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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5633 | ## Number terms
An interesting question on the G+ Mathematics community I co-moderate asked about the difference between “numbers” and “numerals”. We wo...
## Some thoughts on circumference
This is the formula for the circumference of a circle: $C = 2\pi r$ It’s very simple. My recollection of how it was taught is a... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5634 | # What does it mean intuitively to know a pdf “up to a constant”?
I've seen this mentioned numerous times, most recently in motivating the MCMC method and description of the Metropolis-Hastings algorithm. The text (Simulation and the Monte Carlo Method, Second Edition. By R.Y. Rubinstein and D. P. Kroese) says:
An ad... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5635 | # Combinations and Probability
• February 17th 2008, 10:24 PM
mike
Combinations and Probability
If my brother and I can invite 5 friends from a class of 15 to a party how many ways can we each pick 5 friends?
What's the probability 6 different friends are invited?
What's the prob my brother and I invite the same 5 p... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5637 | # Why do large particles scatter more light than smaller particles?
1. ### thewall12
10
1. The problem statement, all variables and given/known data
Silly question, I know. I suspect it's because of a wider reflecting angle due to the diameter, but I'm not quite sure.
2. Relevant equations
3. The attempt at a solut... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5639 | # Continuity of preferences
Let $$\succsim$$ be a transitive and reflexive relation on a metric space $$X$$ with closed upper and lower contour sets. If $$\succsim$$ is not complete, does it hold that: for all converging sequences with $$x_n\succsim y_n$$ for each $$n\geq 1$$ and $$x_n\to x$$, $$y_n\to y$$, we have $$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5641 | # [SOLVED] Torsion invariants check
The torsion invariants of $C_{90} \times C_{12} \times C_{36 } = 6|6|180$. If not, please help. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5642 | # Taking the cube root of a sum of radicals
I am wondering how to derive the following simplification without knowing it beforehand: $$^3\sqrt{10 + 6\sqrt{3}} = 1 + \sqrt{3}$$ After the fact, it is easy to verify algebraically. The problem arose when applying Cardano's method to solve $$y^3 + 6y = 20$$ I was able to d... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5643 | # Why the reflection and transmission?
1. Jun 2, 2007
### tim_lou
in solving the time-dependent Schrödinger's equation for the delta potential, one obtain a set of non-normalizable solutions.
form the boundary condition and comparing the coefficients of the solution, one obtains the probability of transmission and ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5644 | ## Open-Mindedness
Recently I have been thinking a lot about why so many people seem inconvincible of certain things which I hold to be true. And while I could certainly make a list of some of these things, that is not the intention of this blog entry. Instead, I have been reflecting on open-mindedness and wanted to s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5645 | # Why is $\sin(t)\cos(t)$ equal to $\frac{1}{2}\sin(2t)$?
I know that $\sin(t)\cos(t)$ is equal to $\frac{1}{2}\sin(2t)$ but I do not understand why, please explain it to me!
-
This question has some explanations "from the first principles". – Dan Shved Nov 8 '13 at 10:29
$\sin 2t =\sin (t+t)= \sin t \cos t+ \cos t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5647 | # Does A a subset of B imply d(B,C)<=d(A,C)
1. Mar 4, 2013
### gottfried
1. The problem statement, all variables and given/known data
Does A $\subset$B imply d(B,C)<=d(A,C)?
3. The attempt at a solution
So my feeling is yes. But trying to prove this is difficult.
se we know A $\subset$B
Suppose C intersection B is... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5638 | # Coefficient a for partial transient temperature rise
This is the coefficent $a_0$ used for calculating cable partial transient temperature rise acc. to IEC 60853-2.
Symbol
$a_0$
Unit
1/s
Formulae
$\frac{M_0+\sqrt{{M_0}^2-N_0}}{N_0}$
Related
Used in
$\Delta \theta_{c,t}$
$T_{a0}$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5646 | # Inverse of complex number
1. Mar 9, 2010
### plexus0208
How does taking the multiplicative inverse (reciprocal) of a complex number change its magnitude and argument?
