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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10240 | Question
# In the hexaploid wheat, the haploid ($$n$$) and basic ($$x$$) numbers of chromosomes are
A
n=21 and x=21
B
n=21 and x=14
C
n=21 and x=7
D
n=7 and x=21
Solution
## The correct option is B $$n=21$$ and $$x=7$$Ploidy level is the number of complete sets of chromosomes in a cell. Wheat is hexaploid which is ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10241 | # Standard word for a formula that is always true
If it is known from context that variables $x$ and $y$ represent integers, an open Boolean formula such as $x \ge y \Rightarrow x+1 > y$ evaluates to true regardless of the value assigned to variables $x$ and $y$, at least in the standard interpretation of arithmetic. ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10242 | # Question
Two machines are supposed to be producing steel bars of approximately the same length. A sample of 35 bars from one machine has an average length of 37.013 inches, with a standard deviation of 0.095 inches. For 38 bars produced by the other machine, the corresponding figures are 36.974 inches and 0.032 inch... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10243 | # A beam of light from a source L is incident normally on a plane mirror fixed at a certain distance x from the source. The beam is reflected back as a spot on a scale placed just above the source L. When the mirror is rotated through a small angle , the spot of the light is found to move through a distance y on the sc... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10244 | 2.7: Theorems and Conjectures involving prime numbers
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Upon completion, a link will appear to access the found materials.
We have proved that there are infinit... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10245 | # Statistical hypothesis testing and key performance
What is hypothesis testing a statistical hypothesis is an assertion or conjecture concerning one or more populations to prove that a hypothesis is true, or false, with absolute. For testing, you will be analyzing and comparing your results against the null hypothesi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10246 | Is Cobb-Douglas the only output function corresponding to a competitive economy?
Apologies if this is a rather simple question, I appreciate any guidance.
$$Q(K,L) = AK^\alpha L^{\beta}$$
where A is a constant. Identify the conditions on $\alpha$ and $\beta$ for output function Q to correspond to a competitive econo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10247 | # On \ell_3 norm in R^2
Let $v,w\in\mathbb{R}^{2}$ and $v\perp w$. Is it true that $\left\Vert v\right\Vert _{3}\leq\left\Vert v+w\right\Vert _{3}$, in which $\left\Vert \left(x,y\right)\right\Vert _{3}:=\sqrt[3]{\left|x\right|^{3}+\left|y\right|^{3}}$ for $\left(x,y\right)\in\mathbb{R}^{2}$?
Thanks.
-
JFYI: your qu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10248 | # Given that Domain of the rational function is all real numbers. So the rational function should not contain denominator part.
Question
Rational functions
Given that Domain of the rational function is all real numbers.
So the rational function should not contain denominator part.
2020-11-06
So the required rational ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10249 | # Static De Sitter Metric
For static dS metric we have $$x_{0}=\sqrt{H^{-2}-r^{2}}\sinh(Ht)$$$$x_{1}=\sqrt{H^{-2}-r^{2}}\cosh(Ht)$$ and the metric can be written as $$ds^{2}=-dx_{0}^{2}+dx^{2}_{1}+d\bar x$$ where the barred $x$ will be just the spherical part of the final metric lets focus on the first two term of abo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10250 | # Erdős cardinals and ineffable cardinals
In Cantor's Attic it is stated that an $\omega$-Erdős cardinal is a stationary limit of ineffable cardinals, and Jech book is given as a reference, but I cannot find this result in that book. I have seen proofs in other sources using that Erdős cardinals are subtle, but since ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10251 | +0
# Quick Question
+1
117
4
+475
Suppose that x,y,z are positive integers satisfying x is less than or equal to y is less than or equal to z, and such that the product of all three numbers is twice their sum. What is the sum of all possible values of z?
Sep 18, 2020
#2
+112080
+1
Suppose that x,y,z are positive ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10252 | # Constructible Polygons
Geometry Level 3
What is the sum of the sides of all constructible (with compass and straightedge) regular $$n$$-gons $$3 \leq n \leq 100$$?
