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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4754 | # Statistics¶
## Arithmetic mean¶
The arithmetic mean of a set of inputs is:
## Correlation¶
The correlation between two random variables and is:
## Covariance¶
The covariance between two random variables and is defined as:
### Covariance matrix¶
A square matrix where and and are two variables.
There are three... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4756 | NULL
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IMR Press / RCM / Volume 22 / Issue 3 / DOI: 10.31083/j.rcm2203066
Open Access News and Views
FDA PLATO deaths list challenges aspirin dose—ticagrelor interaction
Show Less
1 Department of Neurology, Jo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4757 | ## Diyadiya Group Title Integration 2 years ago 2 years ago
$\int\limits\limits_{-a}^{a} \sqrt{\frac{a-x}{a+x}}$
2. FoolForMath Group Title
Lets say, $$f(x)= \sqrt{\frac{a-x}{a+x}}$$ , now f(X) is even or odd?
even or odd?
i dont know :/@Fool
5. DHASHNI Group Title
multiply and divide by the numerator
6. FoolFo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4758 | MathSciNet bibliographic data MR308669 42A18 Fefferman, Charles; Shapiro, Harold S. A planar face on the unit sphere of the multiplier space $M\sb{p}$$M\sb{p}$, \$1
For users without a MathSciNet license , Relay Station allows linking from MR numbers in online mathematical literature directly to electronic journals an... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4760 | Lemma 100.41.1. Let $f : \mathcal{X} \to \mathcal{Y}$ be a morphism of algebraic stacks. Consider a $2$-commutative solid diagram
$\xymatrix{ \mathop{\mathrm{Spec}}(K) \ar[rr]_-x \ar[d]_ j & & \mathcal{X} \ar[d]^{\Delta _ f} \\ \mathop{\mathrm{Spec}}(A) \ar[rr]^{(a_1, a_2, \varphi )} \ar@{..>}[rru] & & \mathcal{X} \ti... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4761 | +0
# Prove that if $w,z$ are complex numbers such that $|w|=|z|=1$ and $wz\ne -1$, then $\frac{w+z}{1+wz}$ is a real number.
0
114
1
+16
Prove that if $$w,z$$ are complex numbers such that $$|w|=|z|=1$$ and $$wz\ne -1$$, then $$\frac{w+z}{1+wz}$$ is a real number.
Dec 25, 2019
#1
0
Let w = a + bi and z = c + di. ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4762 | ×
# Number Theory
Prove that there exists no integer n such that $$n^7 + 7$$ is a perfect square.
Note by Raushan Sharma
1 year, 5 months ago |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4763 | # Trig question.
1. Oct 1, 2006
### Checkfate
I don't really understand a step in my textbook, and I think it is better that I understand why they are doing it this way instead of just brushing it off and it coming back to haunt me later!
The question is : Solve for $$\Theta, 0\leq\Theta\leq2\pi$$
$$2\tan\Theta-2=... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4765 | ## Algebra 1
$33\geq q\geq-21$
$-3\leq\frac{6-q}{9}\leq3\longrightarrow$ multiply all 3 parts by 9 $-3\times9\leq\frac{6-q}{9}\times9\leq3\times9\longrightarrow$ multiply $-27\leq6-q\leq27\longrightarrow$ subtract 6 from all 3 parts $-27-6\leq6-q-6\leq27-6\longrightarrow$ subtract $-33\leq -q\leq21\longrightarrow$ mul... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4752 | 1
JEE Main 2021 (Online) 20th July Evening Shift
+4
-1
With what speed should a galaxy move outward with respect to earth so that the sodium-D line at wavelength 5890 $$\mathop A\limits^o$$ is observed at 5896 $$\mathop A\limits^o$$ ?
A
306 km/sec
B
322 km/sec
C
296 km/sec
D
336 km/sec
2
JEE Main 2021 (Online) 20th Jul... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4755 | # Network operator matrix
Network operator matrix (NOM) is a representation of mathematical expressions in computer memory.
NOM is a new approach to the problem of automatic search of mathematical equations. The researcher defines the sets of operations, variables and parameters.[1] The computer program generates a n... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4759 | # How are the two natural ways to define ''the category of models of a first-order theory T'' related?
