The command line for that is:
node -v
Or
node --version
Note:
If node -v doesn’t work, but nodejs -v does, then something’s not set up quite right on your system. See this other question for ways to fix it.
## The Answer 2
83 people think this answer is useful
If you’re referring to the shell command line, either of the following will work:
node -v
node --version
Just typing node version will cause node.js to attempt loading a module named version, which doesn’t exist unless you like working with confusing module names.
## The Answer 3
39 people think this answer is useful
Try nodejs instead of just node
>process.version
v8.x
## The Answer 7
9 people think this answer is useful
find the installed node version.
$node --version or $ node -v
And if you want more information about installed node(i.e. node version,v8 version,platform,env variables info etc.)
then just do this.
$node > process process { title: 'node', version: 'v6.6.0', moduleLoadList: [ 'Binding contextify', 'Binding natives', 'NativeModule events', 'NativeModule util', 'Binding uv', 'NativeModule buffer', 'Binding buffer', 'Binding util', ... where The process object is a global that provides information about, and control over, the current Node.js process. ## The Answer 8 6 people think this answer is useful By default node package is nodejs, so use $ nodejs -v
or
$nodejs --version You can make a link using $ sudo ln -s /usr/bin/nodejs /usr/bin/node
then u can use
$node --version or $ node -v
## The Answer 9
6 people think this answer is useful
Just type npm version in your command line and it will display all the version details about node, npm, v8 engine etc.
## The Answer 10
2 people think this answer is useful
One cool tip if you are using the Atom editor.
$apm -v apm 1.12.5 npm 3.10.5 node 4.4.5 python 2.7.12 git 2.7.4 It will return you not only the node version but also few other things. ## The Answer 11 1 people think this answer is useful On an Arm7 (armhf) device running Debian Stretch, I had to issue either of the following: $ nodejs -v
$nodejs -h The following did not work: $ node -v
$node -h$ apm -v
Hope this helps someone else.
## The Answer 12
1 people think this answer is useful
open node.js command prompt
run this command
node -v
## The Answer 13
1 people think this answer is useful
You can simply do
node --version
or short form would also do
node -v
If above commands does not work, you have done something wrong in installation, reinstall the node.js and try. | 2021-01-26 08:00:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.42516258358955383, "perplexity": 5955.656256601444}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610704799711.94/warc/CC-MAIN-20210126073722-20210126103722-00436.warc.gz"} |
https://www.physicsforums.com/threads/moment-of-a-couple-need-help-making-sure-answer-is-reasonable.693212/ | # Moment of a Couple, need help making sure answer is reasonable
## Homework Statement
Given the following structure, determine the value of F such that the resultant couple moment on the structure is 200 pound-feet clockwise.
I'm not looking for help here per se, just if this is a valid method of solution:
Because the moment of a couple is a free vector, it seems to me that the moments of the two couples can be placed at point B without any problem.
Then it would also make sense to me that: $M_{\text{couple with F}}=F\cdot 2\sqrt{2}$ pound-feet clockwise, and $M_{\text{150 lb couple}}=600\sqrt{2}$ pound-feet counterclockwise, which gives me that $F\cdot 2\sqrt{2}-600\sqrt{2}=-200$, which implies that $F=229 \text{ lb}$.
Is this a valid method of solution? It makes sense to me, but I'm not sure if it makes sense to anyone else.
Last edited:
Related Engineering and Comp Sci Homework Help News on Phys.org
CWatters | 2020-08-08 11:08:31 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.661251425743103, "perplexity": 377.5980415297735}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737645.2/warc/CC-MAIN-20200808110257-20200808140257-00299.warc.gz"} |
https://gamedev.stackexchange.com/questions/179409/box-collisions-between-vehicles-in-traffic-pattern/187230#187230 | # Box collisions between vehicles in traffic pattern
I'm working on a traffic simulator. Right now, I have ways to manage 4-way stop intersections and a solution for efficiently determining which vehicles are colliding with one another. All vehicles operate independently of each other and will overlap/ignore any vehicles they pass.
I'm looking to build a way to resolve collisions between vehicles such that a Vehicle will follow the Vehicle in front of it. If a Vehicle stops at an intersection, any Vehicles that follow thereafter should stop and wait as well.
Below are the relevant components I already implemented:
• TileGrid containing road segments.
• TravelGraph graph of waypoints for Vehicles to travel along the TileGrid.
• CollisionTracker for efficiently determining which vehicles are colliding, i.e. O(1) lookup for get_collisions(<vehicle_id>) -> List[<vehicle_ids>]
• Intersection for determining which vehicles are waiting at an intersection and determining which Vehicles may pass through it.
The only seemingly-viable algorithm right now is:
1. Calculate velocities and position of all vehicles after tick
2. Determine which vehicles are in a collision
3. Determine which vehicles are in a "collision group" (e.g. if A collides with B, collides with C, then (A, B, C) are in a group)
4. Determine the order of the vehicles in each group based on their velocities (e.g. if A, B, and C are moving to the right and C is the rightmost, followed by B, followed by A, then the order is [C, B, A]).
5. Recalculate the positions of all vehicles, in order from front to back (e.g. C, B, A) such that they reside adjacent to, but not touching the Vehicle in front of them.
Problems with this solution:
• This requires a lot of recalculations. If there's a line of n vehicles waiting on a light, I'd effectively compute 2*n positions per tick in addition to all other overhead for establishing groups, order, etc.
• If the vehicles are following each other around a turn, the logic for finding the "vehicle order" becomes more complex, adding on to the computations per tick.
Ideally moving the vehicles would require n calculations per tick.
I'm open to any/all suggestions here. I've tried building my code as modular as possible, so I'll happily rewrite large parts of it if there's a better architecture to solve this problem.
Below is the visual representation of the TileGrid (black), TileGraph (purple), and Vehicles (circles).
This is commonly achieved by casting rays out from the front of your vehicle.
If your engine doesn't have an implementation of that, at a high level you could implement it manually as:
For each vehicle:
• Find all vehicles in a radius r (or just round up to a bounding square to save the maths)
• Determine whether a line projected forward from the vehicle passes through the bounding box of any target vehicle¹.
• Check line length < radius (or don't bother an instead account for overshoot in the next step)
• Perform some scaling/clamping to get a "braking" factor.
The closer your vehicle gets to one in front, the more rapidly it will brake. Cars behind will follow in turn.
You'll probably want to fire 3 or 5 rays per vehicle in a fan pattern to handle corners/lane changes.
¹ For this step, it's basically just checking whether the ray crosses any of the 4 lines defining the bounding box, althoughn I'm guessing you have this already.
Couldn't you create an event collision box in or around your vehicles to detect if there is another vehicle in front of them?
Then, on that collision you could get the id of the leading car, and create the chain. Since it'll compute once, on_collision_enter, you won't have to keep constant track of every cars speed and velocity.
• Hmm. That’s sounds like a good potential optimization, but I may still need velocity and maybe other data to “undo” a vehicle’s action if it collides with another vehicle after the initial movement calculation, right? Feb 27 '20 at 20:32 | 2021-09-26 15:02:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3399321734905243, "perplexity": 1408.3273370533236}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057882.56/warc/CC-MAIN-20210926144658-20210926174658-00042.warc.gz"} |
https://sails.readthedocs.io/en/1.0.0/api/diagnostics.html | # Model Diagnostics¶
Several classes and/or routines are available to help with examining and diagnosing model fits.
class sails.diags.ModelDiagnostics[source]
Class to store and display LinearModel diagnostic information. Several diagnostic criteria are computed including:
R_square (R_square)
the percentage of variance explained in each channel
Stability Index (SI)
Indicator of the stability of the MVAR parameters (SI<1 indicates a stable model)
Stability Ratio (SR)
A stronger test of stability computed from the ratio of the largest eigenvalue of A to all others.
Durbin-Watson (DW)
A test of autocorrelation in residuals of the model fit. Values should be close to 2 indicating no autocorrelation, values close to 0 indicate a positive autocorrelation and 4 and negative autocorrelation.
Log Likelihood (LL)
The log-likelihood of the model.
Akaike’s Information Criterion (AIC)
An indication of the model ‘quality’, lower values indicate a more accurate, less complex model.
Bayesian Information Criterion (BIC)
An indication of the model ‘quality’, lower values indicate a more accurate, less complex model.
Percent Consistency (PC)
Indicates how well a model captures the auto and cross correlation in a time-series. Only computed if compute_pc is passed to the relevant function.
classmethod combine_diag_list(diags)[source]
Helper function for combining diagnostics from a list of ModelDiagnostics instances for easy comparison and visualisation.
Parameters: diags (list of ModelDiagnostics instances) – The ModelDiagnostics to concatenate sails ModelDiagnostics instance
classmethod compute(model, data, compute_pc=False)[source]
Classmethod for computing a set of model diagnostics from a fitted model applied to a time-series dataset.
Parameters: model (sails LinearModel class) – A fitted linear model data (ndarray) – A 3d time-series of size [nchannels x nsamples x ntrials] compute_pc (bool) – Flag indicating whether to compute the percent consistency, this can be time-consuming for large datasets (Default=False). sails ModelDiagnostics instance
summary(all_models=True)[source]
Print the ModelDiagnostics in a pre-formatted table
class sails.diags.DelayDiagnostics[source]
Class which computes the mutual information as a function of lag from zero lag to the first zero crossing of the autocorrelation function.
Compute MI as a function of lag from zero lag to the first zero crossing of the autocorrelation function
Parameters: data (numpy.ndarray) – array of [signals, samples, trials] maxdelay (int) – maximum delay to consider step (int) – step to increment the delay by sample_rate (float) – sample rate of data constant_window (bool) – Flag indicating that the same number of datapoints should be included at each delay. Default is True Populated object containing diagnostics for each value in delay DelayDiagnostics
sails.modelfit.get_residuals(data, parameters, delay_vect, backwards=False, mode='valid')[source]
This is a helper function for computing the residuals of a dataset after the MVAR predictions have been removed.
Parameters: data (ndarray) – Data to compute the residuals from, of size [nchannels x nsampes x nrealisations] parameters (ndarray) – MVAR parameter matrix, of size [nchannels x nchannels x model order] delay_vect (ndarray) – Vector of lag indices corresponding to the third dimension of the parameter matrix backwards (bool) – Flag indicating whether the forwards or backwards parameters havebeeen passed (Default value = False) mode ({'valid','full_nan','full'}) – Options for excluding or replacing residuals which do not have a full model prediction ie the third sample of an order 5 model. ‘valid’ removes samples without a full model prediction, ‘full_nan’ returns resids of the same size as the data with nans replacing excluded samples and ‘full’ returns resids keeping non-full model samples in place. Residual data, of size [nchannels x nsamples x nrealisations] ndarray | 2021-04-14 10:20:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3756493628025055, "perplexity": 7052.624930147978}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038077810.20/warc/CC-MAIN-20210414095300-20210414125300-00333.warc.gz"} |
https://www.zbmath.org/?q=an%3A0805.35010 | # zbMATH — the first resource for mathematics
Continuity with respect to the domain in the Neumann problem. (Continuité par rapport au domaine dans le problème de Neumann.) (French) Zbl 0805.35010
Summary: It is proved the continuity of the solution of the Neumann problem for the Laplacian in terms of its integration domain, if this presents cracks and satisfies some capacitary constraints. On the space of domains it is considered the Hausdorff complementary topology in which the family of constrained domains is compact.
##### MSC:
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs 35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation 35J25 Boundary value problems for second-order elliptic equations
##### Keywords:
Hausdorff complementary topology | 2021-09-21 03:26:17 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8358756303787231, "perplexity": 1255.511034666501}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057131.88/warc/CC-MAIN-20210921011047-20210921041047-00345.warc.gz"} |
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DVB-T is an abbreviation for Digital Video Broadcasting — Terrestrial; it is the DVB European-based consortium standard for the broadcast transmission of digital terrestrial television that was first published in 1997[1] and first broadcast in the UK in 1998.[1] This system transmits compressed digital audio, digital video and other data in an MPEG transport stream, using coded orthogonal frequency-division multiplexing (COFDM or OFDM) modulation.
Basics of DVB-T
Rather than carrying the data on a single radio frequency (RF) carrier, OFDM works by splitting the digital data stream into a large number of slower digital streams, each of which digitally modulate a set of closely spaced adjacent carrier frequencies. In the case of DVB-T, there are two choices for the number of carriers known as 2K-mode or 8K-mode. These are actually 1,705 or 6,817 carriers that are approximately 4 kHz or 1 kHz apart.
DVB-T offers three different modulation schemes (QPSK, 16QAM, 64QAM).
DVB-T has been adopted or proposed for digital television broadcasting by many countries (see map), using mainly VHF 7 MHz and UHF 8 MHz channels whereas Taiwan, Colombia, Panama, Trinidad and Tobago and the Philippines use 6 MHz channels. Examples include the UK's Freeview.
The DVB-T Standard is published as EN 300 744, Framing structure, channel coding and modulation for digital terrestrial television. This is available from the ETSI website, as is ETSI TS 101 154, Specification for the use of Video and Audio Coding in Broadcasting Applications based on the MPEG-2 Transport Stream, which gives details of the DVB use of source coding methods for MPEG-2 and, more recently, H.264/MPEG-4 AVC as well as audio encoding systems. Many countries that have adopted DVB-T have published standards for their implementation. These include the D-book in the UK, the Italian DGTVi,[2] the ETSI E-Book and Scandivia NorDig.
DVB-T has been further developed into newer standards such as DVB-H (Handheld), now in operation, and DVB-T2, which was recently finalised.
DVB-T as a digital transmission delivers data in a series of discrete blocks at the symbol rate. DVB-T is a COFDM transmission technique which includes the use of a Guard Interval. It allows the receiver to cope with strong multipath situations. Within a geographical area, DVB-T also allows single-frequency network (SFN) operation, where two or more transmitters carrying the same data operate on the same frequency. In such cases the signals from each transmitter in the SFN needs to be accurately time-aligned, which is done by sync information in the stream and timing at each transmitter referenced to GPS.
The length of the Guard Interval can be chosen. It is a trade off between data rate and SFN capability. The longer the guard interval the larger is the potential SFN area without creating intersymbol interference (ISI). It is possible to operate SFNs which do not fulfill the guard interval condition if the self-interference is properly planned and monitored.
Technical description of a DVB-T transmitter
Scheme of a DVB-T transmission system
With reference to the figure, a short description of the signal processing blocks follows.
Source coding and MPEG-2 multiplexing (MUX)
compressed video, compressed audio, and data streams are multiplexed into MPEG program streams (MPEG-PSs). One or more MPEG-PSs are joined together into an MPEG transport stream (MPEG-TS); this is the basic digital stream which is being transmitted and received by TV sets or home Set Top Boxes (STB). Allowed bitrates for the transported data depend on a number of coding and modulation parameters: it can range from about 5 to about 32 Mbit/s (see the bottom figure for a complete listing).
Splitter
two different MPEG-TSs can be transmitted at the same time, using a technique called Hierarchical Transmission. It may be used to transmit, for example a standard definition SDTV signal and a high definition HDTV signal on the same carrier. Generally, the SDTV signal is more robust than the HDTV one. At the receiver, depending on the quality of the received signal, the STB may be able to decode the HDTV stream or, if signal strength lacks, it can switch to the SDTV one (in this way, all receivers that are in proximity of the transmission site can lock the HDTV signal, whereas all the other ones, even the farthest, may still be able to receive and decode an SDTV signal).
the MPEG-TS is identified as a sequence of data packets, of fixed length (188 bytes). With a technique called energy dispersal, the byte sequence is decorrelated.
External encoder
a first level of error correction is applied to the transmitted data, using a non-binary block code, a Reed-Solomon RS (204, 188) code, allowing the correction of up to a maximum of 8 wrong bytes for each 188-byte packet.
External interleaver
convolutional interleaving is used to rearrange the transmitted data sequence, in such a way that it becomes more rugged to long sequences of errors.
Internal encoder
a second level of error correction is given by a punctured convolutional code, which is often denoted in STBs menus as FEC (Forward error correction). There are five valid coding rates: 1/2, 2/3, 3/4, 5/6, and 7/8.
Internal interleaver
data sequence is rearranged again, aiming to reduce the influence of burst errors. This time, a block interleaving technique is adopted, with a pseudo-random assignment scheme (this is really done by two separate interleaving processes, one operating on bits and another one operating on groups of bits).
Mapper
the digital bit sequence is mapped into a base band modulated sequence of complex symbols. There are three valid modulation schemes: QPSK, 16-QAM, 64-QAM.
the complex symbols are grouped in blocks of constant length (1512, 3024, or 6048 symbols per block). A frame is generated, 68 blocks long, and a superframe is built by 4 frames.
Pilot and TPS signals
in order to simplify the reception of the signal being transmitted on the terrestrial radio channel, additional signals are inserted in each block. Pilot signals are used during the synchronization and equalization phase, while TPS signals (Transmission Parameters Signalling) send the parameters of the transmitted signal and to unequivocally identify the transmission cell. The receiver must be able to synchronize, equalize, and decode the signal to gain access to the information held by the TPS pilots. Thus, the receiver must know this information beforehand, and the TPS data is only used in special cases, such as changes in the parameters, resynchronizations, etc.
Spectrum of a DVB-T signal in 8k mode (note the flat-top characteristics).
OFDM Modulation
the sequence of blocks is modulated according to the OFDM technique, using 1705 or 6817 carriers (2k or 8k mode, respectively). Increasing the number of carriers does not modify the payload bit rate, which remains constant.
Guard interval insertion
to decrease receiver complexity, every OFDM block is extended, copying in front of it its own end (cyclic prefix). The width of such guard interval can be 1/32, 1/16, 1/8, or 1/4 that of the original block length. Cyclic prefix is required to operate single frequency networks, where there may exist an ineliminable interference coming from several sites transmitting the same program on the same carrier frequency.
DAC and front-end
the digital signal is transformed into an analogue signal, with a digital-to-analogue converter (DAC), and then modulated to radio frequency (VHF, UHF) by the RF front-end. The occupied bandwidth is designed to accommodate each single DVB-T signal into 5, 6, 7, or 8 MHz wide channels. The base band sample rate provided at the DAC input depends on the channel bandwidth: it is $f_s = \frac{8}{7} B$ samples/s, where $B$ is the channel bandwidth expressed in Hz.
Available bitrates (Mbit/s) for a DVB-T system in 8 MHz channels
Modulation Coding rate Guard interval
1/4 1/8 1/16 1/32
QPSK 1/2 4.976 5.529 5.855 6.032
2/3 6.635 7.373 7.806 8.043
3/4 7.465 8.294 8.782 9.048
5/6 8.294 9.216 9.758 10.053
7/8 8.709 9.676 10.246 10.556
16-QAM 1/2 9.953 11.059 11.709 12.064
2/3 13.271 14.745 15.612 16.086
3/4 14.929 16.588 17.564 18.096
5/6 16.588 18.431 19.516 20.107
7/8 17.418 19.353 20.491 21.112
64-QAM 1/2 14.929 16.588 17.564 18.096
2/3 19.906 22.118 23.419 24.128
3/4 22.394 24.882 26.346 27.144
5/6 24.882 27.647 29.273 30.160
7/8 26.126 29.029 30.737 31.668
The receiving STB adopts techniques which are dual to those ones used in the transmission.
• Front-end and ADC: the analogue RF signal is converted to base-band and transformed into a digital signal, using an analogue-to-digital converter (ADC).
• Time and frequency synchronization: the digital base band signal is searched to identify the beginning of frames and blocks. Any problems with the frequency of the components of the signal are corrected, too. The property that the guard interval at the end of the symbol is placed also at the beginning is exploited to find the beginning of a new OFDM symbol. On the other hand, continual pilots (whose value and position is determined in the standard and thus known by the receiver) determine the frequency offset suffered by the signal. This frequency offset might have been caused by Doppler effect, inaccuracies in either the transmitter or receiver clock, and so on. Generally, synchronization is done in two steps, either before or after the FFT, in such way to resolve both coarse and fine frequency/timing errors. Pre-FFT steps involve the use of sliding correlation on the received time signal, whereas Post-FFT steps use correlation between the frequency signal and the pilot carriers sequence.
• Guard interval disposal: the cyclic prefix is removed.
• OFDM demodulation: this is achieved with an FFT.
• Frequency equalization: the pilot signals are used to estimate the Channel Transfer Function (CTF) every three subcarriers. The CTF is derived in the remaining subcarriers via interpolation. The CTF is then used to equalize the received data in each subcarrier, generally using a Zero-Forcing method (multiplication by CTF inverse). The CTF is also used to weigh the reliability of the demapped data when they are provided to the Viterbi decoder.
• Demapping: since there are Gray-encoded QAM constellations, demapping is done in a "soft" way using nonlinear laws that demap each bit in the received symbol to a more or less reliable fuzzy value between -1 and +1.
• Internal deinterleaving
• Internal decoding: uses the Viterbi algorithm, with a traceback length larger than that generally used for the basic 1/2 rate code, due to the presence of punctured ("erased") bits.
• External deinterleaving
• External decoding
• MPEG-2 demultiplexing and source decoding
Countries and territories using DVB-T
Digital terrestrial television systems worldwide. Countries using DVB-T are shown in blue.[3]
Notes
1. ^ a b "What is DVB-T". Retrieved 2009-07-19.
2. ^
3. ^ DVB.org, Official information taken from the DVB website
4. ^ DVB - Digital Video Broadcasting - Bermuda
5. ^
6. ^
8. ^ The Falkland Islands adopts DVB-T
9. ^ "Plan for the introduction of terrestrial digital television broadcasting(DVB-T) in the Republic of Bulgaria" (in Bulgarian). Ministry of Transportation, Information Technology and Communications. Retrieved 2012-12-17.
10. ^ "Digital Television" (in English). NURTS (TV tower operator). Retrieved 2012-12-17.
11. ^ "Digital Ísland" (in Icelandic). fjarskiptahandbokin.is. Retrieved 2009-10-27.
12. ^
13. ^ "ETV: trial DVB-T2 network" (in Serbian). Retrieved 2012-03-22.
14. ^ Standar Penyiaran Televisi Digital
15. ^ Lankanewspapers.com, Dialog TV launches another South Asia's first DVBT, 2008-01-24. Retrieved on 2008-01-26.
16. ^ "BusinessDay - State U-turn on Nyanda's digital-TV signal plan". Retrieved 2010-11-26.
17. ^ "DVB-T2 chosen as digital TV standard". Retrieved 2011-01-03.
References
• ETSI Standard: EN 300 744 V1.5.1, Digital Video Broadcasting (DVB); Framing structure, channel coding and modulation for digital terrestrial television, available at ETSI Publications Download Area (This will open ETSI document search engine, to find the latest version of the document enter a search string; free registration is required to download PDF.)
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https://blog.theleapjournal.org/2021/05/backdoors-to-encryption-analysing.html | ## Monday, May 10, 2021
### Backdoors to Encryption: Analysing an Intermediary's Duty to Provide 'Technical Assistance'
by Rishab Bailey, Vrinda Bhandari, and Faiza Rahman.
The rising use of encryption is often said to be problematic for law enforcement agencies (LEAs) in that it directly impacts their ability to collect data required to prosecute online offences. While certainly not a novel issue, the matter has risen to global prominence over the last four or five years, possibly due to the increased usage of privacy enhancing technologies across the digital ecosystem.
While there have been a number of policy proposals that seek to address this perceived impasse, no globally accepted best practice or standard has been evolved thus far. In India (as in many other jurisdictions), the government has increasingly sought to regulate the use of encryption. For instance, the recently announced Intermediary Guidelines under the Information Technology Act, 2000, seek to extend the "technical assistance" mandate of certain intermediaries to ensure traceability, by enabling identification of the first originator of the information on a computer resource. The scope of the term "technical assistance" has not been clearly defined. However, the provision appears to go well beyond existing mandates in the law that require holders of encryption keys to provide decryption assistance, when called upon to do so, in accordance with due process, and based on their capability of decrypting the encrypted information. Courts have also weighed in on this debate, with the Madras High Court and the Supreme Court hearing petitions that seek to create mechanisms whereby LEAs could gain access to content protected by end-to-end encryption (E2E), thereby enabling access to user conversations on popular platforms such as WhatsApp. A Rajya Sabha Ad-hoc Committee Report released in 2020 has also recommended that LEAs be permitted to break or weaken E2E to trace distributors of illegal child sexual abuse content.
Against this background, our recently released paper examines the scope of the obligations that ought to be imposed on intermediaries to provide "technical assistance" to LEAs, and whether that should extend to weakening standards of encryption, for instance, through the creation of backdoors. Broadly speaking the term "backdoors" refers to covert methods of circumventing encryption systems, without the consent of the owner or the user. The paper also evaluates, in brief, proposals for alternatives, such as the use of escrow mechanisms and ghost protocols.
We argue that the government should not impose a general mandate for intermediaries to either weaken encryption standards or create backdoors in their products/platforms. This can significantly affect the privacy of individuals and would constitute a disproportionate infringement into the right to privacy. Such a mandate will also likely fail a cost-benefit analysis, not least in view of the possible effects on network security as well as broader considerations such as growth of the Indian market in securities products, geopolitical considerations, etc. This however, does not mean that the law enforcement agencies have no options when faced with the prospect of having to access encrypted digital data. A first step in this regard would be to implement rights-respecting processes to enable law enforcement to access data collected by intermediaries in a timely manner. In addition, there should be greater focus on enhancing government and law enforcement capacities, including by developing hacking capabilities, with sufficient oversight and due process checks and greater funding to research and development efforts in the cybersecurity and crypto spaces.
This post seeks to throw light on the key issues around the encryption debate, and summarises our main arguments and suggestions on how India should address them.
### Understanding the encryption debate
Encryption is the process of using a mathematical algorithm to render plain, understandable text into unreadable letters and numbers (Gill, 2018). Typically, an encryption key is used to carry out this conversion. Reconverting the encrypted text back to plain-text also requires an encryption key. Depending on the manner of encryption, the same encryption key can be used to encrypt or decrypt information, or alternatively, one may require different encryption and decryption keys. Encryption therefore ensures that the message can only be read by the person who has the appropriate decryption key, particularly as newer forms of encryption make it inefficient, if not impossible, to reverse the encryption process (Gill, 2018).
Encryption essentially improves the security of information. It secures information against unwarranted access and ensures the confidentiality and integrity of data, thereby fostering trust in the digital ecosystem and protecting the private information of citizens and businesses alike.
However, the use of encryption can also enable criminals to "go dark", making it difficult for LEAs to carry out their functions. For instance, it is estimated that upwards of 22 percent of global communication traffic uses end-to-end encryption (Lewis et al, 2017). This puts a quarter of communications virtually out of reach for LEAs, not least as the use of modern encryption systems makes it harder for LEAs to use the traditional "brute force" method to access encrypted data (Haunts, 2019). LEAs therefore have increasingly called for limitations to be placed on the use of encryption so as to enable them to have access to information they require to pursue their law enforcement functions. They point to the need to ensure accountability for online harms, and therefore argue that intermediaries must provide them with all data relevant to an investigation.
The concerns with the use of encryption are driven by a number of factors such as the growing instances of cybercrime, the use of data minimisation practices such as disappearing messages and the use of encryption by default in various technology products. For instance, WhatsApp and Signal automatically encrypt communications in transit and also give users the option of automatically deleting their messages. Similarly, Apple uses encryption based authentication on its iPhones (which render the content accessible only if an appropriate passcode is provided. If not, the content on the phone could even be deleted after a certain number of failed attempts) (Lewis et. al, 2017).
These concerns have led to calls for Internet intermediaries to weaken encryption standards or create backdoors in their products/services. These demands are not new. Notably, the 1990s saw the issue being debated in the United States, with the FBI proposing the use of the "Clipper Chip", a mechanism whereby decryption keys would be copied from the devices of users and sent to a trusted third party, where they could be accessed on appropriate authorisation by LEAs. More recently, the FBI has been involved in face-offs with technology companies such as Apple, when it refused to provide exceptional access to an iPhone linked to a terrorist. In India too, the government has encountered similar issues - notably forcing Blackberry manufacturers to relocate their servers to India and hand over plain text of communications. The government also circulated a draft National Encryption Policy in 2015, which sought to implement obligations involving registration of encryption software vendors, and the need for intermediaries to store plain text of user data. The draft was however withdrawn after much criticism.
In response to such proposals, security researchers, cryptographers and service providers, have been near unanimous in pointing out that the creation of backdoors is likely to lead to significant costs to the entire digital ecosystem, especially as it leads to the entire population being exposed to vulnerabilities and security threats. Indeed, the need for stronger encryption and other security standards to protect user data is only heightened by the numerous and frequent data breaches that have been reported in India. Interestingly, even the Telecom Regulatory Authority of India has adopted a similar position in its Recommendations on Regulatory Framework for OTT Communication Services of 2020.
Even two commonly discussed methods of a "balanced solution" to the problem - the use of escrow mechanisms and ghosting protocols - have faced significant criticism. For instance, the use of escrow mechanisms (which, as with the Clipper Chip system described above, involve storage of the decryption key with a trusted third-party, who can then provide the same to LEAs when called upon to do so) is likely to lead to significant vulnerabilities being created in computer systems. Not only will such a system require faith in the integrity of the entity holding the decryption key, such an entity would constitute a single point of failure, which is poor system design (Kaye, 2015). Deployment of complex key recovery infrastructure is also likely to impose huge costs on the ecosystem (Abelson et al., 1997). Similarly, suggestions for using ghost protocols (which would require service providers to secretly add an extra LEA participant to private communications) have also faced significant criticism (Levy and Robinson, 2018). Given that this system would essentially require service providers to convert a private conversation between two individuals into a group chat, with a hidden third participant, critics have argued that it is just another form of a backdoor. It would erode trust between consumers and service providers, and provide for a "dormant wiretap in every user's pocket" that can be activated at will. This would also require fundamental changes in system architecture, thereby introducing vulnerabilities that can create threats for all users on platforms (Access Now et al., 2019).
Thus, while the use of such methods can enable LEAs to access user data more quickly than is currently possible, there are numerous concerns - from a civil liberties, economic and technical perspective. We outline the key concerns in this regard below.
### Concerns with mandating backdoors
• Privacy: In view of the recognition of privacy as a fundamental right, private thoughts and communications are protected from government intrusion subject to satisfaction of tests of necessity and proportionality. Mass surveillance can be considered to be per se disproportionate. It is recognised that government surveillance can lead to unwanted behavioural changes, and create a chilling effect. Encryption therefore serves as a method to protect individual privacy, particularly from government excesses.
• Security: Creating backdoors can weaken network security as a whole since it can be exploited by governments and hackers alike (Abelson et al., 2015). Backdoors can also lead to increased complexity in systems, which can make them more vulnerable to attack (Abelson et al., 2015).
• Right against self-incrimination: Mandating decryption of data can arguably also be seen as violating an individual's right against self-incrimination (Gripman, 1999; ACLU and EFF, 2015).
• Due process requirements: Criminal investigation in general and surveillance in particular is not meant to be a frictionless process. Introducing inefficiencies in the functioning of LEAs is what separates a police state from a democracy (Richards, 2013; Hartzog and Selinger, 2013). As is the case of due process requirements, encryption creates procedural hurdles, ensuring some checks and balances over the functioning of LEAs and the possibility of mass surveillance. It therefore helps re-balance the asymmetric power distribution between the State and citizen.
### Scope of "technical assistance": Should it extend to creating backdoors?
Given the aforementioned concerns, the question arises, should the duty of "technical assistance" that intermediaries are required to provide to LEAs, extend to the creation of backdoors or otherwise weakening encryption systems?
We argue that as far as recoverable encryption is concerned, i.e. encryption where a service provider already has a decryption key in the normal course of service provision, there is no requirement for such a mandate. Indian law already requires service providers to decrypt data in such cases, in addition to providing various other forms of assistance. Here, the need is to focus on implementing proper oversight and other procedural frameworks to ensure that LEAs exercise their powers of surveillance or decryption in an appropriate manner. We find however, that the Indian framework is lacking in this regard. There is no judicial oversight of decryption requests, no proportionality requirements in the law, and no meaningful checks and balances over decryption processes at all. We therefore proposed various changes in order to improve the transparency and accountability of the system. Further, research indicates that the primary problem of LEAs in India may relate to the relatively old and slow processes that must be used by LEAs when accessing data held by intermediaries, particularly those based outside India. This points more to the need for LEA data access processes to be revised/streamlined in accordance with modern needs.
As far as unrecoverable encryption is concerned, i.e. encryption where even the service provider cannot access the content (such as with E2E) as it does not have access to the decryption key, which is retained by the user, the situation is undoubtedly more complex. However, even in such instances, for the reasons elaborated above, we believe that mandating backdoors or weakening encryption is not an appropriate solution.
Moreover, LEAs already have multiple alternatives to collect information, including by accessing metadata and unencrypted backups of encrypted communications. They can also use targeted surveillance methods to conduct investigations (National Academy of Science, Engineering and Medicine, 2018). Indeed, the current Indian framework - governing telecom service providers in particular, but also other intermediaries - already gives significant and arguably excessive powers to the State. It should also be noted that LEAs in India are already using spying technology, as we saw in the Pegasus case. LEAs also have other covert methods of gathering data - from key-stroke logging programmes to exploiting weaknesses in implementation of encryption systems. While one cannot argue against the use of such systems in appropriate cases, it is clear that such powers must only be exercised through institutionalised processes, and importantly, subject to appropriate regulatory oversight. There is therefore a case for formulating a legal framework in India, along the lines of the US vulnerabilities equities process, to ensure due process even when the government resorts to exploitation of vulnerabilities within information systems for national security and law enforcement purposes.
Accordingly, we point to the need to carry out a more detailed cost-benefit analysis before deciding on the need to implement such a mandate (which unfortunately, has not been done in the case of the recent Intermediary Guidelines Rules). We point to how such a cost-benefit analysis should consider:
• Whether the use of unrecoverable encryption is indeed a significant hurdle for LEAs in collecting relevant information. While no data is available in this context in India, data from the US in the period 2012-2015 indicates that of the 14,500 wiretaps ordered under the Communications Assistance for Law Enforcement Act, only about 0.2 percent of wiretaps encountered unrecoverable encryption (Lewis et al., 2017). While this share has likely increased in view of the greater use of unrecoverable encryption in the ecosystem, a similar empirical analysis must be conducted in India to understand the impact of such types of encryption.
• The cost to intermediaries in changing their platform architecture are unlikely to be insignificant. It is also worth keeping in mind that often intermediaries will avoid using certain types of encryption purely to keep in the good books of LEAs in a form of "weakness by design". Notably, companies such as Apple and WhatsApp have dropped plans to encrypt user back-ups stored in the cloud. Such data can therefore be accessed by LEAs without compromising encryption.
• The risk of such laws getting caught up in global geopolitics. This has been the case for example, with Huawei and ZTE, who have faced significant international pressure in view of the Chinese government's purported ability to access data flowing through their networks.
• The possible effectiveness of such laws, considering that many criminals may use open source encryption or encryption from platforms that are not amenable to Indian jurisdiction. Further, the pace of technical development is difficult to keep up with from a regulatory perspective. Notably, institutions such as Europol and Interpol are increasingly concerned about the use of steganography (the technique of hiding the very existence of a message) and open source encryption by international criminals and terrorist groups. Therefore, even if there is a bar on using strong encryption, those who want to break this law, will continue to do so.
We therefore argue that while a mandate for targeted decryption or technical assistance may be constitutional if backed by a law with sufficient safeguards, a general mandate for the creation of backdoors (or an interpretation of the Intermediary Guidelines requirement to provide "technical assistance" to extend to such generic obligations) is unlikely to pass constitutional muster, assuming a high intensity of proportionality review is applied. A higher intensity of review will have to look at not just whether the proposed intervention would substantially improve national security, but would also need to engage with the fact that it would (a) compromise the privacy and security of individuals at all times, regardless of whether there is any evidence of illegal activity on their party, and (b) the existence of alternative means that are available to LEAs to carry out their investigations. Thus, we believe that a general mandate for creating backdoors will not be the least restrictive measure available.
### Conclusions and Recommendations
We argue that a general mandate that requires Internet intermediaries to break encryption, use poor quality encryption, or create backdoors in encryption is not a proportionate policy response given the significant privacy and security concerns, and the relatively less harmful alternatives available to LEAs. Instead, the Indian government should support the development and use of strong encryption systems.
Rather than limiting the use of certain technologies, or mandating significant changes in platform/network architecture of intermediaries that compromises encryption, the government ought to take a more rights-preserving and long-term view of the issue. This will enable a more holistic consideration of interests involved, avoid unintended consequences, and limit costs that come with excessive government interference in the technology space. The focus of the government must be on achieving optimal policy results, while reducing costs to the ecosystem as a whole (including privacy and security costs). A substantive mandate to limit the use of strong encryption would increase costs for the entire ecosystem, without commensurate benefits as far as state security is concerned.
The tussle between LEAs and criminal actors has always been an arms race. Rather than adopting steps that may have significant negative effects on the digital ecosystem, the government could learn from the policies adopted by countries such as Germany, Israel and the USA. This would involve interventions along two axes - legal changes and measures to enhance state capacity.
Legal changes that the government must consider implementing, include:
• Reforming surveillance and decryption processes, to clarify the powers of LEAs, and ensure appropriate transparency, oversight and review. It is also essential to standardise and improve current methods of information access by LEAs at both domestic and international levels. There must be greater transparency in the entire surveillance and information access apparatus, including by casting obligations on intermediaries and the State to make relevant disclosures to the public.
• Adoption of a Vulnerabilities Equities Process, such as that adopted in the United States, which could enable reasoned decisions to be made by the government about the disclosure of software/network vulnerabilities (thereby allowing these to be patched, in circumstances where this would not significantly affect security interests of the State). Such a process, while not without critics, does chart a path forward and must become central to the Indian conversation around due process in LEA access to personal data.
• Amending telecom licenses, which currently give excessive leeway for exercise of executive authority, without sufficient checks or safeguards.
Rather than implement ill-thought out policy solutions that would significantly harm the digital ecosystem and user rights, the government could also focus on enhancing its own capacities. This can include measures such as:
• Developing and enhancing covert hacking capacities (though these must be implemented only subject to appropriate oversight and review processes). To this end, there must be appropriate funding of LEAs, including by hiring security and technical researchers.
• Investing in academic and industry research into cryptography and allied areas. The government should also aid the development of domestic entities who can participate in the global market for data security related products. Enhancing coordination between industry, academia and the State is essential.
• Increasing participation in international standard setting and technical development processes.
To conclude, the crux of this issue can be understood using an analogy. Would it be prudent for a government, engaged in a fight against black money, to require all banks to deposit a key to their customer's safe deposit boxes with it? One would venture that this would be an unworkable proposition in a democracy. It would lead to people looking for alternatives to the use of safe-deposit boxes due to the lack of trust such a system will create. Innocent people will be exposed to increased risks. A preferable solution may be for the government to develop the ability to break into a specific safe deposit box, upon learning of its illegal contents, and subsequent to following due process. This would enable more targeted interventions, that would also preserve the broader privacy interests of innocent customers while protecting banks from increased costs (or loss of business).
### References
Gill, 2018: L Gill, Law, Metaphor and the Encrypted Machine, Osgoode Hall L.J. 55(2) 2018, 440-477.
Lewis et al., 2017: James Lewis, Denise Zheng and William Carter, The Effect of Encryption on Lawful Access to Communications and Data, Center for Strategic and International Studies, February 2017.
Haunts, 2019: Stephen Haunts, Applied Cryptography in .Net and Azure Key Vault: A Practical Guide to Encryption in .Net and .Net Core, APress, February 2019.
Kaye, 2015: David Kaye, Report of the Special Rapporteur on the promotion and protection of the right to freedom of opinion and expression, United Nations, Human Rights Council, May 2015.
Abelson et al., 1997: Hal Abelson, Ross Anderson, Steven Bellovin, Josh Benaloh, Matt Blaze, Whitfield Diffie, John Gilmore, Peter Neumann, Ronald Rivest, Jeffrey Schiller, and Bruce Schneier, The Risks of Key Recovery, Key Escrow, and Trusted Third-Party Encryption, May 27, 1997.
Levy and Robinson, 2018: Ian Levy and Crispin Robinson, Principles for a More Informed Exceptional Access Debate, LawFare Blog, November 29, 2018.
Cardozo, 2019: Nate Cardozo, Give Up the Ghost: A Backdoor by Another Nam et al.e, Electronic Frontier Foundation, January 7, 2019.
Access Now et al., 2019: Access Now, Big Brother Watch, Center for Democracy and Technology, et al., Open Letter to GCHQ, May 22, 2019.
Gripman, 1999: David Gripman, Electronic Document Certification: A Primer on the Technology Behind Digital Signatures, 17 J. Marshall J. Computer and Info. L. 769 (1999).
ACLU and EFF, 2015: American Civil Liberties Foundation of Massachusetts, the American Civil Liberties Union Foundation, and Electronic Frontier Foundation, Brief for Amici Curiae in Support of the Defendant-Appellee in Commonwealth of Massachusetts v. Leon Gelfgatt, 2015
Richards, 2013: Neil Richards, Don't Let US Government Read Your E-Mail, CNN, August 18, 2013.
Hartzog and Selinger, 2013: Woodrow Hartzog and Evan Selinger, Surveillance as Loss of Obscurity, Washington and Lee L.R. 72(3), 2015.
National Academy of Science, Engineering and Medicine, 2018: National Academy of Science, Engineering and Medicine, Decrypting the Encryption Debate: A Framework for Decision Makers, National Academies Press, Washington DC.
Rishab Bailey is a researcher at NIPFP. Vrinda Bhandari is a practising advocate. Faiza Rahman is a PhD candidate at the University of Melbourne.
LaTeX mathematics works. This means that if you want to say $10 you have to say \$10. | 2022-06-28 08:14:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2133135348558426, "perplexity": 3054.6881442546774}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103360935.27/warc/CC-MAIN-20220628081102-20220628111102-00071.warc.gz"} |
https://jeopardylabs.com/play/mcap-jeopardy-3 | "X Gonna Give It To Ya"
Polynomials
Are You Smarter Than a 5th Grader?
Writing EQs
What's That Word?!
100
The value of x in
-4x>20
What is
x<-5?
100
This is
5x^3+6x^4+5x+8x^5
re-written in standard form.
What is
8x^5+6x^4+5x^3+5x?
100
This is the biggest star in our universe.
What is the sun?
100
Linear equations are typically written in this form that describes the slope.
What is y=mx+b?
100
This term can be used to describe the minimum or the maximum of a parabola.
What is a vertex?
200
The expression
x^2-10x+24
is equivalent to _______.
What is
(x-6)(x-4)?
200
What is
5x^2+4x+4?
200
A hexagon has this many sides
What is 6?
200
Ms. Barnet’s dog has just finished taking a bath. There are 65 gallons of water in the tub. She is DRAINING the tub at a rate of 6 gallons of water per minute.
What is
y=-6x+65?
200
This term describes an invisible line that divides a parabola perfectly in half.
What is an axis of symmetry?
300
Hint: graph it!
What is 0 and 9?
300
What is
5x^2+6y+4xy-x+5?
300
This planet in our Solar System is known for having a ring.
What is Saturn?
300
Ms. Le organizes an annual spoken word tournament. After each round, one-half of the performers were eliminated. If there were 64 performers at the start of the tournament, this equation models the number of performers left after 3 rounds.
What is
y=64(1-0.5)^3
300
Another word to refer to roots, zeroes, or solutions.
What is x-intercept?
400
Uber charges $4.99 in fees and then$1.25 per mile. Lyft charges $2.85 in fees but charges$1.40 per mile. After how many miles will the cost be the same?
What is 14.26 miles?
400
The dimensions of a sand volleyball court are represented by a width of 4m-3 and a length of 2m+6 feet. Which of the following expressions represents the area of the court?
What is
8m^2+18m-18?
400
This is the only continent in which spiders don’t exist.
What is Antarctica?
400
Find the equation of the linear function that goes through the points (0,3) and (1,1). Hint: start by finding the slope or average rate of change.
What is
y=-2x+3?
400
This type of function includes an
x^2
as the highest degree.
500
What is -12?
500
What is
20x^4-11x^3+31x^2-16x+12?
500
This country has the Unicorn as its national animal.
What is Scotland?
500
Olivia orders T-shirts for her volleyball camp. Adult-sized T-shirts (x) cost $6.25 each and youth-sized T-shirts (y) cost$4.50 each. Olivia has \$550 to purchase both adult-sized and youth-sized T-shirts. If she purchases 45 youth-sized T-shirts, determine algebraically the maximum number of adult-sized T-shirts she can purchase.
What is 55?
500
This set of straight lines intersect at a 90 degree angle and their slopes are the opposite reciprocals.
What are perpendicular lines?
Click to zoom | 2022-07-04 23:39:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3864474892616272, "perplexity": 3785.116620370488}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104506762.79/warc/CC-MAIN-20220704232527-20220705022527-00633.warc.gz"} |
http://mathonline.wikidot.com/counting-the-number-of-subsets-of-a-finite-set | Counting the Number of Subsets of a Finite Set
# Counting the Number of Subsets of a Finite Set
Consider the finite $3$-element set $A = \{ x_1, x_2, x_3 \}$. Suppose that we want to determine the total number of distinct subsets that can be formed from $A$. It's not too difficult to list these sets, and it turns out that the subsets$\emptyset, \{ x_1 \}, \{ x_2 \}, \{ x_3 \}, \{ x_1, x_2 \}, \{ x_1, x_3 \}, \{ x_2, x_3 \}, \{ x_1, x_2, x_3 \}$ are the only subsets of $A$ and that there are exactly $8$ of them.
In general, it might be convenient to know the total number of distinct subsets that can be formed from a finite $n$-element set $A$ such as:
(1)
\begin{align} \quad A = \{ x_1, x_2, ..., x_n \} \end{align}
The following theorem uses The Binomial Theorem to show us that for any finite $n$-element set there are exactly $2^n$ distinct subsets of $A$.
Theorem 1: If $A$ is a finite $n$-element then there are exactly $2^n$ distinct subsets of $A$.
• Proof: Let $A = \{ x_1, x_2, ..., x_n \}$ be an $n$-element set. Then the total number of subsets containing zero elements is $\binom{n}{0}$, the total number of subsets containing one element is $\binom{n}{1}$, …, and the total number of subsets containing $n$ elements is $\binom{n}{n}$. By the addition principle we see that:
(2)
\begin{align} \quad \mathrm{total \: number \: of \: subsets \: of} \: A = \sum_{k=0}^{n} \binom{n}{k} \end{align}
• Recall that for all $x, y \in \mathbb{R}$ and $n \in \{ 0, 1, 2, ... \}$ we have that the binomial expansion of $(x + y)^n$ is given by the formula:
(3)
\begin{align} \quad (x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^y y^{n-k} \end{align}
• Setting $x = y = 1$ will give us:
(4)
\begin{align} \quad 2^n = \sum_{k=0}^{n} \binom{n}{k} \end{align}
• Therefore we have that:
(5)
\begin{align} \quad \mathrm{total \: number \: of \: subsets \: of} \: A = 2^n \quad \blacksquare \end{align}
For example, consider the five element set $D = \{ v, w, x, y, z \}$. From Theorem 1 above we see that there are $2^5 = 32$ distinct subsets of $D$ (try to list them all). | 2019-10-16 11:54:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 5, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9918310642242432, "perplexity": 192.26429380236274}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-43/segments/1570986668569.22/warc/CC-MAIN-20191016113040-20191016140540-00151.warc.gz"} |
https://realdharma.wordpress.com/category/humor/ | ## The Mad Yogi of Bhutan gets real
“In the rosary of my many lives
I have taken the form of every creature;
I remember it only darkly,
Yet I feel it was something like this:
Since now I thrive on chung,
Once I must have been a bee;
Since now I am so lustful
Once I must have been a cock;
Since now I am so angry,
Once I must have been a snake;
Since now I am so slothful,
Once I must have been a pig;
Since now I am so mean,
Once I must have been a rich man;
Since now I am so shameless,
Once I must have been a madman;
Since now I am such a liar,
Once I must have been an actor;
Since now my manners are so rude,
Once I must have been a monkey;
Since now I have such blood lust,
Once I must have been a wolf;
Since now I have so tight an anal sphincter,
Once I must have been a nun;
Since now I am so punctilious,
Once I must have been a barren woman;
Since now I spend my wealth on food,
Once I must have been a Lama;
Since now I am so avaricious,
Once I must have been a steward;
Since now I am so self-esteeming,
Once I must have been an officer;
Since now I enjoy cheating others,
Once I must have been a business man;
Since now I am so loquacious,
Once I must have been a woman;
But I cannot tell you if this is really true.
Consider the matter yourselves. | 2023-03-30 06:00:07 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8460697531700134, "perplexity": 2252.034278172465}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296949097.61/warc/CC-MAIN-20230330035241-20230330065241-00323.warc.gz"} |
https://socratic.org/questions/how-do-you-factor-y-x-5-x-6-2-x-5-2-x-6 | # How do you factor y= (x-5)(x+6)^2 - (x-5)^2 (x+6) ?
Jul 4, 2018
$y = \left(x - 5\right) \left(x + 6\right) \left(11\right)$
#### Explanation:
When factorising, you want to take out anything that you can find in both parts of the equation ie in $\left(x - 5\right) {\left(x + 6\right)}^{2}$ and ${\left(x - 5\right)}^{2} \left(x + 6\right)$
Hopefully, you will notice that there is one $x - 5$ and one $x + 6$ in both parts
Therefore, you can "take" them out
$y = \left(x - 5\right) \left(x + 6\right) \left(x + 6 - \left(x - 5\right)\right)$
$y = \left(x - 5\right) \left(x + 6\right) \left(x + 6 - x + 5\right)$
$y = \left(x - 5\right) \left(x + 6\right) \left(11\right)$ | 2019-09-21 15:04:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 8, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.654922604560852, "perplexity": 1320.3539319865295}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574532.44/warc/CC-MAIN-20190921145904-20190921171904-00211.warc.gz"} |
https://puzzling.stackexchange.com/questions/48023/maximum-sudoku-puzzle | # Maximum Sudoku Puzzle
As most of you know, there is no Sudoku problem that has less than 17 number of starting clues with one unique solution.
Imagine there is a sudoku problem that has $n$ number of starting clues with one unique solution, where removing any clue in the sudoku will make the puzzle non-unique (more than one answer).
What is the maximum value of $n$ possible with an example?
• I'd guess that would be a hard problem. – Neil W Jan 17 '17 at 22:51
• This sounds like it could be made into a game actually. Two players start with an empty 9x9 sudoku board. Player take turns filling in numbers into the board. If a number is placed whereby a unique (partial or full) solution can be filled in, the other player can automatically fill all of those numbers in. The player who completes the last digit on the board wins. I'd imagine it'd be very nontrivial and no exact strategy however...but the thought process may be similar to the question posed here – skyeriding Jan 18 '17 at 1:13
• @skyeriding: The game you propose will not necessarily lead to the kinds of arrangements that the question is asking for (even if only considering the state just before the first move that allows some empty cells to be deduced). Moves later in the game may make the numbers placed in earlier moves redundant (i.e. deducable from the other numbers even if the board as a whole is not yet solvable). – Jaap Scherphuis Jan 18 '17 at 13:47
• @Jaap-Scherphuis: alternatively, modify the rules then such that whoever makes a move that allows the next player to deduce at least one number from the current setup - loses. This can avoid the redundancy... – skyeriding Jan 19 '17 at 4:40
As of today, the maximum value of n is 40. Two puzzles are known.
This first puzzle was discovered by Mladen Dobrichev in March 2014.
...|...|...
.12|.34|567
.34|5.6|182
---+---+---
..1|.58|2.6
..8|6..|..1
.2.|..7|.5.
---+---+---
..3|7.5|.28
.8.|.6.|7..
2.7|.83|615
See his post here
• interesting :) accepted this an answer then! – Oray Aug 12 '18 at 17:42
• I see that both 40 clue puzzles us only 8 different clues. – Steve B Aug 13 '18 at 4:35
• @Steve True. M. Dobrivhev found also 2650 39-clues minimal puzzles. Out of them only 63 (i.e. 2%) have 9 different digits. – JPF Aug 13 '18 at 10:02
To get the ball rolling, here is an example of a Sudoku with 28 clues, and if my Sudoku generating program is right, none of them are redundant.
.1.|.6.|7.9
3..|...|...
.9.|...|...
---+---+---
7..|..8|4..
.4.|1..|...
9..|.4.|137
---+---+---
.7.|.86|9..
6..|5..|2..
.2.|4.7|.61
This is the unique solution.
412|863|759
387|954|612
596|721|384
---+---+---
761|398|425
243|175|896
958|642|137
---+---+---
175|286|943
634|519|278
829|437|561
My sudoku generator produces these only on the highest difficulty setting, which means that when you solve it you will have to some of the more advanced deduction techniques. There are likely to be unreducible sudokus with more clues, but which are solvable using only simple techniques.
Edit:
I have now looked through the book "Tak1ng Sud0ku Ser10usly", by Jason Rosenhouse and Laura Taalman. It says that the largest known number of clues is 39:
7.5|6..|8.4
64.|...|.27
128|47.|.56
---+---+---
251|.6.|..8
...|...|...
8..|.5.|26.
---+---+---
.8.|.3.|.7.
5.2|74.|.83
3.7|5..|4.2
It is not known (at least at the time of writing that book, 2011) whether there is an irreducible sudoku with 40 clues.