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10253 | # Commutator subgroup and bijective representation
Let $G$ be a finite group and $G' = [G,G]$ be its commutator subgroup, which is defined to be the subgroup generated by elements $[g,h] = g^{-1}h^{-1}gh$ for all $g,h \in G$, where $G'$ is a normal subgroup of $G$. And $G/G'$ is abelian.
Prove that for any field $\ma... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10254 | Home » Math Theory » Algebra » Absolute Value
Absolute Value
Introduction
We often come across the term absolute value in various situations. It is a commonly used term not just in the English language, but in mathematics as well. In mathematics, what do we mean by absolute value and how is it useful in different ca... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10255 | ## Friday, October 25, 2019
### Some comments on convergence in distribution
This is a note for myself.
Proposition. Let $(X_n)_{n\geq 1}$ be a sequence of random variables. Suppose that, for each $\epsilon > 0$, there exist random variables $(Y^{\epsilon}_n)_{n\geq 1}$, $(Z^{\epsilon}_n)_{n\geq 1}$, and $Y^{\epsilo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10208 | # Birational Invariants of Regular Surfaces
Let $$X,Y$$ surfaces (so $$2$$-dimensional proper $$k$$-schemes) which are regular and birational and denote by $$f: X – \ – \to Y$$ the corresponding rational birational morphism between $$X$$ and $$Y$$.
My aim is to show that for regular surfaces the dimensions of cohomol... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10209 | # Growth of Mordell-Weil Rank of Elliptic Curves over Field Extensions
I'm a graduate student just checking to make sure that what he's researching isn't already known.
Let $$\mathbb{F}$$ be a number field, and let $$E$$ be an elliptic curve defined over $$\mathbb{F}$$. Is it already known that, for any integer $$r\g... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10210 | # All Science Fair Projects
## Science Fair Project Encyclopedia for Schools!
Search Browse Forum Coach Links Editor Help Tell-a-Friend Encyclopedia Dictionary
# Science Fair Project Encyclopedia
For information on any area of science that interests you,
enter a keyword (eg. scientific met... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10211 | # Annihilators in matrix rings
Let $R$ be a finite commutative ring. For $n>1$ consider the full matrix ring $M_n(R)$. For a matrix $A\in M_n(R)$ is true that the cardinality of the left annihilator (in $M_n(R)$) of $A$ equals the cardinality of the right annhilator?
-
No, this isn't true in general, but it's true i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10212 | ## The Annals of Probability
### Sets Which Determine the Rate of Convergence in the Central Limit Theorem
Peter Hall
#### Abstract
Rates of convergence in the central limit theorem are frequently described in terms of the uniform metric. However, statisticians often apply the central limit theorem only at symmetri... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10213 | It is currently 21 Jan 2018, 14:42
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customized
for You
we will pick new questions that match your level based o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10214 | # Section 1.5: Problem 5 Solution
Working problems is a crucial part of learning mathematics. No one can learn... merely by poring over the definitions, theorems, and examples that are worked out in the text. One must work part of it out for oneself. To provide that opportunity is the purpose of the exercises.
James R... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10215 | 3,916 views
Let $\text{P, Q, S, R, T, U}$ and $\text{V}$ represent the seven distinct digits from $0$ to $6$, not necessarily in that order. If $\text{PQ}$ and $\text{RS}$ are both two-digit numbers adding up to the three-digit number $\text{TUV}$, find the value of $\text{V}$.
1. $3$
2. $6$
3. $5$
4. Cannot be deter... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10216 | # Lambert summation
In mathematical analysis, Lambert summation is a summability method for a class of divergent series.
Definition
A series $sum a_n$ is "Lambert summable" to "A", written $sum a_n = A \left(mathrm\left\{L\right\}\right)$, if
:$lim_\left\{r ightarrow 1-\right\} \left(1-r\right) sum_\left\{n=1\right... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10217 | # Generating sets of all binary strings of a fixed size
Consider the set $\Sigma^n$ of all binary strings of length $n$.