Background/Motivation: Inspired by an interesting question by Joel, I've been wondering about the relationship between two very natural ways to define the category of ''all models of T'' where T is a first-order theo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4766 | # Math Help - Numerical Analysis Midpoint Rule Help
1. ## Numerical Analysis Midpoint Rule Help
Could someone check if this is the correct way to solve this problem.
For what n will the approximation f(x) be accurate to within .0000001 using
$E_{f} = \frac{(b-a)h^2}{6} f''(\mu)$, for some $\mu$ between a and b is.
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4767 | # Interference in Thin Films?
premed
## Homework Statement
Light of wavelength $$\lambda$$ strikes a pane of glass of thickness T and refractice index n, as shown in figure(I attached a diagram I made). Part of the beam is reflected off the upper surface of the glass, and part is transmitted and then reflected off t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_4764 | zbMATH — the first resource for mathematics
Fractional resolution and minimum aberration in blocked $$2^{n-k}$$ designs. (English) Zbl 0913.62073
Summary: Systematic sources of variation can be reduced in fractional factorial experiments by grouping the runs into blocks. This is accomplished through the use of blockin... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14817 | # Rastrigin function
Rastrigin function of two variables
In 3D
Contour
In mathematical optimization, the Rastrigin function is a non-convex function used as a performance test problem for optimization algorithms. It is a typical example of non-linear multimodal function. It was first proposed by Rastrigin [1] as a 2-... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14818 | ## CryptoDB
### Paper: Encryption-Scheme Security in the Presence of Key-Dependent Messages
Authors: J. Black P. Rogaway T. Shrimpton URL: http://eprint.iacr.org/2002/100 Search ePrint Search Google Encryption that is only semantically secure should not be used on messages that depend on the underlying secret key; al... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14820 | ## A note on the separation problem for the matching matroid
For a given graph G(V,E) and a given vector (......) the problem of finding a hyperplane which separates x form the polyhedron P of the matching matroid on G or proving that x belongs to P is solved by finding a minimum capacity cut on an auxiliary digraph.
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14822 | # A grammar is defined asA → BCB → x | BxC → B | DD → y | EyE → z The non-terminal alphabet of the grammar is
1. {A, B, C, D, E}
2. {B, C, D, E}
3. {A, B, C, D, E, x, y, z}
4. {x, y, z}
Option 1 : {A, B, C, D, E}
## Detailed Solution
Concept:
Set of all non-terminal symbols are those from which all the strings in ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14823 | # Tag Info
6
The proof has nothing to do with the Schwartz space per se; nor with $i$ or $t$, or that $P$ and $Q$ are symmetric. If $P,Q$ are operators on a Hilbert space $H$ with domain $D$ and such that $PD\subset D$, $QD\subset D$, and $QP-PQ=\mathbb I$, then at least one of $P$ and $Q$ is unbounded. This applies ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14824 | # The sum of four consecutive integers is 74. What is the first integer?
Apr 27, 2016
The integers are :
$17 , 18 , 19$ and $20$.
#### Explanation:
Let us denote the four consecutive integers as:
$x , \left(x + 1\right) , \left(x + 2\right)$ and $\left(x + 3\right)$
As per the data provided:
$x + x + 1 + x + 2 + x... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14825 | # Derivative of Matrix elements w.r.t. to scalar
First of all, excuse the stupid question. Unfortunately, I couldn't find something similar already asked.
Consider the matrix
$$A(r_1, r_2) = \begin{pmatrix} r_1^2 & 3 \\ 2 & r_2 \end{pmatrix}.$$
I'd like to know how I can get the Jacobian of this matrix. I'd suggest... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14826 | # Introduction to turbulence/Statistical analysis/Multivariate random variables
(Difference between revisions)
Revision as of 07:41, 1 June 2006 (view source)Michail (Talk | contribs)← Older edit Revision as of 18:21, 1 June 2006 (view source)Michail (Talk | contribs) (→Joint pdfs and joint moments)Newer edit → Line ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14828 | # Asymptotics of $\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}}$
I am fairly sure that asymptotically $$\frac{\sum _{i=0}^{\lfloor n/2 \rfloor} {2(n-2i) \choose n-2i} {n \choose 2i} {4i \choose 2i}}{2^{3n - 1}} \sim \frac{2}{\pi n}.$$
I tried
Limit[n*Sum[B... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14829 | ## anonymous one year ago PLEASE HELP WILL FAN AND MEDAL In the figure above , OACB is a square with area 4x^2. If OA and OB are radii of a sector of a circle O, what is the perimeter, in terms of x, of the unbroken figure? A) x(4+3 π) B) x(3+4π) C) x(6+4 π) D) 4(x+2 π) E) 7 πx
1. anonymous
2. anonymous
3. anonymous... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14830 | ## University Calculus: Early Transcendentals (3rd Edition)
a) $dy/dx=1$ b) $dy/dx=1$
a) $y=(u/5)+7$ and $u=5x-35$ We have $$\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}=\Big(\frac{u}{5}+7\Big)'(5x-35)'=\frac{1}{5}\times5=1$$ b) $y=1+(1/u)$ and $u=1/(x-1)$ We have $$\frac{dy}{dx}=\frac{dy}{du}\frac{du}{dx}=\Big(1+\frac{1}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14831 | # Thread: parameter restrictions HELP ??