• While it's obviously super cumbersome and wouldn't format very well in a post, it would be interesting to see the 28 alternate endings for each of the removals. – Ian MacDonald Jan 18 '17 at 18:53
• @IanMacDonald thonky.com/sudoku/… Yes this is valid answer. You can remove one number, and you will see multiple answer for each... – Oray Jan 18 '17 at 19:15
• @Oray I'm glad there's something that exists. That's really all I wanted to see. :) – Ian MacDonald Jan 18 '17 at 19:43
• @Oray: I have now added one with 39 clues, taken from a book. I have not verified it. – Jaap Scherphuis Jan 18 '17 at 20:08
• @JaapScherphuis very good job! It is valid answer! – Oray Jan 18 '17 at 20:19 | 2020-12-04 20:34:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.554469108581543, "perplexity": 1018.8422576836566}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141743438.76/warc/CC-MAIN-20201204193220-20201204223220-00511.warc.gz"} |
http://www.opensource.apple.com/source/shell_cmds/shell_cmds-118/printf/printf.1 | # printf.1 [plain text]
.\" $NetBSD: printf.1,v 1.10 1998/08/22 14:54:48 garbled Exp$
.\"
.\" Copyright (c) 1989, 1990, 1993
.\"
.\" This code is derived from software contributed to Berkeley by
.\" the Institute of Electrical and Electronics Engineers, Inc.
.\"
.\" Redistribution and use in source and binary forms, with or without
.\" modification, are permitted provided that the following conditions
.\" are met:
.\" 1. Redistributions of source code must retain the above copyright
.\" notice, this list of conditions and the following disclaimer.
.\" 2. Redistributions in binary form must reproduce the above copyright
.\" notice, this list of conditions and the following disclaimer in the
.\" documentation and/or other materials provided with the distribution.
.\" 3. All advertising materials mentioning features or use of this software
.\" must display the following acknowledgement:
.\" This product includes software developed by the University of
.\" California, Berkeley and its contributors.
.\" 4. Neither the name of the University nor the names of its contributors
.\" may be used to endorse or promote products derived from this software
.\" without specific prior written permission.
.\"
.\" THIS SOFTWARE IS PROVIDED BY THE REGENTS AND CONTRIBUTORS AS IS'' AND
.\" ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
.\" IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
.\" ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE
.\" FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
.\" DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
.\" OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
.\" HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
.\" LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
.\" OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
.\" SUCH DAMAGE.
.\"
.\" from: @(#)printf.1 8.1 (Berkeley) 6/6/93
.\"
.Dd November 5, 1993
.Dt PRINTF 1
.Os
.Sh NAME
.Nm printf
.Nd formatted output
.Sh SYNOPSIS
.Nm
.Ar format
.Op Ar arguments ...
.Sh DESCRIPTION
The
.Nm
utility formats and prints its arguments, after the first, under control
of the
.Ar format .
The
.Ar format
is a character string which contains three types of objects: plain characters,
which are simply copied to standard output, character escape sequences which
are converted and copied to the standard output, and format specifications,
each of which causes printing of the next successive
.Ar argument .
.Pp
The
.Ar arguments
after the first are treated as strings if the corresponding format is
either
.Cm b ,
.Cm c
or
.Cm s ;
otherwise it is evaluated as a C constant, with the following extensions:
.Pp
.Bl -bullet -offset indent -compact
.It
A leading plus or minus sign is allowed.
.It
If the leading character is a single or double quote, the value is the
.Tn ASCII
code of the next character.
.El
.Pp
The format string is reused as often as necessary to satisfy the
.Ar arguments .
Any extra format specifications are evaluated with zero or the null
string.
.Pp
Character escape sequences are in backslash notation as defined in
.St -ansiC .
The characters and their meanings
are as follows:
.Bl -tag -width Ds -offset indent
.It Cm \ee
Write an <escape> character.
.It Cm \ea
Write a <bell> character.
.It Cm \eb
Write a <backspace> character.
.It Cm \ef
Write a <form-feed> character.
.It Cm \en
Write a <new-line> character.
.It Cm \er
Write a <carriage return> character.
.It Cm \et
Write a <tab> character.
.It Cm \ev
Write a <vertical tab> character.
.It Cm \e\'
Write a <single quote> character.
.It Cm \e\e
Write a backslash character.
.It Cm \e Ns Ar num
Write an 8-bit character whose
.Tn ASCII
value is the 1-, 2-, or 3-digit
octal number
.Ar num .
.El
.Pp
Each format specification is introduced by the percent character
(%'').
The remainder of the format specification includes,
in the following order:
.Bl -tag -width Ds
.It "Zero or more of the following flags:"
.Bl -tag -width Ds
.It Cm #
A #' character
specifying that the value should be printed in an alternative form''.
For
.Cm c ,
.Cm d ,
and
.Cm s ,
formats, this option has no effect. For the
.Cm o
formats the precision of the number is increased to force the first
character of the output string to a zero. For the
.Cm x
.Pq Cm X
format, a non-zero result has the string
.Li 0x
.Pq Li 0X
prepended to it. For
.Cm e ,
.Cm E ,
.Cm f ,
.Cm g ,
and
.Cm G ,
formats, the result will always contain a decimal point, even if no
digits follow the point (normally, a decimal point only appears in the
results of those formats if a digit follows the decimal point). For
.Cm g
and
.Cm G
formats, trailing zeros are not removed from the result as they
would otherwise be;
.It Cm \&\-
A minus sign \-' which specifies
of the output in the indicated field;
.It Cm \&+
A +' character specifying that there should always be
a sign placed before the number when using signed formats.
.It Sq \&\ \&
A space specifying that a blank should be left before a positive number
for a signed format. A +' overrides a space if both are used;
.It Cm \&0
A zero 0' character indicating that zero-padding should be used
rather than blank-padding. A \-' overrides a 0' if both are used;
.El
.It "Field Width:"
An optional digit string specifying a
.Em field width ;
if the output string has fewer characters than the field width it will
has been given) to make up the field width (note that a leading zero
is a flag, but an embedded zero is part of a field width);
.It Precision:
An optional period,
.Sq Cm \&.\& ,
followed by an optional digit string giving a
.Em precision
which specifies the number of digits to appear after the decimal point,
for
.Cm e
and
.Cm f
formats, or the maximum number of characters to be printed
from a string; if the digit string is missing, the precision is treated
as zero;
.It Format:
A character which indicates the type of format to use (one of
.Cm diouxXfwEgGbcs ) .
.El
.Pp
A field width or precision may be
.Sq Cm \&*
In this case an
.Ar argument
supplies the field width or precision.
.Pp
The format characters and their meanings are:
.Bl -tag -width Fl
.It Cm diouXx
The
.Ar argument
is printed as a signed decimal (d or i), unsigned octal, unsigned decimal,
or unsigned hexadecimal (X or x), respectively.
.It Cm f
The
.Ar argument
is printed in the style
.Sm off
.Pf [\-]ddd Cm \&. No ddd
.Sm on
where the number of d's
after the decimal point is equal to the precision specification for
the argument.
If the precision is missing, 6 digits are given; if the precision
is explicitly 0, no digits and no decimal point are printed.
.It Cm eE
The
.Ar argument
is printed in the style
.Sm off
.Pf [\-]d Cm \&. No ddd Cm e No \\*(Pmdd
.Sm on
where there
is one digit before the decimal point and the number after is equal to
the precision specification for the argument; when the precision is
missing, 6 digits are produced.
An upper-case E is used for an E' format.
.It Cm gG
The
.Ar argument
is printed in style
.Cm f
or in style
.Cm e
.Pq Cm E
whichever gives full precision in minimum space.
.It Cm b
Characters from the string
.Ar argument
are printed with backslash-escape sequences expanded.
.It Cm c
The first character of
.Ar argument
is printed.
.It Cm s
Characters from the string
.Ar argument
are printed until the end is reached or until the number of characters
indicated by the precision specification is reached; however if the
precision is 0 or missing, all characters in the string are printed.
.It Cm \&%
Print a %'; no argument is used.
.El
.Pp
In no case does a non-existent or small field width cause truncation of
a field; padding takes place only if the specified field width exceeds
the actual width.
.Sh RETURN VALUES
.Nm
exits 0 on success, 1 on failure.
.Xr echo 1 ,
.Xr printf 3
.Sh STANDARDS
The
.Nm
utility mostly conforms to
.St -p1003.2-92 .
.Sh BUGS
Since the floating point numbers are translated from
.Tn ASCII
to floating-point and
then back again, floating-point precision may be lost.
.Pp
Parsing of - arguments is also somewhat different from
.Xr printf 3 ,
where unknown arguments are simply printed instead of being
flagged as errors.
` | 2013-05-24 18:15:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.34606435894966125, "perplexity": 8531.325750924798}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368704943681/warc/CC-MAIN-20130516114903-00084-ip-10-60-113-184.ec2.internal.warc.gz"} |
https://a-coding.com/tag/ai/ | For the last few months I have been working with neural networks, trying to figure out exactly what the inputs to the network and the network »
A* (A-star) is the typical textbook algorithm: it is a simple concept and can be easily explained. It is also widely known, one of the first » | 2019-02-17 17:03:11 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8750284910202026, "perplexity": 176.2367539437826}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-09/segments/1550247482186.20/warc/CC-MAIN-20190217152248-20190217174248-00060.warc.gz"} |
http://mathhelpforum.com/math-topics/25493-families-functions.html | 1. ## Families of functions
When is a function neither odd or even?For example why is x^3/2 neither odd or even?
When the domain is R\{0}, is the range always R+?
How do u find {x:x^3/2>x^2 } and {x:x^-3/2<x^-2}?
2. Originally Posted by chaneliman
When is a function neither odd or even?For example why is x^3/2 neither odd or even?
$\displaystyle \frac {x^3}2$ is odd. did you mean to say $\displaystyle x^{3/2}$ ?
a function f(x) is even if f(-x) = f(x)
a function is odd if f(-x) = -f(x)
otherwise, it is neither
When the domain is R\{0}, is the range always R+?
consider the function f(x) = 1/x
How do u find {x:x^3/2>x^2 } and {x:x^-3/2<x^-2}?
set up your inequalities and solve for x
can you solve $\displaystyle x^{3/2} > x^2$ for x? (is the power 3/2? type clearly)
3. yea i typed it right
4. Originally Posted by chaneliman
yea i typed it right
i do not know what you are refering to. you should quote the part of my message that you are responding to so i can respond
5. i can't solve x^3/2>x^2 for x. Does it have something 2 do with logs
?
6. Originally Posted by chaneliman
i can't solve x^3/2>x^2 for x. Does it have something 2 do with logs
?
$\displaystyle x^{3/2} > x^2$
Divide by $\displaystyle x^{3/2}$
$\displaystyle 1 > \sqrt{x}$
$\displaystyle 0 < x < 1$
7. Originally Posted by colby2152
$\displaystyle x^{3/2} > x^2$
Divide by $\displaystyle x^{3/2}$
$\displaystyle 1 > \sqrt{x}$
$\displaystyle 0 \le x < 1$
Before you divide by $\displaystyle x^{3/2}$ you should say that $\displaystyle x^{3/2} > 0$ because otherwise the inequality is flipped.
8. Originally Posted by ThePerfectHacker
Before you divide by $\displaystyle x^{3/2}$ you should say that $\displaystyle x^{3/2} > 0$ because otherwise the inequality is flipped.
True, but I kept that as an unstated assumption since it holds in the end o fthe solution with the square root.
9. Originally Posted by colby2152
[tex]
$\displaystyle 0 \le x < 1$
another technical note, which i'm sure was just a typo or something on your part. we can't have x = 0, since dividing by x^{3/2} would be invalid, and also the original inequality would not hold in the first place. we need x > 0 here for it to make sense
10. Originally Posted by Jhevon
another technical note, which i'm sure was just a typo or something on your part. we can't have x = 0, since dividing by x^{3/2} would be invalid, and also the original inequality would not hold in the first place. we need x > 0 here for it to make sense
I didn't see that at last glance, but I originally had a regular greater than sign, but changed it for some reason.
11. i understand it till the point u got 0<x<1
12. Originally Posted by chaneliman
i understand it till the point u got 0<x<1
we have $\displaystyle 1 > \sqrt{x}$
note that the domain of the square root function is $\displaystyle x \ge 0$, so we must have that for $\displaystyle \sqrt{x}$ to make sense. however, we drop the $\displaystyle x = 0$ part, because that does not work in the original inequality.
now, if we square both sides, we get: $\displaystyle 1 > x$
so we have $\displaystyle 0< x$ and $\displaystyle x < 1$, hence $\displaystyle 0 < x < 1$
13. then shouldn't it be 0>x if the domain of the square root function is more then or equal to 0
14. Originally Posted by chaneliman
then shouldn't it be 0>x if the domain of the square root function is more then or equal to 0
yes. more than or equal to zero is $\displaystyle x \ge 0$. we reject the = (for the afore mentioned reason) and make it $\displaystyle x > 0$. we cannot have x < 0, because the square root is not defined for such x's | 2018-03-18 15:55:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8852212429046631, "perplexity": 672.892809512068}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257645824.5/warc/CC-MAIN-20180318145821-20180318165821-00588.warc.gz"} |
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question commented on On the Configuration Space of a Scalar Field in 1+1D | 2021-11-30 05:05:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.784509539604187, "perplexity": 9534.758944999501}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358953.29/warc/CC-MAIN-20211130050047-20211130080047-00065.warc.gz"} |
http://www.ams.org/mathscinet-getitem?mr=713063 | MathSciNet bibliographic data MR713063 58C27 (14B10) Damon, James The unfolding and determinacy theorems for subgroups of \${\scr A}\$${\scr A}$ and \${\scr K}\$${\scr K}$. Singularities, Part 1 (Arcata, Calif., 1981), 233–254, Proc. Sympos. Pure Math., 40, Amer. Math. Soc., Providence, RI, 1983. Links to the journal or article are not yet available
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews. | 2016-06-25 20:43:50 | {"extraction_info": {"found_math": true, "script_math_tex": 2, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9809070825576782, "perplexity": 4402.259520132363}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-26/segments/1466783393518.22/warc/CC-MAIN-20160624154953-00083-ip-10-164-35-72.ec2.internal.warc.gz"} |
http://atozmath.com/Default.aspx?q1=Is%20lower%20triangle%20matrix%20%5B%5B1%2C0%2C0%5D%2C%5B2%2C3%2C0%5D%2C%5B4%2C5%2C6%5D%5D%60521&do=1 | Home > Matrix Algebra calculators > is Lower Triangle Matrix calculator
Solve any problem (step by step solutions) Input table (Matrix, Statistics)
Mode :
SolutionHelp
Solution
Find Is lower triangle matrix [[1,0,0],[2,3,0],[4,5,6]] [ Calculator, Method and examples ]
Solution:
Your problem -> Is lower triangle matrix [[1,0,0],[2,3,0],[4,5,6]]
A square matrix, in which all elements above the main diagonal are zero, is called a lower triangle matrix.
A =
1 0 0 2 3 0 4 5 6
Here, all elements above the main diagonal are zero, so it is a lower triangle matrix.
Solution provided by AtoZmath.com
Any wrong solution, solution improvement, feedback then Submit Here
Want to know about AtoZmath.com and me | 2019-06-19 12:04:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6018322706222534, "perplexity": 1863.382641495207}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627998959.46/warc/CC-MAIN-20190619103826-20190619125826-00151.warc.gz"} |
https://socratic.org/questions/how-do-you-write-and-solve-an-inequality-represents-the-values-of-x-for-which-th | # How do you write and solve an inequality represents the values of x for which the area of the rectangle will be at least 35 square feet?
Jan 6, 2017
#### Answer:
$x \ge \frac{35}{w}$ where $w > 0$ is the width of the rectangle (assuming $x$ is the length)
#### Explanation:
There really is not enough information here. You have not indicated how $x$ is related to the rectangle.
Perhaps (as an alternative to the assumption I made [above]), you meant for $x > 0$ to be the length of one side of a square.
In this case:
$\textcolor{w h i t e}{\text{XXX}} {x}^{2} \ge 35$
$\textcolor{w h i t e}{\text{XXX}} \rightarrow x \ge \sqrt{35}$ | 2019-03-21 15:40:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 7, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9661628007888794, "perplexity": 186.16482924522057}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-13/segments/1552912202526.24/warc/CC-MAIN-20190321152638-20190321174638-00406.warc.gz"} |
http://mathandmultimedia.com/2010/01/11/how-to-use-the-summation-symbol/ | # How to use the summation symbol
If we want to add the expression $x_1,x_2$ all the way up to $x_{10}$, it is quite cumbersome to write $x_1 +x_2 + x_3 + x_4 + x_5 + x_6 + x_7 + x_8 +x_9 +x_{10}$. Mathematical notations permit us to shorten such addition using the $\cdots$ symbol to denote “all the way up to” or “all the way down to”. Using the this symbol, the expression above can be written as $x_1 + x_2 + \cdots + x_{10}$.
There is, however, a more compact way of writing sums. We can use the Greek letter $\Sigma$ as shown below.
Figure 1 – The Sigma Notation
In the figure above, is the first index, and letter b is the last index. The variable(s) are the letters or the numbers that appear constantly in all terms. In the expression
$x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 + x_8 + x_9 + x_{10}$
$1$ is the first index, $10$ is the last index and $x$ is the variable. We use the letter $i$ as our index variable, or the variable that will hold the changing quantities. Hence, if we are going to use the sigma or the summation notation for the expression $x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 + x_8 + x_9 + x_{10}$, we have
$\displaystyle\sum_{i=1}^{10} x_i$
Some of the examples are shown below. Observe the colors of the indices and the variables, to familiarize yourself how the summation symbol works.
Figure 2 – Examples of Summation Notation
In using the summation symbol, take note of the following:
• An index variable is just a “dummy” variable. It means that you can use a different index variable without changing the value of the sum. The sum $\displaystyle\sum_{i=1}^{10} a_i$ is the same as $\displaystyle\sum_{j=1}^{10} a_j$ and is the same as $\displaystyle\sum_{k=1}^{10} a_k$.
• The indices are the natural numbers $1, 2, 3, \cdots$ and so on.
• The last index is always greater than the first index.
• A variable without an index most of the time represent an infinite sum or a sum from $1$ through $n$
More Examples
1 $(a - 1) + (a^2 - 2) + (a^3 - 3) + (a^4 -4)$ $\displaystyle\sum_{i=1}^{4} (a^i - i)$ 2 $3p_5 + 3p_6 + 3p_7 + 3p_8$ $\displaystyle\sum_{j=5}^{8} 3p_j$ 3 $5 + 5 + 5 + 5 + 5 + 5 + 5$ $\displaystyle\sum_{k=1}^{7} 5$ 4 $1 + 2 + 3 + \cdots + 99 + 100$ $\displaystyle\sum_{m=1}^{100} m$ 5 $(a_3 + b_3) + (a_4 + b_4) +(a_5 + b_5)$ $\displaystyle\sum_{n=3}^{5} (a_n + b_n)$
Properties of the Summation Symbol
1.) The expression $(x_1 + x_2 + x_3 + x_4) + (x_5 + x_6 + x_7 + x_8 + x_9 + x_{10})$ equals $(x_1 + x_2 + x_3 + x_4 + x_5 + x_6 + x_7 + x_8 + x_9 + x_{10})$ which means that $\displaystyle\sum_{i=1}^{4} x_i + \displaystyle\sum_{j=5}^{10} x_j = \displaystyle\sum_{i=1}^{10} x_i$. In general, $\displaystyle\sum_{i=1}^{m} x_i + \displaystyle\sum_{j=m+1}^{n} x_j = \displaystyle\sum_{i=1}^{n} x_i$.
2.)The expression $(x_1 + x_2 + x_3 + x_4) + (y_1 + y_2 + y_3 + y_4) = \displaystyle\sum_{i=1}^{4} x_i + \displaystyle\sum_{j=1}^{4} y_j$. Regrouping the expression, we have $(x_1 + y_1) + (x_2 + y_2) + (x_3 + y_3) + (x_4 + y_4) = \displaystyle\sum_{i=1}^{4} (x_i + y_i)$. This means that $\displaystyle\sum_{i=1}^{4} x_i + \displaystyle\sum_{i=j}^{4} y_j = \displaystyle\sum_{i=1}^{4} (x_i + y_i)$ Generalizing, we have $\displaystyle\sum_{i=1}^{n} x_i \pm \displaystyle\sum_{j=1}^{n} y_j = \displaystyle\sum_{i=1}^{n} (x_i \pm y_i).$
3.) The expression $c + c + c + \cdots + c$ ($k$ of them) $= \displaystyle\sum_{i=1}^{k} c$. But $c + c + c + \cdots + c = c( 1 + 1 + 1 + \cdots + 1)$ ($k$ of them) $= kc$. Therefore, $\displaystyle\sum_{i=1}^{k} c = kc$.
4.) The expression $2x_1 + 2x_2 + 2x_3 + 2x_4 = \displaystyle\sum_{i=1}^{4} 2x_i$. But $2x_1 + 2x_2 + 2x_3 + 2x_4 = 2(x_1 + x_2 + x_3 + x_4) = 2 \displaystyle\sum_{i=1}^{4} x_i$. In general, $\displaystyle\sum_{i=1}^{k} cx_i = c \displaystyle\sum_{i=1}^{k} x_i$.
1. ?
∑ 3n-10= 175
n=1
Can you help me with this problem. Has something to do with partial sums.
2. This is not a math tutorial site, but since you are the only one who asked, I’ll answer for now.
I don’t answer questions directly but I am going to give you a hint.
Try to see the pattern:
3(1) – 10 = -7
3(2) – 10 = – 4
3(3) – 10 = – 1
So basically, you have an arithmetic sequence with constant difference 3, first term -7 and sum of 175. I guess that hint is more than enough for you to solve the problem.
If you want math help, you should see this post. It has helped me in the past.
http://mathandmultimedia.com/2010/01/08/the-best-free-math-tutorial-website/
3. @misugrrl
You’re welcome. I am glad it has helped you.
4. jennifer
hi i was just wondering, how would you type that into an excel spreadsheet?
• I do not know of any way that you can write summation in excel. Maybe you should try writing it in MS Word first, the copy and paste to Excel.
• sonia
hi! do u know if there is any way to calculate it in excel? imagine u have from n=1 to n=100… u cannot write it manually, thanks!
• Well, as far as I know, excel has no summation function. The best thing that you can do is to place the numbers in excel (you don’t have to type them all, just use a formula), and then use the sum function.
5. toto | 2015-03-05 02:29:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 47, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8964651823043823, "perplexity": 325.61341409410255}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-11/segments/1424936463679.20/warc/CC-MAIN-20150226074103-00180-ip-10-28-5-156.ec2.internal.warc.gz"} |
https://stats.stackexchange.com/questions/225144/in-medical-statistics-when-to-use-chi2-and-when-to-use-kruskal-wallis-h | # In medical statistics, when to use $\chi^2$ and when to use Kruskal-Wallis H?
I am conducting a retrospective analysis on the effect of three different treatment option (intervention treatment) on a special type of cancer, so I have three groups: 1, 2, and 3.
In the baseline patient demographic table for the three groups, I have multiple variables like age, gender, presence of other disease, presence of lymph node involvement, etc. All of them are coded categorical variables (0,1), I want to know if there is a significant difference in each variable for the three groups.
Some articles use the Chi-Squared test and others use Kruskal-Wallis H test.
Which one is the correct one? Or if there is another possibility? | 2019-12-06 00:53:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.20817826688289642, "perplexity": 854.769527854335}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540482954.0/warc/CC-MAIN-20191206000309-20191206024309-00473.warc.gz"} |
http://www.zora.uzh.ch/122850/ | # Search for the rare decays ${B}^{0}{\rightarrow}J/{\psi}{\gamma}$ and ${B}_{s}^{0}{\rightarrow}J/{\psi}{\gamma}$
LHCb collaboration; Abellán Beteta, C; Anderson, J; Bernet, R; Bowen, E; Bursche, A; Chiapolini, N; Chrzaszcz, M; Elsasser, C; Graverini, E; Lionetto, F; Mauri, A; Müller, K; Steinkamp, O; Serra, N; Silva Coutinho, R; Storaci, B; Straumann, U; Tresch, M; Vollhardt, A; Weiden, A; et al (2015). Search for the rare decays ${B}^{0}{\rightarrow}J/{\psi}{\gamma}$ and ${B}_{s}^{0}{\rightarrow}J/{\psi}{\gamma}$. Physical Review D (Particles, Fields, Gravitation and Cosmology), 92:112002.
## Abstract
A search for the rare decay of a $B^{0}$ or $B^{0}_{s}$ meson into the final state $J/\psi\gamma$ is performed, using data collected by the LHCb experiment in $pp$ collisions at $\sqrt{s}=7$ and $8$ TeV, corresponding to an integrated luminosity of 3 fb$^{-1}$. The observed number of signal candidates is consistent with a background-only hypothesis. Branching fraction values larger than $1.7\times 10^{-6}$ for the $B^{0}\to J/\psi\gamma$ decay mode are excluded at 90% confidence level. For the $B^{0}_{s}\to J/\psi\gamma$ decay mode, branching fraction values larger than $7.4\times 10^{-6}$ are excluded at 90% confidence level, this is the first branching fraction limit for this decay.
A search for the rare decay of a $B^{0}$ or $B^{0}_{s}$ meson into the final state $J/\psi\gamma$ is performed, using data collected by the LHCb experiment in $pp$ collisions at $\sqrt{s}=7$ and $8$ TeV, corresponding to an integrated luminosity of 3 fb$^{-1}$. The observed number of signal candidates is consistent with a background-only hypothesis. Branching fraction values larger than $1.7\times 10^{-6}$ for the $B^{0}\to J/\psi\gamma$ decay mode are excluded at 90% confidence level. For the $B^{0}_{s}\to J/\psi\gamma$ decay mode, branching fraction values larger than $7.4\times 10^{-6}$ are excluded at 90% confidence level, this is the first branching fraction limit for this decay.
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Item Type: Journal Article, refereed, original work 07 Faculty of Science > Physics Institute 530 Physics English 2015 18 Feb 2016 11:46 05 Apr 2016 20:09 American Physical Society 1550-7998 https://doi.org/10.1103/PhysRevD.92.112002 arXiv:1510.04866
Permanent URL: https://doi.org/10.5167/uzh-122850
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## TrendTerms
TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents. | 2016-10-22 07:39:28 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9025099873542786, "perplexity": 2871.642883459944}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988718840.18/warc/CC-MAIN-20161020183838-00422-ip-10-171-6-4.ec2.internal.warc.gz"} |
https://www.aimsciences.org/article/doi/10.3934/dcdsb.2003.3.255 | American Institute of Mathematical Sciences
May 2003, 3(2): 255-262. doi: 10.3934/dcdsb.2003.3.255
Recurrent motions in the nonautonomous Navier-Stokes system
1 Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, United States, United States 2 State University of Moldova, Department of Mathematics and Informatics, A. Mateevich Street 60, MD–2009 Chişinău, Moldavia
Received June 2002 Revised December 2002 Published February 2003
We prove the existence of recurrent or Poisson stable motions in the Navier-Stokes fluid system under recurrent or Poisson stable forcing, respectively. We use an approach based on nonautonomous dynamical systems ideas.
Citation: Vena Pearl Bongolan-walsh, David Cheban, Jinqiao Duan. Recurrent motions in the nonautonomous Navier-Stokes system. Discrete & Continuous Dynamical Systems - B, 2003, 3 (2) : 255-262. doi: 10.3934/dcdsb.2003.3.255
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2019 Impact Factor: 1.27 | 2020-12-04 15:10:30 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4784075915813446, "perplexity": 8653.18150309443}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141737946.86/warc/CC-MAIN-20201204131750-20201204161750-00499.warc.gz"} |
https://tex.stackexchange.com/questions/25798/how-can-i-add-abstract-and-acknowledgement-pages-into-the-table-of-contents | I followed Mike's solution from my first question:
Roman numeral page numbering
Assuming that the abstract and acknowledgement contents is typeset using a \chapter*{...}, you could do the following:
\chapter*{Abstract}%
...
\chapter*{Acknowledgements}%
...
This will add a chapter-level (chapter) entry to the table of contents (toc) without a chapter number (\numberline{}).
• what do i do if i am adding abstract.tex to my main thesis.tex file ? in this case how do i add page numbering in roman ? Mar 21, 2016 at 7:40
• @Hirak: Either \renewcommand{\thepage}{\roman{page}} or \pagenumbering{roman}. The latter also resets the page counter. However, I'm not sure whether this is what you're asking about.
– Werner
Mar 21, 2016 at 15:28
• While this is the accepted answer and technically correct, the hyperlinks in the TOC will not go to the correct location without \phantomsection. See Stefan's answer for a complete solution.
– jds
May 13, 2021 at 15:33
• @gwg: Correct, if you're using hyperref (which there is no mention of in the OP).
– Werner
May 13, 2021 at 15:49
While you can manually add an entry to the TOC by \addtocontents or \addcontentsline, the order of commands can be important, especially
• if you use hyperref, to get the hyperlink above the heading, not below
• or if you add a section to the TOC, which is done by a macro but several pages long, such as by \listoffigures, \listoftables or \bibliography. A wrong order would add the last page to the TOC
So
• use \addtocontents or \addcontentsline before \chapter* of \listof...
• ensure the required page break before \addtocontents or \addcontentsline
• for hyperref, add an anchor for the target
\cleardoublepage
\phantomsection
\chapter*{Abstract}
If you need that several times, you could define a macro for it.
Regarding the commands:
• \cleardoublepage ends the page, prints out remaining floats if necessary, and ensures that the following text starts on a right hand page, as chapters in books commonly do, if in twoside mode. \clearpage, in contrast, would start the new page on a left or a right side.
• \phantomsection is a command of the hyperref package, which creates an anchor at this location, similar to \hypertarge, which can be referred to - \addcontentsline does it implicitely. Without \phantomsection, \addcontentsline would refer to the previous anchor which could be undesired.
The package tocbibind makes putting commonly added chapters/sections (bibliography, TOC, index) to the TOC easier. It's integrated in the memoir class, while KOMA-Script classes support this purpose by class options such as bibliography=totoc.
• You've used \cleardoublepage, \phantomsection - could you be more specific about those two ? Feb 1, 2012 at 18:47
• @GrzegorzWierzowiecki I updated my answer and explained the commands. Feb 1, 2012 at 19:04
• Thank you, it's educative piece of tex code for learning latex :). Feb 1, 2012 at 19:11
Instead of tinkering with \cleardoublepage, \phantomsection, and \addcontentsline, I suggest to
• use \chapter (the non-starred version) also for the Abstract and Acknowledgements,
• set the secnumdepth counter to -2 (i.e., no sectioning level is numbered) before the Abstract,
• resetsecnumdepth to 2 (default for the report class) before the first proper chapter.
Works also with hyperref.
\documentclass{report}
\usepackage{hyperref}
\begin{document}
\tableofcontents
\setcounter{secnumdepth}{-2}% default for "report" is 2
\chapter{Abstract}
\chapter{Acknowledgements}
\setcounter{secnumdepth}{2}
\chapter{First}
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https://www.gradesaver.com/textbooks/math/calculus/calculus-8th-edition/chapter-6-inverse-functions-6-2-the-natural-logarithmic-functions-6-2-exercises-page-446/49 | ## Calculus 8th Edition
$y'=\frac{2x}{(x^{2}+y^{2}-2y)}$
First simplify the given function using the properties of logarithms and then apply chain rule of differentiation. $y'=\frac{d}{dx}[ln(x^{2}+y^{2})]$ $=\frac{1}{(x^{2}+y^{2})}(2x+2y\frac{dy}{dx})$ $=\frac{2x}{(x^{2}+y^{2})}+\frac{2yy'}{(x^{2}+y^{2})}$ $y'-\frac{2yy'}{(x^{2}+y^{2})}=\frac{2x}{(x^{2}+y^{2})}$ $y'(x^{2}+y^{2}-2y)=2x$ Hence, $y'=\frac{2x}{(x^{2}+y^{2}-2y)}$ | 2018-11-18 05:31:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9853482246398926, "perplexity": 172.3329773434431}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-47/segments/1542039743968.63/warc/CC-MAIN-20181118052443-20181118073817-00018.warc.gz"} |
http://www.ams.org/mathscinet-getitem?mr=2113894 | MathSciNet bibliographic data MR2113894 (2005k:46189) 46L80 (19K33 46L05) Toms, Andrew On the independence of \$K\$$K$-theory and stable rank for simple \$C\sp *\$$C\sp *$-algebras. J. Reine Angew. Math. 578 (2005), 185–199. Article
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews. | 2015-01-26 00:29:55 | {"extraction_info": {"found_math": true, "script_math_tex": 2, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9973125457763672, "perplexity": 9226.150999368494}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-06/segments/1422115867691.21/warc/CC-MAIN-20150124161107-00199-ip-10-180-212-252.ec2.internal.warc.gz"} |
https://math.stackexchange.com/questions/4035260/a-doubt-about-differentiability-and-increasing-function | # A doubt about differentiability and increasing function
Suppose $$f:(a,b)\rightarrow (a,b)$$ is differentiable on $$(a,b)$$ and for an $$x_{0}$$ such that $$a , $$f'(x_{0}) >0$$ then is $$f$$ increasing in some neighborhood of $$x_{0}$$?
I have seen examples on this site on disproving this for the interval $$(0,1)$$ by taking the function $$x+2x^{2}\sin(\frac{1}{x})$$ when $$x\neq 0$$ and $$0$$ if $$x=0$$. But I have a doubt whether this would be true for $$x_{0}$$ being an interior point of the open interval $$(a,b)$$ . Can someone please clarify . I have tried to prove it using LMVT but since nothing is said about continuity on $$[a,b]$$ I am unable to proceed.
• "in some neighborhood of $(a,b)$" : what do you mean ? – TheSilverDoe Feb 22 at 10:39
• Oh no...typo...I meant in some neighborhood of $x_{0}$ . Thanks for noticing – Arghyadeep Chatterjee Feb 22 at 10:56
• Take the same counterexample $x+2x^{2}\sin(x)$ on $(-1,1)$. – TheSilverDoe Feb 22 at 10:59
• I think the result holds true when $f'$ is continuous at $x_0$. – cxh007 Feb 22 at 11:08
• @cxh007 math.stackexchange.com/questions/1603958/… see this . – Arghyadeep Chatterjee Feb 22 at 11:21
If we can assume that $$f'$$ is continuous at $$x_0$$, then by $$f'(x_0)>0$$ we know that there exists a closed interval $$[c,d]$$ satisfying $$x_0 \in [c,d]\subset (a,b)$$ and s.t. $$\forall t \in [c,d], f'(t)>0$$. Moreover $$f$$ is differentiable on $$(c,d)$$, $$f$$ is continuous at $$[c,d]$$. Then we apply LMVT: if $$x,y\in[c,d], x, then $$f(y)-f(x)=f'(\xi)(y-x)$$ where $$\xi \in [c,d]$$, and thus $$f'(\xi)>0, (y-x) >0$$, finally for $$x,y\in [c,d]$$, $$f(y)>f(x)$$ whenever $$y>x$$.
As noted, for counterexample just take $$(a,b)=(-1,1), x_0=0,f(x)=x+2x^2 \sin(\frac{1}{x})$$ when $$x \neq 0$$, $$f(x)=0$$ when $$x=0$$. | 2021-05-13 07:00:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 36, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9999903440475464, "perplexity": 756.7926273688374}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-21/segments/1620243991537.32/warc/CC-MAIN-20210513045934-20210513075934-00630.warc.gz"} |
https://stats.hohoweiya.xyz/2022/04/07/big-data-paradox/ | # Big Data Paradox
##### Posted on Apr 07, 2022
Tags: Big Data
By developing measures for data quality, this article suggests a framework to address the following question
Which one should I trust more: a 1% survey with 60% response rate or a self-reported administrative dataset covering 80% of the population?
A 5-element Euler-formula-like identity shows that for any dataset of size $n$, probabilistic or not, the difference between the sample average $\bar X_n$ and the population average $\bar X_N$ is the product of three terms:
• a data quality measure, $\rho_{R,X}$, the correlation between $X_j$ and the response/recording indicator $R_j$
• a data quantity measure, $\sqrt{(N-n)/n}$
• a problem difficulty measure, $\sigma_X$
The decomposition provides multiple insights:
• probabilistic sampling ensures high data quality by controlling $\rho_{R,X}$ at the level of $N^{-1/2}$ (???)
• when lose this control, the estimation error, relative to the benchmarking rate $1/\sqrt n$, increased with $\sqrt N$
• the bigness of such Big Data (for population inferences) should be measured by the relative size $f=n/N$, not the absolute size $n$
• when combining data sources for population inferences, those relatively tiny but higher quality ones should be given far more weights than suggested by their sizes
Without taking data quality into account, population inferences with Big Data are subject to a Big Data Paradox: the more the data, the surer we fool ourselves.
data defect index
For population inferences, a key “policy proposal” of the paper is to shift from the traditional focus on assessing probabilistic uncertainty
$\text{Standard Error}\prop \frac{\sigma}{\sqrt n}$
to the practice of ascertaining systematic error in non-probabilistic Big Data captured by
$\text{Relative Bias} \prop \rho \sqrt N$
The key question is
how to compare two datasets with different quantities and different qualities?
Consider finite population indexed by $j=1,\ldots,N$.
• $\bar G_N$: population average of $\{G_j\equiv G(X_j),j=1,\ldots,N\}$
When we have a sample, the sample average
$\bar G_n = \frac 1n\sum_{j\in I_n}G_j = \frac{\sum_{j=1}^NR_jG_j}{\sum_{j=1}^NR_j}$
where “R” leads to R-mechanism.
the difference between $\bar G_n$ and $\bar G_N$ can be written as
$\bar G_n-\bar G_N = \frac{\Cov_J(R_J, G_J)}{E_J(R_J)}$
Let
• $\rho_{R,G}=\Corr_J(R_J, G_J)$ be the population correlation between $R_J$ and $G_J$,
• $f=E_J(R_J）=n/N$ be the sampling rate,
• $\sigma_G$ be the standard deviation of $G_J$.
Then
$\bar G_n - \bar G_N = \rho_{R, G} \times \sqrt{\frac{1-f}{f}} \times \sigma_G$
The most critical, yet most challenging to assess is data quality.
Published in categories Note | 2022-10-01 14:27:59 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5005196332931519, "perplexity": 2126.6094472230507}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-40/segments/1664030336674.94/warc/CC-MAIN-20221001132802-20221001162802-00792.warc.gz"} |
http://www.aamt.edu.au/Topdrawer/Fractions/Good-teaching/Equivalence/Grids-and-arrays/Overlay-grids/(language)/eng-AU | ## Featured resource
### A Guide to Mathematics Coaching
Mathematics coaching can be an effective method of changing teacher practice and improving student achievement. But the processes in this book do not just apply to coaches—they are applicable to any mathematics leader.
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# Overlay grids
It is important that students experience the decision-making process of selecting grids for themselves, and physically positioning them to make the new fractions.
Watch the video Using Overlay Grids.
Photocopy the overlay templates onto transparencies and make a set for each pair of students.
The grids can be used for a number of tasks.
• Find and record equivalent fractions for $$\frac{1}{2}$$, $$\frac{1}{3}$$, $$\frac{1}{5}$$ etc.
• Make a grid and record all the equivalent fractions (e.g. $$\frac{1}{3}$$ = $$\frac{2}{6}$$, $$\frac{2}{3}$$ = $$\frac{4}{6}$$, $$\frac{3}{3}$$ = $$\frac{6}{6}$$).
• Explore different ways to represent twelfths and record the equivalent fractions.
Use of overlay templates.
Encourage students to look for patterns and relationships among the groups of equivalent fractions they find, particularly multiplicative relationships.
As students become familiar with finding equivalent fractions, ask them to predict what they will find (e.g. if looking for fractions equivalent to $$\frac{2}{3}$$). Students should explain their prediction strategies. | 2017-12-16 09:17:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6669250130653381, "perplexity": 1771.423285362692}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948587496.62/warc/CC-MAIN-20171216084601-20171216110601-00683.warc.gz"} |
https://www.sanfoundry.com/finite-element-method-questions-answers-shear-deformable-plate-model/ | # Finite Element Method Questions and Answers – Shear Deformable Plate Model
«
This set of Finite Element Method Multiple Choice Questions & Answers (MCQs) focuses on “Shear Deformable Plate Model”.
1. In FEM, which theory is an extension of the Timoshenko beam theory?
a) Classical Plate Theory
b) Hencky-Mindlin plate theory
c) Kirchhoff plate theory
d) Shell theory
Explanation: The two most commonly used displacement-based plate theories are the Classical Plate Theory (CPT) and first-order Shear Deformation Theory (SDT). CPT is an extension of the Euler-Bernoulli beam theory from one dimension to two dimensions and is also known as the Kirchhoff plate theory. Shear Deformation Theory is an extension of the Timoshenko beam theory and it is often called the Hencky-Mindlin plate theory.
2. In displacement-based plate theories, if a linear theory based on infinitesimal strains and orthotropic material properties is used, then the in-plane displacements are coupled with the transverse deflection.
a) True
b) False
Explanation: For a linear theory based on infinitesimal strains and orthotropic material properties, the in-plane displacements(ux, uy) are uncoupled from the transverse deflection uz=w. The plane elasticity equations govern the in-plane displacements (ux, uy). The in-plane displacements are zeroin the absence of in-plane forces, andhence, we discuss only the equations governing the bending deformation.
3. In FEM, what are the primary variables in the Shear Deformation Theory of plate deformation (w)?
a) The transverse deflection w only
b) The transverse deflection w and the normal derivative of w
c) The transverse deflection w and the angles of rotation of the transverse normal about in-plane axes
d) The angles of rotation of the transverse normal about in-plane axes only
Explanation: An examination of the boundary terms in the weak form of Shear Deformation Theory suggests that the essential boundary conditions involve specifying the transverse deflection w and the angles of rotation of the transverse normal about in-plane axes (φx, φy), which constitute the primary variables of the problem (like in the Timoshenko beam model). Hence, the finite element interpolation of w must be such that w, (φx and φy are continuous across the inter-element boundaries in SDT elements.
4. Which equation correctly describes Hamilton’s principle used in FEM?
a) 0=$$\int_{t_1}^{t_2}$$[δK-(δU+δV)]dt
b) 0=$$\int_{t_1}^{t_2}$$t[δK-(δU+δV)]dt
c) 0=$$\int_{t_1}^{t_2}$$[δK+(δU+δV)]dt
d) 0=$$\int_{t_1}^{t_2}$$t[-δK+(δU+δV)]dt
Explanation: Governing equations of displacement-based plate theories are derived using the principle of virtual displacements. The principle of virtual displacements or Hamilton’s principle requires that 0=$$\int_{t_1}^{t_2}$$[δK-(δU+δV)]dt where δU, δV and δK denote the virtual strain energy, virtual work done by externally applied forces, and virtual kinetic energy, respectively. These quantities are expressed in terms of actual stresses and virtual strains, which depend on the assumed displacement functions and their variations.
5. In displacement-based plate theories, which option is correct about Shear Deformation Theory (SDT)?
a) It is also called Kirchhoff plate theory
b) It is an extension of Euler-Bernoulli beam theory from one dimension to two dimensions
c) It does not involve Timoshenko beam theory
d) It is often known as Hencky-Mindlin plate theory
Explanation: The two most commonly used displacement-based plate theories are the Classical Plate Theory (CPT) and first-order Shear Deformation Theory (SDT). CPT is an extension of the Euler-Bernoulli beam theory from one dimension to two dimensions and is also known as the Kirchhoff plate theory. Shear Deformation Theory is an extension of the Timoshenko beam theory and it is often called the Hencky-Mindlin plate theory.
6. In displacement-based plate theories, which assumption of Classical Plate Theory is relaxed in Shear Deformation Theory?
a) A straight-line perpendicular to the plane of the plate is inextensible
b) A straight line perpendicular to the plane of the plate remains straight
c) A straight line perpendicular to the plane of the plate rotates such that it remains perpendicular to the tangent to the deformed surface
d) A straight line perpendicular to the plane of the plate rotates
Explanation: In the SDT, we relax the normality assumption of CPT, i.e., transverse normal may rotate without remaining perpendicular to the mid-plane. The Classical Plate Theory is based on the assumption that a straight line perpendicular to the plane of the plate is (1) inextensible, (2) remains straight, and (3) rotates such that it remains perpendicular to the tangent to the deformed surface.
7. Which option specifies an assumption made in Shear Deformation Theory for a plate lying in the plane XY?
a) εzz≠0
b) εxz=0
c) εyz≠0
d) εxy=0
Explanation: The Classical Plate Theory is based on the assumption that a straight line perpendicular to the plane of the plate is (1) inextensible, (2) remains straight, and (3) rotates such that it remains perpendicular to the tangent to the deformed surface, but In the SDT, we relax the normality assumption of CPT, i.e., transverse normal may rotate without remaining normal to the mid-plane. Thus, for a plate in the XY plane, the assumptions are equivalent to specifying εzz=0 only whereas εyz and εxz are non-zero.
8. In SDT, what are the boundary conditions for a plate that is clamped if ф represents the rotation of the transverse normal about an in-plane axis and w is the transverse deflection?
a) w=0,$$\frac{\partial w}{\partial n}$$=0
b) w=0,ф=0
c) w=0,$$\frac{\partial w}{\partial n}$$≠0
d) w=0, Mnn=0
Explanation: Geometrically, plate problems are similar to the plane stress problems except that plates are also subjected to transverse loads that cause bending about axes in the plane of the plate. In SDT, the boundary condition for a clamped plate is the absence of deflection and rotation of the transverse normal about any in-plane axis, i.e., w=ф=0. Because a simply supported end does not restrict rotation, the reactive moment is zero, i.e., w=Mnn=0. For a free end, both, the reactive moment and the shear force are absent, i.e., Mnn=Qn=0.
9. In SDT, what are the boundary conditions for a plate that is simply supported if ф represents the rotation of the transverse normal about an in-plane axis and w is the transverse deflection?
a) w=0,$$\frac{\partial w}{\partial n}$$=0
b) w=0,ф=0
c) w=0,$$\frac{\partial w}{\partial n}$$≠0
d) w=0, Mnn=0
Explanation: Plate problems are geometrically similar to the plane stress problems except that plates are also subjected to transverse loads. In SDT, a clamped plate has no deflection and rotation of the transverse normal about any in-plane axis, i.e., w=ф=0. In a simply supported end, rotation is not restricted; thusthe reactive moment is zero, i.e., w= Mnn=0. A free end does not have reactive moment and the shear force, i.e., Mnn=Qn=0.
10. In FEM, which option is correct for a linear plate theory based on infinitesimal strains and orthotropic material properties?
a) The plane elasticity equations govern the transverse deflections
b) The transverse deflections are coupled with in-plane displacements
c) The in-plane displacements are zero in the absence of in-plane forces
d) The transverse deflections are zero in the absence of in-plane forces
Explanation: For a linear theory based on infinitesimal strains and orthotropic material properties, the in-plane displacements (ux, uy) are uncoupled from the transverse deflection uz=w. The plane elasticity equations govern the in-plane displacements (ux, uy). The in-plane displacements are zero if there are no in-plane forces and hence, we discuss only the equations governing the bending deformation and the associated finite element models.
11. In the Shear Deformation plate theory, when does the transverse shear strains in the element equations present computational difficulties?
a) If the plate is thick
b) If the side to thickness ratio of the plate is large
c) If the side to thickness ratio of the plate is small
d) If higher-order finite elements are used
Explanation: The transverse shear strains in the element equations of Shear Deformation Theory present computational difficulties when the side-to-thickness ratio of the plateis large (say 50, i.e., when the plate becomes thin). For thin plates, the transverse shear strains are negligible, and consequently, the element stiffness matrix becomes stiff and yields erroneous results for the generalized displacements. This phenomenon is known as shear locking.
12. In the Shear Deformation plate theory, what characteristic contributes to shear locking?
a) Transverse shear strains in thick plates present computational difficulties
b) Transverse shear strains in thin plates present computational efficiency
c) For thick plates, the element stiffness matrix yields erroneous results for the generalized displacements
d) For thin plates, the element stiffness matrix becomes stiff and yields erroneous results | 2021-09-26 04:20:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6679466366767883, "perplexity": 1330.0551515053637}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057796.87/warc/CC-MAIN-20210926022920-20210926052920-00366.warc.gz"} |
http://bestwwws.com/confidence-interval/confidence-interval-margin-of-error-for-a-population-proportion.php | Home > Confidence Interval > Confidence Interval Margin Of Error For A Population Proportion
# Confidence Interval Margin Of Error For A Population Proportion
## Contents
ProfessorSerna 164,245 views 27:18 Confidence Intervals about the Mean, Population Standard Deviation Unknown - Duration: 5:15. Why? All Rights Reserved. Welcome to STAT 500! http://bestwwws.com/confidence-interval/compute-population-mean-margin-error-95-confidence-interval.php
Rumsey You can find the confidence interval (CI) for a population proportion to show the statistical probability that a characteristic is likely to occur within the population. Each possible sample gives us a different sample proportion and a different interval. Because we are estimating the smallest sample size needed to produce the desired error. Working...
## Does The Confidence Interval Provide A Good Estimate Of The Population Proportion
Select the Summarized data option button. Identify a sample statistic. Use Minitab to obtain the exact interval: The exact interval is (0.4609, 0.5666). Transcript The interactive transcript could not be loaded.
Compute margin of error (ME): ME = critical value * standard error = 2.58 * 0.012 = 0.03 Specify the confidence interval. Take the square root of the calculated value. For convenience, we repeat the key steps below. Confidence Interval Margin Of Error Calculator Luckily, this works well in situations where the normal curve is appropriate [i.e.
Sign in Transcript Statistics 42,821 views 196 Like this video? Find A 95 Confidence Interval For The True Population Proportion Find standard deviation or standard error. For example, suppose you want to estimate the percentage of the time (with 95% confidence) you're expected to get a red light at a certain intersection. https://onlinecourses.science.psu.edu/stat200/node/48 Sign in to add this video to a playlist.
The margin of error is, therefore, plus or minus 1.96 ∗ 0.0499 = 0.0978, or 9.78%. Confidence Interval Margin Of Error Formula Since we cannot sample a portion of a subject - e.g. Specify the confidence interval. statslectures 23,883 views 4:30 Using the TI-84 to Find a Confidence Interval for a Population Proportion (1-PropZInt) - Duration: 5:37.
1. Stephanie Glen 1,627 views 1:50 Large-Sample Hypothesis Test for a Population Proportion - Duration: 13:43.
2. statslectures 60,121 views 5:15 86 videos Play all Statisticsstatslectures Large Sample Confidence Interval for a Population Proportion - Duration: 6:10.
3. Hand Computation.
4. The key steps are shown below.
5. Use the sample proportion to estimate the population proportion.
6. In terms of percent, between 47.5% and 56.5% of the voters favor the candidate and the margin of error is 4.5%.
7. What is the 99% confidence interval for the proportion of readers who would like more coverage of local news? (A) 0.30 to 0.50 (B) 0.32 to 0.48 (C) 0.35 to 0.45
8. The sample size obtained from using the educated guess is usually smaller than the one obtained using the conservative method.
## Find A 95 Confidence Interval For The True Population Proportion
Often, researchers choose 90%, 95%, or 99% confidence levels; but any percentage can be used. http://onlinestatbook.com/2/estimation/proportion_ci.html This smaller sample size means there is some risk that the resulting confidence interval may be wider than desired. Does The Confidence Interval Provide A Good Estimate Of The Population Proportion Can we use the formulas above to make a confidence interval in this situation?Solution: No,in such a skewed situation- with only 1 home that does not have a refrigerator - the Conservative 95 Confidence Interval Using the t Distribution Calculator, we find that the critical value is 2.58.
Sign in to make your opinion count. his comment is here The general formula for the margin of error for a sample proportion (if certain conditions are met) is where is the sample proportion, n is the sample size, and z* is In this analysis, the confidence level is defined for us in the problem. Since we are trying to estimate a population proportion, we choose the sample proportion (0.40) as the sample statistic. Find The Margin Of Error For The 95 Confidence Interval Used To Estimate The Population Proportion
a. The standard deviation of the sample proportion σp is: σp = sqrt[ P * ( 1 - P ) / n ] * sqrt[ ( N - n ) / ( Welcome to STAT 100! http://bestwwws.com/confidence-interval/compute-population-mean-margin-error-99-confidence-interval.php The exact interval is always appropriate.
AGodboldMath 28,665 views 5:37 95% Confidence Interval - Duration: 9:03. Confidence Interval Margin Of Error Ti 83 Advertisement Autoplay When autoplay is enabled, a suggested video will automatically play next. Because the sampling distribution is approximately normal and the sample size is large, we can express the critical value as a z score by following these steps.
## Therefore, the 99% confidence interval is 0.37 to 0.43.
For this problem, it will be the t statistic having 1599 degrees of freedom and a cumulative probability equal to 0.995. They can be time-consuming and complex. And since the population is more than 20 times larger than the sample, we can use the following formula to compute the standard error (SE) of the proportion: SE = sqrt Confidence Interval Margin Of Error Equation Remember that this is the minimal sample size needed for our study.
Loading... The probability that your interval captures the true population value could be much lower if your survey is biased (e.g. It turns out that 49 of the 50 homes in our sample have a refrigerator. navigate here Margin of Error Note: The margin of error E is half of the width of the confidence interval. $E=z_{\alpha/2}\sqrt{\frac{\hat{p}\cdot (1-\hat{p})}{n}}$ Confidence and precision (we call wider intervals as having poorer precision):
The standard error (SE) can be calculated from the equation below. This step gives you the margin of error. This condition is satisfied; the problem statement says that we used simple random sampling. In other words, if you have a sample percentage of 5%, you must use 0.05 in the formula, not 5.