Consider some set $S_k \subseteq \Sigma^k$ of binary strings of length $k$. We call $S_k$ a `generating set' of $\Sigma^n$ if for any string $s \in \Sigma^n$, there exists a string $s' \in S_k$ suc... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10218 | # Numerical algorithm: Spectral function -> Continued Fraction
I am trying to code up a numerical algorithm which takes a spectral function of the form $$c(\zeta) = w_0 +\sum_{m=1}^N \frac{w_m}{\lambda_m+\zeta}$$ into a continued fraction of the form $$c(\zeta) = d_0+\frac{1}{a_0\zeta+}\;\;\frac{1}{b_1+}\;\;\frac{1}{a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10219 | Xinyu Wang, Yanjing Wang
Proceedings of LORI 2019
Publication year: 2019
Abstract: In this paper, we propose a logical framework extending the standard epistemic logic with a new knowledge operator $\G_i$ which captures the knowledge about (physically) necessary facts, e.g., scientific knowledge. Semantically, the tru... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10220 | # All of the following are names of European islands except __________. A.Ireland B.Iceland C.Sicily D.Jutland
2 answers
###### Question:
All of the following are names of European islands except __________. A.Ireland B.Iceland C.Sicily D.Jutland
## Answers
2 answers
### That car is so expensive; it costs an arm a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10221 | # Rossby number
(Difference between revisions)
Revision as of 20:28, 22 September 2005 (view source)← Older edit Latest revision as of 20:29, 22 September 2005 (view source) Line 1: Line 1: + [[Category:Dimensionless parameters]] + In [[rotating flows]] (e.g. [[geophysical flows]]), the Rossby number is defined as th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10222 | 00:00 - 14:0014:00 - 22:00
2:00 PM
@HDE226868 hah
user116211
> Please correct me if I am wrong.
@slereah are you around
user54412
Then internet: proof that a large fraction of the population is mentally unhinged.
But is the sample representative :P
user116211
2:04 PM
@ChrisWhite There are people in internet who s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10223 | # Math Help - Prove || x|-|y|| ≤ |x-y|
1. ## Prove || x|-|y|| ≤ |x-y|
Prove || x|-|y|| ≤ |x-y|, ∀x, y ∈ R
2. Hint: Use the triangle inequality and the fact that for all $x,y$, $|x| = |x + (y-y)| = |(x-y) + y|$. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15152 | # Intuitive Definition of Electric Potential
1. Jul 22, 2012
### Skoth
Hello all,
For a few months, I've been (off and on) trying to come up with a more intuitive definition for Electric Potential (or Voltage, if you prefer), as all I can seem to find are mathematical equations. I believe I have finally come up wit... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15153 | # Tag Info
-1
Have you had a 3rd or 4th year QM course yet? The simple answer is that the angular momentum is in the wave-function. For spherically symmetric (3-D) potentials the solution to the Schrodinger equation is in terms of spherical harmonics (at least the radial part of the solution.) For any of the solution... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15154 | # Solution for Least Squares Problem $\min \limits_{\mathbf{x}} \| \mathbf{Ax}-\mathbf{b} \|^2$ With Non Negativity Constraint
Let $\mathbf{x}=[x_1,\ldots,x_K]$. I have the following optimization problem:
\begin{array}{rl}
\min \limits_{\mathbf{x}} & \| \mathbf{Ax}-\mathbf{b} \|^2 \\
\mbox{s.t.} & x_k\ge 0, \forall k
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15155 | # A stochastic version of Stein Variational Gradient Descent for efficient sampling
We propose in this work RBM-SVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful for Bayesian inference. The method is to apply the Ran... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15156 | # fourier transform normalization constant
I'm confused about the two Fourier transform formulas that crop up. One where the constant of $\frac{1}{\sqrt{2\pi}}$ is used in both the forward and reverse transform and the other where just $\frac{1}{{2\pi}}$ is used for the inverse. I understand that it's a normalization ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15157 | # When is a linear combination of the elementary symmetric polynomials reducible?