1. ## parameter restrictions HELP ??
hey, i just realli realli dont understand the restrictions for parameters in trig
so for this question
4. x = 2cos theta , y = 2sin theta
and 0<theta<2 pi
the equation is x squared +y squared = 4
i understand that
but then the restriction... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14816 | # categorical quantum LM- logic algebras
\xyoption
curve
## 0.1 Quantum LM-algebraic Logic
### 0.1.1 Fundamental concepts of space and time in quantum theory vs. space-times in general relativity
A notable feature of current 21-st century physical thought involves a close examination of the validity of the classic... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14821 | Problems – We Solve Problems
Filter Problems
Showing 1 to 11 of 11 entries
#### Tilings with ordinary and domino tiles
Fill an ordinary chessboard with the tiles shown in the figure.
#### Odd and even numbers , Tilings with ordinary and domino tiles
Is it possible to fill a $5 \times 5$ board with $1 \times 2$ domi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14819 | # zbMATH — the first resource for mathematics
The independence of the continuum hypothesis. I, II. (English) Zbl 0192.04401
These two papers contain the solution of the famous Continuum Hypothesis. The author shows that the continuum hypothesis cannot be derived from the axioms of set theory. The proof is based an his... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_14827 | Compute the charitable contribution deduction (ignore the percentage limitation) for each of the ...
Compute the charitable contribution deduction (ignore the percentage limitation) for each of the following C corporations.
Ruby Corporation donates a sculpture held as an investiment and worth $223200 to a local museu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19360 | Sunday, September 27, 2020
# Grade 8 PARCC math: scientific notation
#### The following multiple-choice question, explained here in hopes of helping eighth-grade students and their parents in Maryland and Illinois prepare for the PARCC test near the end of this school year, appears on the released version of PARCC’s ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19362 | # Numerical Policy Error Bounds for $$\eta$$ η -Concave Stochastic Dynamic Programming with Non-interior Solutions
Listed:
• Huiyu Li
()
## Abstract
This paper derives explicit error bounds for numerical policies of $$\eta$$ η -concave stochastic dynamic programming problems, without assuming the optimal policy is ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19363 | # tangram cannot get a square with a little square hole in the center
From a tangram or seven-piece puzzle (first picture), we cannot get a square with a little hole in the center (the second cartoon), the hole is also a square
Why?
-
The picture is not consistent with your link. – WimC Dec 22 '13 at 20:00
@WimC so... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19364 | Theorem 33 q is ultra freely sub linear Proof We proceed by induction Clearly
Theorem 33 q is ultra freely sub linear proof we
• Essay
• 8
This preview shows page 3 - 5 out of 8 pages.
Theorem 3.3. q is ultra-freely sub-linear. Proof. We proceed by induction. Clearly, if ˜ y is homeomorphic to Γ then | j | 2 K . Ob... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19365 | # Real Analysis Help
• March 4th 2009, 10:54 AM
Real Analysis Help
Let X be a topological space and let ${f_n}$ be a sequence of continuous functions from X to the real numbers. If f(x)= $\lim_{n->\infty} f_n(x)$ for all x in X, show that the set of points where f is continuous is a $G_\delta$ set.
• March 4th 2009, 1... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19368 | # Is this sentence referring to joint or conditional probability?