Your 95% confidence interval for the percentage of times you will ever hit a red light at that particular intersection is 0.53 (or 53%), plus or minus 0.0978 (rounded to 0.10 Toggle navigation Search Submit San Francisco, CA Brr, it´s cold outside Learn by category LiveConsumer ElectronicsFood & DrinkGamesHealthPersonal FinanceHome & GardenPetsRelationshipsSportsReligion LearnArt CenterCraftsEducationLanguagesPhotographyTest Prep WorkSocial MediaSoftwareProgrammingWeb Design & DevelopmentBusinessCareersComputers Online Courses In other words, our actually sample size would need to be 19,363 given the 40% response rate. Estimation Requirements The approach described in this lesson is valid whenever the following conditions are met: The sampling method is simple random sampling.
To change a percentage into decimal form, simply divide by 100. For example, consider the percentage of people in favor of a four-day work week, the percentage of Republicans who voted in the last election, or the proportion of drivers who don't Applied Statistical Decision Making Lesson 6 - Confidence Intervals6.1 - Inference for the Binomial Parameter: Population Proportion 6.2 - Sample Size Computation for Population Proportion Confidence Interval 6.3 - Inference for Sign in to make your opinion count.
Loading... Using the sample size by the conservative method has no such risk. They asked whether the paper should increase its coverage of local news. | 2018-09-19 22:14:36 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7981322407722473, "perplexity": 745.0492602736801}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-39/segments/1537267156311.20/warc/CC-MAIN-20180919220117-20180920000117-00145.warc.gz"} |
http://openstudy.com/updates/51002f1de4b0426c6368742c | andry.chowanda Group Title Why we are using LaTeX? one year ago one year ago
Mainly to format math equations. It makes them a lot easier to read! :) Here's an example: y=((ln x)^2)/((x-1)^2+2) All those extra brackets can be confusing! If I format it in LaTeX, I don't need to worry about the outer brackets because it will be very clear which term is on top of the fraction.$\large y=\frac{(\ln x)^2}{(x-1)^2+2}$ | 2014-09-02 17:04:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8624827265739441, "perplexity": 893.119472832538}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1409535922089.6/warc/CC-MAIN-20140901014522-00233-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://es.mathworks.com/help/reinforcement-learning/ref/rl.replay.rlreplaymemory.sample.html | # sample
Sample experiences from replay memory buffer
## Syntax
``experience = sample(buffer,batchSize)``
``experience = sample(buffer,batchSize,Name=Value)``
``[experience,Mask] = sample(buffer,batchSize,Name=Value)``
## Description
example
````experience = sample(buffer,batchSize)` returns a mini-batch of N experiences from the replay memory `buffer`, where N is specified using `batchSize`.```
````experience = sample(buffer,batchSize,Name=Value)` specifies additional sampling options using one or more name-value pair arguments.```
````[experience,Mask] = sample(buffer,batchSize,Name=Value)` returns a sequence padding mask indicating which the padded experiences at the end of a sampled sequence.```
## Examples
collapse all
Define observation specifications for the environment. For this example, assume that the environment has a single observation channel with three continuous signals in specified ranges.
```obsInfo = rlNumericSpec([3 1],... LowerLimit=0,... UpperLimit=[1;5;10]);```
Define action specifications for the environment. For this example, assume that the environment has a single action channel with two continuous signals in specified ranges.
```actInfo = rlNumericSpec([2 1],... LowerLimit=0,... UpperLimit=[5;10]);```
Create an experience buffer with a maximum length of 20,000.
`buffer = rlReplayMemory(obsInfo,actInfo,20000);`
Append a single experience to the buffer using a structure. Each experience contains the following elements: current observation, action, next observation, reward, and is-done.
For this example, create an experience with random observation, action, and reward values. Indicate that this experience is not a terminal condition by setting the `IsDone` value to 0.
```exp.Observation = {obsInfo.UpperLimit.*rand(3,1)}; exp.Action = {actInfo.UpperLimit.*rand(2,1)}; exp.NextObservation = {obsInfo.UpperLimit.*rand(3,1)}; exp.Reward = 10*rand(1); exp.IsDone = 0;```
Append the experience to the buffer.
`append(buffer,exp);`
You can also append a batch of experiences to the experience buffer using a structure array. For this example, append a sequence of 100 random experiences, with the final experience representing a terminal condition.
```for i = 1:100 expBatch(i).Observation = {obsInfo.UpperLimit.*rand(3,1)}; expBatch(i).Action = {actInfo.UpperLimit.*rand(2,1)}; expBatch(i).NextObservation = {obsInfo.UpperLimit.*rand(3,1)}; expBatch(i).Reward = 10*rand(1); expBatch(i).IsDone = 0; end expBatch(100).IsDone = 1; append(buffer,expBatch);```
After appending experiences to the buffer, you can sample mini-batches of experiences for training of your RL agent. For example, randomly sample a batch of 50 experiences from the buffer.
`miniBatch = sample(buffer,50);`
You can sample a horizon of data from the buffer. For example, sample a horizon of 10 consecutive experiences with a discount factor of 0.95.
```horizonSample = sample(buffer,1,... NStepHorizon=10,... DiscountFactor=0.95);```
The returned sample includes the following information.
• `Observation` and `Action` are the observation and action from the first experience in the horizon.
• `NextObservation` and `IsDone` are the next observation and termination signal from the final experience in the horizon.
• `Reward` is the cumulative reward across the horizon using the specified discount factor.
You can also sample a sequence of consecutive experiences. In this case, the structure fields contain arrays with values for all sampled experiences.
```sequenceSample = sample(buffer,1,... SequenceLength=20);```
Define observation specifications for the environment. For this example, assume that the environment has two observation channels: one channel with two continuous observations and one channel with a three-valued discrete observation.
```obsContinuous = rlNumericSpec([2 1],... LowerLimit=0,... UpperLimit=[1;5]); obsDiscrete = rlFiniteSetSpec([1 2 3]); obsInfo = [obsContinuous obsDiscrete];```
Define action specifications for the environment. For this example, assume that the environment has a single action channel with one continuous action in a specified range.
```actInfo = rlNumericSpec([2 1],... LowerLimit=0,... UpperLimit=[5;10]);```
Create an experience buffer with a maximum length of 5,000.
`buffer = rlReplayMemory(obsInfo,actInfo,5000);`
Append a sequence of 50 random experiences to the buffer.
```for i = 1:50 exp(i).Observation = ... {obsInfo(1).UpperLimit.*rand(2,1) randi(3)}; exp(i).Action = {actInfo.UpperLimit.*rand(2,1)}; exp(i).NextObservation = ... {obsInfo(1).UpperLimit.*rand(2,1) randi(3)}; exp(i).Reward = 10*rand(1); exp(i).IsDone = 0; end append(buffer,exp);```
After appending experiences to the buffer, you can sample mini-batches of experiences for training of your RL agent. For example, randomly sample a batch of 10 experiences from the buffer.
`miniBatch = sample(buffer,10);`
## Input Arguments
collapse all
Experience buffer, specified as an `rlReplayMemory` or `rlPrioritizedReplayMemory` object.
Batch size of experiences to sample, specified as a positive integer.
If `batchSize` is greater than the current length of the buffer, then `sample` returns no experiences.
### Name-Value Arguments
Specify optional pairs of arguments as `Name1=Value1,...,NameN=ValueN`, where `Name` is the argument name and `Value` is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.
Example: `DiscountFactor=0.95`
Sequence length, specified as a positive integer. For each batch element, sample up to `SequenceLength` consecutive experiences. If a sampled experience has a nonzero `IsDone` value, stop the sequence at that experience.
N-step horizon length, specified as a positive integer. For each batch element, sample up to `NStepHorizon` consecutive experiences. If a sampled experience has a nonzero `IsDone` value, stop the horizon at that experience. Return the following experience information based on the sampled horizon.
Sampling an n-step horizon is not supported when sampling sequences. Therefore, if `SequenceLength` > `1`, then `NStepHorizon` must be `1`.
Discount factor, specified as a nonnegative scalar less than or equal to one. When you sample a horizon of experiences (`NStepHorizon` > `1`), `sample` returns the cumulative reward R computed as follows.
`$R=\sum _{i=1}^{N}{\gamma }^{i}{R}_{i}$`
Here:
• γ is the discount factor.
• N is the sampled horizon length, which can be less than `NStepHorizon`.
• Ri is the reward for the ith horizon step.
`DiscountFactor` applies only when `NStepHorizon` is greater than one.
Data source index, specified as one of the following:
• `-1` — Sample from the experiences of all data sources.
• Nonnegative integer — Sample from the experiences of only the data source specified by `DataSourceID`.
## Output Arguments
collapse all
Experiences sampled from the buffer, returned as a structure with the following fields.
Observation, returned as a cell array with length equal to the number of observation specifications specified when creating the buffer. Each element of `Observation` contains a DO-by-`batchSize`-by-`SequenceLength` array, where DO is the dimension of the corresponding observation specification.
Agent action, returned as a cell array with length equal to the number of action specifications specified when creating the buffer. Each element of `Action` contains a DA-by-`batchSize`-by-`SequenceLength` array, where DA is the dimension of the corresponding action specification.
Reward value obtained by taking the specified action from the observation, returned as a 1-by-1-by-`SequenceLength` array.
Next observation reached by taking the specified action from the observation, returned as a cell array with the same format as `Observation`.
Termination signal, returned as a 1-by-1-by-`SequenceLength` array of integers. Each element of `IsDone` has one of the following values.
• `0` — This experience is not the end of an episode.
• `1` — The episode terminated because the environment generated a termination signal.
• `2` — The episode terminated by reaching the maximum episode length.
Sequence padding mask, returned as a logical array with length equal to `SequenceLength`. When the sampled sequence length is less than `SequenceLength`, the data returned in `experience` is padded. Each element of `Mask` is `true` for a real experience and `false` for a padded experience.
You can ignore `Mask` when `SequenceLength` is 1.
## Version History
Introduced in R2022a | 2022-11-28 21:28:50 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 1, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5898156762123108, "perplexity": 1710.7107779540245}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446710662.60/warc/CC-MAIN-20221128203656-20221128233656-00283.warc.gz"} |
https://email.esm.psu.edu/pipermail/macosx-tex/2006-January/019685.html | [OS X TeX] Unwanted blank page
Maarten Sneep maarten.sneep at xs4all.nl
Thu Jan 5 16:48:38 EST 2006
On 5 Jan 2006, at 0:26, Josep M. Font wrote:
> Some years ago I used a different trick which does not force one to
> modify the source file every time one wants to include or exclude
> the exercises. It uses some TeX mechanisms (which of course work
> with LaTeX), which ask interactively what option you want. Adapting
> my own code to your situation, I think the following should work:
While the interactive option will work, it will be very tedious when
finalising your document, correcting the overfull boxes, etc. Since
it is possible to include (la)tex code on the command line, you can
use a make file to get the final bits right.
pdflatex \\PassOptionsToPackage{draft}{graphics} \\input yourfile.tex
will run the the file yourfile through pdflatex, but prevent
inclusion of the graphics, without editing the file itself. This can
be done in a normal script of a makefile. The speed increase is
considerable (the same is true for passing draft to hyperref). Ideal
when you need multiple runs for the cross-references, the first run
passes much more quickly in this case. The thing is that the commands
will appear _before_ the \documentclass command, and that limits your
options to either plain tex commands, or latex kernel commands (i.e.
not a command defined in a package). However, your definition of a
boolean fits in those categories:
to typeset with exercises:
pdflatex \\newif\\ifexercises\\exercisestrue \\input yourfile.tex
to typeset without:
pdflatex \\newif\\ifexercises \\input yourfile.tex
You may want to add some code to set a default inside the tex file,
and you'll need to remove the \typein.
I tried some code to test whether the \if was defined, but that is
hard. Perhaps try a different approach (note this is untested, and
unsupported by me):
with exercises:
pdflatex \\def\\IncludeExercisesThisRun{} \\input yourfile.tex
without exercises:
pdflatex yourfile.tex
with the following in the file:
\newif\ifexercises
\ifx\IncludeExercisesThisRun\undefined
\exercisesfalse
\else
\exercisestrue
\fi
and the rest as before. This basically turns the existence of a macro
into a boolean flag, which you then use to define the flag you're
really interested in.
HTMH,
Maarten
------------------------- Info --------------------------
Mac-TeX Website: http://www.esm.psu.edu/mac-tex/
& FAQ: http://latex.yauh.de/faq/
TeX FAQ: http://www.tex.ac.uk/faq
List Archive: http://tug.org/pipermail/macostex-archives/ | 2020-09-18 10:23:41 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9830594062805176, "perplexity": 7969.619442355393}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-40/segments/1600400187390.18/warc/CC-MAIN-20200918092913-20200918122913-00126.warc.gz"} |
https://proxieslive.com/tag/process/ | ## Interpretability of feature weights from Gaussian process classifier
Suppose I trained a Gaussian process classifier with a linear kernel (using GPML toolbox) and got some feature weights for each input feature.
My question is then:
Does it/When does it make sense to interpret the weights to indicate the real-life importance of each feature or interpret at group level the average over the weights of a group of features?
## Failed to migrate privileged process to lsass.exe in Windows 10
as part of a study lab I get a privileged reverse shell on a Windows 10 box and trying to migrate the process to lsass.exe to get credential hashes, etc, Windows Defender is detecting that and automatically rebooting the machine. I did the same thing on a Windows 8.1 machine and it worked just fine. Is it a different behaviour in Windows 10? Do you have any suggestinos on how I can get through this to get the hashes?
Thank you
## Passively read key from process memory without invoking kernel (windows 10)
I have a process that loads into memory like any other process. It contains a special key. Our goal is to read this key inside memory…or while it is in transit across the data bus from cpu. The catch is that our solution has to be stealthy and undetected by the kernel, so no DMA, drivers or anything that invokes traditional system calls/routines. Anything that leverages the kernel can be detected by the kernel.
Assume the system in question is infected by a rootkit. Assume the rootkit is employing everything specified here and more unknown anti-debug routines: https://github.com/LordNoteworthy/al-khaser So all the traditional windows routines, (like ObRegisterCallbacks) are hooked.
Is there a digital forensic device for this use case? In so far as I can tell the conventional means of volatile memory collection for forensic purposes can be detected (scraping/dumping).
Note1: There is a “magic” number associated with the bytes surrounding the key, so we don’t have to worry about being overwhelmed by heaps of data, we can filter for those magic bytes.
Note2: We can in theory configure this to use non volatile memory for RAM… then shutoff the computer while the key is in there. However, the key is only good as long as the process remains open. It is random gen, key cannot be cracked. This is also somewhat of a side-channel attack question I suppose. Reading cache I would assume be out of the question since its usually embedded on the cpu or motherboard.
Note3: Running this in a hypervisor might be the call. But there still exists the extra hurdles of avoiding detection of sandboxing. Would rather use a solution that avoids virtualization.
Note4: I originally asked this in EE section about using some type of logic analyzer to read the key as it was coming over the PCI-e bus, but that would disrupt some of the data coming over (resistance and properties of impedance would be disrupted).
## Thought process on Network Protocol Attack
I’m preparing for an introductory information security examination in university and this is one of the tutorial question on Network Protocol attacks. I tried (a) and came to this conclusion: Since the EPbX() is a public key encryption operation, C can decrypt any encrypted message to get back its original message, m as though it is anyone in the pair of people exchanging messages.
However, when I re-read the question, the decryption requires the use of private keys, which means it might be impossible to get the message unless C impersonates as the other to each of A and B, and is involved in the key exchange, generating 2 pairs of private keys, which seems repetitive. This confusion prevents me from doing the later part (b).
Can anyone suggest the thought process and solution to the above problem?
Here is the question description. Sorry the actual paper document is not formatted such that it allows copy over.
## seDebugPrivilege and OpenProcess() – Trying to understand how Windows restricts access to a process’ virtual memory
I’ve been trying to understand how operating systems protect processes from each other. My understanding of Windows security is that a process can call OpenProcess() (thereby allowing read and write access to the virtual memory of another process) as long as it has seDebugPrivilege and an integrity level at least as high as that of the other process.
It also looks as if a process can call OpenProcess() without seDebugPrivilege when targeting a process that belongs to the same user.
FYI: my testing to confirm this was done on a Win2008 R2 server. My method for testing whether a process could write to another process was using Meterpreter’s migrate function, which (among other things) makes an OpenProcess() call to a target process to create a Meterpreter thread inside of it.
My questions:
1. Are the statements above correct, or have I screwed up my testing somewhere?
2. What are the specific criteria that need to be met for an OpenProcess call to work? At the moment, it looks like it’s:
• has correct integrity level
• has seDebugPrivilege OR has same SID as the other process
3. If this is true, isn’t there a crazy amount of information an attacker can read or tamper from a computer they’ve compromised but don’t have root access to?
4. What is the Unix equivalent of this? By default, can all of a user’s processes read and write to each other? Is this true for root too?
## I want to design a page where i put fields as trip no,estimated time and process icon.Suggest me an effective solution
I want to design a page where i put fields as trip no,estimated time and process icon.Suggest me an effective solution
## Is there an intelligent, maybe machine learning C library I can use to parse and process English?
I have a *description character array in a multidimensional binary tree in my small neural network library, I want to process data using a function, so I can do this
``*nX = parse("add 30 dimensions to data structure"); process(nX) // takes data and processes the output to description MDMDBT->description = NX $$``$$ ``
## Minimum steps involved for an effective and efficient website redesign process?
I just started working for a web development agency, we work mainly with government so we want to align ourselves within that market with a professional, creative and functional website. We have a great blog and want to highlight our content and whitepapers, plus who we are, our vision and services.
We just started the Discovery phase of the project, and are in the process of doing personas and user journey mapping. I work there in project support and partly as a junior UX designer, alongside the contract designer, who is more of a UI designer than a UX designer, so it’s a bit of a learn as we go process. BUT we have a pretty strict deadline of Christmas where we’d like to have the final designs signed off, so we can start developing the site in January.
Our current plan/timeline is: – initial planning including pain points and wants for our existing website (done) – persona planning (done) – user journey mapping and doing value journey canvas for our 4 personas (in process) – content analysis – IA card sorting, treejacking, review and iteration – component mapping and content architecture – sketching session of new components – wireframing all vanilla pages – wireframing custom pages – prototyping key user journeys for customer testing – customer testing script – audience testing – prepare customer insights deck to present – presentation of customer insights – refine prototypes/wireframes – UI: Theme and Brand – UI Review
Which is quite a lot and definitely won’t get done by Christmas this year. So my question, is what is the absolute minimum process required for doing a website redesign? | 2019-12-11 09:58:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 1, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.278652548789978, "perplexity": 1738.6534523876494}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-51/segments/1575540530452.95/warc/CC-MAIN-20191211074417-20191211102417-00537.warc.gz"} |
https://www.physicsforums.com/threads/inequality-proof.788755/ | # Inequality Proof
1. Dec 22, 2014
### Bashyboy
Hello,
In Principles of Mathematical Analysis, the author is attempting to demonstrate that, if $x > 0$ and $y < z$, then $xy < xz$, which essentially states that multiplying by a positive number does not disturb the inequality.
I am hoping someone will quickly denounce this with an adequate explanation, but I feel as though the author is using the result to prove it.
He begins by noting that, if $z > y$, $z - y > 0$. He multiplies both sides by $x > 0$, and gets $x(z-y) > 0$.
This seems to be a special case of the theorem which we are trying to prove. Wouldn't this be an invalid step as we do not know what results from multiplying both sides of an inequality? Let $c = z - y$, and replace $y$ with zero in the theorem. This would give us
If $x > 0$ and $0 < c$, then $x \cdot 0 < xc$.
Am I mistaken?
2. Dec 22, 2014
### ShayanJ
He is assuming that if you multiply two positive numbers, you will get a positive number. I don't think for knowing this, you need to know the theorem mentioned, so I see no problem with the proof.
3. Dec 22, 2014
### Bashyboy
I am sorry, but I do not quite follow what you are saying here.
4. Dec 22, 2014
### ShayanJ
The product of two numbers is negative only when one of them is negative. You can't get a negative number by multiplying two positive numbers. | 2018-02-21 11:43:42 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.850261390209198, "perplexity": 203.86461286546208}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-09/segments/1518891813608.70/warc/CC-MAIN-20180221103712-20180221123712-00487.warc.gz"} |
http://www.chegg.com/homework-help/questions-and-answers/inductor-hooked-ac-voltage-source-voltagesource-emf-frequency--current-amplitude-inductor--q799861 | An inductor is hooked up to an AC voltage source. The voltagesource has EMF and frequency .The current amplitude in the inductor is .
What is the reactance of the inductor?
=
What is the inductance of the inductor? | 2014-08-31 04:32:40 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9689445495605469, "perplexity": 864.7544933947656}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500836106.97/warc/CC-MAIN-20140820021356-00225-ip-10-180-136-8.ec2.internal.warc.gz"} |
https://proofwiki.org/wiki/Order_of_Squares_in_Ordered_Field | Order of Squares in Ordered Field
It has been suggested that this article or section be renamed. One may discuss this suggestion on the talk page.
Theorem
Let $\struct {R, +, \circ, \le}$ be an ordered field whose zero is $0_R$ and whose unity is $1_R$.
Suppose that $\forall a \in R: 0 < a \implies 0 < a^{-1}$.
Let $x, y \in \struct {R, +, \circ, \le}$ such that $0_R \le x, y$.
Then $x \le y \iff x \circ x \le y \circ y$.
That is, the square function is an order embedding of $\struct {R_{\ge 0}, \le}$ into itself.
When $R$ is one of the standard fields of numbers $\Q$ and $\R$, then this translates into:
If $x, y$ are positive then $x \le y \iff x^2 \le y^2$.
Proof
From Order of Squares in Ordered Ring, we have:
$x \le y \implies x \circ x \le y \circ y$
To prove the reverse implication, suppose that $x \circ x \le y \circ y$.
Thus:
$\displaystyle x \circ x$ $\le$ $\displaystyle y \circ y$ $\displaystyle \leadsto \ \$ $\displaystyle x \circ x + \paren {-\paren {x \circ x} }$ $\le$ $\displaystyle y \circ y + \paren {-\paren {x \circ x} }$ $\displaystyle \leadsto \ \$ $\displaystyle 0_R$ $\le$ $\displaystyle y \circ y + \paren {-\paren {x \circ x} }$ $\displaystyle \leadsto \ \$ $\displaystyle 0_R$ $\le$ $\displaystyle \paren {y + \paren {-x} } \circ \paren {y + x}$ Difference of Two Squares, which applies because a field is a commutative ring.
As $0_R \le x, y$ we have $0_R \le x + y$.
Hence by the premise we have $0_R \le \paren {x + y}^{-1}$.
So as $0_R \le \paren {y + \paren {-x} } \circ \paren {y + x}$ we can multiply both sides by $\paren {x + y}^{-1}$ and get $0_R \le \paren {y + \paren {-x} }$.
Adding $-x$ to both sides gives us $x \le y$.
$\blacksquare$ | 2020-08-07 14:52:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 2, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9244421720504761, "perplexity": 106.35484781470679}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737204.32/warc/CC-MAIN-20200807143225-20200807173225-00476.warc.gz"} |
http://stats.stackexchange.com/questions/24776/what-method-is-suitable-for-short-term-forecast-for-a-trendless-oscillatory-bo | # What method is suitable for short-term forecast for a trendless, oscillatory, bounded time series?
I am new to time series analysis and I would appreciate if anyone could provide me some insight on it. I am trying to analyse a past series of numbers that fluctuates between 107 & 210 with a normal frequency bell curve distribution of mean 162. What is a suitable approach to forecast short-term future range for a trendless but oscillatory, range bound type of time series?
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Lottery sum of 6numbers frequency follows a normal distribution – Shelagh Mar 16 '12 at 20:24
It would help if you give us more details. For example, how long is the series, what the frequency is, if there's any obvious seasonality/cyclicality, whether the volatility appears constant over time, and what the correlogram looks like. It would also help if you described what sort of software you are using. – Dimitriy V. Masterov Mar 16 '12 at 20:51
Thanks for the response. I am using a free software called Zaitun. I have tried most of the forecast methods in it, including neural network sigmoid and bipolar sigmoid though I am not sure how to really use it efficiently for the time series given in the link below. Perhaps someone could give me some pointers on how to use Zaitun NN for my problem. – Shelagh Mar 20 '12 at 21:04
zaitunsoftware.com – Shelagh Mar 20 '12 at 21:35
@Shelagh, it seems to me that the root of your problem is that you lack a firm understanding of the basic concepts of time series analysis. Answering this question may help you temporarily, but you'll be better off in the long run if you study an introduction to time series. – Firefeather Mar 22 '12 at 17:31
You might want to refer to this and the forecasted upper-lower limit plot in it. Problem in discrete valued time series forecasting
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The example actual/fit/forecast upperlower limit plot given in the 2nd answer looks similar to the discrete SUM time series I am looking for. How can I obtain it for a layman like myself? – Shelagh Mar 21 '12 at 20:33
When you say normal , I assume you don't mean independent and identically distributed observations. If you do then proceed with the standard prediction of the mean. If each observation in the set is not independent from every other observation then one studies the auto-regressive structure and forms an ARIMA Model. After forming such a model you need to verify that there are no level shifts ( i.e. different means ) over time and that there are no trends in the residuals and the parameters of your ARIMA Model are constant over time and the variance of the residuals is homogeneous and here are no outliers/inliers biasing estimated parameters. If the variance of the residuals is not homogeneous you might have to perform Weighted Least Squares or transform your data via a power transform e.g. logs/reciprocals etc or actually identify an ARIMA model for the squared residuals aka a Garch Model. Now if you have some idea as to possible right-hand side/supporting/auxiliary/helping Exoneous Series you would have to seamlessly incorporate these variables into the above and culminate in a Transfer Function. Your question is simple but with most things the answer is complex due to the sample space of opportunities.
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Thanks for the reply. The time series is trendless, range bounded and perhaps close to white noise. Maybe someone can identify if the SUM is forecastable or not .i.e.does not need to be an exact number but as a next period target range sg.myfreepost.com/… – Shelagh Mar 20 '12 at 21:16
catchalotto.co.uk/post/sum-it-up – Shelagh Mar 20 '12 at 21:33
@Shelagh Perhaps it is "trendless over all" but may contain local trends. Perhaps there are "level/step shifts" . Perhaps you could post an example time series. Often free software in the area of time series is not worth what you paid for it. – IrishStat Mar 21 '12 at 13:15
The time series SUM is posted above in this link. Please check if it is forecastable?sg.myfreepost.com/… – Shelagh Mar 21 '12 at 14:36
If your series oscillates with smooth cycles you may use a spectral approach to forecasting. If you are interested in one step ahead forecasts, use an adaptive model such as an ARIMA(0,1,1) model or exponential smoothing model which models the change from period to period.
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Can a discrete time series be projected/forecasted with continuous smooth cycles and moving averages models? Is Arima model more for series with trending & seasonal components? – Shelagh Mar 22 '12 at 7:12
The SUM time series looks more like cyclical spikes similar to the example plot given above in the other post. – Shelagh Mar 22 '12 at 7:21
Since each "sum" of the time series you have is Independent and Normally distributed, you need a different approach from autocorrelated time series models:
I leave it for the experts here to illustrate how to go about with methodology(1) as I have no idea of the detailed steps to construct Prediction Intervals for your discrete time series.
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Is it implied that the time series is ergodic and not directly forecastable? How about Bayesian approach of credible interval? – Shelagh Mar 22 '12 at 12:49 | 2013-12-06 07:32:13 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8382610082626343, "perplexity": 805.9970681222499}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-48/segments/1386163049967/warc/CC-MAIN-20131204131729-00070-ip-10-33-133-15.ec2.internal.warc.gz"} |
https://www.physicsforums.com/threads/principle-of-superposition.228083/ | # Principle of superposition
## Homework Statement
Apply the principle of superposition to a beam to calculate or show beam deflection.
## Homework Equations
Maximum Deflection.
(WL^3) / (48EI)
Equation for possition two, when possition two is 3/4 or 1/4 of the total beam lengh
(Cant figure out the above)
## The Attempt at a Solution
I think i need to sum the two figure, however, cant get a figure for point two.
Think i need an equation to calculate deflection at a given point?
Thanks for any help... | 2020-12-06 01:36:04 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8775091171264648, "perplexity": 2241.4871249047956}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141753148.92/warc/CC-MAIN-20201206002041-20201206032041-00573.warc.gz"} |
http://openstudy.com/updates/55b72976e4b039df908de54d | ## anonymous one year ago Find the most general antiderivative of the function. G ( t ) = 4 + t + t^2/ sqrt t
• This Question is Open
1. Astrophysics
$G(t) = 4+t+ \frac{ t^2 }{ \sqrt{t} }$ we can write this as $G(t) = 4+t+t^{3/2}$ so what do you get when you integrate this expression $\int\limits (4+t+t^{3/2}) dt$
2. Astrophysics
@Cocheso
3. Astrophysics
I wonder if the whole thing is over sqrt t, or just that...
4. Astrophysics
$G(t) = \frac{ 4+t+t^2 }{ \sqrt{t} }$ if so, we can split them up or express it as $\int\limits (4+t+t^2)t^{-1/2} dt$ | 2016-10-24 21:59:02 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9008103609085083, "perplexity": 619.933343027261}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-44/segments/1476988719784.62/warc/CC-MAIN-20161020183839-00541-ip-10-171-6-4.ec2.internal.warc.gz"} |
http://www.gradesaver.com/textbooks/science/physics/conceptual-physics-12th-edition/chapter-8-plug-and-chug-page-155/43 | Chapter 8 - Plug and Chug: 43
It will double. The angular momentum is proportional to speed.
Work Step by Step
Angular momentum $= mvr = (80 kg)(6 m/s)(2 m) = 960 \frac {kg \cdot m^{2}}{s}$.
After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback. | 2017-05-25 20:33:08 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8382129669189453, "perplexity": 2617.500263126951}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-22/segments/1495463608416.96/warc/CC-MAIN-20170525195400-20170525215400-00517.warc.gz"} |
https://www.futilitycloset.com/ | # A Broken Promise
The Los Angeles Times called this “the most horrible crime of the 1920s”: On Dec. 18, 1927, a man appeared at the junior high school attended by Marion and Marjorie Parker, 12-year-old twin daughters of banker Perry H. Parker. The man said that he was a bank employee and that Marion was wanted immediately by her father.
Marion departed with him, and no one suspected anything until Marjorie came home alone. Police searched the city but had found nothing when a ransom note arrived the following morning asking Parker to gather \$1,500 and await further instructions. The kidnapper sent an appeal from Marion and then called that evening with directions to a dropoff location. Parker obeyed, but police were visible in the area and the kidnapper stayed away.
A new letter was delivered the following afternoon:
I am vexed and disgusted with you … You will never know how you disappointed your daughter … Pray to God for forgiveness for your mistake last night.
Fate — Fox
He included a note from Marion:
Dear Daddy and Mother:
Daddy, please don’t bring any one with you today. I am sorry for what happened last night. We drove right by the house. I cried all the time last night. If you don’t meet us this morning, you will never see me again.
Love to all
Marion Parker
A call came at 7:15 telling Parker where to go. He parked his car and turned off the lights as instructed. A car parked beside him and a man pointed a gun and told him to hand over the money. Parker demanded to see his daughter. The stranger lifted the girl’s head from beside him; she appeared to be asleep. Parker assumed she’d been drugged and handed over the money.
The man drove 200 feet forward, stopped, got out, and lifted the girl’s body onto the sidewalk. Then he got in and drove away. Parker ran to the girl and lifted her head, then screamed. Her legs had been cut off near the hips. She had been dead for hours.
Police tracked down 18-year-old bank messenger William Hickman, who said he’d wanted the money to go to college. He did say that he’d strangled Marion with a towel before he’d amputated her legs. He was hanged the following October.
(From Hank Messick and Burt Goldblatt, Kidnapping: The Illustrated History, 1974.)
# Shelter Morality
At a 1962 meeting on civil defense, one local resident of Hartford, Conn., warned the rest that his fallout shelter contained only enough food and water for his immediate family, and so during a nuclear attack he’d be forced to shoot any who tried to join them. His neighbor appealed to him:
‘John,’ she said, ‘you and your family have been our closest friends for ten years. Do you mean to say that if this city was bombed and my baby and I were caught in the open, and we were hurt, and came to your shelter you would turn us away?’
John nodded in the affirmative. His neighbor pressed the point.
‘But suppose we wouldn’t turn away and begged to get in?’
‘It would be too bad,’ John said. ‘You should have built a shelter of your own. I’ve got to look out for my own family.’
‘But suppose we had built a shelter of our own, yet were caught by surprise, being out in the open at the time of an attack, and we discovered that the entrance to our shelter was covered with rubble and we had no place to turn except to you. Would you still turn us back?’
The answer was still yes.
‘But suppose I wouldn’t go away and kept trying to get in. Would you shoot us?’
John said that if the only way he could keep his friend out would be by shooting her and her baby, he would have to do it.
These questions raised disagreements even among clergymen during the Cold War. In an article titled “Ethics at the Shelter Doorway,” Father L.C. McHugh urged his readers to “think twice before you rashly give your family shelter space to friends and neighbors or to the passing stranger.” The nondenominational Christian Century opposed this sentiment. “Men and women who manage to survive a nuclear attack by locking doors on imperiled neighbors or shooting them down to save themselves might conceivably survive,” the editors wrote. “But who would want to live in the kind of social order such people would create out of the shambles?”
(From Kenneth D. Rose, One Nation Underground: The Fallout Shelter in American Culture, 2001.)
# Yar!
According to legend, when the pirate Olivier Levasseur was hanged in 1730, he flung a necklace into the crowd, crying, “Find my treasure, the one who may understand it!” The necklace (supposedly) contained this cryptogram, which people have been trying to decipher ever since. The will of fellow pirate Bernardin Nageon de L’Estang (allegedly) refers to “considerable treasure … buried on my dear île de France” (now Mauritius), and the puzzle may or may not be related to carvings found in the rocks at Bel Ombre beach in the Seychelles by L’Estang’s descendant Rose Savy in 1923.
Does any of this add up to anything? Who knows? Nick Pelling has a good skeptical discussion here, including an interpretation of the cryptogram as a pigpen cipher.
# Wisdom
Proverbs of the 11th century, from Egbert of Liège’s The Well-Laden Ship:
• Not every cloud you see threatens rain.
• A boy is consumed by envy, an old man by anger.
• A reasonable sufficiency is more righteous than dishonorable riches.
• One does well to distrust a stream, even one that is calm.
• Sometimes an old dog growls the truth.
• It is a hard cheese that the greedy man does not give to his dogs.
• He who cannot conceal, ought not to become a thief.
• Whose bread I eat, his songs I sing.
• All the gold that a king has does not equal this rain.
• No thief will be hanged, if he himself is the judge.
• What earned this one praise gets that one a beating.
• Smoky things appear by day, and fiery things by night.
• The living husband is incensed by praise of the dead one.
• A stupid person who is corrected, immediately hates his admonisher.
• It is not the lowliest of virtues to have placed a limit on your wealth.
• No mother-in-law is pleasing to her daughter-in-law unless she is dead.
• A frog on a throne quickly gives up the honor.
• When you trade one fish for another, one of them stinks.
• Whoever hates his work, surely hated himself first.
• To a man hanging, any delay seems too long.
And “One way or another, brothers, we will all pass from here.”
# All’s Well That Ends Well
In 2003 Carl Libis of Assumption College in Worcester, Mass., received this solution from a student in an algebra course:
\begin{aligned} \frac{1}{x+1} + \frac{1}{x-2} &= \frac{x+3}{x^2-x-2} \\ \frac{x+1}{1} + \frac{x-2}{1} &= \frac{x^2-x-2}{x+3} \\ x+1+x-2 &= \frac{x^2 - \frac{x}{x}-2}{3} \\ 2x-1 &= \frac{x^2 - 1 - 2}{3} \\ 3(2x-1) &= x^2 - 3 \\ 6x &= x^2 - 2 \\ \frac{6x}{2x} &= \frac{x^2 - 2}{2x} \\ 3 &= \frac{x^2}{x} - \frac{2}{2} \\ 3 &= x-1 \\ 4 &= x \end{aligned}
(Via Ed Barbeau, “Fallacies, Flaws, and Flimflam,” College Mathematics Journal 34:1 [January 2003], 50-54.)
# Appearances
South Korean artist Dain Yoon uses her face as a canvas for endlessly inventive illusions.
More on her Instagram page.
# A Visitation
A striking scene from the coast of Massachusetts, summer 1894:
I was brought, from my sitting posture, down on the flat of my back. The force produced a motor disturbance of my head and jaws. My mouth made automatic movements; till, in a few seconds, I was distinctly conscious of another’s voice — unearthly, awful, loud, and weird — bursting through the woodland from my own lips, with the despairing words: ‘Oh! My People!’
The victim, Albert Le Baron, had for some time found himself talking involuntarily in a language he didn’t understand, a language he believed had some ancient or remote origin. He became convinced that he was conveying the words of dead speakers. That September, back in New York City, he received a similar communication from the “psycho-automatism,” with a translation:
I have seen all thy ways, O son of the Nile! I have heard all thy songs, O son of the Nile! I have listened to all thy woes, O son of the Nile! I have been with thee, O son of the Nile! I have been near thee when thy days were full of glory. I have been near thee when thy days were covered in sadness. I have heard thy voice, O son of Egypt! I have counted thy tears, O son of Egypt! I have heard thy voice of wailing, O son of Egypt! I have watched thee when thy men of might have flown; I have watched thee when thy glory has faded; I have watched thee when thy sun has set; I have watched thee, O son of the Nile! Thy tears have been my tears; thy joys have been my joys; thy woes have been my woes. O son of the Nile, I love thee! O son of the Nile, I love thee!
William James, who communicated all this to the Society for Psychical Research, wasn’t impressed. “I know no stronger example of the subjective sense of genius, or rather of positive inspiration, accompanying a subliminal uprush of absolutely meaningless matter,” he wrote. The whole article is here.
(Albert LeBaron, “A Case of Psychic Automatism, Including ‘Speaking With Tongues,'” Proceedings of the Society for Psychical Research 12 [1896-1897], 277-297.)
# Legacy
In 1924 the eccentric Lord Berners composed a “Funeral March for a Rich Aunt”:
The musical direction is Allegro giocoso — “fast and cheerful.”
# The Unreality of Time
Take any event — the death of Queen Anne, for example — and consider what changes can take place in its characteristics. That it is a death, that it is the death of Anne Stuart, that it has such causes, that it has such effects — every characteristic of this sort never changes. ‘Before the stars saw one another plain’, the event in question was the death of a queen. At the last moment of time — if time has a last moment — it will still be the death of a queen. And in every respect but one, it is equally devoid of change. But in one respect it does change. It was once an event in the far future. It became every moment an event in the nearer future. At last it was present. Then it became past, and will always remain past, though every moment it becomes further and further past.
— J.M.E. McTaggart, The Nature of Existence, 1927
(McTaggart argued that these varying properties of Anne’s death constitute a paradox. “Past, present, and future are incompatible determinations,” he wrote. “Every event must be one or the other, but no event can be more than one. … But every event has them all.” Hence time is unreal.)
# The Mascot Moth
On Aug. 7, 1905, magician David Devant premiered an effect that had occurred to him in a dream: A woman appears to vanish instantaneously from a bare stage.
Devant left behind a description of only 310 words explaining how he’d accomplished the illusion. He called it “the best I have ever done.” The lady descends into the floor, leaving behind the dress, supported by a tube covered with black velvet. The dress is pumped full of oil fog, and at the critical instant it’s whisked down through the tube, leaving (apparently) nothing but smoke hanging in the air.
The brief, blurry advertisement above, for Doug Henning’s 1983 Broadway musical Merlin, appears to be the only video online of this illusion. That’s a shame; it would be wonderful to see it more clearly. Devant’s partner John Nevil Maskelyne called it the “trickiest trick he had ever seen.” | 2019-07-21 13:32:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 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, "math_score": 0.780754029750824, "perplexity": 6830.852426338134}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-30/segments/1563195527000.10/warc/CC-MAIN-20190721123414-20190721145414-00355.warc.gz"} |
http://blog.dragonsector.pl/2013/07/sigint-ctf-2013-task-fenster-400-pts.html | ## Monday, July 22, 2013
### SIGINT CTF 2013: Task fenster (400 pts)
In this task we have a binary - fenster.exe (link to original exe: click), which checks if the given text is our sought flag. The executable is obfuscated and contains some anti-debug. The first step is to remove all garbage and produce a clean exe.
So, let's start!
The first debug check is inside TLS callback at 0x4019CB. All it does is:
encrypt(check_for_debugger, 0x1B, 0xEC, 0x00409CD8);
bool debugger = check_for_debugger();
encrypt(check_for_debugger, 0x1B, 0xEC, 0x00409CD8);
if (debugger) {
exit(0);
}
encrypt(void* data, int size, int key, int* some_data) is a lengthy function (address: 0x40194B) responsible for data encryption / decryption, but its exact implemenation is not relevant to us. As you can see, we can just remove this TLS callback entry from the executable without any consequence later on.
If we enter the check_for_debugger routine, we can see three further anti-debugging techniques:
push ss
pop ss
This is quite tricky. Any modification of the ss register (excluding the lssinstruction) register causes interrupts to be delayed until the end of execution of next instruction. So, if we step through this code using a debugger (step into/over) the code will "escape" the single-stepping mode immediately after one steps into/over "pop ss". We can safely nop these instructions out.
pushfd
pop eax
This was probably inserted only to fool automatic analyzers and decompilators such as Hex-Rays. We can also nop it out.
call <jmp.&KERNEL32.IsDebuggerPresent>
Standard anti-debugging check, we can replace it with "xor eax,eax" or anything else. Those anti-debugs would often show up inside other functions, so watch out while stepping through the executable. ;)
The main function is located at 0x401EF9. It loads user input from stdin and then does the following with different dataA and dataB pointers in seven iterations (anti-debugging code is skipped, check is a function at 0x00401ab5):
encrypt(check, 0x24, KEY, SOME_PTR);
input_ok &= check(dataA, dataB, user_input);
encrypt(check, 0x24, KEY, SOME_PTR);
To make further analysis easier, we should dump the decrypted check function (and all sub-functions, which are encrypted too) and get rid of all calls to encrypt(). Once this is done, we are ready to dive into the check code and switch from OllyDbg to IDA.
After a brief analysis, it is clear that the function passes our input through finite-state machines (compiled regular expressions). The first subfunction at 0x401C44 performs some kind of initialization, the second one at 0x401C9D executes the machine and the last one at 0x401AD9 checks if the machine completed in a final state. The two pointers passed to check are:
• int*** dataA - machine specification, dataA[state][letter] is a NULL-terminated list of states that we can reach from the given state after a specific letter. Note that states are numbered from 1 to 255 and dataA[0] refers to the first state. Only capital letters cause transitions. Index=0 corresponds to 'A' and index 25 to 'Z'.
• int* dataB - a null-terminated list of final state indexes
Once we know the meaning of those structures, we can write some visualization and crack the regular expressions. I wrote a small C++ program which reads data from the "fenster" process, generates a graph description for dot and then compiles it to svg. The results are shown below (rectangles = final states, * = all capital letters, ^XY = all capitals without X and Y):
machine0.svg:
machine1.svg:
machine2.svg:
machine3.svg:
machine4.svg:
machine5.svg:
machine6.svg:
Solving them by hand would be painful (look at machine4.svg!), so the next step was to write an optimized brute-force solver. Analyzing the machines shows that:
• machine0 - input must end with "EN" and the second letter is "E"
• machine1 - input is a concatenation of pairs: {"NW", "EN", "ES", "CH", "SW", "RG", "GS", "SE", "RE", "GE", "NE"}
• machine3 - input length is 16
With the above knowledge, we only have to check around 4*11^6 different inputs. The simplest way for me to check if the input was correct was to just reuse the original check function from fenster.exe loaded as a DLL. The solver's code was as follows:
#include <cstring>
#include <cstdio>
#include <Windows.h>
#include <cassert>
using namespace std;
int machines[7] = { 0x4077A0, 0x407E40, 0x4082E0, 0x408BA0, 0x4098C0, 0x409B48, 0x409C68 };
int end_states[7] = { 0x4077DC, 0x407E70, 0x408300, 0x408BE4, 0x409920, 0x409B58, 0x409C70 };
const int pairscnt = 11;
char* pairs[pairscnt] = {"NW", "EN", "ES", "CH", "SW", "RG", "GS", "SE", "RE", "GE", "NE"};
char key[17] = " E EN";
int it[7] = {7};
__declspec(naked) bool __cdecl check()
{
__asm
{
push edi
push ebp
mov ebp, esp
and esp, 0xFFFFFFF0
mov edi, 0
looop:
sub esp,4
push offset key
push end_states[edi*4]
push machines[edi*4]
call regex_match
test eax,eax
jz hop
inc edi
cmp edi, 7
jnz looop
hop:
mov esp, ebp
pop ebp
pop edi
retn
}
}
int main()
{
// It doesn't work on bases different from 0x400000,
// because the binary has no relocations (e.g. final states list pointers)
// just run it until it works
assert(fenster == 0x400000);
regex_match = 0x401d97;
// Resolving imports
// Assert that last pair is set
assert(strlen(key) == 16);
while(it[6] < pairscnt)
{
for(int i=0; i<7; i++)
key[i*2] = pairs[it[i]][0],
key[i*2+1] = pairs[it[i]][1];
if(check())
puts(key);
it[0]++;
for(int i=0; i<6 && it[i]==pairscnt; i++)
it[i+1]++,
it[i] = 0;
}
return 0;
}
where ~fenster2.dll is a deobfuscated executable, you can download it here: https://docs.google.com/file/d/0B-L9DIAuaV7STkNjNGdBY1RnQ2M/edit?usp=sharing. After running the application for a short while, it spit out the "REGENECHENSESWEN" textual string, which indeed turned out to be the correct flag. +400pts :) | 2018-08-16 12:05:47 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3120391070842743, "perplexity": 11816.430737924486}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-34/segments/1534221210735.11/warc/CC-MAIN-20180816113217-20180816133217-00467.warc.gz"} |
http://www.ams.org/mathscinet-getitem?mr=0520481 | MathSciNet bibliographic data MR520481 49F99 (58C20) Rockafellar, R. T. Clarke's tangent cones and the boundaries of closed sets in ${\bf R}\sp{n}$${\bf R}\sp{n}$. Nonlinear Anal. 3 (1979), no. 1, 145–154 (1978). Article
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals and original articles. Subscribers receive the added value of full MathSciNet reviews. | 2016-05-04 08:11:34 | {"extraction_info": {"found_math": true, "script_math_tex": 1, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9980402588844299, "perplexity": 5263.263409842702}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2016-18/segments/1461860122533.7/warc/CC-MAIN-20160428161522-00219-ip-10-239-7-51.ec2.internal.warc.gz"} |
https://trac.sagemath.org/ticket/18408 | Opened 6 years ago
Closed 5 years ago
# List of packages in the documentation of sage.misc.package
Reported by: Owned by: ncohen major sage-7.1 documentation vdelecroix, leif Nathann Cohen Javier Honrubia González N/A 15b9583 (Commits) 15b95833e3928fb055ca8d34f2cea2ca646dc236
### Description
It seems that we do not have an up-to-date list of Sage's packages in our documentation.
This branch solves the problem, by adding the list of packages in our reference manual (in sage.misc.package, where all functions dealing with packages are defined). This list is *generated* from python lists, so that they are:
• Easy to read (in a nice sorted table)
• Checked by a doctest, so that we get a warning if they are not up to date anymore
Nathann
### comment:1 Changed 6 years ago by ncohen
• Branch set to public/18408
• Status changed from new to needs_review
### comment:2 Changed 6 years ago by git
• Commit set to f43eb0119fb60ea1367247bcf383506782e4e81a
Branch pushed to git repo; I updated commit sha1. New commits:
c400ee6 trac #18407: Fix standard_packages(), optional_packages(), and experimental_packages() 10933bc Fix exception message of _package_lists_from_sage_output() (#18407) cc02304 trac #18407: better parsing of package name f43eb01 trac #18408: List of packages in the documentation of sage.misc.package
### comment:3 Changed 6 years ago by git
• Commit changed from f43eb0119fb60ea1367247bcf383506782e4e81a to 4a968a88a8eb55bad8dd0f88ccaa1a856eb9c092
Branch pushed to git repo; I updated commit sha1. New commits:
4a968a8 trac #18408: A leftover from a past test
### comment:4 Changed 6 years ago by leif
As mentioned, those package lists refer to Sage versions < 6.0.
### comment:5 Changed 6 years ago by jdemeyer
• Status changed from needs_review to needs_info
What's up with this?
singular-3-1
(there are many more optional packages like this)
Last edited 6 years ago by jdemeyer (previous) (diff)
### comment:6 follow-up: ↓ 10 Changed 6 years ago by jdemeyer
• Status changed from needs_info to needs_work
Some packages from build/pkgs don't appear in your list (arb is the first, but there are more).
### comment:7 Changed 6 years ago by jdemeyer
And extcode, seriously? That's no longer a package...
### comment:8 Changed 6 years ago by jdemeyer
gcc appears in every list :-)
### comment:9 Changed 6 years ago by git
• Commit changed from 4a968a88a8eb55bad8dd0f88ccaa1a856eb9c092 to 869b195106b1fcd06332a38d12ac2a5bcd2d86ec
Branch pushed to git repo; I updated commit sha1. New commits:
869b195 trac #18408: Change the regexp
### comment:10 in reply to: ↑ 6 ; follow-up: ↓ 12 Changed 6 years ago by ncohen
Some packages from build/pkgs don't appear in your list (arb is the first, but there are more). And extcode, seriously? That's no longer a package... gcc appears in every list :-)
Jeroen, please do not ask me to rewrite everything at once. I am no magician. As you can see from the source code, the list of packages is generated from the output of sage -standard, sage -optional and sage -experimental. And yes, all three contain gcc. And extcode. The point of this branch is that we see the list somewhere, and apparently it also helps us notice other bugs. Please do not force me to rewrite everything here.
Nathann
### comment:11 Changed 6 years ago by ncohen
• Status changed from needs_work to needs_review
### comment:12 in reply to: ↑ 10 Changed 6 years ago by jdemeyer
• Status changed from needs_review to needs_work
Jeroen, please do not ask me to rewrite everything at once. I am no magician. As you can see from the source code, the list of packages is generated from the output of sage -standard, sage -optional and sage -experimental. And yes, all three contain gcc. And extcode. The point of this branch is that we see the list somewhere, and apparently it also helps us notice other bugs. Please do not force me to rewrite everything here.
Well, the logical thing to do would be to first fix sage --standard, sage --optional and sage --experimental and then add the lists to the documentation.
I really do not see the point of adding wrong and outdated lists to the documentation.
And in any case, this is wrong: singular-3-1
### comment:13 Changed 6 years ago by ncohen
Why is singular wrong? It displays singular, and only singular?..
### comment:14 follow-ups: ↓ 16 ↓ 17 Changed 6 years ago by leif
FWIW, I'm currently working on categorizing the packages (obsolete, removed, renamed, replaced, newly added...)
If we fix sage-list-packages w.r.t. this, Nathann's work still makes sense (without modifying his code, just regenerating the "hardcoded" lists, I think).
### comment:15 Changed 6 years ago by jdemeyer
Sorry, I didn't realize that you changed the singular thing. Never mind...
### comment:16 in reply to: ↑ 14 ; follow-ups: ↓ 18 ↓ 19 Changed 6 years ago by jdemeyer
If we fix sage-list-packages w.r.t. this, Nathann's work still makes sense (without modifying his code, just regenerating the "hardcoded" lists, I think).
Of course Nathann's work makes sense, but obviously this ticket should depend on fixing the lists.
### comment:17 in reply to: ↑ 14 Changed 6 years ago by ncohen
If we fix sage-list-packages w.r.t. this, Nathann's work still makes sense (without modifying his code, just regenerating the "hardcoded" lists, I think).
Indeed. Plus my goal is also to add a list more exhaustive than the one our doc currently contains:
I am rewriting the doc of that manual currently, and moving a lot of things around. See #18405
Nathann
### comment:18 in reply to: ↑ 16 ; follow-up: ↓ 21 Changed 6 years ago by ncohen
Of course Nathann's work makes sense, but obviously this ticket should depend on fixing the lists.
Why should it *depend* on it? The list currenty generated by sage -standard is wrong at the moment (not caused by this patch) and what this patch does will still work when that will be fixed.
In the meantime we will have a "more correct" list of packages, I will be able to remove the list of Sage packages from the 'installation' document (and instead link to that list). There is no gain in blocking this ticket until the other problem is fixed.
Nathann
### comment:19 in reply to: ↑ 16 Changed 6 years ago by leif
obviously this ticket should depend on fixing the lists.
Well, it's just as borked as sage-list-packages and our package repositories, so I wouldn't even mind merging it as is... ;-)
Remove this:
pname = re.sub("(\.|-)p[0-9]+$","",pname) # strip .p0 (version numbers are always separated by a -, the .p0 is added in addition to a version number) ### comment:21 in reply to: ↑ 18 Changed 6 years ago by jdemeyer Replying to ncohen: In the meantime we will have a "more correct" list of packages The lists in this ticket are far from correct. There is no gain in blocking this ticket until the other problem is fixed. Yes, there is gain: Sage will have less wrong documentation. I think wrong documentation is worse than no documentation. ### comment:22 in reply to: ↑ 20 ; follow-up: ↓ 25 Changed 6 years ago by leif Replying to jdemeyer: Remove this: pname = re.sub("(\.|-)p[0-9]+$","",pname) # strip .p0
(version numbers are always separated by a -, the .p0 is added in addition to a version number)
Nope, we do have packages with a patchlevel but no version.