Let $n\ge 2$ and consider the polynomial ring $\mathbb F [X_1,...,X_n]$, where $\mathbb F$ is a field. Let $e_j:=e_j(X_1,...,X_n)$ be the elementary symmetric polynomial of degree $j$ in $X_1,...,X_n$ (https://en.wikipedia.org/wiki/Eleme... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15158 | Paul's Online Notes
Home / Calculus I / Review / Functions
Show Mobile Notice Show All Notes Hide All Notes
Mobile Notice
You appear to be on a device with a "narrow" screen width (i.e. you are probably on a mobile phone). Due to the nature of the mathematics on this site it is best views in landscape mode. If your dev... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15159 | # Freezing point of a 4% aqueous solution of X is equal to freezing point of 12% aqueous solution of Y. If molecular weight of X is A, then molecular weight of Y is :Option 1)AOption 2) 4AOption 3) 3AOption 4) 2A
Molar Mass -
The mass of one mole of a substance in grams is called its molar mass.
- wherein
Molar mas... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15160 | # Truncation error (numerical integration)
Truncation errors in numerical integration are of two kinds:
• local truncation errors – the error caused by one iteration, and
• global truncation errors – the cumulative error caused by many iterations.
## Definitions
Suppose we have a continuous differential equation
$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15161 | Corpus ID: 221533945
# On tensor fractions and tensor products in the category of stereotype spaces.
@article{SSAkbarov2020OnTF,
title={On tensor fractions and tensor products in the category of stereotype spaces.},
author={S.S.Akbarov},
journal={arXiv: Functional Analysis},
year={2020}
}
• S.S.Akbarov
• Published 20... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15162 | Standard playing card deck without jokers: Deal 13 cards. What is the probability at least 1 suit is not present?
Similar questions:
What is the probability that 13 cards drawn from a standard deck has at least one card from each suit?
Deal 4 cards from a deck. What is the probability that we get one card from each ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15163 | MathOverflow will be down for maintenance for approximately 3 hours, starting Monday evening (06/24/2013) at approximately 9:00 PM Eastern time (UTC-4).
2 downcase
2) linking numbers defined for disjoint subsets of $\mathbb{R}^n$ using the vector space structure of $\mathbb{R}^n$. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15164 | # The GLIMMIX Procedure
#### Quasi-likelihood for Independent Data
Quasi-likelihood estimation uses only the first and second moment of the response. In the case of independent data, this requires only a specification of the mean and variance of your data. The GLIMMIX procedure estimates parameters by quasi-likelihoo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15165 | Groupe d’études et de recherche en analyse des décisions
# Decomposition theorems for linear programs
## Jean-Bertrand Gauthier, Jacques Desrosiers et Marco E. Lübbecke
Given a linear program (LP ) with m constraints and n lower and upper bounded variables, any solution $$x^0$$ to LP can be represented as a nonnegat... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15166 | # sin 0°
## Definition
The value of sine when the angle of the right angled triangle equals to $0^\circ$ is called $\sin 0^\circ$.
The exact value of $\sin 0^\circ$ is obtained mathematically by calculating the ratio of lengths of opposite side to hypotenuse when the angle of the right angled triangle is $0^\circ$.
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_15167 | GCSE Maths Algebra
Functions
# Functions in Algebra
Here we will learn about functions in algebra, including function machines, composite functions and inverse functions.
There are also functions worksheets based on Edexcel, AQA and OCR exam questions, along with further guidance on where to go next if you’re still... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23232 | Its square root is an integer
How many positive integral value(s) of $$n$$ exist such that $$n^2+96$$ is a perfect square?
× |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23233 | # Bold text and newlines inside equations.