The following is a quote from my textbook, in a chapter discussing the Viterbi algorithm (Durbin, Richard, et al. Biological sequence analysis: probabilistic models of proteins and nucleic acids. 1st edition p56)
...The most probable path $$π^∗$$ can b... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19370 | # show a mapping is homomorphism
Assume a complex number $z=a+bi$ has the length $|z|=\sqrt{a^2+b^2}$, and it has the property that $|z_1z_1|=|z_1||z_2|$. A function $\phi$ from the multiplicative group $\mathbb{C^*}$ of non-zero complex numbers to the additive group $\mathbb{R}$ of real numbers by $\phi(z)=ln(|z|)$.
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19371 | 1. ## Polynomials
The polynomial p(x)=x^3+mx^2+nx-56 is exaclty divisible by x-7 and x+2.
a) Find the values of m and n
b) Find the third factor
c) Sketch
How do I do this? I have no idea...
2. Originally Posted by Unwelcome
The polynomial p(x)=x^3+mx^2+nx-56 is exaclty divisible by x-7 and x+2.
If they both divi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19373 | Dear friends, Please read our latest blog post for an important announcement about the website. ❤, The Socratic Team
0
# A ball with a mass of 2 kg and velocity of 4 m/s collides with a second ball with a mass of 5 kg and velocity of - 7 m/s. If 20% of the kinetic energy is lost, what are the final velocities of the... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19374 | # Cyanide's Lewis structure - electronegativity or octet rule?
The formula for the cyanide ion is $\ce{CN-}$. That gives us a total of ten valence electrons to work with. There are two obvious ways to build the Lewis structure.
$\ce{:^-C#N:}$
$\ce{:C=N^-::}$
(I hope that was clear. I'm not sure how to make ASCII Le... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19375 | # Basic Bra-Ket Question
1. Feb 17, 2013
### Bobbo Snap
1. The problem statement, all variables and given/known data
Consider a three-dimensional vector space spanned by an orthonormal basis $|1\rangle, |2 \rangle, |3 \rangle$. Kets $|\alpha \rangle, |\beta \rangle$ are given by
$$|\alpha \rangle = i|1\rangle -2|2 ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19361 | ## Saturday, July 31, 2021
### A scheduling problem: a modeling approach
Here is a simple scheduling problem [1]:
• We have $$T$$ time periods (weeks)
• and $$N$$ jobs to be scheduled.
• Each job has a duration or processing time (again expressed in weeks), and a given resource (personnel) requirement during the exe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19367 | • # question_answer If the sum of LCM and HCF of two number is 1260 and their LCM is 900 more than of their HCF, then the product of two numbers is A) 203400 B) 194400 C) 198400 D) 205400
Let HCF be$x$ Then LCM$=900+x$ $900+x+x=1260$ $900+2x=1260$ $2x=360$ $x=180$ Nos. are 180, ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19369 | +1 vote
306 views
The sum of $n$ terms of the series $4+44+444+ \dots \dots$ is
1. $\frac{4}{81}\left[10^{n+1}-9n-1\right]$
2. $\frac{4}{81}\left[10^{n-1}-9n-1\right]$
3. $\frac{4}{81}\left[10^{n+1}-9n-10\right]$
4. $\frac{4}{81}\left[10^{n}-9n-10\right]$
edited | 306 views
+1
take only 4 and put n=1
option C sum ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19372 | # 2x-6 = 3x+1-X-7 Solve the equation.
###### Question:
2x-6 = 3x+1-X-7
Solve the equation.
### How do air sacs of birds help make body lighter
How do air sacs of birds help make body lighter...
### Solve quadratic equation by completing the square x²+2x-15=0
solve quadratic equation by completing the square x²+2x... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_19366 | # Hyperbolic Boundary Valued Problem
1. Dec 18, 2011
### robby991
Hi, I am trying to understand solving boundary valued partial differential equations and it's relation to hyperbolic functions. In one of my problems, there is a PDE and the solution contains the hyperbolic function "cosh". I was just curious if anyon... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15200 | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# 2.2: Conditional Statements
Difficulty Level: At Grade Created by: CK-12
## Learning Objectives
• Identify the hypothesis and conclusion of an if-then statement.
• Write the converse... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15202 | ## theDevonator 2 years ago Half the difference of eight and six times a certain number is the same as the number. Find the Number
1. PhoenixFire
${{8-6}\over 2}x=x$${2 \over 2}x=x$$x=x$
2. theDevonator
Thanks! |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15203 | # Arithmetico Geometric Series
A series is said to be in arithmetico geometric series if each of its term is the product of the corresponding terms of an AP and a GP.