### comment:23 in reply to: ↑ 20 Changed 6 years ago by ncohen
(version numbers are always separated by a -, the .p0 is added in addition to a version number)
That's what I also believed at first
~\$ sage -experimental | grep -- "-p"
pynifti-p0 ............................. not installed
Last edited 6 years ago by ncohen (previous) (diff)
### comment:24 Changed 6 years ago by jdemeyer
That's -p0, not .p0
### comment:25 in reply to: ↑ 22 ; follow-up: ↓ 26 Changed 6 years ago by leif
(version numbers are always separated by a -, the .p0 is added in addition to a version number)
Nope, we do have packages with a patchlevel but no version.
Such as database_stein_watkins_mini.p0.spkg for example.
### comment:26 in reply to: ↑ 25 Changed 6 years ago by jdemeyer
Such as database_stein_watkins_mini.p0.spkg for example.
1. The name of that package actually is database_stein_watkins_mini.p0 (of course, that's a wrong name).
2. That package no longer exists anyway (the wrong name was fixed).
### comment:27 follow-up: ↓ 29 Changed 6 years ago by ncohen
Let's see it this way Jeroen: if you have reasons to believe that the list from sage -standard (which I believe is the same as what you see there [1]) is wrong then why don't you report it so that we update it (and my code will match it)?
My question at [2] was about whether we have some (any) reliable source containing our packages, for each category. It seems that we have none, so here is the deal: if you see something wrong in the list (i.e. the online one, or sage -standard) then let us fix that. Otherwise you are telling me that "the list is wrong" without telling me how exactly.
On the other hand, you cannot block this patch until the "problematic way in which the packages are handled in Sage" is fixed. All I want to do here is clear our doc, and make it more reliable *than it is*.
Nathann
Last edited 6 years ago by ncohen (previous) (diff)
### comment:28 Changed 6 years ago by leif
So, here it is.
As of Sage 6.7.beta4, we have:
Obsolete packages (since Sage 6.0), *.spkg:
• extcode
• sage (also used to be versioned)
• sage_root
• sage_scripts
Renamed packages:
• libm4ri -> m4ri
• libm4rie -> m4rie
• database_stein_watkins_mini.p0 -> database_stein_watkins_mini (optional)
• TOPCOM -> topcom (optional; "new-style" is lowercase)
• gd -> libgd ? (probably replaced, see below)
Removed (standard) packages:
• genus2reduction (now part of the Sage library IIRC)
• mercurial (in principle replaced by git, but no "drop-in" replacement)
• sqlalchemy
Replaced (standard) packages:
• pil -> Pillow
• gd, gdmodule -> libgd (I think)
• backports_ssl_match_hostname (WTF?)
• certifi
• combinatorial_designs
• configure (see below)
• csage (see below)
• dateutil
• git (used to be optional, so there's still an old one, too)
• jsonschema
• libgd (presumably the replacement of gd, gdmodule; see above)
• markupsafe
• mathjax
• mistune
• pari_galdata
• pip
• pkgconf
• pkgconfig
• prereq (see below)
• pyparsing
• pyzmq
• six
• zeromq
Then we have some weirdness with the following "packages":
• in build/pkgs/, but not (listed as) installed:
• configure
• (listed as) installed, but not in build/pkgs/, and without version:
• csage
• sage ("conflicts" with the previous, versioned spkg in Sage 5.x)
• prereq
And then we have new "new-style" packages (just in the git repo) which have no legacy (*.spkg) counterpart, hence currently not listed by sage-list-packages:
• arb (optional)
• ...
... besides that so far only some optional packages have been converted to "new-style"; the versions in the git repo might meanwhile be newer than their legacy counterparts. (Similar for packages that used to be optional but are standard now, cf. "newly added packages" above.)
### comment:29 in reply to: ↑ 27 ; follow-up: ↓ 30 Changed 6 years ago by jdemeyer
All I want to do here is clear our doc, and make it more reliable *than it is*.
Again, please tell me why adding wrong documentation is making it more reliable.
### comment:30 in reply to: ↑ 29 Changed 6 years ago by ncohen
Again, please tell me why adding wrong documentation is making it more reliable.
Well, because that new page will match the most reliable information we have (i.e. sage -standard) in the future, and because by having this new page I will be able to remove the other pages whose information is even older, and redirect them toward that page.
Nathann
### comment:31 follow-up: ↓ 33 Changed 6 years ago by jdemeyer
gdmodule has genuinly been removed. And gd was renamed to libgd.
Last edited 6 years ago by jdemeyer (previous) (diff)
### comment:32 follow-up: ↓ 45 Changed 6 years ago by ncohen
You seem really bothered by the information I am adding, and not bothered at all by the wrong information which stays available for as long as we do nothing.
### comment:33 in reply to: ↑ 31 ; follow-up: ↓ 34 Changed 6 years ago by ncohen
gdmodule has genuinly be removed. And gd was renamed to libgd.
I just generated the list from our build/install file:
I was about to write to sage-devel to ask <whoever can> to put it online, but in the meantime I noticed that the official list has been removed: http://www.sagemath.org/packages/standard/list
So something is apparently happening.
Nathann
### comment:34 in reply to: ↑ 33 Changed 6 years ago by leif
I was about to write to sage-devel to ask <whoever can> to put it online, but in the meantime I noticed that the official list has been removed: http://www.sagemath.org/packages/standard/list
The site is currently moving, while packages/ is obsolete anyway, since it is incompatible with the mirrors. Take spkg/standard/list from some mirror instead.
### comment:35 follow-up: ↓ 37 Changed 6 years ago by ncohen
Well I do not want to take that list, I want to replace it with the list I just generated from the latest beta :-P
### comment:36 Changed 6 years ago by ncohen
Even the reference manual was removed O_o
### comment:37 in reply to: ↑ 35 Changed 6 years ago by leif
Well I do not want to take that list, I want to replace it with the list I just generated from the latest beta :-P
That doesn't make much sense, since
• the list files are generated from the directory contents,
• the site is moving, as I said.
We'll have to wait with such at least until the infrastructure is stable again (hopefully in a few days).
### comment:38 Changed 6 years ago by ncohen
• Dependencies changed from #18407 to #18407, #18456
### comment:39 Changed 6 years ago by git
• Commit changed from 869b195106b1fcd06332a38d12ac2a5bcd2d86ec to 868fa71f00ed26bf97158e184a93fe8517dd211e
Branch pushed to git repo; I updated commit sha1. Last 10 new commits:
3efc9fb trac #18431: package-specific 'dependencies' files 308ceff trac #18431: Auto-generate make rules for standard packages 77f293f trac #18431: auto-generated Make target "sage-standard-packages" e114874 trac #18431: typo 766798e trac #18431: tab->spaces 47e438d Merge tag '6.7' into t/18441/base_packages_except_configure_should_be_standard 4de8e37 Various changes to build system f83b0c4 Correct variable name 39cc007 trac #18456: Re-Fix standard_packages(), optional_packages(), and experimental_packages() 868fa71 trac #18408: Merged with #18456
### comment:40 Changed 6 years ago by ncohen
• Status changed from needs_work to needs_review
### comment:41 Changed 6 years ago by git
• Commit changed from 868fa71f00ed26bf97158e184a93fe8517dd211e to ac93f992452bebd569183f8f032d5b71c086dbf4
Branch pushed to git repo; I updated commit sha1. New commits:
fe40c54 Edge connectivity working 9a0e868 Improved code for conversion b0ca92c Added sig_on, sig_off, and corrected edge_connectivity 7d12ea9 trac #18408: Merged with 6.8.beta2 ac93f99 trac #18408: python2/python3 were missing
### comment:42 Changed 6 years ago by ncohen
• Status changed from needs_review to needs_work
(small problems with git history)
### comment:43 Changed 6 years ago by git
• Commit changed from ac93f992452bebd569183f8f032d5b71c086dbf4 to a8b9103987226c9a5768c4f571840da3fd7aef19
Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:
a3402c9 trac #18456: Re-Fix standard_packages(), optional_packages(), and experimental_packages() 687e426 trac #18456: Column names d671f1b trac #18456: don't use explicitly '/' in file paths b093007 trac #18456: doc and doctest a8b9103 trac #18408: List of packages in the documentation of sage.misc.package
### comment:44 Changed 6 years ago by ncohen
• Status changed from needs_work to needs_review
### comment:45 in reply to: ↑ 32 ; follow-up: ↓ 46 Changed 6 years ago by jdemeyer
• Milestone changed from sage-6.7 to sage-6.8
• Status changed from needs_review to needs_work
• Work issues set to Remove obsolete packages
You seem really bothered by the information I am adding, and not bothered at all by the wrong information which stays available for as long as we do nothing.
I am bothered by both. The fact that one thing is wrong is not an excuse to add a second wrong thing.
This patch should not be merged as long as stuff like extcode is listed.
### comment:46 in reply to: ↑ 45 Changed 6 years ago by ncohen
This patch should not be merged as long as stuff like extcode is listed.
What is wrong with extcode?
### comment:47 Changed 6 years ago by jdemeyer
• Status changed from needs_work to needs_review
• Work issues Remove obsolete packages deleted
It seems that updating the online packages is harder than I thought. And I also feel slightly guilty for "forcing" #18581 against your will. So I will stop complaining about this ticket.
### comment:48 Changed 6 years ago by ncohen
Thanks. And I hope that they will end up updating the lists at some point :-/
### comment:49 Changed 6 years ago by git
• Commit changed from a8b9103987226c9a5768c4f571840da3fd7aef19 to a9a45bf4314373cda000c34cf8296b457acb5fde
Branch pushed to git repo; I updated commit sha1. New commits:
10a0222 trac #18408: Merged with 6.8.beta7 a9a45bf trac #18408: Updated lists
### comment:50 Changed 6 years ago by ncohen
The lists have been updated. And so, this patch too!
Nathann
### comment:51 follow-up: ↓ 53 Changed 6 years ago by jdemeyer
These are no longer standard:
gd...................................... 2.0.35.p7 (not_installed)
gdmodule................................ 0.56.p8 (not_installed)
genus2reduction......................... 0.3.p8 (not_installed)
mercurial............................... 2.2.2.p0 (not_installed)
pil..................................... 1.1.6.p4 (not_installed)
python.................................. 2.7.5.p1 (not_installed)
sage.................................... 5.13 (not_installed)
sage_root............................... 5.13 (not_installed)
sage_scripts............................ 5.13 (not_installed)
sqlalchemy.............................. 0.5.8 (not_installed)
### comment:52 Changed 6 years ago by jdemeyer
Concerning Python, I do find it very confusing that ./sage -i python installs the old python-2.7.5.p1.spkg (the new-style package is called python2)
### comment:53 in reply to: ↑ 51 ; follow-up: ↓ 54 Changed 6 years ago by ncohen
These are no longer standard:
This conversation again? Didn't you say in 47 that you would give it up?
These packages appear there: http://mirror.switch.ch/mirror/sagemath/spkg/standard/
If you do not agree with the list, please write to Harald. I already did it once, you were in Cc.
### comment:54 in reply to: ↑ 53 ; follow-up: ↓ 55 Changed 6 years ago by jdemeyer
This conversation again? Didn't you say in 47 that you would give it up?
I'm not complaining, just informing...
### comment:55 in reply to: ↑ 54 Changed 6 years ago by ncohen
I'm not complaining, just informing...
I see...
Nathann
Pom Pom Pom ...
### comment:57 Changed 5 years ago by jdemeyer
• Dependencies changed from #18407, #18456 to #19158
### comment:58 Changed 5 years ago by jdemeyer
• Dependencies #19158 deleted
• Milestone changed from sage-6.8 to sage-6.9
### comment:59 Changed 5 years ago by git
• Commit changed from a9a45bf4314373cda000c34cf8296b457acb5fde to 15b95833e3928fb055ca8d34f2cea2ca646dc236
Branch pushed to git repo; I updated commit sha1. New commits:
15b9583 Merge branch 'public/18408' of git://trac.sagemath.org/sage into public/18408
### comment:60 Changed 5 years ago by jhonrubia6
• Milestone changed from sage-6.9 to sage-7.1
• Reviewers set to Javier Honrubia González
• Status changed from needs_review to positive_review
### comment:61 Changed 5 years ago by vbraun
• Branch changed from public/18408 to 15b95833e3928fb055ca8d34f2cea2ca646dc236
• Resolution set to fixed
• Status changed from positive_review to closed
Note: See TracTickets for help on using tickets. | 2021-01-19 09:07:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19359123706817627, "perplexity": 10621.197330349247}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703518201.29/warc/CC-MAIN-20210119072933-20210119102933-00729.warc.gz"} |
http://mail-archives.apache.org/mod_mbox/tomcat-users/200509.mbox/%3C431D4ED0.6030304@liland.org%3E | # tomcat-users mailing list archives
##### Site index · List index
Message view
Top
From Edmund Urbani <...@liland.org>
Subject Re: getRealPath() returns real path plus context path
Date Tue, 06 Sep 2005 08:09:52 GMT
Franz-Josef Herpers wrote:
> Hi,
>
> I've a problem when using ServletContext#getRealPath() with Tomcat 5.5.9.
>
> My web application resides under the name "tool" in the webapps
> directory. When I call
> servletContext.getRealPath(request.getContextPath() I get the real
> path but always with the context path added at the end. That means a
> path like C:\path\to\tomcat\webapps\tool\tool.
>
> Is there any explanation for this behaviour? Or am I doing something
> wrong?
>
> Thanks for any hints in advance
>
> Regards
> Franz
>
the getRealPath method simply returns a path inside the webapp's
directory. eg. you can do getRealPath("images/someimg.jpg") and get the
actual filesystem path for that file, so you can access it using
java.io.File and do something with it. getRealPath("/") should give you
the webapp directory itself.
note that you probably should not use this method, if you ever want to
be able to run your webapp directly from a .war file.
Edmund
---------------------------------------------------------------------
To unsubscribe, e-mail: tomcat-user-unsubscribe@jakarta.apache.org | 2014-10-30 17:00:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6421363949775696, "perplexity": 10099.978988488996}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637898611.54/warc/CC-MAIN-20141030025818-00221-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://www.matecdev.com/posts/julia-fft-derivative.html | # FFT Derivative
## Introduction
In many applications, we want to take advantage that the derivative operator is transformed into a multiplication operator in Fourier space. By applying a subsequent inverse transform, we can expect to obtain the derivative of a function using FFTs, using the well-known relation:
$$\mathcal{F}[g’](\xi) = \frac{2\pi}{L} \xi \mathcal{F}[g](\xi)$$
However, this is not so simple to translate into the discrete setting.
## Common Gotcha: Alising
For example, let’s compute the FFT-derivative of a periodic function defined in $$(0,L)$$. The following code yields an incorrect result:
using FFTW
using plots
N = 20;
L = 1;
xj = (0:N-1)*L/N;
f = sin.(2π*xj)
df = 2π*cos.(2π*xj)
k = 1:N
df_fft = ifft( 2π/L * k.* fft(f) )
plot(xj,real(df),label="Exact derivative")
plot!(xj,real(df_fft),label="incorrect FFT derivative",markershape=:circle)
The reason this doesn’t work is related to aliasing, which we discussed in the previous section. In detail, what’s going on under the hood is that, even though in our grid, we have the equality
$$\sin(5 x_j) = \frac{e^{-5 i x_j} + e^{5 i x_j}}{2i} + \frac{e^{15 i x_j} + e^{5 i x_j}}{2i},$$
clearly, the frequency corresponding to k=15 should not be employed when computing the derivative.
The correct derivative algorithm uses the negative frequencies mentioned in the previous section.
## Correct FFT-Derivative Algorithm
In order to obtain the correct result, we to correct these two lines:
k = fftfreq(N)*N;
df_fft = ifft( 2π*im/L * k.* fft(f) ); | 2022-01-29 05:17:48 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8776353597640991, "perplexity": 1701.064440746483}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-05/segments/1642320299927.25/warc/CC-MAIN-20220129032406-20220129062406-00523.warc.gz"} |
https://leetcode.com/articles/construct-string-from-binary-tree/ | ## Solution
#### Approach #1 Using Recursion [Accepted]
This solution is very simple. We simply need to do the preorder traversal of the given Binary Tree. But, along with this, we need to make use of braces at appropriate positions. But, we also need to make sure that we omit the unnecessary braces. To do the preorder traversal, we make use of recursion. We print the current node and call the same given function for the left and the right children of the node in that order(if they exist). For every node encountered, the following cases are possible.
Case 1: Both the left child and the right child exist for the current node. In this case, we need to put the braces () around both the left child's preorder traversal output and the right child's preorder traversal output.
Case 2: None of the left or the right child exist for the current node. In this case, as shown in the figure below, considering empty braces for the null left and right children is redundant. Hence, we need not put braces for any of them.
Case 3: Only the left child exists for the current node. As the figure below shows, putting empty braces for the right child in this case is unnecessary while considering the preorder traversal. This is because the right child will always come after the left child in the preorder traversal. Thus, omitting the empty braces for the right child also leads to same mapping between the string and the binary tree.
Case 4: Only the right child exists for the current node. In this case, we need to consider the empty braces for the left child. This is because, during the preorder traversal, the left child needs to be considered first. Thus, to indicate that the child following the current node is a right child we need to put a pair of empty braces for the left child.
Just by taking care of the cases, mentioned above, we can obtain the required output string.
Complexity Analysis
• Time complexity : . The preorder traversal is done over the nodes of the given Binary Tree.
• Space complexity : . The depth of the recursion tree can go upto in case of a skewed tree.
#### Approach #2 Iterative Method Using stack [Accepted]
Algorithm
In order to solve the given problem, we can also make use of a . To see how to do it, we'll go through the implementation and we'll also look at the idea behind each step.
We make use of a onto which various nodes of the given tree will be pushed during the process. The node at the top of the represents the current node to be processed. Whenever a node has been processed once, it is marked as visited. The reasoning behind this will be discussed soon.
We start off by pushing the root of the binary tree onto the . Now, the root acts as the current node. For every current node encountered, firstly, we check if it has not been visited already. If not, we add it to the set of visited nodes.
Since, for the preorder traversal, we know, we need to process the nodes in the order current-left-right. Thus, we add a ( followed by the current node to the string to be returned.
Now, if both the left and the right children of the current node exist, we need to process them in the order left-right. To do so, we need to push them onto the in the reverse order, so that when they are picked up later on, their order of processing gets corrected.
Since we've already added to the string , if only the right child of the current node exists, as discussed in case 4 in the last approach, we need to put a () in representing the null left node. We need not push anything onto the for the left node and we can directly add the () to for this. But, we still need to push the right child onto the for future processing.
If only the left child exists, we need not consider the right child at all, as discussed in case 3 in the last approach. We can continue the process by just pushing the left child onto the .
Now, we need to note that even when a node is being processed, if it has not already been visited, it isn't popped off from the . But, if a node that has already been processed(i.e. its children have been considered already), it is popped off from the when encountered again. Such a situation will occur for a node only when the preorder traversal of both its left and right sub-trees has been completely done. Thus, we need to add a ) to mark the end of the preorder traversal of the current node as well.
Thus, at the end, we get the required pre-order traversal in the substring . Here, represents the length of . This is because, we need not put the parentheses(redundant) at the outermost level.
The following animation better depicts the process.
!?!../Documents/Construct_Binary_Tree_stack.json:1000,563!?!
Complexity Analysis
• Time complexity : . nodes are pushed and popped in a stack.
• Space complexity : . size can grow upto .
Analysis written by: @vinod23 | 2019-05-22 07:21:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6720095276832581, "perplexity": 367.47479963376315}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232256764.75/warc/CC-MAIN-20190522063112-20190522085112-00077.warc.gz"} |
http://support.sas.com/documentation/cdl/en/statug/67523/HTML/default/statug_spp_details05.htm | # The SPP Procedure
#### Statistics Based on Second-Order Characteristics
Statistics that are based on second-order characteristics include Ripley’s K function, Besag’s L function, and the pair correlation function (also called the g function). To understand why these functions are based on second-order characteristics, see Illian et al. (2008, p. 223-243). These functions usually involve computation of pairwise distances between points.
The K function of a stationary point process is defined such that is the expected number of points within a distance of r from an arbitrary point of the process. The empirical K function of a set of points is the weighted and renormalized empirical distribution function of the set of pairwise distances between points. The empirical K function can be written as
where is the border edge correction that is described in the section Border Edge Correction for Distance Functions.
For a homogeneous Poisson process, can be written as
Exploratory analysis usually involves computing both the empirical K function, , and the K function for a Poisson process, . A comparison of and might indicate clustering or regularity depending on whether or .
Besag’s L function is a transformation of the K function and is defined as
For a homogeneous Poisson process, .
The pair correlation function, g(r), can also be expressed as a transformation of the K function:
Illian et al. (2008), Stoyan (1987), and Fiksel (1988) suggest an alternative expression for :
where is the second-order product density function. Cressie and Collins (2001) provides an expression for as
where can be written as a kernel estimate,
where a is the area, , and is a kernel such as the uniform kernel or the Epanechnikov kernel (Silverman, 1986). PROC SPP uses the version that is based on the uniform kernel; for more information about the uniform kernel, see the section Nonparametric Intensity Estimation. Based on the formula for the second-order product density in terms of the kernel estimate, Stoyan (1987) gives an edge-corrected kernel estimate for as
Based on the preceding expression for the product density and a planar version of Moller and Waagepetersen (2004), can be written as
A border-edge-corrected version of can be written as
where and are points within the boundary at a distance greater than or equal to r; where is the distance of to the boundary of , ; and where for a kernel , such as the uniform kernel or the Epanechnikov kernel. For more information about the uniform kernel, see the section Nonparametric Intensity Estimation. For a homogeneous Poisson process, . For any point pattern, values of greater than 1 indicate clustering or attraction at distance r, whereas values of less than 1 indicate regularity. | 2017-12-17 16:19:32 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9048987627029419, "perplexity": 669.3436747038346}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-51/segments/1512948596115.72/warc/CC-MAIN-20171217152217-20171217174217-00618.warc.gz"} |
https://calculus7.org/2012/02/25/playing-with-numbers-998001-explained/ | Playing with numbers: 1/998001 and others
A post in response to Colin’s “Patterns in numbers”:
1/998001 = 0.000 001 002 003 004 005 006 007…
goes through all integers 000 through 999, skipping only 998. Maple confirms this:
This fraction made rounds on the internet a while ago.
I begin with two general claims:
• Integer numbers are more complicated than polynomials
• Decimal fractions are more complicated than power series
To illustrate the first one: multiplying 748 by 367 takes more effort than multiplying the corresponding polynomials,
$(7x^2+4x+8)(3x^2+6x+7) = 21x^4+54x^3+97x^2+76x+56$
The reason is that there’s no way for the product of $4 x$ and $3x^2$ to “roll over” into $x^4$. It’s going to stay in the $x^3$ group. Mathematically speaking, polynomials form a graded ring and integers don’t. At the same time, one can recover the integers from polynomials by setting $x=10$ in $21x^4+54x^3+97x^2+76x+56$. The result is $274516$.
Moving on to the second claim, consider the power series
$\displaystyle (*) \qquad \frac{1}{1-t}=1+t+t^2+t^3+\dots = \sum_{n=0}^{\infty} t^n$
I prefer to use $t$ instead of $x$ here, because we often want to replace $t$ with an expression in $x$. For example, setting $t=2x$ gives us
$\displaystyle \frac{1}{1-2x}=1+2x+4x^2+8x^3+\dots = \sum_{n=0}^{\infty} 2^n x^n$
which is nothing surprising. But if we now set $x=0.001$ (and, for neatness, divide both sides by 1000), the result is
$\displaystyle \frac{1}{998}=0.001\ 002\ 004\ 008\ 016\ 032 \dots$
which looks like a magical fraction producing powers of 2. But in reality, setting $x=0.001$ did nothing but mess things up. Now we have a complicated decimal number, in which powers of 2 break down starting with “513” because of the extra digits rolled over from 1024. In contrast, the neat power series keeps generating powers of 2 forever.
By the way, $\displaystyle \frac{1}{1-2x}$ is the generating function for the numbers 1,2,4,8,16…, i.e., the powers of 2.
So, if you want to cook up a ‘magical’ fraction, all you need to do is find the generating function for the numbers you want, and set the variable to be some negative power of 10. E.g., the choice $x=0.001$ avoids digits rolling over until the desired numbers reach 1000. But we could take $x=10^{-6}$ and get many more numbers at the cost of a more complicated fraction.
For example, how would one come up with 1/998001? We need a generating function for 1,2,3,4,…, that is, we need a formula for the power series $\sum nt^n$. No big deal: just take the derivative of (*):
$\displaystyle \frac{1}{(1-t)^2}=\sum_{n=0}^{\infty} nt^{n-1}$
and multiply both sides by $t$ to restore the exponent:
$\displaystyle (**) \qquad \frac{t}{(1-t)^2}=\sum_{n=0}^{\infty} nt^{n}$
Now set $t=0.001$, which is easiest if you expand the denominator as $1-2t+t^2$ and multiply both the numerator and denominator by $1000000$. The result is
$\displaystyle \frac{1000}{998001} = \sum_{n=0}^{\infty} n\,0.001^{n} = 0.001002003\dots$
Dropping 1000 in the numerator is a matter of taste (cf. xkcd 163).
Let’s cook up something else. For example, again take the derivative in (**) and multiply by $t$:
$\displaystyle \frac{t(1+t)}{(1-t)^3}=\sum_{n=0}^{\infty} n^2t^{n}$
Now set $t=0.001$ to get
$\displaystyle \frac{1001}{997002999} = 0.000\ 001\ 004\ 009\ 016\ 025\ 036\ 049\dots$
Admittedly, this fraction is less likely to propagate around the web than 1/998001.
For the last example, take the Fibonacci numbers 1,1,2,3,5,8,13,… The recurrence relation $F_{n+2}=F_n+F_{n+1}$ can be used to find the generating function, $\displaystyle \frac{1}{1-t-t^2} = \sum F_n t^n$. Setting $t=0.001$ yields
$\displaystyle \frac{1}{998999} = 0.000\ 001\ 002\ 003\ 005\ 008\ 013\ 021\ 034\ 055\dots$
3 thoughts on “Playing with numbers: 1/998001 and others”
1. Fantastic explanation. So I guess the answer to the question “why was 998 skipped?” is really that it was not, but there was a domino effect with one of the digits from 1000 “rolling over” onto the 999, which picked up an extra digit and “rolled over” to 998, making it look like 999.
2. Lianxin says:
It is easy to remove the domino effects of 1/998001. Notice we want to subtract $1000\sum_{n=1001}^2000 0.001^n$, $2000\sum_{n=2001}^3000 0.001^n$, and so on. Upon simplification this becomes $\sum_{n=1}^\infty n [10^{-3000}]^{n-1} \frac{1-10^{-3000}}{0.999 \times 10^{3000}}$. Exchanging derivative and limit, we have the result as exactly $\frac{1}{0.999 \times 10^{3000}}$. So the “ideal” faction should be 1/998001-$\frac{1}{0.999 \times 10^{3000}}$
3. Lianxin says:
As another remark we should not pre-assume M and d discussed in the reply of the first comment; we have no idea of the magnitude of the coefficients of the power series. Thus additional computations should be used to determine M and d first. | 2017-09-26 02:02:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 42, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9015360474586487, "perplexity": 389.5089171693824}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-39/segments/1505818693940.84/warc/CC-MAIN-20170926013935-20170926033935-00069.warc.gz"} |
https://mathoverflow.net/questions/227612/can-we-compute-every-definable-number-with-knowledge-of-the-halting-problem | # Can we compute every definable number with knowledge of the halting problem?
Suppose we knew the answer to the halting problem, and the halting problem for this new system with the old halting problem solved. And so on. Would this allow us to compute every definable number?
• When you say definable number, do you mean a subset of natural numbers definable in the first-order structure $(\mathbb{N},0,1,*,+)$? (This is the interpretation that made most sense to me in connection with the halting problem.) Saying "definable number" by itself is pretty dangerous as shown here. – Burak Jan 4 '16 at 10:23
• Wikipedia definition en.wikipedia.org/wiki/Definable_real_number – T45665 Jan 4 '16 at 10:24
• You should check out this answer by Joel Hamkins that explains why the Wikipedia article does not make sense. – Burak Jan 4 '16 at 10:27
• OK. I am still interested in an answer to my question under any reasonable definition of definable. – T45665 Jan 4 '16 at 10:40
Depending on exactly what you mean by "and so on" (continue through the finite? the computable infinite?), you've described either the arithmetic or the hyperarithmetic sets of natural numbers. The former correspond to those sets which are first-order definable in the structure $(\mathbb{N}; +, \times)$; the latter, to those sets which are definable by a computable infinitary first-order formula in the structure $(\mathbb{N}; +, \times)$.
But these certainly aren't the only kinds of definability out there. We could consider other logics (non-computable infinitary first order? second-order? etc.) or other structures (first-order definability in the set-theoretic universe is extremely powerful); each provides a way to leap well outside even the hyperarithmetic sets.
The bottom line is: what do you mean by "definable"? Definability only makes sense once we specify both
• a structure,
and
• a logic;
and the precise answer to your question will vary wildly depending what you mean.
If you want to continue your process past the computable infinite, you run into trouble. Let $\omega_1^{CK}$ be the least noncomputable ordinal: what is the "$\omega_1^{CK}$th Halting Problem?" Unlike, say, the first infinite ordinal $\omega$ - where "the $\omega$th Halting Problem" $0^{(\omega)}$ is quite reasonably defined as $$\{\langle m, n\rangle: m\in 0^{(n)}\},$$ and in fact we can prove that any other reasonable way of "stitching together" the first $\omega$-many halting problems yields the same Turing degree - the fact that $\omega_1^{CK}$ is not computable prevents any nice definition. There are ways we can get past this, but that's a bit of a digression.
No.
For any model of computation; the set of computable reals is countable.
Through cantors diagnolisation argument we can prove the existence of a real which is not in this countably infinite set : --- simultaneously defining it and proving it's incomputability in the chosen model.
eg. If for computation (even if) we have a Universal Turing Machine with the access to the n- th oracle; the set of all programs which halt on it;
is in-computable on the same setup : But the set is definable.(this being the definition)
• Of course, this depends on the definition of "definable." E.g. if "definable" means "first-order definable in $(\mathbb{N}; +, \times)$," then the answer is "yes". – Noah Schweber Jan 4 '16 at 19:56 | 2020-06-06 16:02:52 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9128132462501526, "perplexity": 561.437213162422}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590348517506.81/warc/CC-MAIN-20200606155701-20200606185701-00159.warc.gz"} |
https://math.stackexchange.com/questions/3226420/assumption-on-mirror-descent-convergence | # Assumption on Mirror Descent convergence?
I am studying Mirror descent and nonlinear projected subgradient methods. At page 171 Theorem 4.1., the author claims that the method converges provided $$\sum_s t_s= \infty , \,\,\,t_k \rightarrow 0 \,\,\,\,\,\text{as} \,\,\,\ k \rightarrow \infty$$ beacuse the right hand side of the following goes to zero:
$$\min_{1\leq s \leq k} f(x^s) - \min_{x \in X} f(x) \leq \frac{B_{\psi(x^*,x^1)}+(2\sigma)^{-1}\sum_{s=1}^kt_s^2\|f'(x^k)\|_*^2}{\sum_{k=1}^s t_s}$$
My question is that how we know $$\sum_{s=1}^kt_s^2\|f'(x^k)\|_*^2$$ is bounded provided aforementioned assumption? Although $$t_k \rightarrow 0$$ does not guarantee that $$\sum_{s=1}^kt_s^2\|f'(x^k)\|_*^2$$ is bounded.
Section (b) of Assumption A states that $$f$$ is $$L_f$$-Lipschitz. A standard result of optimization asserts that if $$f'(x)\in \partial f(x)$$, then $$\|f'(x)\|_*\leq L_f$$ where $$\|\cdot\|_*$$ denotes the dual norm of $$\|\cdot\|$$.
Thus $$\displaystyle \frac{\sum_{k=1}^n t_k^2\|f'(x^k)\|_*^2}{\sum_{k=1}^n t_k}\leq L_f\frac{\sum_{k=1}^n t_k^2}{\sum_{k=1}^n t_k}$$.
Let us show that $$\displaystyle \frac{\sum_{k=1}^n t_k^2}{\sum_{k=1}^n t_k} \to 0$$. Remember that the $$t_n$$ are $$\geq 0$$.
Let $$\epsilon >0$$. There exists $$N$$ such that $$n\geq N\implies t_n\leq \epsilon$$. For $$n\geq N$$, $$\sum_{k=1}^n t_k^2\leq \sum_{k=1}^N t_k^2 + \epsilon \sum_{k=N+1}^n t_k$$ The sequence $$\displaystyle \epsilon \sum_{k=N+1}^n t_k$$ (indexed by $$n$$) diverges to $$\infty$$, so there exists some $$N'>N$$ such that $$n\geq N' \implies \sum_{k=1}^N t_k^2\leq\epsilon \sum_{k=N+1}^n t_k$$ For $$n\geq N'$$, $$\sum_{k=1}^n t_k^2\leq 2\epsilon \sum_{k=N+1}^n t_k\leq 2\epsilon \sum_{k=1}^n t_k$$ and we're done.
• Thank you so much. It was very instructive. – Saeed May 17 at 23:37
You don't have that $$\sum_{s=1}^k t_s^2 \lVert f'(x^k)\rVert^2$$ is bounded. However, for any series $$\sum_{s=1}^\infty a_s$$ that diverges, but the summands converge to zero, you have that $$\frac{\sum_{s=1}^k a_s^2}{\sum_{s=1}^k a_s} \to 0, \quad \text{for k\to\infty}.$$ You can find this for example here.
So in fact, it doesn't really have anything to do with optimization (and just as a comment: it's not really relevant for the paper).
• I do not have $\frac{\sum_{s=1}^k a_s^2}{\sum_{s=1}^k a_s}$, I have $\frac{\sum_{s=1}^k a_s^2b_k^2}{\sum_{s=1}^k a_s}$ where $b_k^2$ is the dual norm of the gradient. How would you handle that? – Saeed May 16 at 2:29
• Also, on the cited question, we have have sum of the $a_n$ at the denominator. – Saeed May 16 at 2:34
• The gradient is bounded though so you effectively do have the series they posted... – Tony S.F. May 16 at 8:17 | 2019-05-23 18:44:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 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": 30, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9717270731925964, "perplexity": 162.4628877493121}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-22/segments/1558232257361.12/warc/CC-MAIN-20190523184048-20190523210048-00261.warc.gz"} |
https://learn.saylor.org/mod/book/view.php?id=30723&chapterid=6703 | ## The History of Government Monetary Intervention
Read this section on the West's monetary breakdown by Murray Rothbard. Are the monetary standards we live under today the result of free voluntary choice? If not, what were the government monetary interventions along the way?
### The Monetary Breakdown of the West
#### Phase IX: Fluctuating Fiat Currencies, March 1973-?
With the dollar breaking apart, the world shifted again, to a system of fluctuating fiat currencies. Within the West European block, exchange rates were tied to one another, and the U.S. again devalued the official dollar rate by a token amount, to $42 an ounce. As the dollar plunged in foreign exchange from day to day, and the West German mark, the Swiss franc, and the Japanese yen hurtled upward, the American authorities, backed by the Friedmanite economists, began to think that his was the monetary ideal. It is true that dollar surpluses and sudden balance of payments crises do not plague the world under fluctuating exchange rates. Furthermore, American export firms began to chortled that falling dollar rates made American goods cheaper abroad, and therefore benefitted exports. It is true that governments persisted in interfering with exchange fluctuations ("dirty" instead of "clean" floats), but overall it seemed that the international monetary order had sundered into a Friedmanite utopia. But it became clear all too soon that all is far from well in the current international monetary system. The long fun problem is that the hard money countries will not sit by forever and watch their currencies become more expensive and their exports hurt for the benefit of their American competitors. If American inflation and dollar depreciation continues, they will soon shift to the competing devaluation, exchange controls, currency blocs, and economic warfare of the 1930s. But more immediate is the other side of the coin: the fact that depreciating dollars means that American imports are far more expensive, American tourists suffer abroad, and cheap exports are snapped up by foreign countries so rapidly as to raise prices of exports at home (e.g., the American wheat-and-meat price inflation). So that American exporters might indeed benefit, but only at the expense of the inflation-ridden American consumer. The crippling uncertainty of rapid exchange rate fluctuations was brought starkly home to Americans with the rapid plunge of the dollar in foreign exchange markets in July 1973. Since the U.S. went completely off gold in August 1971 and established the Friedmanite fluctuating fiat system in March 1973, the United States and the world have suffered the most intense and most sustained bout of peacetime inflation in the history of the world. It should be clear by now that this is scarcely a coincidence. Before the dollar was cut loose from gold, Keynesians and Friedmanites, each in their own way devoted to fiat paper money, confidently predicted that when fiat money was established, the market price of gold would fall promptly to its non-monetary level, then estimated at about$8 an ounce. In their scorn of gold, both groups maintained that it was the mighty dollar that was propping up the price of gold, and not vice versa. Since 1971, the market price of gold has never been below the old fixed price of $35 an ounce, and has almost always been enormously higher. When, during the 1950s and 1960s, economists such as Jacques Rueff were calling for a gold standard at a price of$70 an ounce, the price was considered absurdly high. It is now even more absurdly low. The far higher gold price is an indication of the calamitous deterioration of the dollar since "modern" economists had their way and all gold backing was removed.
It is now all too clear that the world has become fed up with the unprecedented inflation, in the U.S., and throughout the world, that has been sparked by the fluctuating fiat currency era inaugurated in 1973. We are also weary of the extreme volatility and unpredictability of currency exchange rates. This volatility is the consequence of the national fiat money system, which fragmented the world's money and added artificial political instability to the natural uncertainty in the free market price system. The Friedmanite dream of fluctuating fiat money lies in ashes, and there is an understandable yearning to return to an international money with fixed exchange rates.
Unfortunately, the classical gold standard lies forgotten, and the ultimate goal of most American and world leaders is the old Keynesian vision of a one-world fiat paper standard, a new currency unit issued by a World Reserve Bank (WRB). Whether the new currency be termed "the bancor" (offered by Keynes), the "unita" (proposed by World War II U.S. Treasury official Harry Dexter White), or the "phoenix" (suggested by The Economist) is unimportant. The vital point is that such an international paper currency, while indeed free of balance-of-payment crises (since the WRB could issue as much bancors as it wished and supply them to its country of choice, would provide for an open channel for unlimited world-wide inflation, unchecked by either balance-of-payment crises or by declines in exchange rates. The WRB would then be the all-powerful determinant of the world's money supply and its national distribution. The WRB could and would subject the world to what it believes will be a wisely-controlled inflation. Unfortunately, there would then be nothing standing in the way of the unimaginably catastrophic economic holocaust of world-wide runaway inflation, nothing, that is, except the dubious capacity of the WRB to fine-tune the world economy.
While a world-wide paper unit and central bank remain the ultimate goal of world's Keynesian-oriented leaders, the more realistic and proximate goal is a return to a glorified Bretton Woods scheme, except this time without the check of any backing in gold. Already the world's major central banks are attempting to "coordinate" monetary and economic policies, harmonize rates of inflation, and fix exchange rates. The militant drive for a European paper currency issued by a European central bank seems on the verge of success. This goal is being sold to the gullible public by the fallacious claim that a free-trade European Economic Community (EEC) necessarily requires an overarching European bureaucracy, a uniformity of taxation throughout the EEC, and, in particular, a European central bank and paper unit. Once that is achieved, closer coordination with the Federal Reserve and other major central banks will follow immediately. And then, could a World Central Bank be far behind? Short of that ultimate goal, however, we may soon be plunged into yet another Bretton Woods, with all the attendant crises of the balance-of-payments and Gresham's Law that follow from fixed exchange rates in a world of fiat moneys.
As we face the future, the prognosis for the dollar and for the international monetary system is grim indeed. Until and unless we return to the classical gold standard at a realistic gold price, the international money system is fated to shift back and forth between fixed and fluctuating exchange rates, with each system posing unsolved problems, working badly, and finally disintegrating. And fueling this disintegration will be the continued inflation of the supply of dollars and hence of American prices which show no sign of abating. The prospect for the future is accelerating and eventually runaway inflation at home, accompanied by monetary breakdown and economic warfare abroad. This prognosis can only be changed by a drastic alteration of the American and world monetary system: by the return to a free market commodity money such as gold, and by removing government totally from the monetary scene. | 2023-02-04 00:16:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2592279613018036, "perplexity": 4107.445893960032}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-06/segments/1674764500076.87/warc/CC-MAIN-20230203221113-20230204011113-00452.warc.gz"} |
https://www.elastic.co/blog/found-elasticsearch-top-down | RSS
15 October 2014
## Elasticsearch from the Top Down
UPDATE: This article refers to our hosted Elasticsearch offering by an older name, Found. Please note that Found is now known as Elastic Cloud.
The previous article in this series, Elasticsearch from the Bottom Up, covered essential data structures within a single shard. In this article, we will look at the distributed nature of Elasticsearch.
## Introduction
In the previous article, Elasticsearch from the Bottom Up, we started with fairly low level data structures, and ascended up the abstraction layer to put them into context. We focused on what happens within a single shard, however.
To look at how all of this fits together in a distributed setting, it is easier to start at the other end: from the “top”, as observed from a user’s perspective.
We will look at what happens when a user sends an index and a search request to Elasticsearch, and how the requests ripple through the network, until we reach the lower level structures covered earlier. First, we’ll look at the node accepting the request and its role as a coordinator. We’ll look at how it routes requests to the shards’ primaries for indexing requests, and load balances across replicas for search requests.
After having been routed to the right shards, we’ll look at what happens at the shard level — such as what constitutes a “successfull” index operation, and transformations necessary to convert documents and searches to their Lucene equivalents. For search request, we’ll also look at the scatter/gather process, which can happen in multiple rounds.
## A Cluster of Nodes
To describe how Elasticsearch works, we need some sort of cluster topology. The cluster in the figure describes the kind of cluster we assume. We have one Elasticsearch index with two shards, replicated across nodes in two different “zones” for availability — with master only nodes running across three zones. Also, we have two client nodes, which we will be sending requests through.
Different nodes in a cluster can have different roles (data and/or master – or none as a client) as well as properties (such as zone). We have data nodes, master nodes and client nodes - in different zones, i.e. with different node.zone properties. We focus on the data nodes in this article. To learn more about the other kinds of nodes, we recommend reading Elasticsearch in Production, and Java Clients for Elasticsearch.
## Request Coordinators
When you send a request to a node in Elasticsearch, that node becomes the coordinator of that request. It will decide which nodes and shards to route a request to, how to merge different nodes’ responses, as well as decide when the request is “done”. While Elasticsearch handles this transparently for you, advanced partitioning schemes require knowledge about internal processing and routing. Given the cluster described above, the client node will act as the coordinator.
To be able to act as a coordinator, the node needs to know the cluster’s state. The cluster state is replicated to every node in the cluster. It has things like the shard routing table (which nodes host which indexes and shards), metadata about every node (such as where it runs and what attributes the node has), and index mappings (which can contain important routing configuration) and templates. The cluster state being replicated to all nodes is an important reason why the mappings need to be reasonably sized
For a search request, coordinating means picking replicas of shards to send the request to for further processing, possibly in multiple rounds, which we’ll look more into later. Picking a replica is done either at random, or influenced by the request’s preference.
An index request (i.e. one where you create, update or delete a document) is slightly different. In this case, the request must be routed to the primaries of the shards, and also to a certain amount of replicas - depending on the index request’s write_consistency. Write consistency can be either one, quorum (the default, though equivalent to one unless you have ≥2 replicas), or all — i.e. requiring one, most or every replica to have acknowledged.
## Index a Document to an Index of … Indexes?
The term “index” is used in a lot of contexts, with different meanings. You index documents, to an Elasticsearch index. The Elasticsearch index has shards, which are Lucene indexes. And those have inverted indexes. This can get confusing.
An important insight is that, conceptually, an Elasticsearch index with two shards is exactly the same as two Elasticsearch indexes with one shard each. Ultimately, they are two Lucene indexes. The difference is largely the convenience Elasticsearch provides via its routing feature. It is possible to achieve the same “manually” having just single shard indexes. (Not that you should!)
The important part is realizing that an Elasticsearch index is an abstraction on top of a collection of Lucene indexes, through the concept of shards. This helps when you need to wrap your head around more advanced partitioning strategies.
## Index Requests
An index request is one that creates or changes documents in an index. Whether it’s the creation of a new document, a deletion or an update is not very important, so we’ll refer to them all as an “index request”.
Consider the following bulk request:
{"index": {"_index": "tweets", "_type": "tweet", "_id": "502878691740090369"}}
{"user": "mikepluta", "tweet": "Moore's Law for #BigData: The amount of nonsense packed into the term \"BigData\" doubles approximately every two years"}
{"index": {"_index": "tweets", "_type": "tweet", "_id": "475944863175671808"}}
{"user": "viktorklang", "tweet": "For resilient software, \"What could possibly go wrong?\" should be the famous first words; not last."}
{"index": {"_index": "logs-2014-10-14", "_type": "log", "_consistency": "all"}}
{"@timestamp": "2014-10-14T12:34:56Z", "message": "Suddenly the Dungeon collapses!! - You die..."}
There are several questions the node that processes this request needs to consider:
• What is the routing configuration for the tweets and the logs? This can be determined by looking at the mappings in the cluster state. For the tweets, it’s possible that user based routing is in place, so the tweet’s user attribute should determine which shard to route the documents to. We look at some examples in the next section.
• After having determined the shards for the two tweets, when can we consider the document to actually be indexed? Since nothing is specified, this defaults to the node’s default action.write_consistency, which defaults to quorum.
• The log message does not have an ID associated with it. All documents must have one, so the coordinator will have to assign one to it. The document ID is what the coordinator will use to route the request, if the action or mapping does not override it. (It’s a best practice to assign IDs and have idempotent requests, however)
• The log action specifies a strict _consistency-setting, so the request cannot be acknowledged until every single replica has returned success.
• When can the bulk request as a whole finish?
## Routing
Routing specifies which documents go where, and is therefore an important part of how requests flow internally in Elasticsearch, both for search and index requests. It’s integral to designing proper data flow and index partitioning. Here, we focus on the mechanics, since index and shard design is a big topic.
Documents are routed based on a routing key, and are placed on shard number $$\mathrm{hash}\left(key\right) \bmod n$$, where $$n$$ is the number of shards in the index. (For the curious, the hash function used is djb2)
Shard design is largely about deciding on what that key is. If we use the document IDs for the above tweets as the routing key, and assume the tweets index has two shards, we would get $$\mathrm{hash}\left(502878691740090369\right) \bmod 2 = 1$$ and $$\mathrm{hash}\left(475944863175671808\right) \bmod 2 = 0$$ respectively. The two tweets would be stored in different shards. However, if the mapping would rather specify routing based on the user key, we would find that $$\mathrm{hash}\left(mikepluta\right) \bmod 2 = \mathrm{hash}\left(viktorklang\right) \bmod 2 = 1$$. The documents would thus be stored in the same shard. That can be helpful if we only want to search a particular user’s documents.
## Primary Concerns
When an index operation has been routed, it is forwarded to the “primary” for that shard. A shard has exactly one “primary”, and zero or more replicas. In this regard, the primary can be considered the “master” for the shard, and the replicas as “slaves”.
The primary will act as a coordinator for index operations for that specific shard. It will send the index operations to the relevant replicas, and wait until the required number has acknowlegded before indicating success.
When a sufficient number of replicas have acknowledged, the primary will report success back to the originating request coordinator, in our case the client node. For the default write consistency of “quorum”, two out of three operations is sufficient, so it is not necessary to wait for the third operation before passing on success.
The coordinator/client node sends out operations to separate shards’ primaries in parallel. When all operations have returned, the originating bulk request can also finally be returned.
The definition of a “successful” operation is worth looking into.
In the previous article, we looked at how indexes are built, and how there is a tradeoff between search speed, index compactness, indexing speed, and the time it takes for operations to become visible. Lucene internals like immutable segments were covered, and we emphasized that building these in batches and delaying costly disk synchronization operations were important.
All of that seems to run counter to what we want from an index operation: safe and durable, yet quickly acknowledged. To achieve that, Elasticsearch has a “transaction log” (“translog” in the documentation), or a “write-ahead log”, like almost every database system. Being written to the append-only translog is what defines success for a shard, not whether the document is actually part of a live index through a searchable segment.
During normal operation, Elasticsearch does not replicate already built pieces of indexes (i.e. segments), but the operations necessary to reapply the same change. (During recovery or shard migration, on the other hand, segments are replicated.) Therefore, all the replicas are essentially doing the same amount of work, for the same CPU cost. A replica cannot “reuse” the work the primary has already done. This is an important reason why adding replicas decreases the overall indexing throughput — you need to wait for even more nodes to acknowledge the operations. Also, you cannot expect to have “write only” nodes and “read only” nodes.
## All in a Shard
While putting an operation in the shard’s transaction log is a great start, ultimately the effect of the operation is supposed to end up in the index structures. In the previous article, we covered how the inverted index works, and how it’s built. We said nothing about mappings, but focused on the fact that a shard is a Lucene index.
Lucene does not have a concept of a mapping, nor does a Lucene index or document have types. In Lucene, a document is typeless and has an arbitrary number of fields. These fields have certain types (string/numeric) and properties (stored/indexed/…). The Mapping is an excellent abstraction to express how to transform a source document to a Lucene document with a bunch of fields. Mappings have concepts like types, dynamic properties, multi-fields, scripted transforms and so on. Lucene, however, knows nothing of these. Lucene is happy as long as Elasticsearch produces a document in the way Lucene expects. There is nothing special with fields like _all, _source, or even _type as far as Lucene is concerned.
Many compare an Elasticsearch index to a database, and a type to a table. Personally, I think this comparison can cause more confusion than clarity. With two different tables, you can reasonably assume that the tables have nothing in common in how or where they are stored. Conversely, you can construct mappings that will cause Elasticsearch to produce fields with the same name, but with disparate types. Since everything is a bunch of terms in the same inverted index, this can cause problems. If you have a filter that is numeric for some documents and a string for others, you will eventually get errors or possibly unexpected results. The same goes for fields with the same type (e.g. string), but with different analyzers. Dynamic mapping is great for jumpstarting development, but probably not something you want to rely entirely on.
## Index Request Summary
To summarize the flow of index requests, this is what happens:
1. The node accepting the request will be the coordinator. It consults the mappings to determine which shard to send the request to.
2. The request is sent to the primary of that shard.
3. The primary writes the operation to its translog, and relays the request to the replicas.
4. When a sufficient number of replicas have acknowledged, the primary returns success.
5. The coordinator returns success when all the sub-operations (in e.g. a bulk request) have succeeded.
While this happens, each shard will continuously process its queue of documents, transforming the input documents to Lucene documents. These are then added to the index buffer, eventually flushed in a new segment, and even later completely committed. When this happens is up to the node hosting the shard. The flushing is not synchronized across nodes, so it is possible for searchers to briefly see separate “timelines” as refreshes propagate.
## Search Requests
We’ve seen the amount of back and forth required to turn a request with an index operation into an actual index change. The process for search requests is similar in some ways, and different in many others.
Like with index requests, the search requests must be routed. A search will either hit all distinct shards, if no routing is specified — or a specific shard, if routing is specified.
When the relevant shards have been identified, the coordinator will choose amongst the available replicas of that shard, trying to balance load.
Let’s assume we have the following search. We have a multi_match-query on the fields title and description, searching for “Holy Grail”. We want the top ten authors, and the top ten books, preferring a match in the title.
POST /books/book/_search
query:
filtered:
filter:
term:
tag: python
query:
multi_match:
query: Holy Grail
fields: [title^5, description]
aggregations:
author_id:
terms:
field: author_id
size: 10
shard_size: 100
size: 10
We have not specified the search’s type, so the default will be used – query_then_fetch. This “search type” is not to be confused with the types discussed above! Naming is difficult.
Essentially, “query then fetch” means that there will be two rounds of searching. We will compare this search type with others later.
First, the shards will each find the top 10 hits and send back their IDs. These IDs (up to $$10 * n$$ of them) will then be merged by the coordinator to find the true top 10, after which it will request the actual documents for the winners. For finding the global top 10 hits, it is sufficient to ask for the top 10 from every shard. We’ll see why this is different for aggregations later.
But first, let’s look closer at the first round, and see what happens at the shard level for a search.
## Query Rewriting
Before a search request can be executed on a shard, the search needs to be rewritten and adapted to Lucene query graphs. Elasticsearch is often criticized for having a deeply nested and verbose search DSL, which to some extent assumes Lucene familiarity. Personally, I find the search DSL to be awesome — for precisely the same reasons:
First, the nested nature makes it easier to work with programatically. It is certainly verbose for simple things, but real search needs with heavily customized scoring and matching are not simple.
Secondly, the queries and the filters in the DSL are quite close to their Lucene counterparts. This is important to understand what is really going on.
There are a few exceptions, however. As mentioned above, the mapping concept is foreign to Lucene. Yet, some queries utilize the mappings. For example, the match family of queries have no Lucene counterpart. They will process the query text according to the fields’ mappings, and compose a Lucene query. Our example will be rewritten to something like the following:
Note that the query text “Holy Grail” has been tokenized and lowercased, according to the analyzers configured for the respective fields. A common source of frustration when not getting the results you want is to have incompatible index- and query time text processing. For example, a terms query would not have transformed Holy Grail into holy, grail, and therefore would not match.