What I'm doing:
\usepackage{amsmath}
\usepackage{amsthm}
\usepackage{eucal}
\usepackage{amssymb}
\usepackage{mathrsfs}
% don't know what some of those do, but i think all the math related ones are
% there
% there are more packages being imported though
Then I try:
\textb... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23234 | 1. ## Sets
Let A and B be sets. Prove each of the following statements. Remember, using a Venn diagram might help to visualize the problem, but it's not a proof!
a. (A B) ⊆ A
b. A ⊆ A ∪ B
c. A (B - A) = 0
2. a) (A B) ⊆ A
Let x be in (A B), then x is in A and x is in B. Hence x is in A. Thus (A B) ⊆ A
b) A ⊆ A ∪ B
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23235 | # Clarification in the definition of presheaf
I need a clarification in the definition of presheaf. If $X$ is a topological space then we define presheaf on $X$ to be an assignment to every open subset $U \subset X$ and to every pair of open sets $U,V$ ($V \subset U$) a map (restriction map) $res_{UV} : \jmath(U) \rig... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23236 | 18.2 Conductors and insulators (Page 3/10)
Page 3 / 10
Neutral objects can be attracted to any charged object. The pieces of straw attracted to polished amber are neutral, for example. If you run a plastic comb through your hair, the charged comb can pick up neutral pieces of paper. [link] shows how the polarizatio... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23237 | What am I missing when solving this integral with trigonometric substition?
The integral
$$\int\frac{x^2}{\sqrt{9-x^2}}dx$$
What I've tried
I've tried doing the substitution with
$$x^2=9\sin^2\theta$$ $$x=3\sin\theta$$ $$dx=3\cos\theta$$
my solving...
$$=\int\frac{27\sin^2\theta\cos\theta}{\sqrt{9-9\sin^2\theta}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23238 | # Categories for which Natural Transformations are the Set of Arrows
From Categories for the Working Mathematician pg. 43:
Theorem 1. The collection of all natural transformations is the set of arrows of two different categories under two different operations of composition, $\cdot$ and $\circ$, which satisfy the int... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23239 | # How to evaluate the expectation value of the Hamiltonian for a three electron Slater determinant?
I'm having trouble with a few concepts dealing with slater determinants and many electron systems. In particular, when dealing with 3 electron systems, I know that
$$\psi_0 = \frac{1}{\sqrt{6}} \det \begin{bmatrix} 1s(... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23240 | # Estimating normalization constant with Monte Carlo integration
Be $f(x)$ a function. Suppose that $f(x)$ integrates to a finite value $k$:
$$\int_{-\infty}^{\infty}f(x)dx=k$$
The normalization constant of $f(x)$ is $1/k$. Monte Carlo integration can give an estimate $\hat{k}$ of $k$, so we can estimate the normaliza... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23241 | ## Wednesday, 4 September 2013
### Linear Regression
The linear regression model is a fairly simple model, nevertheless it is used in many applications.
What follows is a fairly mathematical derivation of the linear regression parameters.
Let us denote the observations as $y[n]$ and $x[n]$ for $n=0,1,..,N-1$ for th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23242 | # Why has there been no unification of topology axioms and measure theory axioms?
The axioms of a topological space and a measure space at the outset seem very similar. They differ in the closure axioms of unions and intersections. The uncanny resemblance between a metric and a measure makes me wonder as to why these ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23243 | # zbMATH — the first resource for mathematics
Posets of copies of countable non-scattered labeled linear orders. (English) Zbl 07204024
Summary: We show that the poset of copies $$\mathbb{P} (\mathbb{Q}_n )=\langle \{ f[X]: f\in \text{Emb} (\mathbb{Q}_n ) \},\subset \rangle$$ of the countable homogeneous universal $$n... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23244 | Search
# Dynamical system
In engineering and mathematics, a dynamical system is a deterministic process in which a function's value changes over time according to a rule that is defined in terms of the function's current value.