2. Mar 9, 2010
### WiFO215
A complex number z, when inverted, will have its magnitude also inverted, $$|z^{-1}| = \frac{1}{|z|}$$ and its argumen... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5636 | # String brownian motion
+ 0 like - 1 dislike
118 views
I construct a string brownian motion, replacing the paths in the manifold by surfaces. On the real line, the string can be developed by Fourier series, so that the string brownian motion can be decomposed in the Fourier coefficient as :
$$x(t) (\theta ) =\sum_n... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_5640 | The Cohen's d effect size is immensely popular in psychology. However, its interpretation is not straightforward for clinicians and laypersons, as it requires prior knowledge about what a standard deviation is. Even practicing scientists often turn to general guidelines, such as small (0.2), medium (0.5) and large (0.8... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_128 | 1
In a computer system where the best-fit' algorithm is used for allocating jobs' to memory partitions', the following situation was encountered:$\begin{array}{|l|l|} \hline \textbf{Partitions size in$KB$} & \textbf{$4K \ 8K \ 20K \ 2K$} \\\hline \textbf{Job sizes in$KB$} & \text{$2K ... $} \\\hline \end{array}$When wi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_129 | # Modulus of a composite sheet
1. Aug 11, 2012
### iceman5
1. The problem statement, all variables and given/known data
A crossply composite is comprised of 3 plys of fiberglass reinforced epoxy with the fiber direction parallel to the test direction and 2 plys of carbon fiber reinforced epoxy with the fiber direct... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_131 | Reflected line
Geometry Level 5
A ray of light is sent along the line $$2x-3y=5$$. After reflecting across the line $$x+y=1$$ it enters the opposite side by turning $$15^{o}$$ away from the line $$x+y=1$$, The slope of line along which the reflected ray travels is
$m= \frac{ a \sqrt{b} - c } { d }$
where $$a,b,c,d$... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_132 | Courses
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# Show that the points $\left( {1,1,1} \right)$ and $\left( { - 3,0,1} \right)$ are equidistant from the plane $\overrightarrow r .\left( {3\widehat i + 4\widehat j - 12\widehat k} \right) + 13 = 0$
Last updated date: 25th Mar 2023
Total views: 308.4... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_133 | # What is the Ka chemistry constant?
Dec 9, 2016
${K}_{a}$ is the acid dissociation constant that has been measured for many different acids.
#### Explanation:
In aqueous solution, an acid dissociates according to the following reaction:
$H A \left(a q\right) + {H}_{2} O \left(l\right) r i g h t \le f t h a r p \i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_134 | # Series counterexample
Give an example of series
$$\sum_{n=1}^{\infty} a_n \quad \text{ and } \quad \sum_{n=1}^{\infty} b_n$$
such that both converge, and the series
$$\sum_{n=1}^{\infty} c_n$$
defined by
$$c_n = a_{n-1}b_1 + a_{n-2}b_2 + \cdots + a_1b_{n-1}$$
diverges.
-
The canonical example is $$a_n=b_n=\f... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_135 | Convergence Series [duplicate]
Below is a question that I came across while studying real analysis. Given that $\{a_k\}_{k=1}^{\infty}$ is a sequence of complex numbers where $\sum_k{a_k}{b_k}$ converges for every complex sequence $\{b_k\}_{k=1}^{\infty}$ such that $\lim_kb_k=0$. Prove that $\sum_k|{a_k}|<\infty$. As ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_136 | # Center of a group of order p
1. Oct 27, 2011
### Locoism
1. The problem statement, all variables and given/known data
Let G be a finite p-group, where p is a positive prime. Show that G has nontrivial center. In other words Z(G) $\neq$ {e}.
3. The attempt at a solution
So the centre is pretty much the "abelian su... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_138 | # What is the geometrical action of a skew-symmetric matrix on an arbitrary vector?
What is the geometrical action of a skew-symmetric matrix on an arbitrary vector?
The rotation matrix is a skew-symmetric matrix when $\theta$ is some multiple of $\frac{\pi}{2}$. But it cannot be true that every skew-symmetric matrix... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_140 | A retangular block of wood is measured to have the dimensions11.2cm*3.4cm*4.10cm. Compute the volume of the block, showingexplicity (by underling) how doubtful figures are carried throughth calculations, and report the final answer with the correctnumber of significant figures.
Calulations ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_141 | Select Page
# Understand the problem
The multiplicative group $F^*_7$ is isomorphic to a subgroup of the multiplicative group $F^*_{31}$.
##### Source of the problem
TIFR GS 2018 Part A Problem 17
Abstract Algebra
Medium
##### Suggested Book
Dummit and Foote
Do you really need a hint? Try it first!
We will write t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_143 | ## Access
You are not currently logged in.
Access your personal account or get JSTOR access through your library or other institution:
## If You Use a Screen Reader
This content is available through Read Online (Free) program, which relies on page scans. Since scans are not currently available to screen readers, pl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_137 | # Math Help - Need help with a graph (I have picture)
1. ## Need help with a graph (I have picture)
I am so confused by this, any help?