## Searching a Shard
At this point, we have a Lucene query operator ready to be executed on every shard. We’re in search phase one — i.e. “query”, to be followed by “fetch” — so we need the following:
• A list of the top ten document IDs. (Not the entire document) These will be merged by the coordinator, which will do a second “fetch” phase to fetch the actual documents.
• An iterator of all hits (though we don’t need scores for them all), for aggregation purposes.
• A way to quickly find a book’s author_id given a document ID: i.e. a field cache or document values.
• The top 100 authors. (Note the shard_size being 100)
The section on inverted indexes and index terms in the bottom up article describes how the search is executed per segment, so we will skip repeating that here. However, it is worth repeating that a search happens across multiple independent segments and merged - much like how the sharding works. There are several caches that can boost the performance of the search, all scoped by segment:
• If the tag:python filter is cached, it can immediately be reused.
• The author_id field must be in the field cache, if document values are not enabled. If not, all author_ids for all documents must be loaded into memory.
• If document values are used for author_id, it’s possible that the disk pages holding the needed values is in the page cache. If so, great!
Queries are not cached, however. So for these, and any uncached filters and fields, we will need to hit the inverted index. For anything that needs to use the underlying index, it would be great if the relevant pages are present in the operating system’s page cache. (If you assign all the memory to the Elasticsearch process, there is nothing left for the operating system.)
Ultimately, with filters and aggregations, you are essentially manipulating bitmaps to summarize values you already have cached. This is why Elasticsearch can be so mind-boggingly fast.
## … Then Fetch
After every shard has provided its contribution to the results, the coordinator will merge them. Specifically, there are two things it needs to find out:
• The true top 10 hits. The shards will provide the IDs of up to 10 documents, and their scores.
• An approximation of the top 10 authors. The shards have provided the counts for up to 100 authors each. If we did not do this, and only requested the top 10 per shard, what would happen if one of the true top 10 authors were actually the 11th in one of the shards? It would not have been submitted as a candidate, and caused that particular outer to have fallen out. This is still possible, if one of the true top 10 authors is actually the 101st on one of the shards, but it should be less likely. To have complete accuracy, Elasticsearch needs to gather the counts for all authors for every shard. This can be prohibitively expensive to do, so trading accuracy for speed is common in this case.
The merge process will determine the true top 10 hits, then reach out to the shards that host the documents and ask for the entire document. Whether this extra step is helpful or an optimization that ends up adding to the overall latency depends on your use case. If you have a big number of shards and rather big documents, it’s probably worthwhile to do it in two rounds. If you have tiny documents and few shards, you can consider the query_and_fetch search type. As always, test and verify.
## Summary
The goals of this article was to start out with an index and a search request, as sent from a client, and reach the bits covered in the first part of this series. We’ve looked at shard routing, with the help of cluster state, mappings and possibly customized routing. With shards routed, we’ve seen how the shards’ primaries coordinate changes to its replicas, and how the transaction log balances durability and timely responses.
Similarily, we’ve traced the flow of search requests — through routing, balancing, scattering, query rewriting, response gathering, merging, subsequent fetching, and more.
Also, we’ve looked at mappings and types, how they do not exist in “Lucene land”, and what kinds of rewriting is necessary. Both when indexing, and when searching.
Hopefully, you have learned a bit more about the distributed nature of Elasticsearch, and the boundaries between Elasticsearch and Lucene! | 2017-07-24 16:37:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.28878092765808105, "perplexity": 1863.9524796123528}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424889.43/warc/CC-MAIN-20170724162257-20170724182257-00607.warc.gz"} |
https://binghamtonlaser.com/storage-bscin/7913aa-what-is-an-inverse-relationship-in-science | what is an inverse relationship in science
There is an inverse relationship between distance and light intensity - as the distance increases, light intensity decreases.. Two conventional explanations for the inverse relationship have emerged in the literature: (i) factor market imperfections that cause cross-sectional variation in household-specific shadow prices and (ii) the omission of soil quality measurements. Answer. A typical example of this type of relationship is between interest rates and consumer spending. The law of demand illustrates this inverse relationship. We call this type of relationship inverse proportionality. Data Science Stack Exchange is a question and answer site for Data science professionals, Machine Learning specialists, and those interested in learning more about the field. An inverse relationship is one which is the reverse of another or one in which when one variable factor increases, another decreases. The inverse relationship is a relationship between two numbers in which an increase in the value of one number results in a decrease in the value of the other number. 1. We use the same symbol as for proportionality, but represent one quantity by its inverse, so: $A \propto \frac{1}{B}$ , or to use our previous example: $\text{speed} \propto \frac{1}{\text{journey time}}$. Inverse proportion is the relationship between two variables when their product is equal to a constant value. Hence, a variable is inversely proportional to another variable. Graphs of inverse relationships always slope down and to the right (Figure 2.16) . Information and translations of Inverse relation in the most comprehensive dictionary definitions resource on the web. DIRECT AND INVERSE RELATIONSHIPS. Ok, rookie question.. but I have no one to verify it other than you folks. Inverse relationship of Addition and Subtraction. What is the definition of inverse relationship?The inverse relationship is also known as negative correlation in regression analysis; this means that when one variable increases, the other variable decreases, and vice versa. To understand how inverse correlation works in the world of finance, consider the relationship between gold and the stock market. Thus, if for a given function f ( x ) there exists a function g ( y ) such that g ( f ( x )) = x and f ( g ( y )) = y , then g is called the inverse function of f and given the notation f −1 , where by convention the variables are interchanged. Science. How to use inverse in a sentence. Other. A negative relationship between two variables usually implies that the correlation between them is negative, or — what is in some contexts equivalent — that the slope in a corresponding graph is negative. It … The inverse relationship is also known as negative correlation in regression analysis; this means that when one variable increases, the other variable decreases, and vice versa. There are many real-life examples of inverse relationships. In a direct relationship, both physical quantities may increase or decrease simultaneously. The curve itself shows an inverse relationship between force and velocity, meaning that an increase in force would cause a decrease in velocity and vice versa. I did some observation about a function and its inverse and I would like to confirm whether these observation are true: The domain and range roles of the inverse and function are 'exchanged' The graph of inverse function is flipped 90degree as compared to the function. First Name. Giving an example, a one repetition maximum (1RM) Back Squat would produce high levels of force but would be lifted at a slow velocity. In an inverse relationship, two things are opposite and react to each other. Children often find themselves either counting up or counting back to solve subtraction, and that is inefficient. Some relationships are inverse. Top Answer. An inverse relationship in economics is a relationship in which an increase in one variable corresponds with a decrease in another variable. Social Science. Science. In an inverse relationship, when one variable increases, the other decreases. Selection of Terms in an Arithmetic Progression, Acknowledgement Letter Format from Bank for Branch Shifting, Subtract the same number from both sides 3 + 7 – 3 = 10 – 3, On the left side the 3 and -3 produce 0 which leaves 7 = 10 – 3. Science. What is an Inverse Relationship? Languages. 2 3 4. The inverse productivity–size relationship is one of the oldest puzzles in development economics. So the relationships in question are both inverse. Inverse relationship of Addition and Subtraction. Can you explain what an inverse and direct relationship are when related to science? Inverse Agonist. The inverse relationship is also known as negative correlation in regression analysis; this means that when one variable increases, the other variable decreases, and vice versa. If children learn the important inverse relationship between addition and subtraction, subtraction facts will become much easier. The area of a circle is in direct relationship with the … Smart, in-depth coverage of the latest discoveries and research in science, from evolution to space exploration. Inverse relationships. x is treated like y, y is treated like x in its inverse. Whether … The inverse relationship is a relationship between two numbers in which an increase in the value of one number results in a decrease in the value of the other number. It states that, with all things being equal, as price falls, demand rises. An equation is balanced or the same on either side of the equals (=) sign. tive (neg'ă-tiv), Avoid the jargonistic use of this word as a synonym of normal or in expressions that may be obscure or ambiguous, as in negative findings and negative results. A quick way to derive them is by considering the geometry of a right-angled triangle, with one side of length 1 and another side of length x , then applying the Pythagorean theorem and definitions of the trigonometric ratios. In statistics, there is a negative relationship or inverse relationship between two variables if higher values of one variable tend to be associated with lower values of the other. Asked by Wiki User. This inverse relationship is useful when simplifying complex algebraic expressions and solving equations. Every statement in logic is either true or false. Teacher Alice Hart offers examples of how and when your child will be asked to use the inverse operation in school, and practical ways to help them understand the concept. An inverse agonist is a ligand that binds to the same receptor-binding site as an agonist and not only antagonizes the effects of an agonist but, moreover, exerts the opposite effect by suppressing spontaneous receptor signaling (when present). An inverse relationship can be represented by: a straight line a bar chart 0 0 569; Casey. Get ready for your Inverse Relationship tests by reviewing key facts, theories, examples, synonyms and definitions with study sets created by students like you. The same Gold vs Bitcoin to — RBC What to Know About long memory in the correlation with gold may relationship with the stock are negative, which tells in-. On the other hand, firms face higher compensation costs, which are passed to consumers through inflation. The inverse relationship is also known as negative correlation in regression analysis; this means that when one variable increases, the other variable decreases, and vice versa. An inverse correlation, also known as negative correlation, is a contrary relationship between two variables such that when the value of one variable is high then the value of … A similar inverse relationship exists between multiplication and division, but there's an important difference. Plant structures and their functions. Respond to this Question. Recently, it has been suggested instead that the inverse relationship is a statistical artifact resulting from omitted land quality. This is an inverse relationship. There are many examples of moral choices in the face of danger, no matter the IQ of the person. Define Inverse Relationship: Inversely related means two measurements move in the opposite direction when one changes. Often in a physics course, the type of inverse relationship you'll run across is an inversely proportional relationship. In statistics, there is a negative relationship or inverse relationship between two variables if higher values of one variable tend to be associated with lower values of the other. Direct relationships have a clear cause and effect and are fairly "equal". The English term inverse is derived from a Latin word that means “turn upside down”; or opposite in some way. Some relationship questions will work backwards. 9 0. But it is not strong correlation, there are also highly intelligent folks, who are risk-takers. Int.science. When the value of one variable increases, … An inverse relationship means that, if one term increases, the other decreases. Also, f(x) = -x and f(x) = 1/x to eliminate a zero value. Relationship ACT Science Practice Question #2. It is often described as a negative relationship. The mathematical explanation is that if f(x) = x + 2 and y (x) = x -2, the relationship is inverse. Generally, subtraction facts are harder for children to learn than addition facts. The Philips Curve is the most common example of a negative relationship. Sodium and potassium have an inverse relationship. are expressed by mathematical equations, being able to see qualitatively the relationships between variables is often crucial to an understanding of many … Inverse proportion is the relationship between two variables when their product is equal to a constant value. Then the following are also true: The reason for this is that we are dealing with an equation. Home » Accounting Dictionary » What is an Inverse Relationship? Denoting failure of response, absence of a reaction, or absence of an entity or condition in question. Inverse relationship is a relationship between two numbers in which an increase in the value of one number results in a decrease in the value of the other number. Inverse operations are opposite operations – one reverses the effect of the other. Please help me out if you can. The inverse relationship is also known as negative correlation in regression analysis; this means that when one variable increases, the other variable decreases, and vice versa. When you have two relationships with different entities that each point to each other, the "Inverse" field is how you tell XCode that those two relationships "go together". Often you can see relationships between variables by simply examining a mathematical equation. For example, savings is inversely related to expenditure when the income is constant. If a math fact is considered, for example 3 + 7 = 10. Of the two, the line is best. If exactly the same thing is done to both sides of the equation, it will still be balanced or equal. Also, when unemployment increases, consumer spendingdecreases because people hav… Before we define the converse, contrapositive, and inverse of a conditional statement, we need to examine the topic of negation. Imagine the age of a car and its value. A direct relationship means that increasing one term will cause the other term to increase as well. An inverse relationship means that, if one term increases, the other decreases. The inverse relationship is also known as negative correlation in regression analysis; this means that when one variable increases, the other variable decreases, and vice versa. In times of economic turmoil, investors may be concerned about the stock issued by struggling companies and react by investing in gold, which is usually considered to be a safe investment. As distance increases, annual wet deposition decreases for both Cu and Zn. For example, when pressure increases, temperature also increases. the stock market Gold and the - FOREX.com Tail A relationship between. Easy to use and portable, study sets in Inverse Relationship are great for studying in the way that works for you, at the time that works for you. Direct relationship- as x gets bigger, y gets bigger. In the example above we start with the equation 3 + 7 = 10. In an inverse relationship, an increase in one quantity leads to a corresponding decrease in the other. The farther I drive, the longer the time on the road. Not affirmative; refutative; not positive; not abnormal. If I drive 10 hours, I will have traveled some distance. A direct relationship means that increasing one term will cause the other term to … The net result of multiplying and dividing a number by the same factor is to multiply the number by 1, which leaves it unchanged. If A rises when B rises, there is a direct or positive relationship. Mathematically, this is expressed as y = k / x . An inverse correlation, also known as negative correlation, is a contrary relationship between two variables such that when the value of one variable is high then the value of … Inverse- as x gets bigger, y gets smaller. When the interest rates increase, consumers are less willing to spend and more willing to save. The negative relationship is portrayed as a downward sloping curve. When the interest rates increase, consumers are less willing to spend and more willing to save. Inverse definition is - opposite in order, nature, or effect. one which is the reverse of another or one in which when one variable factor increases Then the following are also true: Similar relationships exist for subtraction, for example 10 – 3 = 7. Hence, the lower the unemployment rate, the higher the inflation. The inverse productivity–size relationship is one of the oldest puzzles in development economics. What does Inverse relation mean? In your example, if a higher viscosity leads to a decreased flow rate, the relationship between viscosity and flow rate is inverse. The law of demand illustrates this inverse relationship. Science Explains. If A falls when B rises, the is an inverse or negative relationship. For example, the relationship between time spent at the mall and the amount of money in your pocket is an inverse relationship. Math. This use of thinking of the related addition fact when children encounter a subtraction fact they don’t know should be encouraged. Arts and Humanities. Copyright © 2020 MyAccountingCourse.com | All Rights Reserved | Copyright |. Inverse functions do what their name implies: they undo the action of a function to return a variable to its original state. A typical example of this type of relationship is between interest rates and consumer spending. ... An animal behaviorist confirms to Inverse there are all sorts of chemical goodness going on in puppies’ brains when they’re around us. There is an inverse relationship between distance and light intensity - as the distance increases, light intensity decreases. Reverse causation can occur when people change their diet or other lifestyle habit after developing a disease or perhaps after having a close family member suffer an event like a heart attack. An inverse relationship is one in which the value of one parameter tends to decrease as the value of the other parameter in the relationship increases. The negation of a statement simply involves the insertion of the … The traditional explanation has been imperfect labor markets. inverse meaning: 1. opposite in relation to something else: 2. the opposite: 3. opposite in relation to something…. It states that, with all things being equal, as price falls, demand rises. tive (neg'ă-tiv), Avoid the jargonistic use of this word as a synonym of normal or in expressions that may be obscure or ambiguous, as in negative findings and negative results. If you graph how much money you have against how much you spend, you see an inverse relationship. Explore how we tell when two variables are in quadratic or inverse relationships in this lesson. a there more to the leverage effect as well bitcoin correlation to gold be speculative, its inverse and reliable. Combined Science. An inverse relationship between both farm productivity and labor intensity, and farm size, is a common empirical finding in developing country agriculture. Not affirmative; refutative; not positive; not abnormal. The issue of direct versus inverse is an issue of whether two variables move in the same direction or against each other. Following the higher government spending, employees are better compensated, which means that they have more money to spend. Wiki User Answered . Since many physical relationships in electrostatics, electrodynamics, thermodynamics, etc. As you work with the children, use questions that encourage this strategy of the inverse relationship between addition and subtraction. Definition of Inverse relation in the Definitions.net dictionary. In an inverse relationship, one variable decreases while the other increases. Similar Questions. Converse, Inverse, Contrapositive Given an if-then statement "if p , then q ," we can create three related statements: A conditional statement consists of two parts, a hypothesis in the “if” clause and a conclusion in the “then” clause. Meaning of Inverse relation. Twenty years of relationship science reveals the strongest bonds hinge on the nature of the relationship itself. 2. As an equation, a basic inverse relationship looks like x = 1/y. Rae Paoletta. is it always the case? When pressure falls, the temperature falls too. The inverse relationship is also known as negative correlation in regression analysis; this means that when one variable increases, the other variable decreases, and vice versa. In an inverse relationship, when one quantity increases the other decreases. Subjects. Oct 23, 2014 . The relationship between two variables is a direct relationship if when one increases so does the other or as one decreases so does the other. Your Response. How to use inverse in a sentence. There is an inverse relationship between addition and subtraction. If a child knows that 6 + 9 = 15, and he or she sees the subtraction sentence 15 – 9 = __, the child can think, 9 and what are 15? Inverse relationship is a relationship between two numbers in which an increase in the value of one number results in a decrease in the value of the other number. Oct 23, 2014 . Two conventional explanations for the inverse relationship have emerged in the literature: (i) factor market imperfections that cause cross-sectional variation in household-specific shadow prices and (ii) the omission of soil quality measurements. One of the most obvious everyday examples of an inverse relationship is speed to travel time. Cyclic- a repeating pattern. In fact, when the government spending increases, the unemployment rate decreases because more jobs are created. 1. Denoting failure of response, absence of a reaction, or absence of an entity or condition in question. As far as I know, only the risk taking is statistically significantly related to IQ and yes, it's inverse relationship. 0 0; PsyDAG. For example, if Group 1 moves up, Group 2 subsequently declines, and vice-versa. The more you have, the less you spend. Earth Science 101: Earth Science Psychology 105: Research Methods in Psychology Accounting 101: Financial Accounting Inverse relationship exists between two variables when one increases the other decreases. Inverse relationships follow a hyperbolic pattern. For example, the relation ship between age and size (until maturity) is a direct relationship. an inverse leverage effect other cryptocurrencies. Inverse relationship is a relationship between two numbers in which an increase in the value of one number results in a decrease in the value of the other number. Negation . 2. Take for instance this question: Inverse definition, reversed in position, order, direction, or tendency. An inverse relationship, negative correlation, or inverse correlation is a contrary relationship between two variables. y is inversely proportional to x when the equation takes the form: When the value of one variable increases, the other decreases, so their product is unchanged. A negative relationship between two variables usually implies that the correlation between them is negative, or — what is in some contexts equivalent — that the slope in a corresponding graph is negative. Below is a graph that … Relationships between trigonometric functions and inverse trigonometric functions Trigonometric functions of inverse trigonometric functions are tabulated below. In primary maths we talk about the inverse to explain how addition and subtraction are linked and how multiplication and division are linked. If I run a car rental business, I might have an entity for my cars with a foreign key indicating which lot the car is stored at. Inverse Relationship Thread starter zombeast; Start date Feb 23, 2006; Feb 23, 2006 #1 zombeast. Notionally it can be written as A more technical example is current is inversely proportional to the resistance in the circuit provided the voltage is constant. What is the definition of inverse relationship? If one quantity increases by a certain factor, the other quantity decreases by that same factor. Definition: An inverse relationship is identified between two variables, which are interrelated but the change of one causes the opposite change to the other. For example, when pressure is increased, the volume decreases. The radius of a circle and its area are in a direct relationship since if I increase the radius the area increases also and if I decrease the radius the area decreases. Inverse Relation Because a relation is said to be functional, we can steal a property from functions in mathematics, specifically calculating the inverse of a function. For a journey, travel time = distance ÷ speed, which is an inverse relationship with the distance traveled as a constant. Easy to use and portable, study sets in Inverse Relationship are great for studying in the way that works for you, at the time that works for you. Inverse variation means that a variable is inversely varying with respect to another variable. Our second story is about how mastering relationships led to our success as a species. See more. (of a relationship) containing two variables such that an increase in one results in a decrease in the other the volume of a gas is in inverse ratio to its pressure (of an element) operating on a specified member … In other words, the two variables move in opposite directions. Inverse definition is - opposite in order, nature, or effect. Learn more. Statement: For an inverse relationship between two variables, the sign of the correlation coefficient is +. Reverse causation (also called reverse causality) refers either to a direction of cause-and-effect contrary to a common presumption or to a two-way causal relationship in, as it were, a loop. An inverse relationship in economics is a relationship in which an increase in one variable corresponds with a decrease in another variable. Also, when unemployment increases, consumer spending decreases because people have less disposable income. Given: Inverse relationship between two variables. The speed of travel relative to travel time (the faster one travels from point to point B, the less travel time is required to arrive at point B from point A); current and resistance (the higher the resistance, the lower the current); savings and disposable income (the less the disposable income, the more the savings); government spending and unemployment rate (the higher the government spending, the lower the unemployment rate); unemployment rate and inflation (known as the Phillips Curve). Math and Arithmetic. Get ready for your Inverse Relationship tests by reviewing key facts, theories, examples, synonyms and definitions with study sets created by students like you. For example: if the distance travelled by train at constant speed increases then the time taken by it increases too and vice versa. Turning the equation around to be in more normal form 10 – 3 = 7. Example of an inverse relationship in science: When a higher viscosity leads to a decreased flow rate, the relationship between viscosity and flow rate is inverse. Search 2,000+ accounting terms and topics. It the sort of relationship that appears in many disciplines, including mathematics, economics and finance. The inverse square law - Higher. To be in more normal form 10 – 3 = 7 between addition and.. And subtraction things being equal, as price falls, demand rises and vice-versa, f ( x =!, a basic inverse relationship our success as a constant value and vice-versa measurements move in opposite directions simplifying... Mall and the - FOREX.com Tail a relationship in which an increase in one variable with! Inversely related means two measurements move in opposite directions physical quantities may increase or decrease simultaneously negative correlation, are... 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Unemployment increases, another decreases common empirical finding in developing country agriculture x gets bigger, y bigger... | 2021-09-27 17:02:06 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4813309907913208, "perplexity": 745.6659596822726}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780058456.86/warc/CC-MAIN-20210927151238-20210927181238-00509.warc.gz"} |
https://zbmath.org/?q=an:1034.20009 | # zbMATH — the first resource for mathematics
Character degree graphs and normal subgroups. (English) Zbl 1034.20009
If $$Z$$ is a subset of $$\mathbb{N}$$, then the ‘common-divisor graph’ $${\mathcal G}(Z)$$ of $$Z$$ has vertex set $$Z$$, and distinct vertices $$m$$ and $$n$$ are joined if $$\text{GCD}(m,n)>1$$. For $$N\trianglelefteq G$$, set $$\text{Irr}(G| N)=\{\chi\in\text{Irr}(G)\mid N\nleq\ker(\chi)\}$$, $$\text{cd}(G| N)=\{\chi(1)\mid\chi\in\text{Irr}(G| N)\}$$. Next, denote by $$c(\mathcal G)$$ the number of connected components of a graph $$\mathcal G$$. We retain the notation so introduced.
The author studies the relative degree graph $${\mathcal G}(G| N)={\mathcal G}(\text{cd}(G| N))$$ in great detail. Below the main results are formulated. In what follows $$N\leq G'$$ is a $$G$$-invariant subgroup of $$G$$ and $${\mathcal G}={\mathcal G}(G/N)$$, $$c=c(\mathcal G)$$.
(a) If $$N'<N$$, then $$c\leq 2$$. If $$c=2$$ and $${\mathcal X}_1$$ and $${\mathcal X}_2$$ are connected components of our graph, then all members of $${\mathcal X}_1$$ are coprime to $$| N:N'|$$ and $$\pi(m)=\pi(| N:N'|)$$ for all $$m\in{\mathcal X}_2$$.
(b) Let $$N$$ be solvable and $$c=2$$. Then the nilpotent length of $$G$$ is at most $$3$$. Also, $$N''$$ is either nilpotent or $$G''$$ contains a $$G$$-invariant Abelian subgroup of index $$2$$.
(c) Let $$N$$ be an Abelian $$p$$-group and $$P\in\text{Syl}_p(G)$$. If $$c=2$$, then (i) $$P$$ is normal in $$G$$ and $$G/P$$ and $$P/N$$ are Abelian; (ii) $$N$$ is not central in $$P$$, but every minimal normal subgroup of $$G$$ contained in $$G'$$ is central in $$G$$.
(d) If $$N\leq G'$$ is an Abelian minimal normal subgroup of $$G$$, then $$c=1$$.
(e) Let $$N$$ be solvable and $$c=2$$. Then one component of $$\mathcal G$$ is a complete graph and the other component has diameter $$2$$.
(f) If $$N$$ is a $$p$$-group, then no two vertices of $$\mathcal G$$ can have finite distance exceeding $$3$$. – The proof of (f) is very involved.
This important paper contains a number of interesting related results. It develops some ideas of a paper of I. M. Isaacs and G. Knutson [J. Algebra 199, No. 1, 302-326 (1998; Zbl 0889.20005)].
##### MSC:
20C15 Ordinary representations and characters 20D10 Finite solvable groups, theory of formations, Schunck classes, Fitting classes, $$\pi$$-length, ranks 20D60 Arithmetic and combinatorial problems involving abstract finite groups 05C25 Graphs and abstract algebra (groups, rings, fields, etc.)
Full Text:
##### References:
[1] S. Garrison, On groups with a small number of character degrees. Ph.D. Thesis, University of Wisconsin, Madison, 1973. [2] B. Huppert, Endliche Gruppen. I, Die Grundlehren der Mathematischen Wissenschaften, Band 134, Springer-Verlag, Berlin-New York, 1967 (German). · Zbl 0217.07201 [3] I. Martin Isaacs, Character theory of finite groups, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. Pure and Applied Mathematics, No. 69. · Zbl 0337.20005 [4] I. M. Isaacs and Greg Knutson, Irreducible character degrees and normal subgroups, J. Algebra 199 (1998), no. 1, 302 – 326. · Zbl 0889.20005 [5] Mark L. Lewis, Solvable groups whose degree graphs have two connected components, J. Group Theory 4 (2001), no. 3, 255 – 275. · Zbl 0998.20009 [6] Mark L. Lewis, Bounding Fitting heights of character degree graphs, J. Algebra 242 (2001), no. 2, 810 – 818. · Zbl 0989.20007 [7] Olaf Manz, Degree problems. II. \?-separable character degrees, Comm. Algebra 13 (1985), no. 11, 2421 – 2431. · Zbl 0575.20007 [8] Olaf Manz and Thomas R. Wolf, Representations of solvable groups, London Mathematical Society Lecture Note Series, vol. 185, Cambridge University Press, Cambridge, 1993. · Zbl 0928.20008 [9] J. McVey, Bounding graph diameters of solvable groups, J. of Algebra (Submitted). · Zbl 1077.20010 [10] P. P. Pálfy, On the character degree graph of solvable groups. II. Disconnected graphs, Studia Sci. Math. Hungar. 38 (2001), 339 – 355. · Zbl 1012.20005 [11] Thomas Yuster, Orbit sizes under automorphism actions in finite groups, J. Algebra 82 (1983), no. 2, 342 – 352. · Zbl 0518.20020 [12] Jiping Zhang, A note on character degrees of finite solvable groups, Comm. Algebra 28 (2000), no. 9, 4249 – 4258. · Zbl 0980.20005
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching. | 2021-10-22 05:51:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7842702269554138, "perplexity": 351.94855843152766}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323585460.87/warc/CC-MAIN-20211022052742-20211022082742-00664.warc.gz"} |
https://www.curiosities.dev/tags/topology/ | # Topology
Random Link ¯\_(ツ)_/¯ Sep 17, 2018 » Why Mathematicians Can't Find the Hay in a Haystack [Quanta Magazine] 1 min; updated Feb 5, 2022 Why Mathematicians Can’t Find the Hay in a Haystack. Kevin Hartnett. www.quantamagazine.org . Sep 17, 2018. Irrational numbers occupy most of the number line. If you were to pick a number on the number line at random, there is literally a 100% chance that it will be irrational (probabilities with inifinities are spooky). Yet, we almost never encounter irrational numbers for we can’t write them down.... | 2022-07-05 22:02:53 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8333992958068848, "perplexity": 2146.9352854703816}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104628307.87/warc/CC-MAIN-20220705205356-20220705235356-00250.warc.gz"} |
http://www.popflock.com/learn?s=Pentagonal_prism | Pentagonal Prism
Get Pentagonal Prism essential facts below. View Videos or join the Pentagonal Prism discussion. Add Pentagonal Prism to your PopFlock.com topic list for future reference or share this resource on social media.
Pentagonal Prism
Uniform pentagonal prism
Type Prismatic uniform polyhedron
Elements F = 7, E = 15
V = 10 (? = 2)
Faces by sides 5{4}+2{5}
Schläfli symbol t{2,5} or {5}×{}
Wythoff symbol 2 5 | 2
Coxeter diagram
Symmetry group D5h, [5,2], (*522), order 20
Rotation group D5, [5,2]+, (522), order 10
References U76(c)
Dual Pentagonal dipyramid
Properties convex
Vertex figure
4.4.5
3D model of a (uniform) pentagonal prism
In geometry, the pentagonal prism is a prism with a pentagonal base. It is a type of heptahedron with 7 faces, 15 edges, and 10 vertices.
As a semiregular (or uniform) polyhedron
If faces are all regular, the pentagonal prism is a semiregular polyhedron, more generally, a uniform polyhedron, and the third in an infinite set of prisms formed by square sides and two regular polygon caps. It can be seen as a truncated pentagonal hosohedron, represented by Schläfli symbol t{2,5}. Alternately it can be seen as the Cartesian product of a regular pentagon and a line segment, and represented by the product {5}x{}. The dual of a pentagonal prism is a pentagonal bipyramid.
The symmetry group of a right pentagonal prism is D5h of order 20. The rotation group is D5 of order 10.
Volume
The volume, as for all prisms, is the product of the area of the pentagonal base times the height or distance along any edge perpendicular to the base. For a uniform pentagonal prism with edges h the formula is
${\displaystyle {\frac {h^{3}}{4}}{\sqrt {5(5+2{\sqrt {5}})}}}$
Use
Nonuniform pentagonal prisms called pentaprisms are also used in optics to rotate an image through a right angle without changing its chirality.
In 4-polytopes
It exists as cells of four nonprismatic uniform 4-polytopes in 4 dimensions:
cantellated 600-cell cantitruncated 600-cell runcinated 600-cell runcitruncated 600-cell
Related polyhedra
The pentagonal stephanoid has pentagonal dihedral symmetry and has the same vertices as the uniform pentagonal prism. | 2021-01-21 01:13:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 1, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7018557786941528, "perplexity": 3354.3610427012045}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-04/segments/1610703522150.18/warc/CC-MAIN-20210121004224-20210121034224-00358.warc.gz"} |
https://www.usna.edu/Users/cs/roche/courses/s16si486h/probs/062.php | This is the archived website of SI 486H from the Spring 2016 semester. Feel free to browse around; you may also find more recent offerings at my teaching page.
# Randomized dictionary comparison
Due: March 8
Points: 3
Compare the three randomized data structures we have seen for the dictionary ADT: skip lists, randomized BSTs, and treaps. They all have expected cost $$\Theta(\log n)$$ for every operation, search, insert, and delete. But they aren't exactly the same! So I want you to tell me:
• Which do you think will be fastest for search, and why?
• Which do you think will have the fastest insertion, and why?
• Which do you think will have the fastest deletion, and why?
• Which would be the simplest to implement, and why?
• Which would have the smallest memory footprint, and why? | 2018-10-23 05:29:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.31082063913345337, "perplexity": 1867.9928775073822}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-43/segments/1539583516071.83/warc/CC-MAIN-20181023044407-20181023065907-00414.warc.gz"} |
https://www.transtutors.com/questions/and-q-are-biased-by-two-ideal-current-sources-both-transistors-have-the-following-pa-5162807.htm | # and Q, are biased by two ideal current sources. Both transistors have the following parameters: +s v
and Q, are biased by two ideal current sources. Both transistors have the following parameters: +s v +202 1:-". Do not ignore the base currents. β-40 and la ) 18 points 0 kn 2a) Calculate the DC quiescent currents in @, and Qe 0 1- 3 mA 0.5 mA 2b) Assuming that I-g-05 mA, calculate the input resistance (R,- 7?) seen at the based of O 18 points) | 2021-10-28 18:38:34 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8385855555534363, "perplexity": 8362.442078635515}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588398.42/warc/CC-MAIN-20211028162638-20211028192638-00174.warc.gz"} |
http://cms.math.ca/cmb/kw/sectional%20genus | location: Publications → journals
Search results
Search: All articles in the CMB digital archive with keyword sectional genus
Expand all Collapse all Results 1 - 1 of 1
1. CMB 2001 (vol 44 pp. 452)
Ishihara, Hironobu
Some Adjunction Properties of Ample Vector Bundles Let $\ce$ be an ample vector bundle of rank $r$ on a projective variety $X$ with only log-terminal singularities. We consider the nefness of adjoint divisors $K_X + (t-r) \det \ce$ when $t \ge \dim X$ and $t>r$. As an application, we classify pairs $(X,\ce)$ with $c_r$-sectional genus zero. Keywords:ample vector bundle, adjunction, sectional genusCategories:14J60, 14C20, 14F05, 14J40
top of page | contact us | privacy | site map | | 2017-02-23 02:31:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.506197988986969, "perplexity": 2576.0333709998918}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-09/segments/1487501171070.80/warc/CC-MAIN-20170219104611-00284-ip-10-171-10-108.ec2.internal.warc.gz"} |
http://ssconlineexam.com/onlinetest/SSC-CGL-Tier-1/General-Intelligence-and-Reasoning/GIR-Test-60 | # SSC CGL Tier 1 :: General Intelligence and Reasoning GIR Test 60
## Home SSC CGL Tier 1 / General Intelligence and Reasoning GIR Test 60 Questions and Answers
1 .
From the given alternatives select the word which can be formed using the letters of the given word.
$DICTIONARY$
BINARY
DAIRY
NATION
2 .
3 daily wage workers A, B and C are distributed Rs.178 in such a way that A gets Rs.4 less than C, B gets Rs.15 more than A and C gets Rs.11 less than B. What is the ratio of their shares ?
53 : 68 : 57
57 : 53 : 68
50 : 51 : 52
53 : 56 : 68
3 .
If the $5^ {th}$ date of a month is Tuesday, what date will be 3 days after the $3^ {rd}$ Friday in the month?
17
22
19
18
4 .
Seema's younger brother Sohan is older than Seeta. Sweta is younger than Deepti but elder than Seema. Who is the eldest ?
Seeta
Deepti
Seema
Sweta
5 .
Rahim and his uncle differ in their ages by 30 years. After 7 years, if the sum of their ages is 66, what will be the age of the uncle ?
39
41
51
49
6 .
Sohan ranks seventh from the top and twenty-sixth from the bottom in a class. How many students are there in the class ?
33
34
31
32
7 . In questions below, select the missing number from the given responses
17
23
47
73
8 . In questions below, select the missing number from the given responses
1
8
6
16
9 . Select the related word/letters/number from the given alternatives
DHL : EJO :: KOS : ?
LPV
LQV
LQU
LPU
10 . Select the related word/letters/number from the given alternatives
EOSR : ROSE :: NAIP : ?
APIN
PANI
IAPN
PAIN | 2018-03-17 04:39:33 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2787416875362396, "perplexity": 2546.7203349716356}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-13/segments/1521257644271.19/warc/CC-MAIN-20180317035630-20180317055630-00624.warc.gz"} |
http://tex.stackexchange.com/questions/69782/bar-chart-given-minimum-and-maximum-values?answertab=active | # Bar chart given minimum and maximum values
I want to create a bar chart that looks like the one in the picture.
For each x value I have the minimum and maximum value that represent the height that each bar should have. My problem though is: how to create the bars given the maxinum and minimum value since in the manual I only found how to create them given coordinates like in the following code.
\begin{tikzpicture}
\begin{axis}[
x tick label style={
/pgf/number format/1000 sep=},
ylabel=Population,
enlargelimits=0.05,
legend style={at={(0.5,-0.15)},
anchor=north,legend columns=-1},
ybar interval=0.7,
]
coordinates {(1930,50e6) (1940,33e6)
(1950,40e6) (1960,50e6) (1970,70e6)};
coordinates {(1930,38e6) (1940,42e6)
(1950,43e6) (1960,45e6) (1970,65e6)};
coordinates {(1930,15e6) (1940,12e6)
(1950,13e6) (1960,25e6) (1970,35e6)};
\legend{Far,Near,Here}
\end{axis}
\end{tikzpicture}
-
I think for this you can also just make use of TikZ. Here is a possible solution that allows to customize axis (x and y), bars (aspect and width) and to insert labels (on both x and y axis).
Now an example is shown and after it some explanations on commands are provided.
The complete example show the same graphic twice by using different options:
\documentclass[svgnames]{article} % the option is required for xcolor already called by tikz
\usepackage{xstring}
% Retreive an element from a list - Jake's code from
% http://tex.stackexchange.com/a/21560/13304
\newcommand*{\GetListMember}[2]{%
\edef\dotheloop{%
\noexpand\foreach \noexpand\a [count=\noexpand\i] in {#1} {%
\noexpand\IfEq{\noexpand\i}{#2}{\noexpand\a\noexpand\breakforeach}{}%
}}%
\dotheloop
\par%
}%
\usepackage{tikz}
\usetikzlibrary{calc,backgrounds}
\pgfdeclarelayer{gridlayer}
\pgfdeclarelayer{barlayer}
\pgfsetlayers{background,gridlayer,barlayer,main}
% Declarations
\pgfmathtruncatemacro\scaley{1}
\pgfmathtruncatemacro\scalex{1}
\pgfmathtruncatemacro\minycoord{-5}
\pgfmathtruncatemacro\step{1}
\pgfmathtruncatemacro\maxycoord{5}
\pgfmathtruncatemacro\minxcoord{-5}
\pgfmathtruncatemacro\maxxcoord{5}
\pgfmathsetmacro\barwidth{0.3}
\usepackage{xparse}
% Settings
\newcommand{\setyscale}[1]{\pgfmathtruncatemacro\scaley{#1}}
\newcommand{\setxscale}[1]{\pgfmathtruncatemacro\scalex{#1}}
\newcommand{\setminycoord}[1]{\pgfmathtruncatemacro\minycoord{#1/\scaley}}
\newcommand{\setmaxycoord}[1]{\pgfmathtruncatemacro\maxycoord{#1/\scaley}}
\newcommand{\setmaxxcoord}[1]{\pgfmathtruncatemacro\maxxcoord{#1/\scalex}}
\newcommand{\setminxcoord}[1]{\pgfmathtruncatemacro\minxcoord{#1/\scalex}}
\NewDocumentCommand{\setbarwidth}{m}{\pgfmathsetmacro\barwidth{#1}}
% Specific commands
\NewDocumentCommand{\drawbar}{o m m m o}{
\begin{pgfonlayer}{barlayer}
\draw[#1] ($(#2/\scalex,#3/\scaley)+(-\barwidth,0)$)rectangle($(#2/\scalex,#4/\scaley)+(\barwidth,0)$);
\end{pgfonlayer}
\IfNoValueTF{#5}{}{
\node[below, text width=\step cm,font=\footnotesize,align=flush center] at (#2/\scalex,#3/\scaley) {#5};
}
}
\NewDocumentCommand{\drawaxes}{O{stealth} m m}{
\pgfmathtruncatemacro\finaly\pgfmathresult
\ifnum\minycoord=0
\draw[-#1,very thick](0,\minycoord)--(0,\finaly) node[left]{#3};
\else
\pgfmathparse{subtract(\minycoord,\step)}\pgfmathresult
\pgfmathtruncatemacro\startingy\pgfmathresult
\draw[#1-#1,very thick](0,\startingy)--(0,\finaly) node[left]{#3};
\fi
\pgfmathtruncatemacro\finalx\pgfmathresult
\ifnum\minxcoord=0
\draw[-#1,very thick](\minxcoord,0)--(\finalx,0) node[below right]{#2};
\else
\pgfmathparse{subtract(\minxcoord,\step)}\pgfmathresult
\pgfmathtruncatemacro\startingx\pgfmathresult
\draw[#1-#1,very thick](\startingx,0)--(\finalx,0) node[below right]{#2};
\fi
}
\NewDocumentCommand{\setlabelyaxes}{o O{0.1}}{
\pgfmathtruncatemacro\startingy\minycoord
\pgfmathtruncatemacro\secondy\pgfmathresult
\pgfmathtruncatemacro\lasty\maxycoord
\IfNoValueTF{#1}{% true
\foreach \y [evaluate=\y as \scaledy using \y*\scaley] in {\startingy,\secondy,...,\lasty}
\pgfmathtruncatemacro\labely\scaledy
\draw[very thick] (#2,\y)--(-#2,\y) node[left] {\labely};
}{% false
\pgfmathparse{abs(subtract(\startingy,\lasty))}\pgfmathresult
\pgfmathsetmacro\dimyaxes\pgfmathresult
\foreach \axisitems [count=\axisitem] in {#1} {\global\let\totaxisitems\axisitem}
\pgfmathparse{subtract(\totaxisitems,1)}\pgfmathresult
\pgfmathtruncatemacro\numstep\pgfmathresult
\pgfmathparse{divide(\dimyaxes,\numstep)}\pgfmathresult
\pgfmathsetmacro\incrstep\pgfmathresult
\pgfmathsetmacro\seconditemy\pgfmathresult
\foreach \y [count=\yi] in {\startingy,\seconditemy,...,\lasty}
\draw[very thick] (#2,\y)--(-#2,\y) node[left]{\GetListMember{#1}{\yi}};
}
}
\NewDocumentCommand{\setlabelxaxes}{O{0.1}}{
% X-axis
\pgfmathtruncatemacro\startingx\minxcoord
\pgfmathtruncatemacro\secondx\pgfmathresult
\pgfmathtruncatemacro\lastx\maxxcoord
\foreach \x [evaluate=\x as \scaledx using \x*\scalex] in {\startingx,\secondx,...,\lastx}{
\pgfmathtruncatemacro\labelx\scaledx
\pgfmathparse{notequal(\labelx,0)}\pgfmathresult
\ifnum\pgfmathresult=1
\draw[very thick] (\x,#1)--(\x,-#1) node[below] {\labelx};
\fi
}
}
\NewDocumentCommand{\setytickaxes}{O{0.1}}{
% Y-axis
\pgfmathtruncatemacro\startingy\minycoord
\pgfmathtruncatemacro\secondy\pgfmathresult
\pgfmathtruncatemacro\lasty\maxycoord
\foreach \y[evaluate=\y as \scaledy using \y*\scaley] in {\startingy,\secondy,...,\lasty}{
\pgfmathtruncatemacro\labely\scaledy
\pgfmathparse{notequal(\labely,0)}\pgfmathresult
\ifnum\pgfmathresult=1
\draw[very thick] (#1,\y)--(-#1,\y);
\fi
}
}
\NewDocumentCommand{\setxtickaxes}{O{0.1}}{
% X-axis
\pgfmathtruncatemacro\startingx\minxcoord
\pgfmathtruncatemacro\secondx\pgfmathresult
\pgfmathtruncatemacro\lastx\maxxcoord
\foreach \x [evaluate=\x as \scaledx using \x*\scalex] in {\startingx,\secondx,...,\lastx}{
\pgfmathtruncatemacro\labelx\scaledx
\pgfmathparse{notequal(\labelx,0)}\pgfmathresult
\ifnum\pgfmathresult=1
\draw[very thick] (\x,#1)--(\x,-#1);
\fi
}
}
\NewDocumentCommand{\drawgrid}{o}{
\pgfmathtruncatemacro\finalx\pgfmathresult
\IfNoValueTF{#1}{
\begin{pgfonlayer}{gridlayer}
\draw[help lines] (\minxcoord,\minycoord)grid(\finalx,\maxycoord);
\end{pgfonlayer}
}{
\begin{pgfonlayer}{gridlayer}
\draw[help lines,#1] (\minxcoord,\minycoord)grid(\finalx,\maxycoord);
\end{pgfonlayer}
}
}
\begin{document}
\begin{figure}
\centering
\begin{tikzpicture}[scale=0.8,transform shape]
% Customization of elements
\setyscale{200}
\setxscale{200}
\setminycoord{-1000}
\setmaxycoord{1000}
\setminxcoord{0}
\setmaxxcoord{1400}
\setbarwidth{0.4}
% Axes
\drawaxes{$x$}{$y$}
\setlabelyaxes[label one, label two,label three,label four,label five]
% Bars
\drawbar[top color=gray!10, bottom color=gray!70,thick]{200}{-250}{832}[label a]
\drawbar[top color=orange!10, bottom color=orange!70,thick]{400}{-300}{250}[label b]
\drawbar[fill=AliceBlue!40,thick]{600}{-600}{423}[label c]
\drawbar[top color=BlueViolet!5, bottom color=BlueViolet!70,thick]{800}{-450}{1000}
\drawbar[top color=white, bottom color=FireBrick!80,thick]{1000}{-71}{150}[label d]
\drawbar[top color=GreenYellow!10, bottom color=GreenYellow!70,thick]{1200}{-500}{733}[label e]
\drawbar[top color=Aqua!10, bottom color=Aqua!70,thick]{1400}{-361}{124}[label f]
\end{tikzpicture}
\caption{This a very long caption that incidentally could overwrite the y axis, but actually it doesn't}
\end{figure}
\begin{figure}
\centering
\begin{tikzpicture}[scale=0.8,transform shape]
% Customization of elements
\setyscale{200}
\setxscale{100}
\setminycoord{-1000}
\setmaxycoord{1000}
\setminxcoord{0}
\setmaxxcoord{700}
\setbarwidth{0.45}
% Axes
\drawgrid[dashed]
\drawaxes[latex]{my x axis}{my y axis}
\setlabelyaxes
\setxtickaxes
% Bars
\drawbar[top color=gray!10, bottom color=gray!70,thick]{100}{-250}{832}[label a]
\drawbar[top color=orange!10, bottom color=orange!70,thick]{200}{-300}{250}[label b]
\drawbar[fill=AliceBlue!40,thick]{300}{-600}{423}[label c]
\drawbar[top color=BlueViolet!5, bottom color=BlueViolet!70,thick]{400}{-450}{1000}
\drawbar[top color=white, bottom color=FireBrick!80,thick]{500}{-71}{150}[label d]
\drawbar[top color=GreenYellow!10, bottom color=GreenYellow!70,thick]{600}{-500}{733}[label e]
\drawbar[top color=Aqua!10, bottom color=Aqua!70,thick]{700}{-361}{124}[label f]
\end{tikzpicture}
\caption{The caption}
\end{figure}
\end{document}
The commands that start with \set<element> allow to customize the <element>. The grid could be drawn by the command \drawgrid and the optional argument customizes its aspect while \drawaxes displays the axes, but just the style of the arrows could be customized. For drawaxes two parameters are mandatory that are the labels characterizing the axes.
There are now some commands to set axis ticks and labels: they are distinct for x and y axis; to just set ticks one could use \setxtickaxes and \setytickaxes while \setlabelyaxes inserts not only ticks but also axis marks. If one needs to insert its own labels, it is possible to use setlabelyaxis[<list of labels>]: this modality display axis ticks and labels based on the number of elements in the list. The two examples (figures will be inserted right now) show this difference. There's no \setlabelyaxis equivalent for the x axis; the reason behind this is that IMHO is much more simple set x labels while drawing bars. The command for this is \drawbar and it needs as mandatory arguments the x position, the ymin and ymax coordinate to draw the bar. As optional parameters, one can customize the bar aspect and to insert a label. Thus the syntax of this command is:
\drawbar[<customization>]{<x>}{<ymin>}{<ymax>}[<label>]
Here are the figures of the two examples (the problem with the caption is fixed). In the first one y axis labels are inserted manually by means of \setlabelyaxes[label one, label two,label three,label four,label five] and x ticks are not displayed (personally I prefer this way).
Notice also the options [scale=0.8,transform shape] given to the tikzpicture environment to avoid the picture be too much big.
In the second example y axis labels are given automatically, x ticks are displayed as the grid.
-
I really like the version after the second update but it gives me some problems. When I add a caption in the figure (including the tikzpicture) the caption is relatively close to the plot. That also happens with the text above the plot as well, especially on some scale values. Moreover is it possible somehow to put labels on the axis (xlabel,ylabel, not ticks)? Lastly how can we modify the drawbar to allow drawing the xticks as well? – gkaran89 Sep 6 '12 at 8:00
As soon as possible I'll have a look to this ;). – Claudio Fiandrino Sep 6 '12 at 8:26
I've updated my answer! – Claudio Fiandrino Sep 7 '12 at 8:09
I have to say it is amazing! Thanks for the great help! – gkaran89 Sep 7 '12 at 8:31
You can use PGFPlots to do this. Compared to pure TikZ solutions, this has the advantage of taking care of data scaling for large values, making it easy to provide data in a variety of different formats, and allowing for the many convenient features of PGFPlots such as automatic legends, tick marks, color cycle lists, etc.
You'll just need to split up the negative and positive parts of the columns, and add forget plot to the negative part:
\documentclass[border=5mm]{standalone}
\usepackage{pgfplots}
Year FarMin FarMax NearMin NearMax HereMin HereMax
1930 -20 50 -10 30 -15 40
1940 -10 60 -15 60 -20 70
1950 -15 78 -20 20 -32 42
1960 -20 30 -15 40 -20 10
1970 -5 30 -30 40 -15 20
}\datatable
\begin{document}%
\begin{tikzpicture}
\begin{axis}[
x tick label style={
/pgf/number format/1000 sep=},
ylabel=Population,
ybar,
enlarge x limits=0.15,
bar width=0.8em,
after end axis/.append code={
\draw ({rel axis cs:0,0}|-{axis cs:0,0}) -- ({rel axis cs:1,0}|-{axis cs:0,0});
}
]
\addplot +[forget plot] table [y index=3] {\datatable};
\addplot +[forget plot] table [y index=5] {\datatable};
\legend{Far,Near,Here}
\end{axis}
\end{tikzpicture}
\end{document}
-
Here you a more of less automatic version for monochromatic or colored bars:
## The Code
\documentclass[parskip]{scrartcl}
\usepackage[margin=15mm]{geometry}
\usepackage{tikz}
\usetikzlibrary{arrows}
\pgfdeclarelayer{background}
\pgfsetlayers{background,main}
\newcommand{\drawstacks}[3]% low/high value, baroptions, gridoptions
{ \xdef\minvalue{0}
\xdef\maxvalue{0}
\foreach \low/\high [count=\c] in {#1}
{ \fill[#2] (\c-0.8,\low) rectangle (\c-0.2,\high);
\xdef\stacknumber{\c}
\pgfmathsetmacro{\lower}{min(\minvalue,\low)}
\xdef\minvalue{\lower}
\pgfmathsetmacro{\higher}{max(\maxvalue,\high)}
\xdef\maxvalue{\higher}
}
\pgfmathtruncatemacro{\lowbound}{\minvalue}
\pgfmathtruncatemacro{\highbound}{\maxvalue}
\begin{pgfonlayer}{background}
\draw[#3] (0,\lowbound-1) grid (\stacknumber,\highbound+1);
\end{pgfonlayer}
\draw[thick,-latex] (0,0) -- (\c+0.5,0);
\draw[thick,-latex] (0,\lowbound-1) -- (0,\highbound+1.5);
\pgfmathtruncatemacro{\a}{\lowbound-1}
\pgfmathtruncatemacro{\b}{\highbound+1}
\foreach \x in {\a,...,\b}
{ \pgfmathtruncatemacro{\label}{\x}
\draw (0.07,\x) -- (-0.07,\x) node[left] {\label};
}
}
\newcommand{\drawcolorstacks}[2]% low/high/color, gridoptions
{ \xdef\minvalue{0}
\xdef\maxvalue{0}
\foreach \low/\high/\fillcolor [count=\c] in {#1}
{ \fill[\fillcolor,draw=\fillcolor!50!black] (\c-0.8,\low) rectangle (\c-0.2,\high);
\xdef\stacknumber{\c}
\pgfmathsetmacro{\lower}{min(\minvalue,\low)}
\xdef\minvalue{\lower}
\pgfmathsetmacro{\higher}{max(\maxvalue,\high)}
\xdef\maxvalue{\higher}
}
\pgfmathtruncatemacro{\lowbound}{\minvalue}
\pgfmathtruncatemacro{\highbound}{\maxvalue}
\begin{pgfonlayer}{background}
\draw[#2] (0,\lowbound-1) grid (\stacknumber,\highbound+1);
\end{pgfonlayer}
\draw[thick,-latex] (0,0) -- (\c+0.5,0);
\draw[thick,-latex] (0,\lowbound-1) -- (0,\highbound+1.5);
\pgfmathtruncatemacro{\a}{\lowbound-1}
\pgfmathtruncatemacro{\b}{\highbound+1}
\foreach \x in {\a,...,\b}
{ \pgfmathtruncatemacro{\label}{\x}
\draw (0.07,\x) -- (-0.07,\x) node[left] {\label};
}
}
\colorlet{cola}{red!50!gray}
\colorlet{colb}{orange!50!gray}
\colorlet{colc}{yellow!50!gray}
\colorlet{cold}{green!50!gray}
\colorlet{cole}{blue!50!gray}
\colorlet{colf}{violet!50!gray}
\colorlet{colg}{gray}
\begin{document}
\begin{tikzpicture}
\drawstacks{-2.1/4.3,-1.8/7.1,-5.6/3.7,-4.5/3.5,-3.9/2.0,-6.3/1.7,-1.8/2.4}{red!50,draw=red!50!black}{gray}
\end{tikzpicture}
\begin{tikzpicture}
\drawcolorstacks{-2.1/4.3/cola,-1.8/7.1/colb,-5.6/3.7/colc,-4.5/3.5/cold,-3.9/2.0/cole,-6.3/1.7/colf,-1.8/2.4/colg}{gray, thick, densely dotted}
\end{tikzpicture}
\end{document}
## The Result
To draw high values here's a new version: it has a new optional parameter by which all data is divided for plotting, it's defaults is 500 but can be changed:
## The code
\newcommand{\drawhighstacks}[3][500]% low/high/color, gridoptions
{ \xdef\minvalue{0}
\xdef\maxvalue{0}
\foreach \low/\high/\fillcolor [count=\c] in {#2}
{ \fill[\fillcolor,draw=\fillcolor!50!black] (\c-0.8,\low/#1) rectangle (\c-0.2,\high/#1);
\xdef\stacknumber{\c}
\pgfmathsetmacro{\lower}{min(\minvalue,\low)}
\xdef\minvalue{\lower}
\pgfmathsetmacro{\higher}{max(\maxvalue,\high)}
\xdef\maxvalue{\higher}
}
\pgfmathtruncatemacro{\lowbound}{\minvalue/#1}
\pgfmathtruncatemacro{\highbound}{\maxvalue/#1}
\begin{pgfonlayer}{background}
\draw[#3] (0,\lowbound-1) grid (\stacknumber,\highbound+1);
\end{pgfonlayer}
\draw[thick,-latex] (0,0) -- (\c+0.5,0);
\draw[thick,-latex] (0,\lowbound-1) -- (0,\highbound+1.5);
\pgfmathtruncatemacro{\a}{\lowbound-1}
\pgfmathtruncatemacro{\b}{\highbound+1}
\foreach \x in {\a,...,\b}
{ \pgfmathtruncatemacro{\label}{\x*#1}
\draw (0.07,\x) -- (-0.07,\x) node[left] {\label};
}
}
## The result
\begin{tikzpicture}
\drawhighstacks{-1632/927/cola, -412/1250/colb, -777/1965/colc, -1234/1984/cold, -981/1984/cole, -1004/590/colf, -766/1318/colg}{gray, thick, dashed}
\end{tikzpicture}
\begin{tikzpicture}
\drawhighstacks[300]{-1632/927/cola, -412/1250/colb, -777/1965/colc, -1234/1984/cold, -981/1984/cole, -1004/590/colf, -766/1318/colg}{gray, thick, dashed}
\end{tikzpicture}
-
This looks great. But what happens when I have large values? For example -1200/1023/cola? In this occasion I get a Dimension too large error and using a scalebox didn't help me. How can that be solved? – gkaran89 Sep 2 '12 at 18:15 | 2014-10-31 16:02:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8483220338821411, "perplexity": 12983.242679675546}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-42/segments/1414637900029.49/warc/CC-MAIN-20141030025820-00028-ip-10-16-133-185.ec2.internal.warc.gz"} |
https://artofproblemsolving.com/wiki/index.php?title=1996_AHSME_Problems/Problem_26&diff=prev&oldid=41717 | # Difference between revisions of "1996 AHSME Problems/Problem 26"
## Problem
An urn contains marbles of four colors: red, white, blue, and green. When four marbles are drawn without replacement, the following events are equally likely:
(a) the selection of four red marbles;
(b) the selection of one white and three red marbles;
(c) the selection of one white, one blue, and two red marbles; and
(d) the selection of one marble of each color.