Contents
## Types of dynamical systems
A dynamical system is called discrete if time i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23245 | 3. Force diagrams or generalized coordinates? Typically you are taught in high school that in order to solve problems with interacting bodies you need to draw force diagrams, and write down the force balance equations (based on Newton II law) for x and y components (for three-dimensional problems, also the z-component)... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23246 | # Find the limit
Calculus Level 4
$\large\lim_{n \to \infty}\sum_{k=1}^{n}\dfrac{n}{k^2+n^2}$
The limit above has a closed form. Find this closed form. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_23247 | # What is fastest algorithm for factoring out square from number
I have $n$-digit integer $N=a^2b$, $b$ is square-free. In other words, $a$ is maximal square which divides $N$.
What is fastest known algorithm to find $a$? I can write algorithm of $O(n^2\sqrt{N})$ simply trying all squares that are smaller than $N$ an... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19136 | How to solve related rates problems in calculus
Hot network questions which brake system is this how to solve the problem of people communicating issues late, marketing assignments but demanding an immediate reply. suppose that we are using a how to solve related rates problems in calculus cone-bottomed tank. 2. find ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19137 | # Flexible identity
(Redirected from Flexible algebra)
In mathematics, a flexible binary operation $\circ$ is a binary operation that satisfies the equation
$a \circ \left( b \circ a \right) = \left( a \circ b \right) \circ a .$
for any two elements $a$ and $b$ of an algebraic structure.
Every commutative or assoc... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19138 | # Subgroups of Abelian Groups
## Homework Statement
Let G be a group. if H = ##{x \epsilon G : x = x^{-1}}##, that is H consists of all elements of G which are their own inverses, prove that H is a subgroup of G.
## Homework Equations
to show H is a subgroup of G, show that H is closed under the operation of G and ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19139 | # Number Theory Seminar
Tuesday, March 26, 2019 — 12:30 PM EDT
Vandita Patel, University of Toronto
"A Galois property of even degree Bernoulli polynomials"
Let $k$ be an even integer such that $k$ is at least $2$. We give a (natural) density result to show that for almost all $d$ at least $2$, the equation $(x+1)^... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19140 | # Math Help - Integral
1. ## Integral
I would like to integrate the following with respect to x.
y*e^x
--------
x^2
I can't find the right substitution.
Thanks!
2. $y\int\frac{e^{x}}{x^{2}}dx$.
This is not easily done with elementary methods. That is why you can not find the right substitution.
It can be represent... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19141 | Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2810
Title: Generalized homogeneous Besov spaces and their applications Authors: Mejjaoli, Hatem Keywords: Dunkl OperatorsHomogeneous Littlewood-Paley DecompositionHomogeneous Dunkl-Besov SpaceParaproduct OperatorDifferential-Differe... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19142 | # Solving purely symbolic systems of linear equations
• July 31st 2010, 11:50 PM
jfortiv
Solving purely symbolic systems of linear equations
Hello,
I'm working through a finite element text which provides a symbolic solution to a system of linear equations which I suspect might be incorrect based on some checks that ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19143 | Tricki
I have a problem about a continuous function
Quick description
To use this page, click on the appropriate answers below to be taken to further text and further questions. The page is only just started, so at the moment not much will actually happen if you do this.
Prerequisites
Definition of continuity and ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19144 | # Dilworth’s theorem
###### Theorem.
If $P$ is a poset with width $w<\infty$, then $w$ is also the smallest integer such that $P$ can be written as the union of $w$ chains.
Remark. The smallest cardinal $c$ such that $P$ can be written as the union of $c$ chains is called the chain covering number of $P$. So Dilwort... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19145 | # Simple proof of Prékopa's Theorem: log-concavity is preserved by marginalization
The following result is well-known:
Suppose that $$H(x,y)$$ is a log-concave distribution for $$(x,y) \in \mathbb R^{m \times n}$$ so that by definition we have $$H \left( (1 - \lambda)(x_1,y_1) + \lambda (x_2,y_2) \right) \geq H(x_1,y... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19146 | Abstract
We study the behaviour of a -ES that handles constraints by resampling infeasible candidate solutions for linear optimization problems with a conically constrained feasible region. The analysis generalizes prior work in that no particular orientation of the cone relative to the gradient of the objective funct... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19147 | # Math Help - Convergence in the form p^n/n!