For example, 1, 2x, 3x2, 4x3,…
In the above series, the first part of this series is in an AP (1, 2, 3, 4,…) and the 2nd part is (x0x1x2x3,….) in a GP.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15204 | # If $a=\cos\alpha- i \sin \alpha,b=\cos\beta-i \sin\beta,c=\cos\gamma-i\sin\gamma$ then $(a^{2} c^{2} -b^{2})/abc$ is
$(1)\cos 2(\alpha-\beta+\gamma)+i\sin 2(\alpha-\beta+\gamma)$(2)$-2\cos(\alpha-\beta+\gamma)$(3)$-2 i\sin(\alpha-\beta+\gamma)$(4)$2\cos(\alpha-\beta+\gamma)$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15205 | ## Calculus 8th Edition
$error \leq 6.4 \times 10^{-8}$ and first ten terms $\approx 0.0739293$
$\Sigma_{n=1}^{\infty} 5^{-n}cos^{2}n=\Sigma_{n=1}^{\infty}\frac{cos^{2}n}{5^{n}}$ $T_{n}=\int_{10}^{\infty}\frac{1}{5^{x}}dx=\lim\limits_{t \to \infty} \int_{10}^{t}\frac{1}{5^{x}}dx$ $=\lim\limits_{t \to \infty} [-\frac{5... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15207 | JEDNOSTKA NAUKOWA KATEGORII A+
# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty
## Product preserving bundle functors on fibered fibered manifolds
### Tom 96 / 2003
Colloquium Mathematicum 96 (2003), 17-26 MSC: 58A05, 58A20. DOI: 10.4064/cm96-1-3
#### Streszczenie
We investigate the ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15208 | 11. Find the equation of the circle passing through the points (2,3) and (–1,1) and hose centre is on the line $x - 3y - 11 = 0$.
As we know,
The equation of the circle with centre ( h, k) and radius r is given by ;
$(x-h)^2+(y-k)^2=r^2$
Given Here,
Condition 1: the circle passes through points (2,3) and (–1,1)... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15209 | # Geometric representation of Euler-Maclaurin Summation Formula
When reading Tom Apostol's expository article (or the free link), I was expecting more diagrams to come that follow the figure below (or this from the Wolfram project). It was a disappointment not seeing further decomposition of the "curved triangular pie... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15211 | # The Meaning of Life
Number Theory Level 4
$\large \frac1a+\frac1b+\frac1c= \frac1{42}$
Let $$a\leq b \leq c$$ be positive integers that satisfy the equation above. Find the maximum possible value of $$c$$.
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15212 | # What is Correlation?
Besides not being causation, many pedantically smart laymen don’t know what correlation is. I’m here to fix that with a mathematical, an intuitive explanation and a brief philosophical comment.
### Intuitive Explanation
Correlation is a quantitative measure of how well the highs line up with t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15213 | # Is it possible to obtain joint PDF of set of variables given marginal PDF of each variable?
Say $f(X_1)$, $f(X_2)$, $f(X_3)$, $f(X_4)$ are the empirical marginal PDFs of random variables $X_1$, $X_2$ , $X_3$, $X_4$. Also given is correlation between each pair of variables $X_1$, $X_2$ , $X_3$, $X_4$. Is it possible ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15214 | # Is the Kronecker delta linear?
1. Mar 14, 2015
### entropy1
I don't see how the kronecker delta function is linear, and hence I don't see how it can serve as a dual basis for a ket space.
How is the kronecker delta linear? How can it serve as a dual basis?
Last edited: Mar 14, 2015
2. Mar 14, 2015
### Jazzdude
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15206 | How to deduct the gradient in spherical coordinates?
1. Jul 30, 2013
igorronaldo
2. Jul 30, 2013
vanhees71
The one given in Wikipedia is correct, or what is your question?