What is the smallest number of marbles satisfying the given condition?
$\text{(A)}\ 19\qquad\text{(B)}\ 21\qquad\text{(C)}\ 46\qquad\text{(D)}\ 69\qquad\text{(E)}\ \text{more than 69}$
## See also
1996 AHSME (Problems • Answer Key • Resources) Preceded byProblem 25 Followed byProblem 27 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 All AHSME Problems and Solutions
Invalid username
Login to AoPS | 2020-11-27 08:59:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 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, "math_score": 0.5165821313858032, "perplexity": 5595.330147074482}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-50/segments/1606141191511.46/warc/CC-MAIN-20201127073750-20201127103750-00112.warc.gz"} |
http://www.mathworks.com/help/comm/ref/commscope.eyediagram.html?nocookie=true | # commscope.eyediagram
Eye diagram analysis
## Syntax
`h = commscope.eyediagramh = commscope.eyediagram(property1,value1,...)`
## Description
`h = commscope.eyediagram` constructs an eye diagram object, `h`, with default properties. This syntax is equivalent to:
```H = commscope.eyediagram('SamplingFrequency', 10000, ... 'SamplesPerSymbol', 100, ... 'SymbolsPerTrace', 2, ... 'MinimumAmplitude', -1, ... 'MaximumAmplitude', 1, ... 'AmplitudeResolution', 0.0100, ... 'MeasurementDelay', 0, ... 'PlotType', '2D Color', ... 'PlotTimeOffset', 0, ... 'PlotPDFRange', [0 1], ... 'ColorScale', 'linear', ... 'RefreshPlot', 'on');```
`h = commscope.eyediagram(property1,value1,...)` constructs an eye diagram object, `h`, with properties as specified by property/value pairs.
The eye diagram object creates a series of vertical histograms from zero to T seconds, at Ts second intervals, where T is a multiple of the symbol duration of the input signal and Ts is the sampling time. A vertical histogram is defined as the histogram of the amplitude of the input signal at a given time. The histogram information is used to obtain an approximation to the probability density function (PDF) of the input amplitude distribution. The histogram data is used to generate `'2D Color'` plots, where the color indicates the value of the PDF, and `'3D Color'` plots. The `'2D Line'` plot is obtained by constructing an eye diagram from the last n traces stored in the object, where a trace is defined as the segment of the input signal for a T second interval.
You can change the plot type by setting the `PlotType` property. The following plots are examples of each type.
2D-Color Eye Diagram
3D-Color Eye Diagram
2D-Line Eye Diagram
To see a detailed demonstration of this object's use, type ```showdemo scattereyedemo;``` at the command line.
## Properties
An eye diagram scope object has the properties shown on the following table. All properties are writable except for the ones explicitly noted otherwise.
PropertyDescription
`Type`Type of scope object (`'Eye Diagram'`). This property is not writable.
`SamplingFrequency`Sampling frequency of the input signal in hertz.
`SamplesPerSymbol`Number of samples used to represent a symbol. An increase in `SamplesPerSymbol` improves the resolution of an eye diagram.
`SymbolRate`The symbol rate of the input signal. This property is not writable and is automatically computed based on `SamplingFrequency` and `SamplesPerSymbol`.
`SymbolsPerTrace`The number of symbols spanned on the time axis of the eye diagram scope.
`MinimumAmplitude`Minimum amplitude of the input signal. Signal values less than this value are ignored both for plotting and for measurement computation.
`MaximumAmplitude`Maximum amplitude of the input signal. Signal values greater than this value are ignored both for plotting and for measurement computation.
`AmplitudeResolution`The resolution of the amplitude axis. The amplitude axis is created from `MinimumAmplitude` to `MaximumAmplitude` with `AmplitudeResolution` steps.
`MeasurementDelay`The time in seconds the scope waits before starting to collect data.
`PlotType`Type of the eye diagram plot. The choices are ```'2D Color'``` (two dimensional eye diagram, where color intensity represents the probability density function values), ```'3D Color'``` (three dimensional eye diagram, where the z-axis represents the probability density function values), and ```'2D Line'``` (two dimensional eye diagram, where each trace is represented by a line).
`NumberOfStoredTraces`The number of traces stored to display the eye diagram in ```'2D Line'``` mode.
`PlotTimeOffset`The plot time offset input values must reside in the closed interval [-Tsym Tsym], where Tsym is the symbol duration. Since the eye diagram is periodic, if the value you enter is out of range, it wraps to a position on the eye diagram that is within range.
`RefreshPlot`The switch that controls the plot refresh style. The choices are `'on'` (the eye diagram plot is refreshed every time the update method is called) and `'off'` (the eye diagram plot is not refreshed when the `update` method is called).
`PlotPDFRange`The range of the PDF values that will be displayed in the ```'2D Color'``` mode. The PDF values outside the range are set to a constant mask color.
`ColorScale`The scale used to represent the color, the z-axis, or both. The choices are `'linear'` (linear scale) and `'log'` (base ten logarithmic scale).
`SamplesProcessed`The number of samples processed by the eye diagram object. This value does not include the discarded samples during the `MeasurementDelay` period. This property is not writable.
OperationModeWhen the operation mode is complex signal, the eye diagram collects and plots data on both the in-phase component and the quadrature component. When the operation mode is real signal, the eye diagram collects and plots real signal data.
`Measurements`An eye diagram can display various types of measurements. All measurements are done on both the in-phase and quadrature signal, unless otherwise stated. For more information, see the Measurements section.
The resolution of the eye diagram in `'2D Color'` and ```'3D Color'``` modes can be increased by increasing `SamplingFrequency`, decreasing `AmplitudeResolution`, or both.
Changing `MinimumAmplitude`, `MaximumAmplitude`, `AmplitudeResolution`, `SamplesPerSymbol`, `SymbolsPerTrace`, and `MeasurementDelay` resets the measurements and updates the eye diagram.
## Methods
An eye diagram object is equipped with seven methods for inspection, object management, and visualization.
### update
This method updates the eye diagram object data.
`update(h,x)` updates the collected data of the eye diagram object `h` with the input `x`.
If the `RefreshPlot` property is set to `'on'`, the `update` method also refreshes the eye diagram figure.
The following example shows this method's use:
```% Create an eye diagram scope object h = commscope.eyediagram('RefreshPlot', 'off') % Prepare a noisy sinusoidal as input hChan = comm.AWGNChannel('NoiseMethod', 'Signal to noise ratio (SNR)',... 'SNR', 20); x = step(hChan,0.5*sin(2*pi*(0:1/100:10))+j*cos(2*pi*(0:1/100:10))); % update the eyediagram update(h, x); % Check the number of proccessed samples h.SamplesProcessed```
### plot
This method displays the eye diagram figure.
The `plot` method has three usage cases:
`plot(h)` plots the eye diagram for the eye diagram object `h` with the current colormap or the default linespec.
`plot(h,cmap)`, when used with the `plottype` set to `'2D Color'` or `'3D Color'`, plots the eye diagram for the object `h`, and sets the colormap to `cmap`.
`plot(h,linespec)`, when used with the `plottype` set to `'2D Line'`, plots the eye diagram for the object `h` using `linespec` as the line specification. See the help for plot for valid linespecs.
The following example shows this method's use:
```% Create an eye diagram scope object h = commscope.eyediagram; % Prepare a noisy sinusoid as input hChan = comm.AWGNChannel('NoiseMethod', 'Signal to noise ratio (SNR)',... 'SNR', 20); x = step(hChan, 0.5*sin(2*pi*(0:1/100:10))+ j*0.5*cos(2*pi*(0:1/100:10))); % Update the eye diagram update(h, x); % Display the eye diagram figure plot(h) % Display the eye diagram figure with jet colormap plot(h, jet(64)) % Display 2D Line eye diagram with red dashed lines h.PlotType = '2D Line'; plot(h, 'r--')```
### exportdata
This method exports the eye diagram data.
`[VERHIST EYEL HORHISTX HORHISTRF] = EXPORTDATA(H)` Exports the eye diagram data collected by the eyediagram object H.
`VERHIST` is a matrix that holds the vertical histogram, which is also used to plot '2D Color' and '3D Color' eye diagrams.
`EYEL` is a matrix that holds the data used to plot 2D Line eye diagram. Each row of the EYEC holds one trace of the input signal.
`HORHISTX` is a matrix that holds the crossing point histogram data collected for the values defined by the CrossingAmplitudes property of the MeasurementSetup object. HORHISTX(i, :) represents the histogram for CrossingAmplitudes(i).
`HORHISTRF` is a matrix that holds the crossing point histograms for rise and fall time levels. HORHISTRF(i,:) represents the histogram for AmplitudeThreshold(i).
The following example shows this method's use:
```% Create an eye diagram scope object h = commscope.eyediagram('RefreshPlot', 'off'); % Prepare a noisy sinusoidal as input hChan = comm.AWGNChannel('NoiseMethod', 'Signal to noise ratio (SNR)',... 'SNR', 20); x = step(hChan, 0.5*sin(2*pi*(0:1/100:10))+ j*0.5*cos(2*pi*(0:1/100:10))); % Update the eyediagram update(h, x); % Export the data [eyec eyel horhistx horhistrf] = exportdata(h); % Plot line data t=0:1/h.SamplingFrequency:h.SymbolsPerTrace/h.SymbolRate; plot(t, real(eyel)); xlabel('time (s)');... ylabel('Amplitude (AU)'); grid on; % Plot 2D Color data t=0:1/h.SamplingFrequency:h.SymbolsPerTrace/h.SymbolRate; a=h.MinimumAmplitude:h.AmplitudeResolution:h.MaximumAmplitude; imagesc(t,a,eyec); xlabel('time (s)'); ylabel('Amplitude (AU)'); ```
### reset
This method resets the eye diagram object.
`reset(h)` resets the eye diagram object `h`. Resetting `h` clears all the collected data.
The following example shows this method's use:
```% Create an eye diagram scope object h = commscope.eyediagram('RefreshPlot', 'off'); % Prepare a noisy sinusoidal as input hChan = comm.AWGNChannel('NoiseMethod', 'Signal to noise ratio (SNR)',... 'SNR', 20); x = step(hChan, 0.5*sin(2*pi*(0:1/100:10))+ j*0.5*cos(2*pi*(0:1/100:10))); update(h, x); % update the eyediagram h.SamplesProcessed % Check the number of proccessed samples reset(h); % reset the object h.SamplesProcessed % Check the number of proccessed samples```
### copy
This method copies the eye diagram object.
`h = copy(ref_obj)` creates a new eye diagram object `h` and copies the properties of object `h` from properties of `ref_obj`.
The following example shows this method's use:
```% Create an eye diagram scope object h = commscope.eyediagram('MinimumAmplitude', -3, ... 'MaximumAmplitude', 3); disp(h); % display object properties h1 = copy(h)```
### disp
This method displays properties of the eye diagram object.
`disp(h)` displays relevant properties of eye diagram object `h`.
If a property is not relevant to the object's configuration, it is not displayed. For example, for a `commscope.eyediagram` object, the `ColorScale` property is not relevant when `PlotType` property is set to `'2D Line'`. In this case the `ColorScale` property is not displayed.
The following is an example of its use:
```% Create an eye diagram scope object h = commscope.eyediagram; % Display object properties disp(h); h = commscope.eyediagram('PlotType', '2D Line')```
### close
This method closes the eye diagram object figure.
`close(h)` closes the figure of the eye diagram object `h`.
The following example shows this method's use:
```% Create an eye diagram scope object h = commscope.eyediagram; % Call the plot method to display the scope plot(h); % Wait for 1 seconds pause(1) % Close the scope close(h)```
### analyze
This methods executes eye diagram measurements. analyze(h) executes the eye diagram measurements on the collected data of the eye diagram scope object h. The results of the measurements are stored in the Measurements property of h. See Measurements for more information.
In some cases, the analyze method cannot determine a measurement value. If this problem occurs, verify that your settings for measurement setup values or the eye diagram are valid.
## Measurements
You can obtain the following measurements on an eye diagram:
• Amplitude Measurements
• Eye Amplitude
• Eye Crossing Amplitude
• Eye Crossing Percentage
• Eye Height
• Eye Level
• Eye SNR
• Quality Factor
• Vertical Eye Opening
• Time Measurements
• Deterministic Jitter
• Eye Crossing Time
• Eye Delay
• Eye Fall Time
• Eye Rise Time
• Eye Width
• Horizontal Eye Opening
• Peak-to-Peak Jitter
• Random Jitter
• RMS Jitter
• Total Jitter
Measurements assume that the eye diagram object has valid data. A valid eye diagram has two distinct eye crossing points and two distinct eye levels.
The deterministic jitter, horizontal eye opening, quality factor, random jitter, and vertical eye opening measurements utilize a dual-Driac algorithm. Jitter is the deviation of a signal's timing event from its intended (ideal) occurrence in time [1]. Jitter can be represented with a dual-Driac model. A dual-Driac model assumes that the jitter has two components: deterministic jitter (DJ) and random jitter (RJ). The DJ PDF comprises two delta functions, one at $\mu$L and one at $\mu$R. The RJ PDF is assumed to be Gaussian with zero mean and variance σ.
The Total Jitter (TJ) PDF is the convolution of these two PDFs, which is composed of two Gaussian curves with variance $\sigma$and mean values $\mu$L and $\mu$R. See the following figure.
The dual-Dirac model is described in [5] in more detail. The amplitude of the two Dirac functions may not be the same. In such a case, the analyze method estimates these amplitudes, $\rho$L and $\rho$R.
### Amplitude Measurements
You can use the vertical histogram to obtain a variety of amplitude measurements. For complex signals, measurements are done on both in-phase and the quadrature components, unless otherwise specified.
Note: For amplitude measurements, at least one bin per vertical histogram must reach 10 hits before the measurement is taken, ensuring higher accuracy.
#### Eye Amplitude (EyeAmplitude)
Eye Amplitude, measured in Amplitude Units (AU), is defined as the distance between two neighboring eye levels. For an NRZ signal, there are only two levels: the high level (level 1 in figure) and the low level (level 0 in figure). The eye amplitude is the difference of these two values, as shown in figure [3].
#### Eye Crossing Amplitude (EyeCrossingLevel)
Eye crossing amplitudes are the amplitude levels at which the eye crossings occur, measured in Amplitude Units (AU). The analyze method calculates this value using the mean value of the vertical histogram at the crossing times [3]. See the following figure.
The next figure shows the vertical histogram at the first eye crossing time.
#### Eye Crossing Percentage (EyeOpeningVer)
Eye Crossing Percentage is the location of the eye crossing levels as a percentage of the eye amplitude.
#### Eye Height (EyeHeight)
Eye Height, measured in Amplitude Units (AU), is defined as the 3σ distance between two neighboring eye levels.
For an NRZ signal, there are only two levels: the high level (level 1 in figure) and the low level (level 0 in figure). The eye height is the difference of the two 3σ points, as shown in the next figure. The 3σ point is defined as the point that is three standard deviations away from the mean value of a PDF.
#### Eye Level (EyeLevel)
Eye Level is the amplitude level used to represent data bits, measured in Amplitude Units (AU).
For an ideal NRZ signal, there are two eye levels: +A and –A. The analyze method calculates eye levels by estimating the mean value of the vertical histogram in a window around the EyeDelay, which is also the 50% point between eye crossing times [3]. The width of this window is determined by the EyeLevelBoundary property of the eyemeasurementsetup object, shown in the next figure.
The analyze method calculates the mean value of all the vertical histograms within the eye level boundaries. The mean vertical histogram appears in the following figure. There are two distinct PDFs, one for each eye level. The mean values of the individual histograms are the eye levels as shown in this figure.
#### Eye SNR (EyeSNR)
Eye signal-to-noise ratio is defined as the ratio of the eye amplitude to the sum of the standard deviations of the two eye levels. It can be expressed as:
SNR = $\frac{{L}_{1}-{L}_{0}}{{\sigma }_{1}+{\sigma }_{0}}$
where L1 and L0 represent eye level 1 and 0, respectively, and $\sigma$1 and $\sigma$2 are the standard deviation of eye level 1 and 0, respectively.
For an NRZ signal, eye level 1 corresponds to the high level, and the eye level 0 corresponds to low level.
#### Quality Factor (QualityFactor)
The analyze method calculates Quality Factor the same way as the eye SNR. However, instead of using the mean and standard deviation values of the vertical histogram for L1 and $\sigma$1, the analyze method uses the mean and standard deviation values estimated using the dual-Dirac method. [2] See dual-Dirac section for more detail.
#### Vertical Eye Opening (EyeOpeningVer)
Vertial Eye Opening is defined as the vertical distance between two points on the vertical histogram at EyeDelay that corresponds to the BER value defined by the BERThreshold property of the eyemeasurementsetup object. The analyze method calculates this measurement taking into account the random and deterministic components using a dual-Dirac model [5] (see the Dual Dirac Section). A typical BER value for the eye opening measurements is 10-12, which approximately corresponds to the 7σ point assuming a Gaussian distribution.
### Time Measurements
You can use the horizontal histogram of an eye diagram to obtain a variety of timing measurements.
Note: For time measurements, at least one bin per horizontal histogram must reach 10 hits before the measurement is taken.
#### Deterministic Jitter (JitterDeterministic)
Deterministic Jitter is the deterministic component of the jitter. You calculate it using the tail mean value, which is estimated using the dual-Dirac method as follows [5]:
DJ = $\mu$L$\mu$R
where $\mu$L and $\mu$R are the mean values returned by the dual-Dirac algorithm.
#### Eye Crossing Time (EyeCrossingTime)
Eye crossing times are calculated as the mean of the horizontal histogram for each crossing point, around the reference amplitude level. This value is measured in seconds. The mean value of all the horizontal PDFs is calculated in a region defined by the CrossingBandWith property of the eyemeasurementsetup object.
The region is from -Atotal* BW to +Atotal* BW, where Atotal is the total amplitude range of the eye diagram (i.e., A total = A maxAmin) and BW is the crossing band width, shown in the following figure.
The following figure shows the average PDF in this region. Because this example assumes two symbols per trace, there are two crossing points.
Note: When an eye crossing time measurement falls within the [-0.5/Fs, 0) seconds interval, the time measurement wraps to the end of the eye diagram, i.e., the measurement wraps by 2*Ts seconds (where Ts is the symbol time). For a complex signal case, the analyze method issues a warning if the crossing time measurement of the in-phase branch wraps while that of the quadrature branch does not (or vice versa).To avoid the time-wrapping or a warning, add a half-symbol duration delay to the current value in the MeasurementDelay property of the eye diagram object. This additional delay repositions the eye in the approximate center of the scope.
#### Eye Delay (EyeDelay)
Eye Delay is the distance from the midpoint of the eye to the time origin, measured in seconds. The analyze method calculates this distance using the crossing time. For a symmetric signal, EyeDelay is also the best sampling point.
#### Eye Fall Time (EyeFallTime)
Eye Fall Time is the mean time between the high and low threshold values defined by the AmplitudeThreshold property of the eyemeasurementsetup object. The previous figure shows the fall time calculated from 10% to 90% of the eye amplitude.
#### Eye Rise Time (EyeRiseTime)
Eye Rise Time is the mean time between the low and high threshold values defined by the AmplitudeThreshold property of the eyemeasurementsetup object. The following figure shows the rise time calculated from 10% to 90% of the eye amplitude.
#### Eye Width (EyeWidth)
Eye Width is the horizontal distance between two points that are three standard deviations (3σ ) from the mean eye crossing times, towards the center of the eye. The value for Eye Width measurements is seconds.
#### Horizontal Eye Opening (EyeOpeningHor)
Horizontal Eye Opening is the horizontal distance between two points on the horizontal histogram that correspond to the BER value defined by the BERThreshold property of the eyemeasurementsetup object. The measurement is take at the amplitude value defined by the ReferenceAmplitude property of the eyemeasurementsetup object. It is calculated taking into account the random and deterministic components using a dual-Dirac model [5] (see the Dual Dirac Section).
A typical BER value for the eye opening measurements is 10-12, which approximately corresponds to the 7$\sigma$ point assuming a Gaussian distribution.
#### Peak-to-Peak Jitter (JitterP2P)
Peak-To-Peak Jitter is the difference between the extreme data points of the histogram.
#### Random Jitter (JitterRandom)
Random Jitter is defined as the Gaussian unbounded component of the jitter. The analyze method calculates it using the tail standard deviation estimated using the dual-Dirac method as follows [5]:
RJ = (QL + QR) * $\sigma$
where
${Q}_{L}=\sqrt{2}*erf{c}^{-1}\left(\frac{2*BER}{{\rho }_{L}}\right)$
and
${Q}_{R}=\sqrt{2}*erf{c}^{-1}\left(\frac{2*BER}{{\rho }_{R}}\right)$
BER is the bit error ratio at which the random jitter is calculated. It is defined with the BERThreshold property of the eyemeasuremensetup object.
#### RMS Jitter (JitterRMS)
RMS Jitter is the standard deviation of the jitter calculated from the horizontal histogram.
#### Total Jitter (JitterTotal)
Total Jitter is the sum of the random jitter and the deterministic jitter [5].
## Measurement Setup Parameters
A number of set-up parameters control eye diagram measurements. This section describes these set-up parameters and the measurements they affect.
### Eye Level Boundaries
Eye Level Boundaries are defined as a percentage of the symbol duration. The analyze method calculates the eye levels by averaging the vertical histogram within a given time interval defined by the eye level boundaries. A common value you can use for NRZ signals is 40% to 60%. For RZ signals, a narrower band of 5% is more appropriate. The default setting for Eye level Boundaries is a 2-by-1 vector where the first element is the lower boundary and the second element is the upper boundary. When the eye level boundary changes, the object recalculates this value.
### Reference Amplitude
Reference Amplitude is the boundary value at which point the signal crosses from one signal level to another. Reference amplitude represents the decision boundary of the modulation scheme. This value is used to perform jitter measurements. The default setting for Reference Amplitude is a 2-by-1 double vector where the first element is the lower boundary and the second element is the upper boundary. Setting the reference amplitude resets the eye diagram.
The crossing instants of the input signal are detected and recorded as crossing times. A common value you can use for NRZ signals is `0`. For RZ signals, you can use the mean value of `1` and `0` levels. Reference amplitude is stored in a 2-by-N matrix, where the first row is the in-phase values and second row is the quadrature values. See Eye Crossing Time for more information.
### Crossing Bandwidth
Crossing Bandwidth is the amplitude band used to measure the crossing times of the eye diagram. Crossing Bandwidth represents a percentage of the amplitude span of the eye diagram, typically 5%. See Eye Crossing Time for more information. The default setting for Crossing Bandwidth is 0.0500.
### Bit Error Rate Threshold
The eye opening measurements, random, and total jitter measurements are performed at a given BER value. This BER value defines the BER threshold. A typical value is 1e-12. The default setting for Bit Error Threshold is 1.0000e-12. When the bit error rate threshold changes, the object recalculates this value.
### Amplitude Threshold
The rise time of the signal is defined as the time required for the signal to travel from the lower amplitude threshold to the upper amplitude threshold. The fall time, measured from the upper amplitude threshold to the lower amplitude threshold, is defined as a percentage of the eye amplitude. The default setting is 10% for the lower threshold and 90% for the upper threshold. Setting the amplitude threshold resets the eye diagram. See Eye Rise Time and Eye Fall Time for more information.
### Jitter Hysteresis
You can use the JitterHysteresis property of the `eyemeasurementsetup` object to remove the effect of noise from the horizontal histogram estimation. The default value for Jitter Hysteresis is zero. Setting the jitter hysteresis value resets the eye diagram.
If channel noise impairs the signal being tested, as shown in the following figure, the signal may seem like it crosses the reference amplitude level multiple times during a single 0-1 or 1-0 transition.
See the zoomed—in image for more detail.
To eliminate the effect of noise, define a hysteresis region between two threshold values: Aref + ΔA and Aref - ΔA, where Aref is the reference amplitude value and ΔA is the jitter hysteresis value. If the signal crosses both threshold values, level crossing is declared. Then, linear interpolation calculates the crossing point in the horizontal histogram estimation.
## Examples
```% Construct an eye diagram object for signals in the range % of [-3 3] h = commscope.eyediagram('MinimumAmplitude', -3, ... 'MaximumAmplitude', 3) % Construct an eye diagram object for a signal with % 1e-3 seconds of transient time h = commscope.eyediagram('MeasurementDelay', 1e-3) % Construct an eye diagram object for '2D Line' plot type % with 100 traces to display h = commscope.eyediagram('PlotType', '2D Line', ... 'NumberOfStoredTraces', 100)```
## References
[1] Nelson Ou, et al, Models for the Design and Test of Gbps-Speed Serial Interconnects,IEEE Design & Test of Computers, pp. 302-313, July-August 2004.
[2] HP E4543A Q Factor and Eye Contours Application Software, Operating Manual, http://agilent.com
[3] Agilent 71501D Eye-Diagram Analysis, User's Guide, http://www.agilent.com
[4] 4] Guy Foster, Measurement Brief: Examining Sampling Scope Jitter Histograms, White Paper, SyntheSys Research, Inc., July 2005.
[5] Jitter Analysis: The dual-Dirac Model, RJ/DJ, and Q-Scale, White Paper, Agilent Technologies, December 2004, http://www.agilent.com | 2015-05-05 00:19:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 19, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.718366265296936, "perplexity": 1847.344228955994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-18/segments/1430455162832.10/warc/CC-MAIN-20150501043922-00025-ip-10-235-10-82.ec2.internal.warc.gz"} |
https://replab.github.io/web/ | # Welcome to RepLAB!¶
Current version: 1.0.1 (GitHub / latest release ZIP / installation instructions).
RepLAB provides tools to study representations of finite groups and decompose them numerically. It is compatible with both MATLAB and Octave.
## Key features¶
Provable decompositions
Modular construction
Optimization toolbox integration
Interactive documentation
Open source
RepLAB’s numerical decomposition into irreps can be certified
Construct new groups and representations by simple combination
Solves convex optimization problems with symmetries efficiently
Extensive documentation accessible by a click
Full open source software compatible with the GNU/Octave interpreter
## How to start using RepLAB?¶
Have a look at the tutorials! They have everything to get you started, from installation instructions to hands-on examples.
The documentation of RepLAB is organized along 4 directions, following this approach:
• Tutorials: are short hands-on presentations that give you a taste of the goodness of RepLAB
• How-to guides: are concise recipes showing how to achieve a specific goal
• Topic guides: are understanding-oriented presentations explaining the big picture and key notions on which this software is built
• Technical reference: contains a complete and accurate description of each object of the library
## Work in progress¶
RepLAB is a work-in-progress. In particular:
• We are still working on the estimation/control of numerical errors (a few criteria are currently hard-coded). That said, RepLAB works fine for representations of medium size ($$d$$ equal to a few thousands).
• While RepLAB implements several computational group theory algorithms, their performance is not competitive with dedicated computational group theory software such as GAP or Magma.
• The documentation is still a work in progress, and tutorials/how to guides/… will be added as the project progresses.
## Why RepLAB?¶
Because no open source library decomposes arbitrary permutation/monomial representations into irreducible representations over the reals. RepLAB implements numerical methods that perform this decomposition up to machine precision.
That said, other libraries working on the same problem space include:
• RepLAB follows a category-based approach. This enables preserving the structure of objects under operations, naturally allowing composition of finite and continuous groups/representations together for instance.
• RepLAB integrates with the convex optimization framework YALMIP. This allows to formulate optimizations subject to symmetries easily.
## Contributors¶
RepLAB and the group theory/linear algebra libraries it depends on were initiated by Denis Rosset and Jean-Daniel Bancal. The project now has more contributors.
RepLAB references in the /external directory the following libraries: the MOxUnit test framework by Nikolaas N. Oosterhof, the YALMIP toolbox for optimization modeling by Johan Löfberg, the SDPT3 solver, and the VPI big integer library by John D’Errico.
Feedback and suggestions are always welcome. We ask participants to follow the guidelines of the Typelevel Code of Conduct. | 2023-04-02 10:59:15 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.2886154353618622, "perplexity": 4858.590954351766}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2023-14/segments/1679296950528.96/warc/CC-MAIN-20230402105054-20230402135054-00263.warc.gz"} |
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x identical machines can make x widgets in x minutes. If each machine
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x identical machines can make x widgets in x minutes. If each machine works at the same constant rate, how many widgets can y identical machines make in y minutes, in terms of x and y?
A. x
B. y
C. y^2
D. x/y
E. y^2/x
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x identical machines can make x widgets in x minutes. If each machine [#permalink]
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24 Apr 2017, 10:31
1
x machine-------x minutes---------x widgets
x machine-------1 minutes---------x /x widgets(=1 widget)
1 machine-------1 minutes---------1/x widgets (rate of x machine)
similarly
let Y machine in y minutes make A widget. then
y machine-------y minutes---------A widgets
y machine-------1 minutes---------A/y widgets
1 machine-------1 minutes---------A/y^2 widgets (rate of y machine)
As rates are equal
A/y^2 = 1/x
A =y^2/x
Ans E
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x identical machines can make x widgets in x minutes. If each machine [#permalink]
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24 Apr 2017, 10:57
1
Number of Widgets is directly proportional to Number of machines and Time taken.
So we can write it as $$W ∝T*N$$ ==> $$W=K*T*N$$
Where
W= Number of Widgets
T= Time Taken
N= Number of Machine
From the given Problem
$$x=K*x*x$$
On Solving above equation $$K=\frac{1}{x}$$
$$Wy= K*y*y$$
on substituting $$K=\frac{1}{x}$$ ==> $$Wy=\frac{y^2}{x}$$
Kudos +1
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Re: x identical machines can make x widgets in x minutes. If each machine [#permalink]
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27 Apr 2017, 16:11
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1
Bunuel wrote:
x identical machines can make x widgets in x minutes. If each machine works at the same constant rate, how many widgets can y identical machines make in y minutes, in terms of x and y?
A. x
B. y
C. y^2
D. x/y
E. y^2/x
We are given that x identical machines can make x widgets in x minutes. Thus, the rate for the x machines is x/x or 1 widget per minute. Next we can determine the rate of y machines using the following proportion in which n is the rate for y machines:
x/1 = y/n
n = y/x
Since the rate for y machines is y/x and work = rate x time, y machines can produce (y/x)(y) = y^2/x widgets in y minutes.
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Re: x identical machines can make x widgets in x minutes. If each machine [#permalink]
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02 May 2017, 14:29
1
x identical machines.......working x minutes......can make= x widgets
1 identical machines.......working 1 minutes......can make[less] = x/(x+x) widgets
y identical machines.......working y minutes......can make[more] = (x/(x+x))*(y*y) widgets
= y^2 /x widgets
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x identical machines can make x widgets in x minutes. If each machine [#permalink]
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03 Aug 2018, 10:54
Lets say that R is the rate and W the number of widgets
$$X * R = \frac{X}{X}$$
$$R = \frac{1}{X}$$
(Replacing R)
$$Y * R = \frac{W}{Y}$$
$$Y * \frac{1}{X} = \frac{W}{Y}$$
$$\frac{Y}{X} = \frac{W}{Y}$$
$$W = \frac{Y²}{X}$$
Option E
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x identical machines can make x widgets in x minutes. If each machine [#permalink]
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03 Aug 2018, 16:21
Bunuel wrote:
x identical machines can make x widgets in x minutes. If each machine works at the same constant rate, how many widgets can y identical machines make in y minutes, in terms of x and y?
A. x
B. y
C. y^2
D. x/y
E. y^2/x
Find the individual machine rate from scenario #1 (defined by $$x$$), then use that rate to find the number of widgets in scenario #2.
Scenario 1: x identical machines make x widgets in x minutes
(# of workers) * R * T = W
Plug in variables*
$$x*R*x=x$$
$$Rate=\frac{x}{x^2}$$
At that rate . . .
Scenario 2: y identical machines in y minutes can make how many widgets? (= Work)
(# of workers) * R * T = W
$$y*\frac{x}{x^2}*y=W$$
$$W=\frac{y*x*y}{x2}$$
$$W=\frac{y^2}{x}$$
*In other words, manipulate the equation exactly as RT=W is manipulated with one more variable (# of machines) on LHS. Scenario #1:
$$R=\frac{W}{(No.Of.Machines*T)}$$
Scenario #2:
$$Work=(No.Of.Machines*R*T)$$
x identical machines can make x widgets in x minutes. If each machine &nbs [#permalink] 03 Aug 2018, 16:21
Display posts from previous: Sort by | 2018-12-09 19:40:09 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5713987350463867, "perplexity": 12698.945827889887}, "config": {"markdown_headings": false, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-51/segments/1544376823009.19/warc/CC-MAIN-20181209185547-20181209211547-00033.warc.gz"} |
http://mathhelpforum.com/differential-geometry/86897-metric-spaces-print.html | # metric spaces
• May 2nd 2009, 05:39 AM
jin_nzzang
metric spaces
Let (X,d) and (Y,p) be metric spaces, and assume Y is complete. Let f: X→Y and x∈X.
Show that f has a limit at x if and only if given any ε>0 there exists δ>0 such that whenever y, z ∈B_δ(x)＼｛x｝,p(f(y),f(z)) < ε.
• May 3rd 2009, 01:33 AM
Opalg
Quote:
Originally Posted by jin_nzzang
Let (X,d) and (Y,p) be metric spaces, and assume Y is complete. Let f: X→Y and x∈X.
Show that f has a limit at x if and only if given any ε>0 there exists δ>0 such that whenever y, z ∈B_δ(x)＼｛x｝,p(f(y),f(z)) < ε.
Let $(x_n)$ be a sequence in X that converges to x. Then $(x_n)$ is a Cauchy sequence in X. Use the given ε-δ condition to conclude that $(f(x_n))$ is a Cauchy sequence in Y. The completeness of Y tells you that $(f(x_n))$ converges to some element w in Y.
It remains to show that for every sequence that converges to X, its image under f converges to the same limit in Y. So suppose that $x_n\to x$ with $f(x_n)\to w$, as above, and also that $y_n\to x$ with $f(y_n)\to v$. Then $d(x_n,y_n)\to0$, and therefore $p(f(x_n),f(y_n))\to0$, from which it follows that $p(w,v)=0$ and hence v=w.
Thus for every sequence that converges to x, its image under f converges to w. Therefore $\textstyle\lim_{y\to x}f(y)$ exists and is equal to w. | 2017-01-18 06:32:38 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 12, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9956715703010559, "perplexity": 354.2901247390206}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 5, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-04/segments/1484560280239.54/warc/CC-MAIN-20170116095120-00456-ip-10-171-10-70.ec2.internal.warc.gz"} |
https://lqp2.org/node/811 | # On the net of von Neumann algebras associated with a wedge and wedge-causal manifolds
Hans-Jürgen Borchers
December 12, 2009
A wedge in a flat or curved ordered space can be defined with help of two light-rays passing through a point and the double-cones spanned between these light-rays. Only special manifolds have the property that the space-like complement of a wedge is again a wedge as in the flat situation. Such manifolds will be called wedge-causal. Starting from a wedge and its associated von Neumann algebra then its properties will be investigated in the flat and the wedge-causal situation. It will be shown, that in the flat situation, all local algebras are of von Neumann type III, and that they are all of the same Connes-von Neumann-type III$_1$ . Here the types can be determined, because the modular group of the wedge-algebra acts local. For the situation of the Minkowski space we will show how to construct from the wedge-algebra the algebra of the double cones. In addition we will show how to construct from a double-cone algebra the algebra of larger double cones and of the wedge. For this we will use either the translations or the modular group of the wedge-algebra and the double cone theorem. All these investigations are dimension independent. Moreover, we will develop new methods determining the von Neumann and the Connes types for the wedge- and double-cone algebras.
article file
Keywords:
modular theory, QFT on curved spacetimes, wedges, geometric modular action | 2019-11-13 20:30:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5378393530845642, "perplexity": 614.4866100130406}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-47/segments/1573496667333.2/warc/CC-MAIN-20191113191653-20191113215653-00317.warc.gz"} |
https://www.gradesaver.com/textbooks/math/other-math/thinking-mathematically-6th-edition/chapter-11-counting-methods-and-probability-theory-11-3-combinations-exercise-set-11-3-page-707/18 | ## Thinking Mathematically (6th Edition)
The number of possible combinations if r items are taken from n items is nCr = $\frac{n!}{r!(n-r)!}$ 6C0 = $\frac{6!}{0!(6 -0)!}$ =$\frac{6!}{0!6!}$ 0!=1, so the expression reduces to 1. | 2020-06-03 09:31:22 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19937995076179504, "perplexity": 1229.1762291413636}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-24/segments/1590347432521.57/warc/CC-MAIN-20200603081823-20200603111823-00358.warc.gz"} |
https://tex.stackexchange.com/questions/493343/add-dotted-lines-in-toc-without-changing-spacing | # Add dotted lines in TOC without changing spacing
I would like to add dotted lines to the chapters in my TOC. Currently my PDF and code look like this:
\documentclass[12pt,a4paper,twoside]{report} %openright
%Schriftart Arial - ACHTUNG: Compile with XeLaTeX (not PDFLaTeX)!
\usepackage{fontspec}
\defaultfontfeatures{Scale = MatchLowercase}
\setmainfont{Arial}[Scale = 1.0]
%Seitenlayout
\usepackage[top=2.5cm, bottom=2cm, left=2.5cm, right=2.5cm,paper=a4paper]{geometry}
%Zeilenabstand ändern
\usepackage[onehalfspacing]{setspace}
%Graphiken und Bilder
\usepackage{subfig}
%Kopfzeile
\usepackage{fancyhdr}
%Verzeichnisse
\usepackage[notindex, nottoc, numbib]{tocbibind}
%\usepackage[subfigure]{tocloft}
%\renewcommand\cftchapdotsep{\cftdotsep}
%Längenangaben für den Abstand zwischen zwei Absätzen.
\usepackage{parskip}
%Kapitelanzeige und -platzierung im Text
\usepackage[clearempty]{titlesec}
\titleformat{\chapter}{\normalfont\fontsize{16pt}{0}\bfseries}{\thechapter.}{9pt}{}
\titleformat{\section}{\normalfont\fontsize{14pt}{0}\bfseries}{\thesection}{9pt}{}
\titleformat{\subsection}{\normalfont\fontsize{12pt}{0}\bfseries}{\thesubsection}{9pt}{}
\titlespacing*{\chapter}{0pt}{-22pt}{7pt}
% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
% Formatierung der Kopfzeile
% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
\pagestyle{fancy}
\fancyhf{}
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\fancypagestyle{plain}{
\fancyhf{}
}
% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
% Anfang von Dokumententext
% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
\begin{document}
\pagenumbering{Roman}
% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
% Verzeichnisse
% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
\tableofcontents
\chapter{Chapter 1}
\section{test section}
\subsection{test section}
\section{test section}
\subsection{test section}
\end{document}
But when I use (comment in):
\usepackage[subfigure]{tocloft}
\renewcommand\cftchapdotsep{\cftdotsep}
then the following code line doesn't work any more and it looks like this:
\titlespacing*{\chapter}{0pt}{-22pt}{7pt}
Does anyone know how to fix this issue? I appreciate every help. Thanks in advance!
Edit 1: Thanks to daleif I have come so far to this:
\usepackage{titletoc}
\contentsmargin{2em}
\dottedcontents{section}[3.9em]{}{2.3em}{9.5pt}
\dottedcontents{subsection}[84pt]{}{3.2em}{9.5pt}
\dottedcontents{chapter}[20pt]{\bfseries}{20pt}{9.5pt}
Please don't mind the nonsense titles, this is just for comparing the spacing. As you can see, the spacing between the lines are still not correct as everything is quite close together... Does anyone know how to adjust that?
Edit 2:
I have now added vertical space between the entries of the chapters, sections and subsections:
\usepackage{titletoc}
\contentsmargin{2em}
But now the space between "Contents" and "1 Chapter 1" is too big. Does anyone know how to adjust just this particular spacing (by now adjusting the vertical space in \dottedcontents{chapter}[21pt]{\addvspace{15pt}\bfseries}{20pt}{9.5pt}, since this is the spacing within the TOC itself)? By this I mean how can I position "1 Chapter 1" and everything following a bit further up? With the positioning of "Contents" I am happy so far.
Edit 3: I have not found a solution for the spacing, but discovered that in my template there is the same specific spacing (seems to be normal, no matter whether you do it in LATEX or Word), so I will not search any further. Thanks everyone for helping! :-)
• tocloft and titlesec are not compatible. If you want to use titlesec then titletoc might be the package you should use. May 30, 2019 at 12:15
• @daleif I see! Can you help me out how to implement it? Is \dottedcontents the command I should use? So far I only get error messages. May 30, 2019 at 12:40
• Not really, I don't use titlesec. I'd perhaps starting from scratch May 30, 2019 at 12:53
• @daleif Thanks so far :-) I am making progress and will update this Question. May 30, 2019 at 13:30
Here is a solution with titletoc:
\documentclass[12pt,a4paper,twoside]{report} %openright
%Schriftart Arial - ACHTUNG: Compile with XeLaTeX (not PDFLaTeX)!
\usepackage{fontspec}
\defaultfontfeatures{Scale = MatchLowercase}
\setmainfont{Arial}[Scale = 1.0]
%Seitenlayout
\usepackage[top=2.5cm, bottom=2cm, left=2.5cm, right=2.5cm,paper=a4paper]{geometry}
%Zeilenabstand ändern
\usepackage[onehalfspacing]{setspace}
%Graphiken und Bilder
\usepackage{subfig}
%Kopfzeile
\usepackage{fancyhdr}
%Verzeichnisse
\usepackage[notindex, nottoc, numbib]{tocbibind}
%Längenangaben für den Abstand zwischen zwei Absätzen.
\usepackage{parskip}
%Kapitelanzeige und -platzierung im Text
\usepackage[clearempty]{titlesec}
\titleformat{\chapter}{\normalfont\fontsize{16pt}{0}\bfseries}{\thechapter.}{9pt}{}
\titleformat{\section}{\normalfont\fontsize{14pt}{0}\bfseries}{\thesection}{9pt}{}
\titleformat{\subsection}{\normalfont\fontsize{12pt}{0}\bfseries}{\thesubsection}{9pt}{}
\titlespacing*{\chapter}{0pt}{-22pt}{7pt}
\usepackage{titletoc}
\dottedcontents{chapter}[1.5em]{}{1.5em}{0.78pc}
% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
% Formatierung der Kopfzeile
% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
\pagestyle{fancy}
\fancyhf{}
\renewcommand{\chaptermark}[1]{\markboth{#1}{}}
\fancypagestyle{plain}{
\fancyhf{}
}
% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
% Anfang von Dokumententext
% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
\begin{document}
\pagenumbering{Roman}
% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
% Verzeichnisse
% = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = = =
\tableofcontents
\chapter{Chapter 1}
\section{test section}
\subsection{test section}
\section{test section}
\subsection{test section}
\end{document}
• Thank you very much! I have come so far to "Edit 2" in my original posted Question. Do you have any idea how to adjust the spacing between "Content" and "1 Chapter 1"? May 30, 2019 at 14:29
• You might change the spacing parameters for numberless chapters, with \titlespacing{name=\chapter, numberless}{ ... }. May 30, 2019 at 14:32
• Can I adjust the position of "1 Chapter 1" with this, too? Or is this just for the adjustment of "Contents"? Because I am happy with the positioning of "Contents", just the whole part below ("1 Chapter 1", etc.) should go a bit further up. Sorry for the confusion, I edited my original post to clarify what I mean. May 30, 2019 at 14:51
• To adjust the position of "1 Chapter 1", you can play with the last parameter of \titlespacing, which defines the spacing below Contents. Or you can add vertical spacing in the empty argument of \dottedcontents, which is for abovecode, but it well be applied to every subsequent chapter in the table of contents. Just testand see what's fine for you. May 30, 2019 at 14:57
• Ah I see, thanks a lot! I will try this :-) May 30, 2019 at 14:58
Finally I used this code:
\usepackage{titletoc}
\contentsmargin{2em} | 2022-06-27 00:34:00 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4842240810394287, "perplexity": 192.3331133653842}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656103322581.16/warc/CC-MAIN-20220626222503-20220627012503-00145.warc.gz"} |
http://mathoverflow.net/questions/125408/maximal-zero-sums-partition | # Maximal Zero Sums Partition
You are given $n$ numbers between $-n$ and $n$, the sum of numbers is $0$. Divide the given sequence on disjoint subsequences in such a way that each subsequence has zero sum. Each element should belong to exactly one subsequence. Maximize the number of subsequences. It is not required that elements in subsequences are consecutive.
It seems the problem is NP-hard (or "Can the sequence be partitioned into $k$ subsequences which all have zero sums?" is NP-complete), but can't prove it.
Example: the maximal number of subsequences for the sequence [2, 0, 1, -1, -1, -1] is 3: [0], [2, -1, -1] and [1, -1].
-
this is phrased like HW (imperative tone); might get closed soon. – Suvrit Mar 23 '13 at 22:51
It is not a HW or similar. Maybe my wording is not good. – silentbob Mar 23 '13 at 23:09
Answered on math.stackexchange.com/questions/339148/… How to hide the question? – silentbob Mar 24 '13 at 8:15 | 2015-08-29 09:26:07 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8718788027763367, "perplexity": 1179.400477304822}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2015-35/segments/1440644064420.15/warc/CC-MAIN-20150827025424-00076-ip-10-171-96-226.ec2.internal.warc.gz"} |
https://socratic.org/questions/the-k-a-of-a-monoprotic-weak-acid-is-4-67-x-10-3-what-is-the-percent-ionization- | # The K_a of a monoprotic weak acid is 4.67 x 10^-3. What is the percent ionization of a 0.171 M solution of this acid?
May 9, 2017
$\text{% dissociation = 15%}$
#### Explanation:
We address the equilibrium,
$H A \left(a q\right) + {H}_{2} O \left(l\right) r i g h t \le f t h a r p \infty n s {H}_{3} {O}^{+} + {A}^{-}$
And ${K}_{a} = \frac{\left[{H}_{3} {O}^{+}\right] \left[{A}^{-}\right]}{\left[H A\right]} = 4.67 \times {10}^{-} 3$
Now if $x \cdot m o l \cdot {L}^{-} 1$ $H A$ dissociates then..........
$4.67 \times {10}^{-} 3 = {x}^{2} / \left(0.171 - x\right)$
And this is quadratic in $x$, but instead of using the tedious quadratic equation, we assume that $0.171 \text{>>} x$, and so.......
$4.67 \times {10}^{-} 3 \cong {x}^{2} / \left(0.171\right)$
And thus ${x}_{1} = \sqrt{4.67 \times {10}^{-} 3 \times 0.171} = 0.0283 \cdot m o l \cdot {L}^{-} 1$, and now we have an approx. for $x$, we can recycle this back into the expression:
${x}_{2} = 0.0258 \cdot m o l \cdot {L}^{-} 1$
${x}_{3} = 0.0260 \cdot m o l \cdot {L}^{-} 1$
${x}_{4} = 0.0260 \cdot m o l \cdot {L}^{-} 1$
Since the values have converged, I am willing to accept this answer. (This same answer would have resulted from the quadratic equation, had we bothered to do it.)
And thus percentage dissociation................
="Concentration of hydronium ion"/"Initial concentration of acid"xx100%=(0.0260*mol*L^-1)/(0.171*mol*L^-1)xx100%=15% | 2019-09-22 10:46:40 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 15, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9828563332557678, "perplexity": 1629.989612052494}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514575484.57/warc/CC-MAIN-20190922094320-20190922120320-00175.warc.gz"} |
https://www.jiskha.com/questions/1695056/in-the-exercise-we-want-to-use-a-substitution-to-integrate-integral-xsqrt-x-1-dx-find-the | # Math
In the exercise we want to use a substitution to integrate integral xsqrt(x+1)dx.
Find the substitution u to transform the integral into integral(u-1)u^(1/2)du. u=?
1. 👍
2. 👎
3. 👁
4. ℹ️
5. 🚩
1. If you take u = x + 1
Then, x + 1 = u => sqrt(x+1) = sqrt(u) = u^(1/2)
Then, x = (u - 1)
And, du/dx = 1 => du = dx
So,
x*sqrt(x+1)*dx
Becomes
(u-1)*sqrt(u)*du = (u-1)u^(1/2)du
With the substitution u = x + 1
1. 👍
2. 👎
3. ℹ️
4. 🚩
## Similar Questions
Still need help? You can ask a new question. | 2022-07-05 10:09:27 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9215419888496399, "perplexity": 5241.513203815429}, "config": {"markdown_headings": true, "markdown_code": false, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-27/segments/1656104542759.82/warc/CC-MAIN-20220705083545-20220705113545-00732.warc.gz"} |
https://studydaddy.com/question/how-do-i-use-demoivre-s-theorem-to-solve-z-3-1-0 | Waiting for answer This question has not been answered yet. You can hire a professional tutor to get the answer.
QUESTION
# How do I use DeMoivre's theorem to solve z^3-1=0?
If z^3-1=0, then we are looking for the cubic roots of unity, i.e. the numbers such that z^3=1.
If you're using complex numbers, then every polynomial equation of degree k yields exactly k solution. So, we're expecting to find three cubic roots.
De Moivre's theorem uses the fact that we can write any complex number as \rho e^{i \theta}= \rho (\cos(\theta)+i\sin(\theta)), and it states that, if z=\rho (\cos(\theta)+i\sin(\theta)), then z^n = \rho^n (\cos(n \theta)+i\sin(n \theta))
If you look at 1 as a complex number, then you have \rho=1, and \theta=2\pi. We are thus looking for three numbers such that \rho^3=1, and 3\theta=2\pi.
Since \rho is a real number, the only solution to \rho^3=1 is \rho=1. On the other hand, using the periodicity of the angles, we have that the three solutions for \theta are \theta_{1,2,3}=\frac{2k\pi}{3}, for k=0,1,2.
This means that the three solutions are:
1. \rho=1, \theta=0, which is the real number 1.