1. ## Convergence in the form p^n/n!
Are these sufficient answers? I feel like maybe they are not convincing enough...
2. Originally Posted by davismj
Are these sufficient answers? I feel like maybe they are not convincing enough...
They don't convince me at all. Can you... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19148 | ## Elementary Technical Mathematics
Published by Brooks Cole
# Chapter 1 - Section 1.8 - Multiplication and Division of Fractions - Exercise - Page 49: 69
160 bu/acre
#### Work Step by Step
given a $\frac{1}{20}$ acre plot produces 448 lb shelled corn Therefore we need to find the yield in bushels per acre first c... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19149 | # Abv Formula Plato
references the color of the wort made from the malt at a specific gravity of 8 degrees Plato, which is a specific gravity of approximately 1. Where to Find CB&B Magazine. Forget the decimal point. Altă formulă care foloseşte scara Plato ar fi aşa: P* = (D x 259 - 259) / D , unde "P*" reprezintă gra... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19150 | It is currently 17 Jan 2018, 18:23
GMAT Club Daily Prep
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_19151 | # LAST QUESTION I WILL GIVE BRAINLIEST 3k - 2 = 10
###### Question:
LAST QUESTION I WILL GIVE BRAINLIEST
3k - 2 = 10
### Probability Task - Marbles A jar contains five red marbles and three green marbles. A marble is drawn at random and not replaced. A second marble is then drawn from the jar. 1. Find the probabilit... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10528 | # Group of translations by a fixed distance
I think I need this group ( if it exists) to help solve a physics problem.
Not being a mathematician, what I'd really like is a matrix representation
and a rule for getting the covariant derivative in the event of a broken symmetry.
I'd be much obliged if any one can give m... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10529 | DC FieldValueLanguage
dc.contributor.authorIskandarov, Artur-
dc.date.accessioned2022-07-28T05:33:24Z-
dc.date.available2022-07-28T05:33:24Z-
dc.date.issued2022-
dc.identifier.urihttp://hdl.handle.net/2003/41007-
dc.identifier.urihttp://dx.doi.org/10.17877/DE290R-22856-
dc.description.abstractThe Laplacian operator $\m... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10530 | To install click the Add extension button. That's it.
The source code for the WIKI 2 extension is being checked by specialists of the Mozilla Foundation, Google, and Apple. You could also do it yourself at any point in time.
4,5
Kelly Slayton
Congratulations on this excellent venture… what a great idea!
Alexander Gri... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10531 | What is Magnetic Intensity? [duplicate]
While studying about the magnetic properties of matter, my book defines this vector as
$$\vec{H}=\dfrac{\vec{B}}{\mu_0}-\vec{M}$$
where $$B$$ is the magnetic field and $$M$$ is the intensity of magnetisation.
However it did not provide any definition of this new physical quan... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10532 | # Servois' 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation - The Natural Logarithm Series
Author(s):
In Section 16, Servois applies his expansion formulas to $$F(x) = \varphi ^x(z)$$, where $$\varphi$$ is a distributive function that is commutative with ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10533 | <meta http-equiv="refresh" content="1; url=/nojavascript/"> Chapter 10 Review | CK-12 Foundation
You are reading an older version of this FlexBook® textbook: CK-12 Geometry - Basic Go to the latest version.
# 10.6: Chapter 10 Review
Created by: CK-12
## Keywords, Theorems and Formulas
Triangles and Parallelograms
... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10534 | ### Schwefel
##### Mathematical Definition
###### Latex
f(x) = {418.9829d -{\sum_{i=1}^{n} x_i sin(\sqrt{|x_i|})}}
##### Description and Features
Dimensions: d
The Schwefel function is complex, with many local minima. The plot shows the two-dimensional form of the function.
• The function is continuous.