3. Jul 30, 2013
yungman
Should be this one:
$$\nabla f(r, \theta, \phi) = \frac{\partial f}{\partial r}\mathbf{e}_r+ \frac{1}{r}\frac{\part... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15210 | # Binary Call Option Formula
Jan 16, 2018 · It is also called digital option because its payoff is just like binary signals: i.e. Position trading is less. Binary options are a type of exotic option for which the payoff is determined by whether the final stock price is greater or less than binary call option formula t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15201 | 0 like 0 dislike
193 views
Call a subset $S$ of a vector space $V$ a spanning set if $\operatorname{Span}(S)=V$. Suppose that $T: V \rightarrow W$ is a linear map of vector spaces.
a) Prove that a linear map $T$ is 1-1 if and only if $T$ sends linearly independent sets to linearly independent sets.
b) Prove that $T$ is... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_15215 | # Wigner-Weyl ordering in exponential
If the particle number is $$\hat{a}^\dagger\hat{a}\leftrightarrow|\alpha_w|^2-1/2$$, it can be mapped on the Wigner fields by assuming symmetric ordering:$$|\alpha_w|^2\leftrightarrow\hat{a}^\dagger\hat{a}+\hat{a}\hat{a}^\dagger$$.
My question is: is there a clear way to work wit... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1872 | It is currently 22 Oct 2017, 00:11
### GMAT Club Daily Prep
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1875 | Branched center manifold
# Regularity theory for 2-dimensional almost minimal currents II: branched center manifold
Camillo De Lellis, Emanuele Spadaro and Luca Spolaor
###### Abstract.
We construct a branched center manifold in a neighborhood of a singular point of a -dimensional integral current which is almost mi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1876 | Lemma 29.11.10. Let $X$ be a scheme. Let $\mathcal{L}$ be an invertible $\mathcal{O}_ X$-module. Let $s \in \Gamma (X, \mathcal{L})$. The inclusion morphism $j : X_ s \to X$ is affine.
Proof. This follows from Properties, Lemma 28.26.4 and the definition. $\square$
There are also:
• 2 comment(s) on Section 29.11: Af... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1877 | # Q : 4 If the lateral surface of a cylinder is $\small 94.2\hspace{1mm}cm^2$ and its height is 5 cm, then find (ii) it's volume. (Use $\small \pi =3.14$)
H Harsh Kankaria
Given,
The lateral surface area of the cylinder = $\small 94.2\hspace{1mm}cm^2$
Height of the cylinder = $h = 5\ cm$
The radius o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1878 | # An algebraic property of the simplicial boundary operator
I am working with simplicial homology with coefficients over $$\mathbb{Z}_2$$. Let $$C$$ be a null-homologous cycle in a simplicial complex $$K$$. Let $$\{C_i\}_{i=1}^n$$ be a basis for the cycle space of $$K$$ for some fixed dimension. We have $$C = \oplus_{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1881 | # zbMATH — the first resource for mathematics
Lebesgue constants and approximation of functions by Fourier and Fejér sums. (English. Russian original) Zbl 0587.42008
Sov. Math., Dokl. 30, 182-185 (1984); translation from Dokl. Akad. Nauk SSSR 277, 1033-1035 (1984).
Given a bounded region D in $${\mathbb{R}}^ m$$, the ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1883 | # 4 x 4 determinant
Printable View
• May 24th 2010, 12:42 PM
renlok
4 x 4 determinant
I had the question solve the determinate: $\begin{vmatrix}7 & 11 & 13 & 17\\ 11 & 13 & 17 & 13\\ 13 & 17 & 13 & 11\\ 17 & 13 & 11 & 7\end{vmatrix}$
I know how to do it the normal way of splitting it into 3 x3 determinate then spiti... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1884 | ## Find the 6th number
For the discussion of math. Duh.
Moderators: gmalivuk, Moderators General, Prelates
Posts: 65
Joined: Mon Sep 18, 2006 9:35 pm UTC
Contact:
### Re: Find the 6th number
I have
$f(a)_b = \sum_{k=1}^af(k)_{b-1} + \frac{ab(b+1)}{2}$
with
$f(a)_0=f(0)_b=0$
but I'm not sure how to get more general... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1885 | # Waves of differing frequency are orthogonal - help me understand
I know that sinusoidal waves of different frequencies are orthogonal to each other. For instance:
# Shows that 1Hz and 2Hz waves are orthogonal
import numpy, scipy
x = numpy.linspace(0, 1, 1000)
wave_1hz = scipy.sin(1 * 2*scipy.pi*x)
wave_2hz = scipy.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1886 | # Problems of the Week
Contribute a problem
# 2017-09-11 Intermediate
Which is larger?