2. \rho=1, \theta=\frac{2\pi}{3}, which is the complex number -1/2 + \sqrt{3}/2 i
3. \rho=1, \theta=\frac{4\pi}{3}, which is the complex number -1/2 - \sqrt{3}/2 i | 2019-04-25 20:39:53 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9258449673652649, "perplexity": 1189.441530206384}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-18/segments/1555578733077.68/warc/CC-MAIN-20190425193912-20190425215912-00301.warc.gz"} |
https://math.msu.edu/seminars/TalkView.aspx?talk=14365 | ## Colloquium
• Ken Ono, Emory University
• Jensen–Polya Program for the Riemann Hypothesis and Related Problems
• 03/28/2019
• 4:10 PM - 5:00 PM
• C304 Wells Hall
In 1927 Polya proved that the Riemann Hypothesis is equivalent to the hyperbolicity of Jensen polynomials for Riemann’s Xi-function. This hyperbolicity had only been proved for degrees $d=1,2,3$. We prove the hyperbolicity of all (but possibly finitely many) the Jensen polynomials of every degree $d$. Moreover, we establish the outright hyperbolicity for all degrees $d< 10^{26}$. These results follow from an unconditional proof of the "derivative aspect" GUE distribution for zeros. This is joint work with Michael Griffin, Larry Rolen, and Don Zagier.
## Contact
Department of Mathematics
Michigan State University | 2019-08-20 10:50:19 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8773156404495239, "perplexity": 3683.9982363895874}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-35/segments/1566027315321.52/warc/CC-MAIN-20190820092326-20190820114326-00021.warc.gz"} |
https://socratic.org/questions/a-cup-of-tea-containing-400-0-g-of-liquid-at-20-0-degree-c-was-heated-if-58-5-kj | # A cup of tea containing 400.0 g of liquid at 20.0 degree C was heated. If 58.5 kJ of heat was added to the tea, what would be the final temperature? Assume that the specific heat is the same as that of water( 4.18 J g c)
Mar 31, 2015
The final temperature of the tea is 55.0 °C.
The formula to use is
q = mcΔT,
where $q$ is the heat involved, $m$ is the mass, $c$ is the specific heat capacity, and ΔT is the temperature change.
$q = \text{58 500 J}$
$m = \text{400.0 g}$
$c = \text{4.18 J·g⁻¹°C⁻¹}$
ΔT = "?"
Solve the equation for ΔT.
ΔT = q/(mc) = ("58 500" cancel("J"))/(400.0 cancel("g") × 4.18 cancel("J·g⁻¹")"°C⁻¹") = "35.0 °C"
Δ T = T_2 – T_1
T_2 = T_1 + ΔT = "20.0 °C + 35.0 °C" = "55.0 °C" | 2021-09-27 06:54:55 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 13, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5579103827476501, "perplexity": 2809.338985531331}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780058373.45/warc/CC-MAIN-20210927060117-20210927090117-00291.warc.gz"} |
https://www.physicsforums.com/threads/can-you-append-digits-to-a-variable-in-c-or-python.238197/ | # Can you append digits to a variable in c++ or python
• C/++/#
OrbitalPower
Say you have a variable x, that is of type int.
x = 1;
I just want to create a while or for loop so that each time it runs it adds another digit to it, such as:
12
123
1234
or 1, 11, 111, 1111, and so on.
OrbitalPower
I know you can do this:
char y;
y = '1';
char test[2];
test[0] = y;
test[1] = y;
test[2] = '\0';
But I wouldn't know how to get it back to int in C++
Code:
int num=1;
for (int i=2; i<len; ++i)
{
num*=10;
num+=i;
}
Obviously though, you'd have to watch out for integer overflow.
You could also go with the string method, and if you don't need to actually perform operations on the number then it would work fine and you wouldn't have to worry about overflow. I'd use std::string instead of a char array, though.
Also, since you might need to convert a string to an integer or visa versa at some point:
Code:
#include <sstream>
int str_to_int(std::string str)
{
int num=0;
std::istringstream is(str);
is>>num;
return num;
}
std::string int_to_str(int num)
{
std::ostringstream os;
os<<num;
return os.str();
}
These can be easily modified for use with other numeric types as well (for all the types std::*stringstream objects can handle anyways) You could even write a generic template function if you felt like it.
Strilanc
Say you have a variable x, that is of type int.
x = 1;
I just want to create a while or for loop so that each time it runs it adds another digit to it, such as:
12
123
1234
or 1, 11, 111, 1111, and so on.
To append at the low end, multiply by 10 and add [digit].
To append at the high end, add [digit] * 10 ^ floor(log_10(n)).
You can compute the log relatively quickly using shifts and a constant for 1/log_2(10).
OrbitalPower
Yes, thank you both JaWiB and Strilanc. I guess to do the 1111+ I'd so something like:
Code:
int x;
x = 1;
int num=1;
for (int i=2; i<8; i++)
{
num = num * 10;
num = num + 1;
}
I guess I was so busy thinking about trying to convert between types I didn't think of the simple arithmetic solution.
I also like the append at the high end method.
Dale
Mentor
2021 Award
I don't know how big you want your numbers, but if you want them really big you will need to download an arbitrary precision arithmetic library. There are a bunch available for C++, but I don't know about Python.
In Python, the above would become:
Code:
maxappends = 8 # actually its max appends -2
num = 1
for i in range(2,maxappends):
num = num*10 + 1
You get the added benefit of arbitrary length integers: maxappends could be 1001 or more.
To add digits to the LHS (only makes sense if the digits are different, and if you are not prepending a zero):
Code:
maxappends = 20; num = 0
for i in range(maxappends):
num = num + ((i % 9) + 1) * 10**(i)
print i,num
OrbitalPower
In Python, the above would become:
Code:
maxappends = 8 # actually its max appends -2
num = 1
for i in range(2,maxappends):
num = num*10 + 1
You get the added benefit of arbitrary length integers: maxappends could be 1001 or more.
This is built in natively? What I was doing was constructing a program that return the remainder in a number composed entirely of ones with 50 or so digits. The idea was to determine the remainder by using the divisor only a few times into the dividend, as it was also composed entirely of ones. Obviously, to do that in C++ I'd perhaps need one of those libraries needed above. So, basically I just tested my method with smaller numbers.
*Also fixed an error I made, should be:
char test[3];
test[0] = y;
test[1] = y;
test[2] = '\0';
and not char test[2]. | 2022-05-26 20:02:49 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.25945401191711426, "perplexity": 1398.4692292102404}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-21/segments/1652662625600.87/warc/CC-MAIN-20220526193923-20220526223923-00735.warc.gz"} |
http://jwgcs.com/ntsjkh/vanguard-canada-mutual-funds-54de62 | Since it might not be able to display many digits on its screen, it can be limited in terms of the size of numbers it can add. Which ordered pair below would prevent this table from being a function? So it should point to some other value. an idea ? 1. The following table contains the supported operations and functions: Required only for trigonometric functions. You may recognize this trick from the linear equation y = mx + b. Table 8-1 lists each Calculator function with its keyboard equivalent. This means the function is not returning any value. （ex. 2. If no return type is given, the compiler will normally assume the function returns an int. ; The graph of the linear function is a straight line. What a Four-Function Calculator Does. The function exclud… Otherwise, if displayValue is a non-zero number, the digit is appended to it through string concatenation.. Learn vocabulary, terms, and more with flashcards, games, and other study tools. This is a function. When you enter a function, the calculator will begin by expanding (simplifying) it. Next, the calculator will plot the function over the range that is given. Definition: A function is odd if the equality $$f(x) = -f(-x)$$ is true for all $x$ from the domain of definition. Example. Graphing in the Coordinate Plane. If so, calculator.displayValue is overwritten with whatever digit was clicked. Its simplest form is the linear consumption function used frequently in simple Keynesian models: = + ⋅ where is the autonomous consumption that is independent of disposable income; in other words, consumption when income is zero. You can use function notation as an easy, efficient way of using equations without re-writing them. Start studying Function Notation, Evaluating Function Notation -- GRAPHS, Domain and Range, Function or Not a Function?. Function calculators usually work by allowing users to enter a function to analyze. Thanks to your feedback and relevant comments, dCode has developed the best 'Even or Odd Function' tool, so feel free to write! Graphically, this involves that opposed abscissae have the same ordinates, this means that the ordinate y-axis is an axis of symmetry of the curve representing $f$. The correct way to indicate that a function does not return a value is to use the return type "void". If the calculator did not compute something or you have identified an error, please write it in Another common use of the NOT function in Excel is to reverse the behavior of some other function. Example: Determine whether the function is even or odd: $f(x) = x^2$ (square function) in $\mathbb{R}$, the calculation is $f(-x) = (-x)^2 = x^2 = f(x)$, so the square function $f(x)$ is even. Note that this module is NOT about general plotting of graphs!It discusses functions, their domains, and inverse functions. On the other hand, y 2 + 3x = 6 is not a function, because you can not solve for a unique y: I mean, yes, this is solved for "y =", but it's not unique. Functions []. User defined functions can be further divided into two groups depending on whether a function does or does not return a value. To be a function or not to be a function Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. Regardless, function calculators are designed to shine a spotlight on some function you’ve been considering. Calculator for determining whether a function is an even function and an odd function. (i) Domain of f is A. 0 ⋮ Vote. So this right over here not a function, because it's not clear if you input x what member of the range you're going to get. Developments in convergent power series or polynomials of even (respectively odd) functions have even degrees (respectively odd). Learn vocabulary, terms, and more with flashcards, games, and other study tools. Using a function as one of the arguments in a formula that uses a function is called nesting, and we’ll refer to that function as a nested function. Calculates the table of the specified function with two variables specified as variable data table. The following example uses the CALCULATETABLE function to get the sum of Internet sales for 2006. You’ll be able to see these different types of scenarios by graphing the function on a graphing calculator; the only other way to “see” these events is algebraically. Is there a function that is both even and odd. Write to dCode! Purpose of use academic assignment Comment/Request huh, i was using this to check an assignment using a taylor series approximation and i think i found a misprint in my textbook's function when i checked it against this and another source's taylor series approximation For example, [0, 2pi] or (-pi, oo). It transitions row context to filter context. Tool to check the parity of a function (even or odd functions): it defines the ability of the function (its curve) to verify symmetrical relations. The CALCULATE function used without filters achieves a specific requirement. Please, check our community Discord for help requests! Since it might not be able to display many digits on its screen, it can be limited in terms of the size of … The calculator will find the domain, range, x-intercepts, y-intercepts, derivative, integral, asymptotes, intervals of increase and decrease, critical points, extrema (minimum and maximum, local, absolute, and global) points, intervals of concavity, inflection points, limit, Taylor polynomial, and graph of the single variable function. And an easy test is to just see, look, for one value I have two points for this relationship. In the inputDigit function, the ternary operator (?) a feedback ? A function 'CALCULATE' has been used in a True/False expression - Simple Date comparison 03-05-2018 02:00 PM. 3. Optionally, you can also create a custom calculation. How do you figure out if a relation is a function? Limit of a function: limit_calculator. By using this website, you agree to our Cookie Policy. An odd function will provide an opposite image for opposite values. Thank you! This would not be a function. So: If its vertex is pointing downwards, its vertex will mark the lowest point on the y-axis The following *does work* but will get a little more cumbersome when doing MTD or YTD calculations: Adding the IF function, the formula below would display “Text included in dataset” if any cell in the range B2-B13 were not a number. Hi There, I'm looking for a more elegant way sum based on a prior business day calculation. In this book, if a function does not have a need, we will leave its parentheses empty. Ordered pairs are a fundamental part of graphing. Even if your algebra skills are very … What is an Ordered Pair? If you continue browsing the site, you agree to the use of cookies on this website. If it exists, then you have the derivative, or else you know the function is not differentiable. To get tan(x)sec^3(x), use parentheses: tan(x)sec^3(x). This type of function is often referred to as the "void" function. Start studying Function or Not a Function?. For example, the function name corresponding to the square-root key Q is sqrt. If you get an error, double-check your expression, add parentheses and multiplication signs where needed, and consult the table below. =NETWORKDAYS.INTL(start_date, end_date, [weekend], [holidays]) The NETWORKDAYS.INTL function includes the following arguments: 1. Such a function would look like: $$Y = X + 1$$ In this case, X in the input value, and Y is the output (this is a common convention). Lessons: First read the introduction into functions by longjonsilver.A function is an operation on numbers of some set that gives (calculates) one number for every number from the domain.For example, function 3x is defined for all numbers … It also shows the step-by-step solution, plots of the function and the domain and range. The function declaration of sqrt() is defined in the cmath header file. Calculates the table of the specified function with two variables specified as variable data table. It's required when an expression (not a model measure) that summarizes model data … A four-function calculator typically performs the four most basic operations of math. Definition: A function is even if the equality $$f(x) = f(-x)$$ is true for all $x$ from the domain of definition. The interval can be specified. Except explicit open source licence (indicated CC / Creative Commons / free), any algorithm, applet or snippet (converter, solver, encryption / decryption, encoding / decoding, ciphering / deciphering, translator), or any function (convert, solve, decrypt / encrypt, decipher / cipher, decode / encode, translate) written in any informatic language (PHP, Java, C#, Python, Javascript, Matlab, etc.) The result is the output. It transitions row context to filter context. is used to check if the current value displayed on the calculator is zero. Examples. Students will determine if a graph represents a function by using a moving vertical line. The NOT function reverses the value of its argument. Amazon. The OR function returns TRUE if any of its arguments evaluate to TRUE, and returns FALSE if all of its arguments evaluate to FALSE. So this is not a function! It also shows the step-by-step solution, plots of the function and the domain and range. These needs could be as varied as possible. Example: Determine the parity of $f(x) = x/(x+1)$, first calculation: $f(-x) = -x/(-x+1) = x/(x-1) \neq f(x)$ and second calculation: $-f(-x) = -(-x/(-x+1)) = -x/(x-1) = x/(-x+1) \neq f(x)$ therefore the function $f$ is neither even nor odd. Hey there, I have been tasked with creating a function that calculates the median number of an array without using the inbuilt median function. The term ⋅ is the induced consumption that is influenced by the economy's income level .The parameter is known as the marginal propensity … The grapher understands "pi" as $$\pi$$ and "e" as the Euler constant $$e$$, so that if you type "e^x", the grapher will graph the exponential function. It can: A dd; Subtract; Multiply ; Divide; D epending on the complexity of the operation, a four-function calculator can be limiting. f(x,y) is inputed as "expression". no data, script, copy-paste, or API access will be for free, same for Even or Odd Function download for offline use on PC, tablet, iPhone or Android ! The function machine permits us to alter expressions. Example: How about this piecewise function: that looks like this: It is defined at x=1, because h(1)=2 (no "hole") But at x=1 you can't say what the limit is, because there are two competing answers: "2" from the left, and "1" from the right; so in fact the limit does not exist at x=1 (there is a "jump") And so the function is not continuous. Type something like "4 sin(x)" or "x^2 +2x-3", etc. The calculator can only handle functions. Although sometimes it can be hard to see the ‘real world’ uses of the function at first. Parcc basic four-function calculators for grades 6-7 | schoolmart. A Function Calculator is a free online tool that displays the graph of the given function. Finally, the updateDisplay() function is invoked so that the … A four-function calculator typically performs the four most basic operations of math. If a function does not have a need, leave its parentheses empty. For instance, you can combine NOT and ISBLANK functions to create the ISNOTBLANK formula that Microsoft Excel lacks. Watch this video to learn how to tell which relations are functions and which are not. write sin x (or even better sin(x)) instead of sinx. However, you can change the summary function. Weekend (optional argument) –If we omit the weekend parameter, it will assume that the weekends will contain Sunday & Saturday. Example. The second topic of this lab is function parameters. More than just an online tool to explore the continuity of functions. Example 1 : You could set up the relation as a table of ordered pairs. Limit of a function : limit_calculator . The final logical function to discuss in this article is the NOT function, and we have left the simplest for last. The problem is not with CurrMonthYear measure, it's with your second formula - CALCULATE function does not accept measures as criteria, only values. Graphically, this involves that opposed abscissae have opposed ordinates, this means that the origin (central point) (0,0) is a symmetry center of the curve representing $f$. In general, a function is not differentiable for four reasons: Corners, Cusps, Vertical tangents, Jump discontinuities. All suggestions and improvements are welcome. End_date (required argument) – The end date. Or maybe it could point to e or whatever else. Also, be careful when you write fractions: 1/x^2 ln(x) is 1/x^2 ln(x), and 1/(x^2 ln(x)) is 1/(x^2 ln(x)). If x is 1 or TRUE then NOT (x) returns 0 (= FALSE). On the other hand, relation #2 has TWO distinct y values 'a' and 'c' for the same x value of '5' . So this cannot be a function. Learn vocabulary, terms, … Start_date(required argument) – Start_date will either be earlier than end_date or later than end_date or the same as end_date. The first way of calculating the derivative of a function is by simply calculating the limit that is stated above in the definition. (ii) For each x ∈ A, there is only one y ∈ B such that (x, y) ∈ f. Let us look at some examples to understand how to determine whether a relation is a function or not. For example, you can evaluate a function at a certain point: You can use the notation f(x,y), for example, to define a function with more than one variable: Example 1 : Does the following relation represent a function ? And you can see that right here. Function calculator, linear function calculator, input output. By way of example, say you will need to achieve the second story window of your residence, which is 10 feet off the ground. What is an Ordered Pair? Start studying Function or Not a Function?. The funtool app is a visual function calculator that manipulates and displays functions of one variable. If so, you have a function! Can you refactor it, and then call the function to calculate the area with base of 5 and height of 6? The value of the function at the stationary and critical points and the points where the second derivative is zero or does not exist ; 2. If x does not have an exponent, the function is growing at a constant, steady, unchanging rate. Example input. A mapping diagram can be used to represent a relationship between input values and output values. f(x,y) is inputed as "expression". even,odd,function,parity,symmetry,trigonometric,cosine,sine, Source : https://www.dcode.fr/even-odd-function. ( This is a way of explicitly saying that the function returns nothing. ) What is the parity of trigonometric functions (cos, sin, tan)? where: y y y - function value (the function value at single point x, often marked as f(x)),; x x x - function argument (called also independent value),; a a a, b b b - linear function coefficients (slope and free parameter). Same as for when we learned how to compute the domain, there is not one recipe to find the range, it really depends on the structure of the function $$f(x)$$. Qgis-custom functions not showing in field calculator. Online Discontinuity Calculator Find discontinuities of a function with Wolfram|Alpha. SURVEY . A function assigns only output to each input. Every function is a relation, but not every relation is a function! Therefore, relation #2 does not satisfy the definition of a mathematical function. From the table below, you can notice that sech is not supported, but you can still enter it using the identity sech(x)=1/cosh(x). Some function calculators allow users to enter in output information first in order to determine what function(s) would yield this information. One common use for the OR function is to expand the usefulness of other functions that perform logical tests. It can: A dd; Subtract; Multiply ; Divide; D epending on the complexity of the operation, a four-function calculator can be limiting. A mapping diagram represents a function if each input value is paired with only one output value. where: y y y - function value (the function value at single point x, often marked as f(x)),; x x x - function argument (called also independent value),; a a a, b b b - linear function coefficients (slope and free parameter). How to Figure Out When a Function is Not Differentiable. This function is not supported for use in DirectQuery mode when used in calculated columns or row-level security (RLS) rules. Learn vocabulary, terms, and more with flashcards, games, and other study tools. comments below. IF(condition, x, y) returns x if the condition is TRUE (=1), but returns y if the condition is FALSE (=0).This function is also useful for conversion of continuous data into discrete data.. dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and problems to solve every day!A suggestion ? If you like the website, please share it anonymously with your friend or teacher by entering his/her email: In general, you can skip the multiplication sign, so 5x is equivalent to 5*x. ; Slope of a linear function defines the degree of slope of the line to the OX axis ("horizontal"). Answered: kokeb Dese on 31 Jul 2018 Accepted Answer: Geoff Hayes. Type in any function above then use the table below to input any value to determine the output: How to check if a function neither even nor odd? Sometimes I see expressions like tan^2xsec^3x: this will be parsed as tan^(2*3)(x sec(x)). What a Four-Function Calculator Does. Public Function doubleMe(d As Variant) doubleMe = d * 2 End Function You can also use Application.Volatile , but this has the disadvantage of making your UDF always recalculate - even when it does not need to because the referenced data has not changed. Students will understand the definition of function and use it to identify whether or not an input-output pairing represents a function. It would not be a function if it says, well, it could point to y. Then, test to see if each element in the domain is matched with exactly one element in the range. Calculator for determining whether a function is an even function and an odd function. The value that is put into a function is the input. Since relation #1 has ONLY ONE y value for each x value, this relation is a function. I'll put an exclamation mark. Purpose of use academic assignment Comment/Request huh, i was using this to check an assignment using a taylor series approximation and i think i found a misprint in my textbook's function when i checked it against this and another source's taylor series approximation =IF(ISNUMBER(B2:B13),AVERAGE(B2:B13),"Text included in dataset") Vote. Function . Calculator policy updated july 2018. Students will determine if a table of x- and y-values represents a function. Algebra calculator mathpapa. To compute a square root in a formula, you would use the notation ‘sqrt(x)’. dCode retains ownership of the online 'Even or Odd Function' tool source code. The limit calculator allows the calculation of the limit of a function with the detail and the calculation steps. In trigonometry, the functions are often symmetrical: The cosine function $\cos (x)$ is even. However, a simple function might return the input plus one. In this program, the sqrt() library function is used to calculate the square root of a number. If you need oo, type. The NOT Function. The needs of a function are provided between parentheses. Follow 275 views (last 30 days) Marnie on 11 Apr 2015. At the click of a button, for example, funtool draws a graph representing the sum, product, difference, or ratio of two functions that you specify.funtool includes a function memory that allows you to store functions for later retrieval. So if the logical value is TRUE, then it returns FALSE. The Algebraic Way of Finding the Range of a Function. The Line Test for Mapping Diagrams To check if a relation is a function, given a mapping diagram of the relation, use the following criterion: If each input has only one line connected to it, then the outputs are a function of the inputs. Every function in the Calculator application has a keyboard equivalent associated with it. As you know, the formula =ISBLANK(A2) returns TRUE of if the cell A2 is blank. ; The graph of the linear function is a straight line. For example, 2y + 3x = 6 is a function, because you can solve for y: 2y + 3x = 6 2y = –3x + 6 y = (–3/2)x + 3. Having proved equality for a single value like $f(2) = -f(-2)$ does not allow us to conclude that there is imparity, only to say that 2 and -2 have opposite images by the function $f$. Or it could point to z. 120 seconds . Ordered pairs are a fundamental part of graphing. See the manual page for calctool for a more complete description of each function. Please leave them in comments. By putting any number in for X, we calculate a corresponding output Y by simply adding one. It cannot be a function if for some input into the function you could give me two different values. Even or odd function calculator: is_odd_or_even_function. answer choices . Having proved this equality for a single value like $f(1) = f(-1)$ does not allow to conclude that there is parity, only to say that 1 and -1 have the same image by the function $f$. Most common functions are understood by this graph calculator. The OR function returns TRUE if any of its arguments evaluate to TRUE, and returns FALSE if all of its arguments evaluate to FALSE.. One common use for the OR function is to expand the usefulness of other functions that perform logical tests. An even function will provide an identical image for opposite values. 0. In this lab, we learn how to write user-defined functions that do not return a value. A common solution is to wrap the criteria into FILTER function, something like: x^2*y+x*y^2 ） The reserved functions are located in " Function … ; Slope of a linear function defines the degree of slope of the line to the OX axis ("horizontal"). Creating a function to calculate median. As a function, we take f(x) = x 2. The function NOT (x) reverses the value of its boolean argument x. Watch this video to learn how to tell which relations are functions and which are not. If you skip parentheses or a multiplication sign, type at least a whitespace, i.e. Functions may depend on variables passed to them, called … Wolfram|Alpha is a great tool for finding discontinuities of a function. The calculator will find the domain, range, x-intercepts, y-intercepts, derivative, integral, asymptotes, intervals of increase and decrease, critical points, extrema (minimum and maximum, local, absolute, and global) points, intervals of concavity, inflection points, limit, Taylor polynomial, and graph of the single variable function. x^2*y+x*y^2 ） The reserved functions are located in " Function … Start studying Function VS Not a Function. Details. Free functions calculator - explore function domain, range, intercepts, extreme points and asymptotes step-by-step This website uses cookies to ensure you get the best experience. Instructions: Use this Function Grapher Online to type in the function you want to plot. For example, the IF function performs a logical test and then returns one value if the test evaluates to TRUE and another value if the … Example input. A function is neither odd nor even if neither of the above two equalities are true, that is to say: $$f(x) \neq f(-x)$$ and $$f(x) \neq -f(-x)$$. If a relation is a function, it has to satisfy the following conditions. In some references, instead of leaving the parentheses empty, the programmer would write void. : y is not a function of x (x = 1 has multiple outputs), x is not a function of y (y = 2 has multiple outputs). The graph of a quadratic function is a parabola. The limit calculator allows the calculation of the limit of a function with the detail and the calculation … BYJU’S online function calculator tool makes the calculations faster, and it displays the graph of the function by calculating the x and y-intercept values, slope values in a fraction of seconds. Com: sharp el233sb standard function calculator. Example: Determine whether the function is even or odd: $f(x) = x^2$ (square function) in $\mathbb{R}$, the calculation is $f(-x) = (-x)^2 = x^2 = f(x)$, so the square function $f(x)$ is even. IF function Description. How to Calculate the Derivative of a Function. This function to calculate the area of a rectangle is not very readable. In general, you can skip parentheses, but be very careful: e^3x is e^3x, and e^(3x) is e^(3x). If-then-else function. That's why it works when you put "201704" explicitly but fails when you use the measure. Data in the Values area summarize the underlying source data (not the value that is showing) in the PivotChart report in the following way: numeric values use the SUM function and text values use the COUNT function. Online Discontinuity Calculator Find discontinuities of a function with Wolfram|Alpha. SURVEY . Tags: Question 15 . All intervals between and around the points mentioned in 1 ; 3. NB: if an odd function is defined in 0, then the curve passes at the origin: $f(0) = 0$. Wolfram|Alpha is a great tool for finding discontinuities of a function. It's also possible to return a value from a function. Hi, I am using CALCULATE function to extract sum out of a column if it matches 1 out of 5 criteria. （ex. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. These are the calculation methods utilized by the calc to locate the derivatives. Check out these examples: (4x)' = 4 (x)' = 1 (-23x)' = -23 Variables. I used an OR() function to see if it matches any of those values. A number multiplied by a variable with no exponent: The derivative of a function of this form is always the number. Every function is a relation, but not every relation is a function! Is this graph a function or not a function? To get tan^2(x)sec^3(x), use parentheses: tan^2(x)sec^3(x). Similarly, tanxsec^3x will be parsed as tan(xsec^3(x)). A function, which can also be referred to as subroutine, procedure, subprogram or even method, carries out tasks defined by a sequence of statements called a statement block that need only be written once and called by a program as many times as needed to carry out the same task.. A History of Inverse Calculator Refuted . IF(C2<0,"NEG","POS") returns the string value "NEG" if the number in cell C2 is less than 0 (C2<0 = TRUE). Functions calculator symbolab. Example: Determine whether the function is even or odd: $f(x) = x^3$ (cube function) in $\mathbb{R}$, the calculation is $-f(-x) = -(-x)^3 = x^3 = f(x)$, so the cube function $f(x)$ is odd. You must use … Keywords: Background Tutorials. Parity will also be determined. Calculator Function Keys. More than just an online tool to explore the continuity of functions. Use the following guidelines to enter functions into the calculator. answer choices (10, 10) (2, 4) (6, 1) (-2, 0) Tags: Question 16 . The above mentioned features aren't supported. Functions which do not have operator symbols like ‘+’ and ‘*’ must be entered in formulas using function-call notation. Q. Yes, the function $f(x) = 0$ (constant zero function) is both even and odd because it respects the 2 equalities $f(x) = f(-x) = 0$ and $f(x) = -f(-x) = 0$. If x is 0 or FALSE then NOT (x) returns 1 (= TRUE). a set of mathematical operations performed on one or more inputs (variables) that results in an output To calculate the image of the second degree functions, you could also calculate it by obtaining the mastery of its inverse function, but we will calculate it with another method. Not a Function. This value is later used to calculate the ratio of Internet sales compared to all sales for the year 2006. Watch this tutorial to see how you can determine if a relation is a function. Whether the function is increasing/decreasing between the stationary and critical points 4. Definition: A function is even if the equality $$f(x) = f(-x)$$ is true for all $x$ from the domain of definition.. An even function will provide an identical image for opposite values.. For example, the ISNUMBER formula will calculate to TRUE if all the cells in the dataset are numbers, otherwise it will calculate to FALSE. Keywords: Background Tutorials. a bug ? Explain. The tangent function $\tan (x)$ is odd. Graphing in the Coordinate Plane. , y ) is inputed as expression '' Vertical line functions into the calculator plot! Relationship between input values and output values, then you have identified an error, your. Or you have the derivative, or else you know the function name corresponding the... Declaration of sqrt ( ) function to get the sum of Internet sales for 2006 tool to the... One common use of cookies on this website, you can combine not and ISBLANK functions create. Excel is to just see, look, for one value I have two points for this.!, then it returns FALSE put into a function? given, the (... End_Date ( required argument ) –If we omit the weekend parameter, could. Help requests xsec^3 ( x ) sec^3 ( x ) $is odd functions ( cos sin., I 'm looking for a more elegant way sum based on prior... The calculate function used without filters achieves a specific requirement if so, calculator.displayValue is overwritten whatever. For finding discontinuities of a function does not have a need, we take f ( x ),! In trigonometry, the function returns nothing. logical tests function or not a function calculator functions have even degrees ( respectively odd functions... What function ( s ) would yield this information series or polynomials even... It could point to e or whatever else points 4 Marnie on 11 Apr 2015 (? reverse the of... Range of a function is a parabola, for one value I have two points for relationship... To reverse the behavior of some other function to calculate the area with base of 5 and height 6... Area with base of 5 and height of 6 not satisfy the definition online tool explore! Error, double-check your expression, add parentheses and multiplication signs where needed, inverse. The parity of trigonometric functions 4x ) ' = 4 ( x ) only. Signs where needed, and other study tools number in for x, y ) is inputed as ''... This is a visual function calculator function or not a function calculator input output = mx + b if so, is. Calculator that manipulates and displays functions of one variable a mapping diagram can be used to represent function. Have left the simplest for last not every relation is a parabola you could set up the relation as function!: Details = x 2 function declaration of sqrt ( x ) reverses the value of function or not a function calculator. Or a function or not a function calculator sign, type at least a whitespace, i.e the did! Tan^2 ( x ) ’ at a constant, steady, unchanging rate studying function notation Evaluating... Sin x ( or even better sin ( x ) sec^3 ( x ) reverses the of!, add parentheses and multiplication signs where needed, and we have left the for! Maybe it could point to e or whatever else are very … function... For determining whether a function, it has to satisfy the definition also! End date, tanxsec^3x will be parsed as tan ( x ) or... Where needed, and other study tools ], [ weekend ], [ ]... ( cos, sin, tan ) function used without filters achieves a specific requirement will normally the... Used without filters achieves a specific requirement a table of ordered pairs is... Exponent, the ternary operator (? it works when you put 201704 '' explicitly fails! Is 0 or FALSE then not ( x ) ’ relation is a great tool for finding discontinuities a... See if it exists, then it returns FALSE for four reasons: Corners, Cusps, tangents... # 2 does not have a need, leave its parentheses empty specified function with two specified... Allow users to enter functions into the calculator did not compute something or you have derivative! Ratio of Internet sales for 2006 x, y ) is inputed as expression '' would the. These are the calculation of the specified function with the detail and the domain matched! Logical value is paired with only one y value for each x value this... 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The updateDisplay ( ) library function is used to represent a relationship between input values and values! | 2021-10-28 10:26:27 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 2, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.6216627359390259, "perplexity": 749.8991533863078}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-43/segments/1634323588284.71/warc/CC-MAIN-20211028100619-20211028130619-00702.warc.gz"} |
http://tomdalling.com/blog/random-stuff/using-git-for-hacky-archive-deduplication/ | Have you ever wished that tar or zip would deduplicate files when creating an archive? Well here’s a hacky solution using git.
## How It Works
Git already has deduplication functionality, due to the way it stores files. Internally, files are named using their own checksums, so if two files have the same checksum then only one copy of the file is stored.
So, to make use of this, if you add all the files to a new git repo then it will perform the deduplication. Then, you archive the .git directory of the repo with zip or tar.
When unarchiving, you just do the opposite. Unzip the .git directory inside the destination directory. Run git reset --hard to bring back all the duplicate files. Then, just delete the .git folder.
Git will also do zlib compression if you run git gc --aggressive. Bzip2 compression is better, but why not have both?!
## The Results
I took some recent work, which I know contains duplicate files, to test if this would actually work. Here are the results:
39M original
3.5M original.gitar
10M original.tar.bz2
2.7M original.tar.lrz *see update below
The original directory contained 39mb of files. Running tar cjf original.tar.bz2 original, which uses bzip2 compression, compressed the folder to about 25% of it’s original size. The git method compressed the folder to about 10% of it’s original size. So it does actually work.
## Update: lrzip is better
After publishing this article, someone suggested trying lrzip, which I hadn’t heard of before. It doesn’t do file deduplication per se, but it does a good job of compressing files with large chunks of redundant data – such as a tarball of duplicate files. By default it uses LZMA compression, which seems to be better than bzip2.
Running tar cf original.tar original && lrzip original.tar produces a file named original.tar.lrz with a size of 2.7M, which is a bit better than the git method.
## The Script
Update: Sam Gleske has written a more robust script here: http://github.com/sag47/drexel-university/tree/master/bin.
Here is a quick and nasty script called gitar.sh that makes these deduplicated archives. Use gitar.sh myfolder to create the myfolder.gitar archive. Then use gitar.sh myfolder.gitar to recreate the original folder.
Do whatever you want with the script. I’ve released it under the MIT license just because I don’t want to get sued if someone copy/pastes it onto a production server and everything explodes.
• beardyjay
Nice and thanks for the script too! :)
• Marshall Levin
Nice work! I made a few small changes to idiot-proof it so I wouldn’t accidentally clobber an existing git repo.
http://pastebin.com/CNecRQRq
• http://www.tomdalling.com/ Tom Dalling
Thanks. I put it in a github gist and applied the patch.
• Tintin
Works good!
But, when i am doing deduplication manually to my file with srot -u, i am getting my file much smaller.
For example:
The original file is 6851852227 kb
The gitar file is 2053674855 kb
The sort -u file is 16123844 kb
What make this big difference? the indexes?
Can i use this script to have better results?
Thanks
• http://www.tomdalling.com/ Tom Dalling
I guess it could be the git indexes if you have millions of files. I’m not exactly sure what you’re doing with sort -u, but if I had to guess I’d say you might be deleting files that aren’t identical – they just have the same file name. See if lrzip gives you a better result.
• Tintin
Not millions of files, but millions of rows in a file.
sort -u is sorting the file and leaving only the unique rows.
• http://www.tomdalling.com/ Tom Dalling
Oh well that explains it. Git will only deduplicate identical files. It doesn’t do anything to the lines within a file.
• Tintin
Thanks Tom!
Do you know what can help me?
Dedup within files..
Thanks
• http://www.tomdalling.com/ Tom Dalling
I would keep using sort -u, then run lrzip on it afterwards. That should give you very good compression.
• Tintin
The problem is that i want also to reconstruct the full file.
and when i am using sort -u i am loosing this information..
i want to combine dedup within file and between files.
• http://www.tomdalling.com/ Tom Dalling
Try lrzip by itself and see what results you get. The file might be too large to get good results. Otherwise, you might have to write your own script that does run-length encoding or something ( http://en.wikipedia.org/wiki/Run-length_encoding).
• Sam Gleske
So I couldn’t resist writing my own CLI utility for gitar :D. I present to you my own gitar.sh. The readme has some benchmarks and other fun information while I explored gitar. I wrote this script from scratch without any reference to your own script. Thanks for the neat hack Tom!
https://github.com/sag47/drexel-university/tree/master/bin#gitarsh—a-simple-deduplication-and-compression-script
• http://www.tomdalling.com/ Tom Dalling
Looks good! I’ve included it in the article. | 2014-07-25 20:33:35 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.27682730555534363, "perplexity": 3279.240458291953}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997894782.90/warc/CC-MAIN-20140722025814-00122-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://dsp.stackexchange.com/questions/71587/how-to-quantify-amplitude-of-oscillations-in-marginally-stable-systems | # How to quantify amplitude of oscillations in marginally stable systems?
Transfer function pole on the Imaginary axis indicates that the system is marginally stable which in time domain can be represented as a sinusoidal motion with constant amplitude and frequency of the Imaginary axis pole. In some applications, oscillations with small amplitude might be acceptable.
1. Is amplitude of oscillation a (only) function of initial condition of the system?
2. How to intuitively quantify amplitude of the oscillations for marginally stable system?
Is amplitude of oscillation a (only) function of initial condition of the system?
No. For a system with a transfer function of the form $$H(s) = \frac{\cdots}{s^2 + \omega_0^2}$$, the amplitude of oscillation will increase any time it is excited by a signal that has a component at $$x(t) = \cos \omega_0 t + \phi$$. Even if you're not exciting it intentionally, random noise will excite that pole. Basically, the output will be of the form $$a(t) \cos \omega_0 t + b(t) \sin \omega_0 t$$, where $$a(t)$$ and $$b(t)$$ will be Wiener (random-walk) processes. Such processes have variances that tend to infinity as $$t \to \infty$$.
How to intuitively quantify amplitude of the oscillations for marginally stable system?
"Big and growing, boss, and I don't think they'll get smaller!"
Possibly by how fast they grow. But grow they will.
In some applications, oscillations with small amplitude might be acceptable.
If you have a system that's exhibiting persistently small oscillations, then you're seeing the signs of a nonlinear phenomenon called a "limit cycle". Basically, there's some oscillator in there that's either inherently small-valued (like the oscillation you may see around the least significant bit of a DAC or ADC), or there's a big oscillation that's mostly not getting to the output. Either way, if it persists at some amplitude, there's some nonlinear process that's keeping it that way.
• I should have clarified that this example is referring to unexcited (inherent) characteristics of the system. Assuming no external force/noise, given eigen values of the system, how to quantify amplitude of oscillations? Do we need to analyze eigen vectors for this purpose ? Nov 22 '20 at 22:02
• If the poles are truly on the stability margin (imaginary axis in the Laplace domain, unit circle in the $z$ domain), then the way to quantify the amplitude is "unbounded". There's only one unbounded -- it's the number that has no bound. It's big. And getting bigger. Without end. Big. Bigger. Bigger yet. If you're dealing with something that isn't described by "unbounded", then you're dealing with something that isn't a linear system with poles on the stability boundary. Nov 22 '20 at 23:23
• I'm not clear on "the way to quantify the amplitude is "unbounded". Could you please elaborate ? Nov 23 '20 at 3:17
• I mean the antonym of "bounded" in the mathematical sense. A signal $x(t)$ is bounded if, for all possible values of $t$, there exists some finite $x_{max}$ such that $\left | x(t) \right | < x_{max}$. If there is no such $x_{max}$ (i.e., if $x_{max}$ is infinity), then $x(t)$ is unbounded. en.wikipedia.org/wiki/Bounded_function Nov 23 '20 at 16:06
• I understand what "bounded" means. But this is not answering my question. I theory, a marginally stable system manifests a finite amplitude oscillation. Again, how one can measure this amplitude? Nov 24 '20 at 17:43
I have to disagree with Tim here. And it's because I once took that position and was shown wrong by James McCartney, the author of SuperCollider.
There's a difference between "marginally stable" and either "stable" or "unstable".
For the marginally-stable oscillator:
\begin{align} y[n] &= 2 \cos(\omega_0) y[n-1] - y[n-2] \\ \\ y[-1] &= A \cos(-\omega_0 + \phi) \\ y[-2] &= A \cos(-2\omega_0 + \phi) \\ \end{align}
will result in this output:
$$y[n] = A \cos(\omega_0 n + \phi) \qquad \forall n \in \mathbb{Z} \ge 0$$
and with double-precision floating point is stable to the extent that I have run it overnight and no change in amplitude. | 2021-11-28 14:59:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 8, "wp-katex-eq": 0, "align": 1, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9797443747520447, "perplexity": 790.2661228364994}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-49/segments/1637964358560.75/warc/CC-MAIN-20211128134516-20211128164516-00302.warc.gz"} |
http://mathhelpforum.com/pre-calculus/103235-area-sector-print.html | # Area of a sector
• Sep 20th 2009, 06:08 AM
Chinnie15
Area of a sector
The area of a circle is 72cm^2. Find the area of a sector of this circle that subtends a central angle of pi/6 rad.
Thanks!
• Sep 20th 2009, 06:53 AM
e^(i*pi)
Quote:
Originally Posted by Chinnie15
The area of a circle is 72cm^2. Find the area of a sector of this circle that subtends a central angle of pi/6 rad.
Thanks!
$A_{sector} = \frac{1}{2}r^2 \theta$
A whole circle may be considered to be a sector:
• $A_{sector} = 72$
• $\theta = 2\pi$
From this you can find r and then find the area of the sector.
Spoiler:
Rearranging the equation to find r and then plugging that expression in provides a way to find A in one step
$r = \sqrt{\frac{2A_{c}}{\theta_{c}}}$
$A_s = A_c \, \frac{\theta_{s}}{\theta_c}$
Where:
• $A_s$= Area of Sector
• $A_c$ = Area of Circle ( $72\, cm^2$)
• $\theta_{c}$ = Angle of Circle ( $2\pi$)
• $\theta_s$ = Angle subtended by sector ( $\frac{\pi}{6}$
• Sep 20th 2009, 07:02 AM
Hello Chinnie15
Quote:
Originally Posted by Chinnie15
The area of a circle is 72cm^2. Find the area of a sector of this circle that subtends a central angle of pi/6 rad.
Thanks!
The whole circle ( $72\,cm^2$) subtends an angle of $2\pi$ at the centre. The sector you want subtends an angle of $\frac{\pi}{6}$ which is $\frac{1}{12}$ of $2\pi$. So its area is ...? | 2017-07-23 11:29:11 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 17, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8602349162101746, "perplexity": 764.8222007104652}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-30/segments/1500549424549.12/warc/CC-MAIN-20170723102716-20170723122716-00266.warc.gz"} |
http://www.gamedev.net/index.php?app=forums&module=extras§ion=postHistory&pid=5011218 | • Create Account
### #ActualBrother Bob
Posted 16 December 2012 - 04:14 AM
I'm not really sure if A is used at all, I did this a long time ago, but B is supposed to be the perspective divide element.
Or at least B and the projection matrix modify the 4th element of the position, so that in clip space if you divide by it, you get the ndc coordinates.
The entire bottom row is used for the perspective division, not just the B-element.
For example, for an orthographic projection, the bottom row is [0, 0, 0, x] where x is some value depending on the parameters of the projection matrix. That means that the fourth component of the resulting vector after multiplication is the fourth component of the in multiplying vector, to some scale factor. For glOrtho, x=1 at all times though, which means that as long as the Z-coordinate of the input is 1.0, which is often the case, there fourth component of the resulting vector is also 1.0, and there is effectively no perspective division, hence no perspective since it is an orthographic projection.
On the other hand, for a perspective matrix, the bottom row is [0, 0, x, 0]. That means that the fourth component of the resulting vector is the third component of the multiplying vector, to some scale factor x. The third component is the depth, and hence the perspective division is now dependent on the depth; you now get a perspective effect.
Likewise, the first two elements of the bottom row can also be non-zero to get a perspective effect along the X and/or the Y-axis instead.
how would I apply A and B to a Vec3? ( I know how to translate and rotate )
It doesn't make much sense to talk about how to apply these elements to a 3-element vector. You simply cannot multiply a 3-element vector by a 4-by-4 matrix in the first place. What you do when adding multiplying the 3-element vector by the rotation part and then adding the translation part as a separate step is really just assuming that the missing fourth component of the 3-element vector is unity. In order to handle the fourth row of the matrix correctly, you have to do the same assumption again, carry out the multiplication, and see how the bottom row affects the other three elements, as well as performing the final perspective division to ensure that the assumption that the fourth component really is unity even after the multiplication.
In the end, you really have to carry out a full 4-vector times 4x4-matrix multiplication, although you can assume that one element is unity and eliminate its multiplication with the corresponding elements of the matrix, and just add them.
### #1Brother Bob
Posted 16 December 2012 - 04:14 AM
I'm not really sure if A is used at all, I did this a long time ago, but B is supposed to be the perspective divide element.
Or at least B and the projection matrix modify the 4th element of the position, so that in clip space if you divide by it, you get the ndc coordinates.
The entire bottom row is used for the perspective division, not just the B-element.
For example, for an orthographic projection, the bottom row is [0, 0, 0, x] where x is some value depending on the parameters of the projection matrix. That means that the fourth component of the resulting vector after multiplication is the fourth component of the in multiplying vector, to some scale factor. For glOrtho, x=1 at all times though, which means that as long as the Z-coordinate of the input is 1.0, which is often the case, there fourth component of the resulting vector is also 1.0, and there is effectively no perspective division, hence no perspective since it is an orthographic projection.
On the other hand, for a perspective matrix, the bottom row is [0, 0, x, 0]. That means that the fourth component of the resulting vector is the third component of the multiplying vector, to some scale factor x. The third component is the depth, and hence the perspective division is now dependent on the depth; you now get a perspective effect.
Likewise, the first two elements of the bottom row can also be non-zero to get a perspective effect along the X and/or the Y-axis instead.
how would I apply A and B to a Vec3? ( I know how to translate and rotate )
It doesn't make much sense to talk about how to apply these elements to a 3-element vector. You simply cannot multiply a 3-element vector by a 4-by-4 matrix in the first place. What you do when adding multiplying the 3-element vector by the rotation part and then adding the translation part as a separate step is really just assuming that the missing fourth component of the 3-element vector is unity. In order to handle the fourth row of the matrix correctly, you have to do the same assumption again, carry out the multiplication, and see how the bottom row affects the other three elements, as well as performing the final perspective division to ensure that the assumption that the fourth component really is unity even after the multiplication.
In the end, you really have to carry out a full 4-vector times 4x4-matrix multiplication, although you can assume that one element is unity and eliminate its multiplication with the corresponding elements of the matrix, and just add them.
PARTNERS | 2014-07-23 11:31:55 | {"extraction_info": {"found_math": false, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.8435227870941162, "perplexity": 288.0690902900076}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-23/segments/1405997877869.73/warc/CC-MAIN-20140722025757-00164-ip-10-33-131-23.ec2.internal.warc.gz"} |
https://worldbuilding.stackexchange.com/questions/140725/practical-reasons-to-have-both-a-large-police-force-and-bounty-hunting-network/140957 | # Practical reasons to have both a large police force and bounty hunting network?
The Hegemony is a global government governing Earth and her colonies. As a global government the Hegemony has a rather large police force (the Hegemony has merged the military and police within the bureaucracy) numbering in the hundreds of millions.
The Hegemony also maintains/condones a large bounty hunting network across Earth and the colonies. To be a bounty hunter all one has to do is pass a simple background check and get issued a permit by the state. The permit gives the hunter in question the legal right to arrest their target (since their target would already be marked a fugitive).
But why? Are there any practical reasons to have a large bounty hunting system when you already have a large police force?
Note: for the most part peace keepers (Hegemony police) are a benevolent force that plays it by the books.
Permit allows hunters to also pick up missing person's cases if that is a factor in any answers.
• If the government is genre savvy, they'll know that bounty hunters are way awesomer than police. – PyRulez Mar 5 at 5:38
• @PyRulez in fact, they'd know ex-police make excellent bounty hunters. So more police force = more ex-police. And of course there is an increased chance they get the rare loner cop who works better by himself and doesn't pay much attention to the law. These guys are really effective, especially when paired with a respectable by-the-book police officer of which there would also be a lot. – VLAZ Mar 5 at 6:46
• Are there any "Dead or alive"-sought fugitives? – DarthDonut Mar 5 at 9:57
• Just a side note, military and police usually have completely different goals. Joining them in a single force sounds very fishy and probably counterproductive. There are examples from Earth's history, but as soon as there is enough "peace" to go around, the law enforcement is generally separated from armed forces. – Gnudiff Mar 6 at 15:34
• The Syfy series Killjoys explores this. – Pureferret Mar 7 at 16:22
Bounty hunters only get paid on results. If they don't succeed, they make nothing and cost the government nothing as where police get paid on success or failure.
Basically bounty hunters are police that work for commission.
The government have enough police to handle most of the routine work but if it starts to get time consuming, they sub it out to bounty hunters. This way they can maximise the return for their money.
An additional bonus is the government has plausible deniability if a bounty hunter uses "questionable" methods to get results. No need for police to beat suspects with phone books and trample suspect's rights (when a bounty hunter will do it for you)
• +1: All for the money... Outsourcing risky jobs that aren't regularly scheduled routines. Especialy in a high bureaucracy where all that matters are the numbers, presented to the higher ups. – T-Me Mar 5 at 15:51
• @nalzok It is in some places. And some bounty hunters have gotten into trouble for it when they get a little too rough. There was even a reality show about one in the US a while back... – Darrel Hoffman Mar 5 at 19:26
• This is good, but also mention that police and sherriff's deputies have to stay within their jurisdiction but bounty hunters don't. – Spencer Mar 5 at 23:27
• If the bounty hunters are not held accountable for "regrettable excesses", they will quickly become essentially mercenary death squads. It's whole lot easier to just kill someone than it is to arrest him. And if the government does not provide effective protection for the bounty hunters, they in turn will become targets. The result will be a lot of civilians killed in the crossfire. This in turn is going to really impact how the government is perceived by the population. Plus, of course, the police will misbehave and blame it on bounty hunters. This trend will not end well. – WhatRoughBeast Mar 6 at 5:52
• @WhatRoughBeast: There are compromises here. E.g. bounty hunters are not allowed to kill a target, but aren't blamed for the fugitive getting hurt. This opens the door to some forms of torture (with no obvious wound patterns), the bounty hunter can claim that it happened while resisting arrest, and the government can choose to not particularly punish this behavior (under the guise of "he shouldn't have resisted arrest!") if they can benefit from asking bounty hunters by skirting (but not provably transgressing) the fugitive's rights. It can lead to death squads but it doesn't have to. – Flater Mar 6 at 9:10
Unregulated Space(s)
Your police force has a heavy presence on-planet, or in dense population centres, but not outside of that - the void between colonies or the wilds of the sparser planets do not have the same infrastructure or law enforcement.
This makes those same locations the perfect hiding place for criminals and outlaws. Bounty Hunters are able to operate in those areas without the Support Network that the Police rely on.
These "buffer zones" also keep the different Departments of your Police Force from coming into conflict with each other - it is always clear which jurisdiction you are in.
• A citation from H2G2 on how big space is would readily explain why maintaining a heavy police presence in space is impractical. – Matthieu M. Mar 6 at 9:39
Note: for the most part peace keepers (Hegemony police) are a benevolent force that plays it by the books.
You actually answered your own question. The setup you're describing would actually be a potential solution to a LOT of the problems that exist in our own society right now.
Basically you're talking about privatizing SWAT, as well as the more offensive arms of the FBI, the DEA, and the ATF.
It's hard to maintain a benevolent police force when one of their responsibilities is trying to control dedicated criminals with no compunctions about using violence. Inevitably the demands of the latter cause your police to become cynical, ruthless, and even corrupt.
Your solution leaves a large, well funded police force handling all the normal 'Protect and Serve' functions and PROTECTS those police from having to deal with heavily armed criminals and gangs. This keeps them benevolent and removes the pressures they might otherwise face to throw out the book in the pursuit of results, or even their own safety. They play it straight, they do the investigation and identify the threats, and put bounties up on them.
Then your heavily armed, licensed bounty hunters go out and THEY get to risk their lives trying to handle the tough criminals. Most importantly, your bounty hunters wouldn't be protected by any laws regarding use of force in the service of duty, which means that if innocent or unarmed civilians are getting shot, it's not a government employee that did it, and it's MUCH easier to throw that contracted bounty hunter to the wolves and let him rot.
Honestly it's a pretty good idea. I might steal it.
• huh I accidentally came up with a good solution. I'd assume if the Hegemony did have swat they'd be comparable to special forces. Maybe they'd retain some offensive cops. Go for it btw (using the idea) I use this sight for inspiration so I'm happy to know I'm having a similar effect – Celestial Dragon Emperor Mar 5 at 18:18
• @CelestialDragonEmperor The police might still maintain heavily armed special forces for one specific purpose only: Taking down rogue bounty hunters :) – Philipp Mar 6 at 9:11
• @Philipp Why even bother? Set a bounty on the rogue bounty hunter, and in specifically those cases tack on "all the properties and possessions of [rogue bounty hunter]" to the bounty. Extra incentive to the rogue to turn himself in (so his family can keep his stuff and not starve), and extra incentive for other bounty hunters; if the rogue is a real threat, it's probably because he has good gear - legally being able to take that as your own is a significant bonus (and if the rogue's not a threat, then the extra incentive isn't really necessary). And no extra funding needed. – Delioth Mar 6 at 17:35
• @Delioth The bounty hunters might have a sense of honor and camaraderie which means they won't turn on each other. – Philipp Mar 6 at 17:38
• @Philipp Contracted workers don't typically form those kinds of bonds - since they're all constantly in direct competition (unless they work in teams, but even then teams likely won't form bonds with other teams, because a sense of honor to another team doesn't put food in their bellies or bullets in their guns). Additionally, you don't need a whole host of hunters to turn on each other. You just need one. Piling up extra incentives (without additional costs to the Hegemony) can make it easier to convince one. – Delioth Mar 6 at 17:44
Another possible concept would be that police and bounty hunters are pursuing different kinds of fugitives, e.g. police searches for persons who are not yet convicted, while bounty hunters search for those who have been sentenced by the courts to prison or death penalty.