• The funct... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10535 | # negative semidefinite function
0
1
Interpretation in terms of second derivative test for a function of multiple variables; Saddle point : The Hessian matrix is neither positive semidefinite nor negative semidefinite. positive definite if x'Ax > 0 for all x ≠ 0 ; negative definite if x'Ax < 0 for all x ≠ 0 ; positiv... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10536 | $SL_2$-action on the free lie algebra on a 2-dimensional vector space
Let $V$ be a 2-dimensional vector space (over, say, $\mathbb{Q}$). Let $FL$ be the free lie algebra on $V$, then there is a natural action of the group $SL(V)$ on $FL$, such that the action of $-I$ is by multiplication by $(-1)^d$ on the $d$th grade... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10537 | ## anonymous 4 years ago evaluate summation as n=1 to infinity (1/2) (1/4)^(n-1)
$\sum_{n=1}^\infty a(r)^{n-1}=\frac{a}{1-r}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10538 | # Uneven Graph
This isn't really about whether a graph is odd or even, but I couldn't think of a better title
How does one make a graph like f(x) = |x|, but in the third quadrant the slope is different from the 1st quadrant?
gb7nash
Homework Helper
f(x) = -|x+1| + 10?
You might want to be more specific in your quest... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10539 | # I Mathematical problem about Buffon's Needle
Tags:
1. Mar 9, 2017
### frostysh
Buffon's Needle
A floor is ruled with equally spaced parallel lines a distance
D apart. A needle of length L is dropped at random on the floor. It is assumed that L no more than D. What is the probability that the needle will intersect... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10540 | # Euler substitution
Euler substitution is a method for evaluating integrals of the form:
$\int\!R(x,\sqrt{ax^2+bx+c})dx$
where $R$ is a rational function of $x$ and $\sqrt{ax^2+bx+c}$. In such cases the integrand can be changed to a rational function of a new variable $t$ by using the following substitutions of Eul... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10541 | Duke Mathematical Journal
Homology of the curve complex and the Steinberg module of the mapping class group
Abstract
By the work of Harer, the reduced homology of the complex of curves is a fundamental cohomological object associated to all torsion-free finite index subgroups of the mapping class group. We call this... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10542 | # Short answer find the quotient 6x^3-x^2-7x-9 ------------ 2x+3
143,010 questions, page 984
1. ## maths
one FOURTH OF A HERD OF CAMELSWAS SEEN IN THE FOREST . TWICE THE SQUARE ROOT OF YHE HERD HAD GONE TO MOUNTAINS AND THE REMAINING15 CAMELS WERE SEEN ON THE BANK OF THE RIVER . FIND THE TOTAL NO. OF CAMELS
asked by... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_10543 | # Integro-differential equation
I found the following differential equation:
$$\frac{\partial}{\partial t}f\left(x,t\right)=xf\left(x,t\right)+g\left(x\right)\int_{0}^{1}f\left(x',t\right)x'\mathrm{d}x'$$
to solve for $f(x,t)$. Here $g(x)$ is a given function of $x$, and we know the initial condition $f(x,0)$.
Befo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18576 | If you find any mistakes, please make a comment! Thank you.
## Using the principle of mathematical induction to show inequalities I
Solution:
### Part a
The $n$-th proposition is
$$P_n: \quad n^2>n+1.$$ Clearly, $P_2$ is true because $2^2=4$ which is greater than $2+1=3$. We have the induction basis.
Now we assume... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18577 | GMAT Question of the Day - Daily to your Mailbox; hard ones only
It is currently 22 Jun 2018, 09:42
### GMAT Club Daily Prep
#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.
Customize... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18578 | • Abstract
# Verifiable Visualization for Isosurface Extraction
Visual representations of isosurfaces are ubiquitous in the scientific and engineering literature. In this paper, we present techniques to assess the behavior of isosurface extraction codes. Where applicable, these techniques allow us to distinguish whet... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00004-of-00114-3158c787ea8296d3_doc_18579 | Theoretical Probability Formula
# Theoretical Probability Formula
## Random Experiment
A Random experiment is an
experiment which satisfies the following three conditions.
a) It must have two or more outcomes.
b) The outcomes must be uncertain
c) The experiment can be repeated any number of times under... |
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