\begin{aligned} A &= \sqrt{2} + \sqrt{4} + \cdots + \sqrt{98} + \sqrt{100} \\\\ B &= \sqrt{1} + \sqrt{3} + \cdots + \sqrt{97} + \sqrt{99} + \sqrt{101} \end{aligned}
Two plane mirrors (shown to the right) both stand perpendicular... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1887 | Rotation operators
cragar
Homework Statement
Determine the matrix representation of the rotation operator
$R(\phi k)$ using the states |+z> and |-z> as a basis. Using your matrix representation verify that $R^{\dagger}R=1$
The Attempt at a Solution
Do I need to write $R| \psi>$ in terms of a matrix.
If I have $|\p... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1873 | ## performance – 4×4 double precision matrix multiply using AVX intrinsics (inc. benchmarks)
An optimised 4×4 double precision matrix multiply using intel AVX intrinsics. Two different variations.
Gist
For quick benchmark (with a compatible system) copy paste the command below. Runs tests on clang and gcc on optimis... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1874 | # Homework Help: Question about Proof
1. Aug 24, 2009
### rbzima
1. The problem statement, all variables and given/known data
One afternoon, a mathematics library had several visitors. A librarian noticed that it was impossible to find three visitors so that no two of them met in the library that afternoon. Prove t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1880 | # 2010-4 Power and gcd
Let n, k be positive integers. Prove that $latex \sum_{i=1}^n k^{\gcd(i,n)}$ is divisible by n.
VN:F [1.9.22_1171] |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1882 | # Tensor product of measure spaces
For a compact topological space $X$, denote by $\mathcal{M}(X)$ the Banach space of finite signed Borel (Radon) measures on $X$ with the total variation norm. This is canonically isometric to the dual space of the space of continuous functions $C(X)$.
If $X$ and $Y$ are compact spac... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1879 | Join Today to Score Better
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_336 | Bureau of Labor
Bureau of Labor is a state institution that provides mike and the rest for their so-called clients. The mission of the Bureau of Labor is spend taxpayer money to provide relaxation and benefits to those who do not want to work. Popularly speaking sense the work of the Bureau of Labor is to create the l... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_339 | # How do you find the coefficient to the x^6 term in the expansion of (x-3)^9?
Dec 8, 2016
The coefficient is ${\textcolor{w h i t e}{1}}_{9} {C}_{6} {\left(\text{-} 3\right)}^{9 - 6} = - 2268.$
#### Explanation:
This is a classic example of binomial expansion.
A few simple expansion of $\left(a + b\right)$ to dif... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_340 | ×
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_341 | # Non-standard Models of Arithmetic 8
JB: So, you were going to tell me a bit how questions about the universe of sets cast their shadows down on the world of Peano arithmetic.
MW: Yup. There are few ways to approach this. Mainly I want to get to the Paris-Harrington theorem, which Enayat name-checks.
First though I... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_342 | # Variance - Definition, Formula, Examples, Properties (2023)
Variance is a statistical measurement that is used to determine the spread of numbers in a data set with respect to the average value or the mean. The standard deviation squared will give us the variance. Using variance we can evaluate how stretched or sque... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_343 | # Category:Definitions/Figurate Numbers
This category contains definitions related to Figurate Numbers.
Related results can be found in Category:Figurate Numbers.
A figurate number is loosely defined as a (natural) number corresponding to a set of objects which can be arranged in a geometric pattern (in an arbitrary ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_344 | group theory
# Cyclic groups
## Definition
A cyclic group is a quotient group of the free group on the singleton.
Generally, we consider a cyclic group as a group, that is without specifying which element comprises the generating singleton. But see Ring structure below.
## Examples
There is (up to isomorphism) on... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_345 | # Energy conservation in elastic collisions and pendulum [closed]
This is my solution but I couldn’t find $$h$$ in term of $$V \rightarrow M_{1} V - M_{2} V = M_{2} V_{2} \implies V \left( M_{1} - M_{2} \right) = M_{2} V_{2} \implies \frac{M_{1}}{M_{2}} = 1 + \frac{V_{2}}{V}$$ and $$V = V_{2} - V$$ so $$V_{2} = 2 V$$ ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_346 | Math Help - Inverse functions
1. Inverse functions
what is the inverse function of 3y=2x+7. How will I do that? thanks
2. Any linear function of the type $y= a\cdot x + b$ , $a \ne 0$ has its inverse of the form $x= \frac {1}{a}\cdot (y-b)$. In your case is $a=\frac {2}{3}$ , $b= \frac{7}{3}$
Kind regards
$\chi$ $... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_347 | # Sketch antiderivative
1. Aug 30, 2006
### swears
Wow, I totally forgot how to do these.