Since the police 'does not kill', the bounty hunters execute the death penalties as soon as they catch the convicted. And since these criminals should already be punished, excessive force is authorized, but frowned upon within the police.
• There may as well be a class of fugitives that legally can't be pursued by police for some reasons, e. g.: citizens of another state which has an agreement with Hegemony for a special status of its citizens; or maybe androids owned by some mighty corporation, which can't have a separate police force but can issue bounty hunter licenses; or something else like that. – ain92 Mar 7 at 16:24
High bureaucracy.
Police can be numerous, but they are bound by countless rules and regulations. Particularly, when a fugitive runs away across district lines, it takes a long time to get other district's force to act on the case. Also, ex-territorial forces (similar to FBI or US Marshals that normally handle this kind of job) are very limited because Hegemony is afraid to make an all-powerful law enforcement agency.
As a result, hunting of fugitives is outsourced to private contractors, who are not limited by district boundaries and not organized to present a threat to the Hegemony.
Simple.
When $$are involved, bounty hunters are a thing. We currently have a large police force right here in the good 'ol USA. And yet--we still have bounty hunters. If you ask why that's true in real life, you'll have your answer. Here's how it works here: Yes, bounty hunting is legal, although state laws vary with regard to the rights of bounty hunters. In general, they have greater authority to arrest than even the local police. "When the defendant signs the bail bond contract, they do something very important. They waive their constitutional rights," says Burton. "They agree that they can be arrested by the bail bond agent. And they waive extradition, allowing bondsmen to take them to any state." All the bounty hunter needs to make an arrest is a copy of the "bail piece" (the paperwork indicating that the person is a fugitive) and, in some states, a certified copy of the bond. He or she doesn't need a warrant, can enter private property unannounced and doesn't have to read a fugitive his or her Miranda rights before making the arrest. But there are rules and regulations to the job. The bail bond contract gives bounty hunters the right to enter the home of a fugitive, but only after establishing without a doubt that the person lives there. They cannot enter the homes of friends or family members to look for the fugitive. In real life, bounty hunters go after people who have jumped bail (basically, that means that you haven't shown up to court after the court released you. When you, the criminal, sign the bail bond contract, you waive normal rights and give bounty hunters the ability to track you down in ways not normally available to police. You might be advocating for a different system, something along the lines of a rewards system, such as what the FBI does with their MOST WANTED. That's completely different and has nothing to do with bounty hunters. In that case, what you would need is lots of$$ being poured into the system, a government that wants order and is willing to pay for it.
To have a lot of either system (Rewards or Bail Bondsmen Bounties) you need a lot of arrests, and motivation to jump bail or run. Motivation can come in the form of unjust punishment or a corrupt system.
I have to say that in real life, bail bondsmen don't want high flight risk clients. They would rather you didn't run, but they will chase you so that they can get their $$back (at least some of it). And they don't go after any fugitives, they go after the ones that their company put money up for... Current rate in the US is something like 50,000-80,000 a year. A decent paycheck, but not enough of a trade-off for it to be worth the risk to most people. You want to make it much, much more profitable or have a more desperate/poor population to make it worthwhile. The difference between the police and bounty hunters in fiction should be risk vs. reward. In real life, police have a risky job, but actual bounty hunters are actively going after desperate fugitives who have fled. Police sort of take things as they come. Police arrest, bounty hunters apprehend AFTER arrest. In a fictional world cops should be saying something like "Pfft, I'm not going in there--let a bounty hunter take it." Cops should get less$$ but take lower risks, and bounty hunters are less bound by law than they are. That's why in real life there's a sort of love hate relationship between bounty hunters and the cops...
• Contrary to what you see on TV, a Police Officer making an arrest does not need to recite the Miranda Rights to the Suspect either: a Miranda Warning is only required when a Suspect in Custody is going to be Interrogated. – Chronocidal Mar 5 at 16:25
• It's standard to give Miranda once the suspect is in custody because if they are asking any questions about the crime at all, they need to be read. Bounty hunters don't ask questions. They don't care. It's apparent that the suspect jumped bail, and it's not their job to ask any questions. Bounty hunters are simply arresting AFTER a suspect has been officially arrested and the suspect has jumped bail. Interrogation is considered ANY question about the crime. So it's often safer to read them for a police officer. – Erin Thursby Mar 6 at 14:50
1: "He Bought The Farm" As far back as the Roman empire and probably beyond, it was recognised that the greatest danger a regime - if not a civilization - can face, is a large number of idle hands belonging to people who have some training in tactics and weaponry and combat experience. It gets worse if they're angry for whatever reason at the current government. To 'combat' this governments began such programs as formalized medals, veteran support programs and REMF promotions, as this regards Bounty Hunters: With such a large military and police force come a lot of retired police officers and soldiers, finding ways to keep them busy is a reason to spend money, let alone if it provides corollary benefits.
Bounty Hunting offers a good professional translation because it can be done part-time(most wanted won't even leave their home neighborhood) and the individuals will already have training in at least a significant proportion of the requirements of the trade, giving them a 'leg up' over other applicants. It will also make them unpopular among the residents, which hinders their inclusion among the part of the community most likely to rebel.
2: Management
Bounty Hunting work should reasonably be irregular and almost more like a taxi office than a police force, irregularity makes for complex management and if there's anything governments can't cope with it's a nonlinear state. Bounty Hunting firms can 'afford' to be more flexible without endangering their jurisdiction.
3: Risk Mitigation
The people (proportional) most likely to present difficult arrest situations are those who know they're already screwed(skipping bail, etc) it makes sense then to give those difficult arrests to people who you don't mind getting hurt, or blamed for hurting others, as much as possible.
4: Collateral
If a police officer harms an innocent in the pursuit of their responsibilities, the police department, county, state or federal authority risks massive costs in legal fees and compensation. Outsourcing to private industry allows the onus of covering insurance to be put on taxpayers, rather than tax recipients.
5: Payment on Delivery vs Full Time Salaried
A Police Forces number one concern must be the integrity of it's own officers, even after actual enforcement of laws, otherwise it's a liability rather than an asset. Police Officers must not be at risk of going bankrupt despite performing their duties and must be disallowed from 'alternative interests,' being relatively poorer, they're relatively easier to bribe or influence with money even than politicians. Regular, dependable payment is essential. That's to say nothing of the requirement for stations and routes to always be staffed as expected and part-time contracts are just asking for flakes to flake.
6: Diversification
A Bounty Hunter can be free to take on non-government work, private security, investigations etc, whilst government contracts must be on average profitable, a diverse portfolio allows recruitment (and a 'Unity'(working for the State) psychological influence) of people who would normally run a mile at police work and subisidize against failure to secure bonds.
7: Arsenal
A Police Force (bearing in mind the earlier requirement for consistency) cannot (it's hard) easily maintain the capacity to deal with all conceivable eventualities, maintain stockpiles and training regimens with/of all relevant materiel and techniques. If they have a budget to balance more equipment means less beat officers or investigative staff. On the other hand, a private individual might be found at any time that has the required licenses, training and equipment to perform a task and the PD might wish it was legal to Deputize, instead they create a contract to a Bounty Hunting team to effectively do the same, getting the results without the overheads for scarce or one-off operations.
If you follow this to it's logical extreme you don't need an army - a police force, contractors and monopoly over space-borne weaponry will do. Even, one might argue an army on the scale of millions of personnel is surplus to requirements if one exists as the sole political entity in known space. No traditionally scaled(that is to say, a tiny fraction of the population actively involved, supported by a few rich folks aka Rev. War) rebellion opposed by the military could hope to succeed in developed nations in modern times(without external support), let alone in times when you can't even see the enemy you're wanting to oppose.
//Military Reserve
Whilst the Hegemony might feel secure in it's integrity, space is big(?) legalizing(promoting, institutionalizing) bounty hunting provides one more method of maintaining a certain core of military readiness that otherwise would not exist.
The Army and 'Navy' might well have biannual mandatory refreshers for reservists, but it's not going to be any substitutute for people who train & use the relevant skills on a daily basis. Depending on the nature of the bounty hunting profession in your world, bounty hunters may provide a tangible asset if it came to war. Those who concentrate on domestic non-violent enforcement could be contracted as 'peacekeepers' and police cadre in occupied territory, members of more militant organizations could be constituted as special operations units, or used as consultants for retraining and readiness by a military that has not seen a wartime action in decades.
Even, in such circumstances where the Army has not had anything much military to do for a long while, it would potentially be the case that a great deal of the more pro-active individuals who can't stomach jobs as placeholders or 'potentially useful' would take up bounty hunting and bounty hunting would attract the prestige historically linked with military units.
Rich and poor
Police is not here to protect every person from violence, it is here to enforce law. (Already ruled and practiced in our world.) In the future there is big difference between those rich and those poor.
There are hight-tech citites (or enclaves), where the rich lives, protected by police and without the need to violently resist (as they could lose their status). The police is benevolent, as usual crimes are white collar crimes (tax evasion and such - solved by penalties) and ocassional interpersonal violence in affect (cheated husband would broke nose his wife and her amant when catch them in flagranti - and then give himself to police without fight - and get away with huge sum to fix cosmetical damage and emocional hurting, maybe even few weeks or month in nice prison - nothing to risk life for). And the police is benevolent, as there is no serious resitance and we are talking rich peoples. In city is total surveliance, cameras everywhere, credit cards with names on them only accepted and so on - nearly impossible to run away from police for more than few hours anyway in bounds of such city.
The cities have good guarded borders and crossing the borders (both ways) is generally frowed upon and is matter of checks like taking intercontinetal airplane today.
Outside are "slums" with poor people, left to themself. No state cameras would stand long there, risky for police to go there without big group and military equipement. Law there is more encorced by customs. Cash is used regularry, IDs are not mandatory to live there and violence is part of the life (also vendetta, low mob mafia, and such).
Well some people are very rich there too, as well as in the city are not-so rich people (gardeners, maids, basically all services) - but those in cities are controlled and wants to keep their good status, those in slums wants to keep their independence and privacy (or are forced to). (basically average person in "slums" can own more, than the lower class in city, except the safe environment and guaranteed good life, including medical care)
There is possible migration both ways, but it is difficult to change status:
poor to rich means give all your privacy, be penalized on all proven crimes and be subject of long time suppresion of police as unttusted person - also you need somebody rich to promise overlook over you (and pay all eventual fines for you) and you would go to the bottom positions anyway and basically be slave for years before having chance to get better position, while your patron can send you back to slums on his/her whim (so you would lose everything in both words)
rich to poor - well, if you think you can survive in jungle, where nobody helps you and everybody hates you, without all those nice thinks you had in city guarantied - you need to be really desperate to go this way - and the city would not like to accept you back. Also all your relatives would lose a lot of credibility aand status for your action, even if they disown you - do not count on some support.
Anyway the cities needs the slums for taking care about agriculture, mining, low tech (which does polution), artworks and such, while slums need cities for high technology, medicines, movies, etc. so there are big trade routes both ways.
And those bounty hunters operates outside the cities, both for locals and citizens, who had problems outside city walls. Maybe even some bounty hunters have homes in cities and high technology (private SWAT), but the main body lives in slums and knows the back streets, gangs and all others, who operate there.
Bounty hunters are not allowed to operate in cities (the police can manage it there good enought), but police cannot operate in slums (as nobody cooperate there and small units would be attacked for equip and ransom, while big units have no chance infiltrate anything), where bounty hunters can move freely as locals. There is tell-telling difference between citizenc and locals not only in body modifications and equipement, but mainly in behavior, street knowledge, language ... they both just stand out on the other side of border.
Referencies: District 9, Battle Angel Alita, Demolition man, Ghost in the Shell, Black Lagoon, ... (or with some exgregation rich countries (as "cities") vs poor countries (as "slums") today)
Edit: It is just on you, what "poor" means in that setting - if common food is soya-ratburgers as real meat (even from vermints) is too expensive, or if it means, that some of them have "just" 2D TV without tactile feedback, only a two or three pieces of cyberware enhancements and have to travel by ground vehicles ... poor and rich is just relative to each other.
# Federal division of powers
Although the Hegemony is a single unified government, in practice it's far too large to be run as a unitary body. It must maintain different levels of bureaucracy, governing areas ranging from cities to what we would think of as countries. Potential competitors for each region's rulers and bureaucrats abound: other regions of similar size, smaller constituents, larger regions they are a part of. Since your police and military forces are controlled by the bureaucracy, they are part of that competition for power.
One natural result is that individual regions of various sizes have their own security forces, with very strict rules about where they are and are not welcome. A nation-like region might not even have the power to send police into individual provinces or cities, depending on whether or not it has a justification that won't make it look like a power play. Because they're effectively in competition, police forces at different levels and in different places aren't likely to have very good communication - this is something that perfectly friendly agencies and nations struggle with in the real world, after all. So criminals (or criminal syndicates) that can move between regions can stay ahead of the local police.
Enter bounty hunters. Unlike police/military forces that represent the encroaching power of a rival power bloc, individual bounty hunters are hardly a threat to the established order. If they cause problems, the host region can easily censure, expel, even kill them without much difficulty. They can take down lone criminals who flee between jurisdictions, and gather information about larger syndicates to feed to the local law. (They might even serve as an informal communications channel for police forces whose superiors are feuding but who must cooperate against a particular threat.)
It gives people an incentive to turn themselves in
The police force is known for being generally pretty fair and reasonable. They're constrained by a number of laws. Also, they can afford to be, partially because they avoid the high-pressure stuff. Everyone knows that if you crank the threat up high enough, the police will just let you go. Wave a gun, and you can walk out of there. At the same time, the police are wearing body cameras at all times, and those update the Panopticon Surveillance State System in real-time. If you wave weaponry at a police officer, your name goes on a list, and the bounty hunters come after you.
The bounty hunters are not fair, and not reasonable, and do not wear body cameras, and they will seriously mess you up. There's likely to be a firefight or two, and anyone you care about in the immediate vicinity might wind up being collateral damage. They get a bonus if you're alive when they bring you in, but it's not that big of a bonus.
Thus, if you're innocent, or even mostly innocent, it's probably a good idea to turn yourself in. The punishment you'll get for whatever crime you committed won't be as bad as what the bounty hunters will do to you trying to "Bring you to justice". If you're guilty s hell, though... well, that's what Bounty Hunters are for.
# Plausible Deniability
What the police do reflects directly on the government. Even a rogue cop who goes to court tarnishes the badge. A rogue cop who does not go to court means the rot is starting.
I hope you realize that giving the legal right to arrest a target means that the bounty hunters have the legal right to arrest anyone who looks like the target. And the right to harass anyone who looks like the target and demand to see papers to prove that they're not the target. Add that the bounty hunters are not trained police officers, and do not get access to police information systems. Either rules are harshly enforced on the bounty hunters, then the first honest mistake sends them to prison for kidnapping and assault. Or the system cuts them some slack if they say "he looked like the perp, honest." Such a force can be useful to people in power.
Note that many jurisdictions allow a citizens's arrest and many post rewards for information on crimes or criminals. But someone who makes a living by seeking out opportunities for a citizen's arrest would be in an awkward position if he or she gets it wrong.
# Lobby Work by the Bond and Prison Industry
The US-style concept of bounty hunters is tied to the practice of bond/bail and the agents who loan this money. Few industrialized countries have similar systems -- a defendant is considered innocent until proven guilty, and held in jail only if there is fear of flight or evidence tampering. Posting a significant bond might reduce the fear of flight, but not if the defendant fears several years in prison.
So why keep it? Because the people involved in it make lots of money, and donate in the right places.
• "I hope you realize that giving the legal right to arrest a target means that the bounty hunters have the legal right to arrest anyone who looks like the target." That's not actually true in the U.S. If a bounter hunter is trying to arrest someone that is not the target, they can get arrested and jailed, even if they honestly think they are the target. It is considered their legally binding responsibility to only arrest the target. That's not to say that mistakes do not happen, but those mistakes are not permitted under the law. – PyRulez Mar 5 at 6:42
Standing armies are dangerous to a polity.
A standing army in the hands of a government placed so independent of the people, may be made a fatal instrument to overturn the public liberties; it may be employed to enforce the collection of the most oppressive taxes, and to carry into execution the most arbitrary measures. An ambitious man who may have the army at his devotion, may step up into the throne, and seize upon absolute power.
The AntiFederalists on Standing Armies, Laurence Vance
Your police and your army are one entity. The writers of the Constitution dreaded having a standing army at all; now the US has one, but there are strict restrictions on its actions and especially its interaction with the populace. On those rare circumstances when armed troops are needed within the borders of the US it is the milita, or National Guard who is called - civilian soldiers, not the professionals.
Having the military interact with the public is dangerous. It is also dangerous to a civilian power structure because the army can simply seize power.
Your armed forces / police force are bound by many rules of interaction which are meant to reduce the danger they pose. Bounty hunters interact intimately with the populace in a way you do not want your military to do, but they are just one aspect of the workaround in this world. Just as in our world paramedics, fire fighters and animal control are bodies of public servants (and possibly volunteer part-timers) who can be called out to help people, so too in your world the bounty hunters, traffic control persons and other aspects of civil society control.
Musing further - their mandate is violence in service of the State and so calling the police / army in your world is tantamount to calling for a person to be killed - because more often than not that is the result when the police / army arrives at the scene. This scenario would make for good high science fiction - exploring our real world from the perspective of a fictonal one. Those interested and aware of current events in the US can consider these aspects of law enforcement as they see fit.
• In my mind once you had a global government the need for a standing army would decrease and would shift more to counter terrorism and combating insurgents. In this way the army got outdated and their work was picked up by the police (technically probably some sort of state security) – Celestial Dragon Emperor Mar 5 at 18:24
I'd imagine they target different demographics.
The police presence would be largely urban, tied into their support networks and fortresses (stations). In the future this would include megalithic surveillance networks and sensors.
The bounty hunters would go where its not cost efficient to set up the supporting infrastructure (yet). Deep country, swamps, off planet, asteroids. Places they haven't built up yet. Or perps that cant be suppressed with standard urban loudouts.
This means seeing a bounty hunter on a city job would cause friction with local cops ("What's he doing here", "Just as bad as the collars he brings in")
## The average citizen is extremely dangerous
Imagine a world not too far into the future where most people own a 3D-printer/replicator, and the personal technology/cybernetic enhancement fields have advanced to a point where people can be stronger and quicker almost without limit.
We have gone post-scarcity, AI governs most high-level systems, leading to a lack of jobs. People get bored, turn to crime for something to do. Those that don't can join the police, solving petty crimes like vandalism, theft, lollygagging etc.
However, the organised crime aspect of the world becomes extremely dangerous, any citizen could print themselves gun parts, and enhance themselves to have super strength and speed. Why would police hunt down these dangerous criminals when they don't need to work? The world is post-scarcity, remember?
That's where the bounty hunters come in. An elite organisation/guild of mercenaries who are also cyber-modded to high heaven, equipped with the very best weaponry. All the government has to do when there's a murder or terrorist attack is post a bounty on the offenders, and the guild will do the rest.
• That implies the State can't win an arms race against criminals: that's true in, like, Somalia, but maybe not usually. And even now criminals can be dangerous (e.g. because of handguns), even so the police do their jobs. – ChrisW Mar 6 at 15:38
See this answer to the question, "How to police a state with high amount of gun ownership where the police are not routinely armed?" -- because the opposite scenario to that might be that it's difficult to police a world where you DON'T have ubiquitous surveillance, and/or where it's easy for private passengers to cross international borders unchecked, and/or where cash is king (or something like cash, i.e. valuable, portable, anonymous, and with a reasonable shelf-life -- cryptocurrency, medicines, or whatever).
Local police work (by definition) against local crime and criminals -- and have no personal experience off-world -- so if ever you want a detective who's hot (or cold) on some fugitive's tail as they flit from one place to another, or try to make a new life elsewhere, that would have to be someone else, e.g. a bounty-hunter.
I don't think they're for "high-risk" arrests because, instead, professional SWAT teams can handle those (and the function of whatever is left of the military is to handle whatever a SWAT team can't).
• maybe the remnants of the military deal with terrorists and insurgencies? All the other functions I believe could be done by the police or a government entity. – Celestial Dragon Emperor Mar 5 at 18:44
• Yeah in Canada I think they task the army when there's an unusual snow-storm and they want the emergency man-power; but also if there's something resembling armed insurgency -- e.g. against the FLQ to act as sentries etc. (to leave the police free to do regular police-work) and in the Oka crisis because the police didn't have the training or discipline or what-have-you required to cope with armed resistance non-violently -- ditto Little Rock in the States. – ChrisW Mar 5 at 18:56
• Dealing with terrorists though is ideally police-work rather than military -- e.g. it's not a (military-grade) anti-tank missile or machine-gun that you want against a "terrorist", rather it's (police-grade) intelligence as to who and where they are (plus sovereignty so that you can go there and arrest them). – ChrisW Mar 5 at 19:08
The answers by Thorne (about the monetary advantages) and Morris the Cat (about the practical benefits to the safety and 'purity' of regular law enforcement) are both great, and cover what I would think are two of the biggest aspects here if you assume a government that isn't fascist and/or authoritarian.
There's one other really big advantage though:
### Once you go interplanetary, you have too much space to cover with traditional canvas policing techniques or even regular patrols.
Quite simply, it's impractical to have law enforcement that comprehensively covers anything beyond planetary orbit, or at most beyond a given star system and established travel routes between systems. There's just way too much area to cover. Even if you had your entire populace providing conventional law enforcement, you still wouldn't be able to reliably cover all your territory. Given this, once you get past planetary orbit, you either need a dedicated force that can track down and retrieve (or terminate) fugitives, or you just treat them as exiles (that is, standing warrants for their incarceration or execution if they show up in areas under jurisdiction of your police, but nobody actively going after them).
This also accentuates both of the aspects of the answers I mentioned above. As the area you need to cover goes up, it makes more sense to pay based on results, and you end up with more and more places for isolated groups of very dangerous criminals to exist.
This aspect of needing an impractical number of officers proportionate to your population to cover a given area is a large part of why bounties were the norm in the American Old West, each town had maybe one or two law enforcement officers, and it was just impractical for them to chase down every last criminal that came through town. You can see the same logic to a lesser extent in the existence of organizations like the US Marshals, there's just too much area for the regular officers at the level of jurisdiction at which they operate to properly cover.
While it's not exactly the primary reason, you can see this in play in a lot of science-fiction settings as well. In Star Wars for example, there actually are planetary and system law enforcement agencies, and even galaxy-wide ones, but bounty hunters are still common enough that outside of certain 'special' areas (the corporate sector or deep core for example), you're more likely to run into them than you are regular law enforcement when traveling the stars.
Cost
If you have a detective squad, they'll be busy inside their jurisdiction working on several cases. Cases go cold and get dropped, police have the safety of their wards as a high priority.
Depending on the bounty system you can either A. Assign bounties to hunters specifically, give each a number of them to accomplish and no real timeline. If they complete the task they get significant pay,less than a dedicated detective squad working the task full time, but plenty for a single individual. The reward is set and the time/resources used are up to the contractor to work out. Other answers have mentioned this.
B. Open bounties, anyone who completes a bounty can claim the reward if they're licensed. Once again the reward per task is static and the investment of resources is on the hunter themselves, failure doesn't add cost to the police themselves.
Specialization
Hunters hunt bounties, they don't do traffic stops, riot suppression, emergency response or anything else. They can spend time on the job because they're specialized and have contacts and licensing to navigate complicated jurisdictional boundaries, they can afford equipment specifically for tracking and hunting people. Their main income is supported by these things, a police department couldn't and shouldn't afford such things at scale.
Networks I mentioned them above but a network of contacts that aren't strictly legal would benefit a bounty hunter and a truly squeaky-clean PD can't be caught doing that. Hunters might network with one another, collaborate on jobs or simply share resources in a way that would not flourish in the bureaucracy of a megacity PD.
Danger Bad folks are gonna kill cops if they're desperate enough, we need cops for a lot of things that aren't hunting fugitives. Better to pay folks that know the risk and chose the line of work than wear out cops you need for more humanitarian cases.
Range Sending a cop far outside their jurisdiction or into seedier areas with a badge risks the officer and almost guarantees failure since they have no effective authority in such a place. Bounty hunters are more discreet because they don't have legal obligations like an officer.
Jurisdictional Respect Sending an officer from my PD to your nation is little problem if we're friendly(Mounties in the US, FBI in Canada, neither are PD but you get the idea), might be a problem if we aren't. Could get some nasty legal battles if we disagree on how something must be handled.
If there's some sort of central registry of bounties that all nations/jurisdictions share, then hunters can collar fugitives anywhere in the world.
Alternatively a bounty hunter might be willing to cross a border, shoot the bad guy and just leave. It's far less of a risk to international relations if a third party that has no official status in my PD gets caught snagging fugitives on a bounty.
The police tend only to do things that are cost effective. They won't go look for your stolen bike even though they know likely locations where it might be stored or for sale. They won't devote more than a certain amount of effort to finding your mugger. They will stop pursuing a fugitive if that fugitive makes it too expensive. They won't try to arrest someone who ripped you off over the internet if they are in a different jurisdiction.
Perhaps it is worth it to me to pay a bounty hunter to do any of those things. Perhaps I'm happy to pay 1000cr to a bounty hunter if I can get my bike back or 50,000cr to get one to track down the man who killed my wife and then disappeared in to the underworld. Maybe a community will club together to pay for a bounty hunter to find the man who said he would broker the sale of their crops and then disappeared with the money.
If you want to differentiate bounty hunters from hired guns you still need the licences and rules that they must follow. So you can pay one to retrieve someone charged with a crime so that the police can arrest them but you can't pay one just to beat up someone you don't like.
This is effectively justice for those who can afford to pay.
• I love the idea of a community pooling money together to hire a bounty hunter. Stuff like finding the corrupt executive that pollutes the water, the serial killer that ravaged their town, etc – Celestial Dragon Emperor Mar 7 at 13:20
Crime, crime and more crime. Why? A black market in a key thing that spawns an underworld that makes prohibition and the drug war look like a tea party (e.g., perhaps touching is a crime, as in the comic Love Not Found; but, unlike the comic where everyone thinks touching is gross, in this world everybody wants it but no one admits it and all touching is covert).
It might be a bit like many aspects of life in the modern People's Republic of China (a 2018 Forbes article captures the feel of it). A totalitarian regime requires lots of watchers. But actually getting things done in a bureaucratic mess like that might take rule breaking bounty hunters.
Extreme economic inequality also creates demand since a lot of gatekeepers and guards must be hired to protect the privileged from the hoi polloi, and the elites then have to hire bounty hunters with better results and service than bureaucratic law enforcement (compare Altered Carbon), not unlike hiring private judges (which exists in real life) with more time to focus on their concerns. Maybe the elites have private prosecutors too.
The two ideas aren't incompatible with each other either.
A short answer is make it challenging to make an honest living and criminals will be numerous. This encourages people to take employment such as bounty hunting as well. Secret Police and informants can be a cheap way of making a highly populated police force and help create an atmosphere of fear and powerlessness. You don't even need to make them fulltime servicemen either.
A corrupt version could be paying for testimony so you can execute someone to set an example...
Another option that I haven't seen mentioned yet is separation of duties. The "Police" branch of the Hegemony's military could be mostly (or entirely) detectives whose job is to determine what happened, who did it, and if it was illegal (in most cases that last one is obvious, but think accidental death vs intentional murder). These people get paid for work done regardless of bodies brought before a judge (or straight to jail). After the police determine something illegal happened, they refer the person to various bounty hunters (or BH networks) who get paid upon bringing the suspect into the system.
Still another option are jurisdictions. Police are bound to an area while a bounty hunter isn't (current world example would be crossing countries to bring someone to justice). That does come with it's own set of legal issues, but that's the hunter's concern, not the cop's.
In the United States, this already exists. Police regularly offer sums of money to anyone who can provide information that leads to the arrest and conviction, banking on a criminal's friend to say "Hey, I think I know who your bank robber is: My buddy has income he can't explain, he paid in multiple large bills... the serial numbers are sequential, and he was drunk at my place last night and said 'I robbed the bank and there's a reward out for me!'. Can I get paid?"
In addition, most common law jurisdictions (basically any country that has it's national origin ties that are related to the United States or The British Empire... serving justice to over 1 billion people daily) have "Citizens Arrest", which basically allows any Joe Schmo to "Arrest" a person who they have a reasonable suspicion of committing a crime... it's frowned upon, but it's not out and out illegal (for a few reasons... it's easy for an untrained citizen to arrest someone in a wrong manner and get the case thrown out... it's dangerous to arrest criminals even if you are a cop.).
Finally there are real life bounty hunters today that work for the police (Almost entirely in the U.S.). Normally the work is done for privately owned "Bail Bondsmen" who are basically loaning criminals the money to put up bail. If they don't pay back, or don't show up to court, the Bondsman will call in a bounty hunter who can go and recover the criminal. Since most of these individuals are not officers of the peace, they don't need warrants to enter property and anyone can citizens arrest. I'm not as up on this enough to post more about the system, but only four U.S. states outlawed this practice.
• A citizens arrest (always for free) is very different from bounty hunting although it can be used by vigilantes (a group in the U.S. called the "Guardian Angels" used it in that way). denver.cbslocal.com/2017/07/22/guardian-angels-colfax-avenue Often bail bond firm employees are the bounty hunters rather than using independent contractors from them to do it. Rewards for snitching are also quite different from paying someone to apprehend someone at large. In medieval Iceland a private person could get authorization from the government to arrest. But, they didn't have any police. – ohwilleke Mar 8 at 0:06
To have bounty hunters you need somebody who has interest in catching the fugitives but cannot use the law enforcements agencies to do so.
In the mythical old west this was because weak police presence, in modern US because it is about a private company enforcing the contract it has with the fugitive.
In your case we can exclude the first option, so we can assume that somebody other than the government pays the bounties. Since you are talking about "a network" we can assume that it is the network paying the money and choosing to pay bounties instead of a salary or a wage.
So three conditions for practical bounty hunters.
1. Private economic interest in catching people, the government does not do it.
2. Interest in accepted by government as legit, so the police do not stop it.
3. The interest is irregular enough that normal employment is not a good option.
The conditions are interconnected. The reason it does not make for normal employment and that the police do not do it are probably related. The private interest and the reason the government accepts it are also probably related.
I hate to say this but this kind of implies some not nice things about the state. Basically, the state is choosing to let a private entity to exploit a specific demographic and looks the other way as long as the private entity keeps it informal by handling it on case by case or bounty by bounty basis. Since the cases involve only individuals there is no systematic pattern of abuse, or rather it can be pretended that the patterns rise from the legitimate individual actions of the individuals involved not from discrimination. The state is not to blame that this particular demographic has lots of this kind of problem.
So we can reduce the three conditions to two
1. A demographic that is considered "outsiders" by the establishment.
2. An action common in that group that can
a. be monetized for profit, some sort of financial transaction is involved
b. serves as an excuse to look the other way, it is their own fault
At this point you kind of need to do the actual world building and fill in the blanks. What kinds of people are on the bottom of the social and political hierarchy to the point of being virtual (but not real) outsiders? What things does this group do to justify being considered fugitive? How can this be monetized? Then just legalize the enforcement of the private contracts involved in the monetization and you have bounty hunters.
You can easily use the modern US as an example how this works or even as a model but it is your world so you can and probably should do something else. This is because even this answer probably reads to most who read this far as a social commentary on the US. With the current political climate that is only one step from seeing this answer as me pushing some sort of liberal political agenda. You want to avoid doing this unless you either actually want to make a political statement or, as with this answer, want to warn against looking like you are making one when you do not.
Naturally it is perfectly possible to write about bounty hunters without going to the social issues behind it. And if you copy those issues from real life instead of making your own you should IMHO.
• The fugitives in my mind where probably going to outcasts (On Earth) both the thug and extremist variety mixed with petty criminals. In my mind they'd be the small fry of their respective groups or at least small fry to the Hegemony. Ex: a dnall time pimp dealing drugs on the side might have a small bounty placed on him by the city council or local peacekeepers busy with other crimes and duties. – Celestial Dragon Emperor Mar 8 at 0:23
• Also you did bring up a good point about how it could come off as me making a point. I think a good example would be Orson Scott Card who's beliefs in enders game seem to be contrary to his own. Tbh I wanted bounty hunters in my setting, but I also wanted to explore the social system behind it so I could have a well developed world. – Celestial Dragon Emperor Mar 8 at 0:25
• @CelestialDragonEmperor Drug users or extremists would both be valid examples of politically and socially marginalized groups. The business could be the rehabilitation services offered as an alternative to serving time. The excuse could be the fugitive running away from treatment he had agreed to in a legally binding contract despite needing it for his "problem". So yeah, that would work, all of my conditions check, but you need to twist it a little to get the private business angle to it or the police will just handle it. – Ville Niemi Mar 8 at 0:43
• maybe the companies who they owe money too or work for hire the bounty hunters to get their investments back. (When it's not private entities putting out the bounties). Also maybe it's the companies that put out the bounties (seeing as all they need to do is prove a crime was committed and the target is currently "on the run"/"evading the law" which could simply be refusing to turn yourself in. – Celestial Dragon Emperor Mar 8 at 1:10 | 2019-09-20 17:08:18 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.19919586181640625, "perplexity": 3137.790822641752}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-39/segments/1568514574050.69/warc/CC-MAIN-20190920155311-20190920181311-00338.warc.gz"} |
https://brilliant.org/problems/who-developed-the-mod-function/ | # Who developed the mod function?
Calculus Level 5
After this problem Mayank and Akul have started hating the mod function;-
Let $$S$$ be $$\{ (x,y):|||x|-2|-1|+|||y|-2|-1|||=1\}$$
If $$S$$ is made up of a wire, find the $$length$$ of the wire.
We've got more for you at the set Mayank and Akul
PS: If brilliantly, it can be solved in a few steps
× | 2017-10-18 16:56:13 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7390826344490051, "perplexity": 2747.275062477604}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2017-43/segments/1508187823016.53/warc/CC-MAIN-20171018161655-20171018181655-00815.warc.gz"} |
https://forum.allaboutcircuits.com/threads/change-dc-voltage.2317/#post-15399 | # Change DC voltage?
#### jhelmick
Joined Mar 24, 2006
4
This simple task is beyond me, but I have a Tach Generator that outputs 110 VDC at its maximum RPM, I need that DC voltage to be 10 volts maximum for an input signal to a inverter drive motor controller.
Here is my problem...I was told 1000 ohms will reduce the voltage by 1, therefore 100K ohms would reduce the voltage by 100, not according to my meter...I tried that and it reduced the voltage maybe 1/2 volt. what am I to do
#### Papabravo
Joined Feb 24, 2006
19,244
Originally posted by jhelmick@Mar 24 2006, 08:36 PM
This simple task is beyond me, but I have a Tach Generator that outputs 110 VDC at its maximum RPM, I need that DC voltage to be 10 volts maximum for an input signal to a inverter drive motor controller.
Here is my problem...I was told 1000 ohms will reduce the voltage by 1, therefore 100K ohms would reduce the voltage by 100, not according to my meter...I tried that and it reduced the voltage maybe 1/2 volt. what am I to do
[post=15399]Quoted post[/post]
A single resistor will not do diddley be-bop for you. What you need is a voltage divider. That's two resistors, call them R1 and R2. What you want is to multiply 110 VDC by 0.090909...
Rich (BB code):
Vout = Vin(R2/(R1+R2)) = 110*(10K/(100K + 10K)) = 10
Connect a 100K resistor and a 10K resistor together. Connect the free end of the 100K to your input and connect the free end of the 10K to ground. If you measure the voltage across the 10K resistor with respect to ground you should measure 0.090909... times the input.
You should stop listening to your little friends with the quaint notions. | 2022-11-26 17:00:01 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3030773103237152, "perplexity": 2663.7234736874684}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2022-49/segments/1669446708010.98/warc/CC-MAIN-20221126144448-20221126174448-00573.warc.gz"} |
https://meta.mathoverflow.net/questions/405/quick-or-easy-methods-to-post-math-or-diagrams-on-chat | # Quick or easy methods to post math or diagrams on chat
One of the seeming obstacles to having scheduled informal seminars on chat is the extra work, probably mostly for the leader of the discussion (should there be one), in presenting ideas on the chat page. One person comapred this to Latexing seminar notes, pointing out this was not much fun.
My friend Dmitry pointed out that there are what he called "scribblers," a pad with a stylus, where one can just write or draw, then create a pdf or jpeg and post that. This may or may not be pleasant enough to induce established mathematicians to agree to participate in such a thing. Evidently Jon Beardsley has a tablet that can do this, including color, and put a couple of sample items on Homotopy Chat. One of them said "it'd be better if chat had a whiteboard area"
What are other devices/services that might make, say, real time posting to Chat less of a chore?
For that matter, has anyone used such a scribbler, and can give an impression of the usefulness of that device for this purpose?
Hmmm. I bought an inexpensive single-page scanner. I could certainly write out pretty much anything by hand that would fit on one piece of paper, not excluding pasting in photocopied excerpts from books I might have, and post that...the thing makes jpegs, for reasons I do not know those work better on SE. Mine is a Canon CanoScan LiDE 210.
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• sigh. ${}{}{}{}$ – Will Jagy Jul 7 '13 at 21:03
• What's wrong? I hope it was not my tag-edit (but I thought now we have them it'd be good to use them). Sorry, I had nothing more substantive to contribute. But perhaps it is just the lack of responses that makes you unhappy. But then meta is not very active at this time, only 10 people saw the post, so there is still hope for good suggestions in the future. – user9072 Jul 7 '13 at 21:07
• @quid, it is the lack of (granted, early) responses. Time will tell. I got very involved with the idea of chat as a useful extension, but there seem to be as many obstacles as opportunities. – Will Jagy Jul 7 '13 at 21:14
• I hope it will work out in the end. The homotopy room you helped to start seems to be doing alright. A lot more going on then in the general room. Perhaps I should have posted this rather in chat to create some traffic there :-) – user9072 Jul 7 '13 at 23:24
• @quid, after I put the jpeg here I put the same one in Homotopy Chat. They were initially impressed by my artwork, but then there was some disagreement about the color, named after the flower named after en.wikipedia.org/wiki/Leonhart_Fuchs as opposed to the mathematician en.wikipedia.org/wiki/Lazarus_Fuchs – Will Jagy Jul 7 '13 at 23:34
• Tangentially related: mathoverflow.net/questions/49384/… – Willie Wong Jul 8 '13 at 11:24
• @WillJagy Oh dear Lord! I can't believe they were arguing over who was the namesake of the flower Fuchsia! Is that why you said sigh? I don't know what to say; I'm kind of appalled. They should ask about that on English Language & Usage SE, and tag it etymology. You are trying to do a good deed, behave in a constructive, helpful manner for the greater good of the MO community. I wish I could chastise them, and hug you, or give you a gold star or something. You are a good person for trying to help others. – Ellie Kesselman Jul 8 '13 at 21:35
• @FeralOink, the sigh was for the lack of early response. To be honest, they did not argue about the flower for very long. However, you are correct that my attempts to push this idea along are no longer being met with much enthusiasm, so I think i will call it a day, and let the kids who are using the chat room work out if and how they wish to extend operations. – Will Jagy Jul 8 '13 at 22:41
• Hey @willJagy we should def talk about this some point. I think it'd be best if you sent me an email. I have some thoughts, and I hate to think that you might feel your efforts have gone unappreciated. I've just been kind of stupid busy with stupid stuff recently. – Jonathan Beardsley Jul 10 '13 at 20:52
• @JonBeardsley, yes, I will find your email and send you something. – Will Jagy Jul 10 '13 at 21:31
• Perhaps some of the links I've collected in the comments here might be interesting for you. – Martin Sleziak Jul 12 '13 at 10:49
• @MartinSleziak, thanks. – Will Jagy Jul 12 '13 at 15:24 | 2021-04-19 15:00:46 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4662264287471771, "perplexity": 1513.3941022833003}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-17/segments/1618038887646.69/warc/CC-MAIN-20210419142428-20210419172428-00074.warc.gz"} |
https://math.stackexchange.com/questions/2702823/is-the-nonzero-vector-b-in-mathrmcol-a-of-the-following-3%C3%973-matrix-a | # Is the nonzero vector $b$ in $\mathrm{Col}\,A$ of the following $3×3$ matrix $A$
$\def\Col{\mathop{\mathrm{Col}}}\def\Nul{\mathop{\mathrm{Nul}}}$In preperation for a linear algebra exam I have coming up I was asked to construct a $3×3$ matrix $A$ and nonzero vector $b$ such that $b$ is in $\Col A$ but $b$ is not the same as any of the columns in $A$. I came up with the following:
Let $$A = \begin{bmatrix}1&-1&-1\\4&-2&-2\\1&-2&0\end{bmatrix}$$
and let $$b = \begin{bmatrix}2\\1\\1\end{bmatrix}.$$
Would this be correct? If not, what is a good answer? Any pointers someone can give on how to answer questions like this?
Can I also say $b$ is in $\Nul A$?
• To check if $b$ is in nul$A$, check if $Ab=0$. Mar 22 '18 at 4:17
So basically you have to find out nonzero vector $b$ which is in columns space of $A$ but not in columns of $A$. Take $b=pC_1+qC_2$, where $C_1$ and $C_2$ are independent columns of $A$ and $p$, $q$ are any non zero real numbers.
For your answer, consider $(2\; 1\; 1)=p(1\;4\;1)+q(-1\;-2\;-2)+r(-1\;-2\;0)$ and check that atleast two of $p,q$ and $r$ is non zero. If such $p,q$ and $r$ does not exist that it is not possible.
So what you should do is take a random column vector $v$ (say all components non-zero) and multiply with the matrix given the result will be the desired one: $b =Av$ | 2021-09-25 15:40:32 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.7855305075645447, "perplexity": 92.24581921100821}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2021-39/segments/1631780057687.51/warc/CC-MAIN-20210925142524-20210925172524-00130.warc.gz"} |
https://electronics.stackexchange.com/questions/340925/how-can-i-set-the-input-signal-to-ltspice-with-equal-intervals?noredirect=1 | # How can I set the input signal to LTspice with equal intervals?
In transient analysis I define a voltage input such as a square wave input and obtain an output voltage. Here I set the input signal:
Export time series:
But when I export the input and export time series signals from LTspice as a text, the time points do not have equal intervals. From the text file time plotted:
Is it possible to set it so we have an input and output with equal time intervals? Such as a sampled input and output with a constant sampling rate fs.
• A very similar question was asked just a couple days ago. – The Photon Nov 20 '17 at 22:03
• I set the max timestep to 0.00008 still same number of samples and same issue nothing change. I think that question is lacking example imao I didnt get the solution which parameter is what ect. – atmnt Nov 20 '17 at 22:10
• Can you put your spice file (the netlist file) on pastebin or somewhere? – The Photon Nov 20 '17 at 22:13
• Yes here is the asc file: wikisend.com/download/511398/fltrtest22.asc – atmnt Nov 20 '17 at 22:21
• Possible duplicate of Exporting LTspice waveforms to txt or csv – laptop2d Nov 21 '17 at 5:52
To 'sample' nodes in LTspice you can use the .WAVE command to create a WAV audio file. The maximum resolution is 32 bits and maximum sampling frequency is 4096MHz.
The plot below was produced from your LTspice schematic. It was created in LTspice with .wave fltrtest22.wav 16 50 V(in) V(out) which specifies 16 bits and 50sps, then converted to csv text data using Sound eXchange (command line: 'sox fltrtest22.wav -t dat fltrtest22.csv'), loaded into Openoffice Calc as merged space-delimited text, and finally plotted on an x-y scatter chart. | 2019-06-20 03:25:43 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.4219629764556885, "perplexity": 3019.861790603248}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2019-26/segments/1560627999130.98/warc/CC-MAIN-20190620024754-20190620050754-00494.warc.gz"} |
https://alexatnet.com/fsharp-how-to-check-that-tail-recursion-calls-are-optimised/ | / F#
# F#: How to check that tail recursion calls are optimised
The tail recursion optimisation happens when a compiler decides that instead of performing recursive function call (and add new entry to the execution stack) it is possible to use loop-like approach and just jump to the beginning of the function. Typically it happens when the compiler is smart, the tail calls optimisation is enabled and the recursive call is a leaf of the expression tree.
Is this can be tail-optimised?
let rec fib n =
if n = 1 || n = 2 then 1
else fib(n-1) + fib(n-2)
No, actually not. In this example recurcive call is not last in the expression tree, which is + (fib (- n 1)) (fib (- n 2)). So the addition happens after recursive calls.
However, the tail call optimisation can be applied in this case:
let fib n =
let rec rfib i p2 p1 =
if i = n then p1
else rfib (i+1) p1 (p2+p1)
rfib 1 0 1
The second version will not exhaust the stack on its way to 10000 Fibonacci number. Tt will hit integer overflow much before that but at least the stack will be fine :-) Not only the stack will be fine, the performance will be much better than in the first version.
So the tail-call optimisation is worth checking for if the number is recursive calls is expected to be more than a hundred or the recursive function is on the hot (performance-critical) execution path.
Unfortunately, the F# compiler does not help you much with that (yet).
This leaves two options: either check it by actually running the code and observing stack overflow exception or check generated IL code.
Observing stack overflow exception is quite simple technically. You just run the code with input causing a lot if recusive calls and wait. However, there is two difficulties: a) it may be quite hard to isolate code from its context; b) it depends on the time and resources the function takes on every iteration. This way is hard to follow in some of the cases.
Checking the generated IL code, in contrast, is very simple if you know what to look for. In the few following paragraphs I will show how to do that for two functions from the beginning of this article so you can do it yourself when needed.
The code will be compiled with .NET core. The tool used for disassemble is monodis. Let's go.
$dotnet new console -lang F# -o fib$ cd fib
Now update the Program.fs file:
open System
[<EntryPoint>]
let main argv =
let rec fib1 n =
if n = 1 || n = 2 then 1
else fib1(n-1) + fib1(n-2)
printfn "%A" (fib1 10)
let fib2 n =
let rec fib3 i p2 p1 =
if i = n then p1
else fib3 (i+1) p1 (p2+p1)
fib3 1 0 1
printfn "%A" (fib2 10000)
0
Build:
$dotnet build Now the fun part. Run monodis on the generated executable: $ monodis bin/Debug/netcoreapp2.0/fib.dll > fib.il
And let's examine the generated file.
The generated file is a mixture of structural statements (.assembly, .mresource, .namespace, .module, .class, .method) and assembly code (IL_0032: ...). Everything with .assembly, .mresource, and .namespace do not look relevant. There are four classes, named Program, fib1, fib2 and fib3. So every function defined with let is compiled into the class.
Body of the function is compiled into the Invoke methods of the generated classes. Let's check these methods of the fib1 and fib3 classes.
.method public virtual strict
instance default int32 Invoke (int32 n) cil managed
{
...
IL_0019: ldarg.0
IL_001a: ldarg.1
IL_001b: ldc.i4.1
IL_001c: sub
IL_001d: callvirt instance !1 class [FSharp.Core]Microsoft.FSharp.Core.FSharpFunc2<int32, int32>::Invoke(!0)
IL_0022: ldarg.0
IL_0023: ldarg.1
IL_0024: ldc.i4.2
IL_0025: sub
IL_0026: callvirt instance !1 class [FSharp.Core]Microsoft.FSharp.Core.FSharpFunc2<int32, int32>::Invoke(!0)
IL_002c: ret
} // end of method fib1@6::Invoke
.method public virtual strict
instance default int32 Invoke (int32 i, int32 p2, int32 p1) cil managed
{
...
IL_000f: ldarg.1
IL_0010: ldc.i4.1
IL_0012: ldarg.3
IL_0013: ldarg.2
IL_0014: ldarg.3
IL_0016: starg.s 3
IL_0018: starg.s 2
IL_001a: starg.s 1
IL_001c: br.s IL_0000
} // end of method fib3@12::Invoke
It is easy to see that differently from the fib1, the fib3 does not have callvirt calls so the tail call optimisation is applied.
At the end, there are two hints on how to make sure that code is optimised:
• check that the result of function being called recursively is returned straight away, without been used in other computations within this function - this should already give you enough confidence that the tail calls are optimised
• if unsure, remember the name of the recursive function (or change it so something inique within your project), decompile and search for the generated function class and its Invoke method. Make sure that it does not contain callvirts of itself
#### Alex Netkachov
Alex likes functional programming, algorithms and code reviews. Apart from programming, his favourites are walking with his family in the parks and national trails and reading books. | 2018-01-18 21:48:44 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.3101719915866852, "perplexity": 4753.204835468311}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2018-05/segments/1516084887621.26/warc/CC-MAIN-20180118210638-20180118230638-00435.warc.gz"} |
http://physics.stackexchange.com/questions/6649/can-the-kramerskronig-relation-be-used-to-correct-transfer-function-measurement/6656 | # Can the Kramers–Kronig relation be used to correct transfer function measurements?
In experimental physics, we often make measurements of linear transfer functions; these are complex-valued functions of frequency. If the underlying system is causal, then the transfer function must be analytic, satisfying the Kramers-Kronig relations. Our measurements, however, are corrupted by random (and perhaps systematic) errors.
Is it possible to improve a measurement of a linear transfer function of a causal system in the presence of noise by applying some kind of constraints derived from the Kramers-Kronig relations?
-
I'm sure the answer is "yes", but I'm very interested how you would actually make such an improvement. Good question +1 – Keenan Pepper Mar 10 '11 at 21:46 I wonder whether this would be equivalent to least-squares fitting an analytic model (trying various numbers of poles and zeroes) à la VECTFIT? – nibot Mar 10 '11 at 22:40
## 1 Answer
The problem you describe is (mathematically) similar to blind deconvolution. Given a signal which is the result of blurring an image (a linear operation) and adding noise, blind deconvolution tries to estimate the blur and the image.
As described here, the blind deconvolution process consists roughly of:
1. Guess the blurring function (transfer function)
2. Construct an image consistent with your signal and your guess of the transfer function
3. Apply physically reasonable constraints to the constructed image. (For example, non-negativity).
4. Modify your guess of the blurring function to better satisfy these constraints
5. Goto 2.
It sounds like your idea would apply to step 3. I've never seen the K-K relations used this way, but I imagine they'd work just fine.
-
Thanks for the link; that looks like a good lead! I like the idea of an iterative technique, but I wonder whether it is really so straight-forward to simply "apply" the K-K relations (i.e. integral relations on sampled data). – nibot Mar 10 '11 at 22:38
Possibly naive, but: Fourier transform your transfer function to give an impulse response. Truncate the part of the impulse response that is acausal, inverse transform, and you have your 'constrained' transfer function. – Andrew Mar 10 '11 at 22:41
Interesting! Sounds very much like the Fienup iterative phase retrieval algorithm. But I would also like to introduce some additional information: I have estimates of the standard error on each of the measurement points (via a coherence measurement). Unclear how to mix this in. – nibot Mar 10 '11 at 22:48
Maybe this iteration: 1. In time domain, truncate acausal portion; 2. In freq domain, nudge towards measured data, with nudging weighted by error estimate, 3. repeat. ? – nibot Mar 10 '11 at 22:51
Also brings up the problem of how to inverse fourier transform an irregularly sampled spectrum (Lomb-Scargle?). – nibot Mar 10 '11 at 22:52
show 1 more comment | 2013-05-23 17:43:39 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 1, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.744135320186615, "perplexity": 1022.989143836226}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 20, "end_threshold": 15, "enable": false}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2013-20/segments/1368703635016/warc/CC-MAIN-20130516112715-00075-ip-10-60-113-184.ec2.internal.warc.gz"} |
http://tex.stackexchange.com/questions/28336/adjust-vspace-between-multiple-align-environments?answertab=votes | # Adjust vspace between multiple align environments
I am using some independant align environments directly one after the other one and it produces some nasty space between them. Is there any workaround to shrink the size of the space a little bit?
Example:
My code looks like this:
\newcounter{eqn}[section]
\newcommand{\eqn}{\refstepcounter{eqn}\tag{\thesection.\arabic{eqn}}}
\newcommand{\xeqn}[1]{\begin{align}\eqn #1\end{align}}
...
\xeqn{foo}
\xeqn{bar}
\xeqn{random}
-
Please post you code so we can comment on it. You are probably leaving a blank line in between the align environments. – Peter Grill Sep 13 '11 at 16:14
Use the gather environment:
\begin{gather}
\text{$x>y$ genau dann, wenn $x-y\in P$,}\\
\text{$x\ge y$ genau dann, wenn $x>y$ oder $x=y$,}\\
\text{$x<y$ genau dann, wenn $y-x\in P$,}\\
\text{$x\ge y$ genau dann, wenn $x<y$ oder $x=y$,}
\end{gather}
Never use two consecutive math environments.
-
Works, but i have "problems" with the tags/numering as i use a very weird method... can you explain me how to adjust the gather code for my needs and my posted code? - EDIT Inserted \eqn before every line and it works! Thanks! – Christian Ivicevic Sep 13 '11 at 16:23
Don't use \eqn, but rather follow barbara's suggestions. – egreg Sep 13 '11 at 17:56
@egreg's recommendations to use the gather environment, and never to use two consecutive math environments, are seconded.
if all (numbered) equations are to be numbered the same way as these, there's a much simpler method: put the command
\numberwithin{equation}{section}
in your preamble and forget about \tag and the definitions for \eqn and \xeqn which would no longer be needed. read the manual for amsmath on this topic -- texdoc amsmath if you have a tex live installation, or follow this link.
- | 2014-11-27 09:36:14 | {"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 1, "mathjax_display_tex": 0, "mathjax_asciimath": 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, "math_score": 0.9420435428619385, "perplexity": 5644.720545164733}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-49/segments/1416931008218.28/warc/CC-MAIN-20141125155648-00215-ip-10-235-23-156.ec2.internal.warc.gz"} |