I have a graph of a line, but it does not say the function. I have to sketch the antiderivative.
TIA
2. Aug 30, 2006
### Staff: Mentor
Remember that the derivative dy/dx is the change in the y value per change in the x val... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_348 | ## delta u
$\Delta U=q+w$
Moderators: Chem_Mod, Chem_Admin
Briana Yik 1H
Posts: 30
Joined: Fri Sep 28, 2018 12:20 am
### delta u
When there is constant temperature, is delta u always 0? Thank you
Nada AbouHaiba 1I
Posts: 77
Joined: Fri Sep 28, 2018 12:28 am
Been upvoted: 1 time
### Re: delta u
I don't think so ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_350 | # How do you find the vertical, horizontal or slant asymptotes for y = (2e^x) / (e^x - 5)?
Oct 21, 2016
We have a vertical asymptote at $x = \ln 5 = 1.6094$
and horizontal asymptotes at $y = 0$ and $y = 2$
#### Explanation:
We have $y = \frac{2 {e}^{x}}{{e}^{x} - 5}$
As $x \to - \infty$, $y \to \frac{0}{0 - 5} = ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_351 | # statsmodels.discrete.discrete_model.Logit.pdf¶
Logit.pdf(X)[source]
The logistic probability density function
Parameters: X (array-like) – X is the linear predictor of the logit model. See notes. pdf – The value of the Logit probability mass function, PMF, for each point of X. np.exp(-x)/(1+np.exp(-X))**2 ndarray
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_337 | Core (graph theory)
In the mathematical field of graph theory, a core is a notion that describes behavior of a graph with respect to graph homomorphisms.
Definition
Graph ${\displaystyle C}$ is a core if every homomorphism ${\displaystyle f:C\to C}$ is an isomorphism, that is it is a bijection of vertices of ${\disp... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_338 | Home > Standard Error > Computing Standard Error Linear Regression
# Computing Standard Error Linear Regression
## Contents
And the uncertainty is denoted by the confidence level. Some regression software will not even display a negative value for adjusted R-squared and will just report it to be zero in that case. J... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_349 | # Existence of a zero-sum subset
Some time ago I heard this question and tried playing around with it. I've never succeeded to making actual progress. Here it goes:
Given a finite (nonempty) set of real numbers, $S=\{a_1,a_2,\dots, a_n\}$, with the property that for each $i$ there exist $j,k$ (not necessarily distinc... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18080 | # 11.2: Non-Commuting Operators
In the previous section, we saw that if a particle can be in a definite state for two observables, then the two operators associated with those observables will commute. The converse is therefore also true; if two operators do not commute, then it is not possible for a quantum state to... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18082 | <img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
# 6.11: Classifying a Polygon Using Sum Theorems
Difficulty Level: At Grade Created by: CK-12
## Graphic Organizer for Unit 6, Lesson 10: Polygons
Name of Polygon Number of Sides (n=)\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18083 | Equilibrium Precipitate
1. Jun 5, 2008
tornzaer
1. The problem statement, all variables and given/known data
What is the maximum [Ca2+] that can exist with 5.2e-4 M c2O4 2- without precipitating? Ksp for CaC2O4 = 2.6e-9.
2. Relevant equations
Well, the Ksp and M is given, I don't know how to apply them.
3. The a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18084 | ## Intermediate Algebra (6th Edition)
Published by Pearson
# Chapter 2 - Review: 4
#### Answer
z=-$\frac{7}{11}$
#### Work Step by Step
Original Equation -(z+12)=5(2z-1) Distribute -z-12=10z-5 Subtract 10z and add 12 to both sides -11z=7 Divide both sides by -11 z=-$\frac{7}{11}$
After you claim an answer you’ll... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_18085 | # Small magmas with identity, inverses, and almost associativity
In constructing a good pedagogical non-example of a group, it would be pleasing to have an example that satisfies all of the properties of being a group except that there is precisely one counterexample to the associative property (especially since this ... |
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