2. Originally Posted by eliteplague
I am so confused by this, any help?
the solution to the system are the points where the two parabolas intersect ... that's where they are equal.... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_139 | # Determine whether the integral $\int_{0}^{\infty}\frac{\cos(x)\sin(1/x)}{x^p}dx$ is convergent or divergent
Determine whether the improper integral $\int_{0}^{+\infty}\frac{\cos(x)\sin(1/x)}{x^p}dx$ is convergent or divergent for $p\in\mathrm{R}$. According to the Dirichlet test, I find it is convergent when $-1<p<2... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_142 | "enter". So a simple solution is to generating all row elements up to nth row and adding them. To build the triangle, start with "1" at the top, then continue placing numbers below it in a triangular pattern. The nth entry of Pascal’s triangle for row is : The formula just use the previous element to get the new one. H... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_130 | # Determining the human owners of stocks
Consider a simple model of corporate ownership.
A corporation's ownership is split into shares. Each share can belong to either a person or another corporation. If a corporation owns shares in another corporation, the ownership of those shares is split between the owning corpo... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11984 | ## LATEX-L@LISTSERV.UNI-HEIDELBERG.DE
Options: Use Forum View Use Monospaced Font Show Text Part by Default Condense Mail Headers Message: [<< First] [< Prev] [Next >] [Last >>] Topic: [<< First] [< Prev] [Next >] [Last >>] Author: [<< First] [< Prev] [Next >] [Last >>]
> Oh yes. One of the really big mistakes peopl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11985 | # How to solve Black Scholes equation directly without using probability
Given constants $r,\sigma, K>0$, considering the Black-Scholes PDE of a Europoean call: \begin{cases} \frac{\partial c}{\partial t}+rs\frac{\partial c}{\partial s}+\frac{1}{2}\sigma^2s^2 \frac{\partial^2 c}{\partial s^2}-rc = 0\\ c(T,s) =(s-K)^+\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11987 | # Natural examples of Reverse Mathematics outside classical analysis?
Harvey Friedman at the 1974 ICM motivated Reverse Mathematics by the following statement:
When the theorem is proved from the right axioms, the axioms can be proved from the theorem.
Reverse Mathematics has had many successes in finding the "right... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11988 | # Factors of 147: Prime Factorization, Methods, Tree, and Examples
The factors of 147 are the numbers that are divisible by 147. Factors can be defined as numbers that are wholly divisible without any remainder. Factors can be positive and negative with the difference of opposite signs.
Figure 1 – All possible Factor... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11989 | ### Home > CALC > Chapter 3 > Lesson 3.3.2 > Problem3-109
3-109.
Curves can be labeled with descriptors such as "concave down" and "increasing." On graph paper, graph them and label their respective parts. Use different colors to represent concavity.
1. $f\left(x\right) = 2x^{2} + x − 15$
2. $g\left(x\right) = x^{3... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11990 | # Chapter 1 - Tools of Geometry - Chapter Test - Page 75: 18
x=7
#### Work Step by Step
The single arcs on the diagram show that $\angle BDK\cong\angle JDR$ so $3x+4=5x-10$ subtract 3x from each side $3x+4-3x=5x-10-3x$ combine like terms $4=2x-10$ add 10 to each side $4+10=2x-10+10$ $14=2x$ divide each side by 2 $14... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11992 | Evaluate a Derivative Using the Differentiation Methods Tutor - Maple Programming Help
# Online Help
###### All Products Maple MapleSim
Home : Support : Online Help : Tasks : Calculus - Differential : Derivatives : Task/CalculateDerivativeByDiffMethodsTutor
Evaluate a Derivative Using the Differentiation Meth... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11993 | # Solve the equation on the interval [0,2pi] sin 4x=(sqrt(3))/(2)
Solve the equation on the interval $\left[0,2\pi \right]$
$\mathrm{sin}4x=\frac{\sqrt{3}}{2}$
You can still ask an expert for help
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11995 | 00-178 Marek Biskup and Wolfgang Koenig
Long-time tails in the parabolic Anderson model with bounded potential (561K, Postscript) Apr 12, 00
Abstract , Paper (src), View paper (auto. generated ps), Index of related papers
Abstract. We consider the parabolic Anderson problem $\partial_t u=\kappa\Delta u+\xi u$ on $(0,\... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11996 | # Schutz's geometrical proof that spacetime interval is invariant
I'm trying to understand the proof that spacetime interval is invariant under for any two inertial observers. I know it's easy to arrive at the result using Lorentz transformation but I'm trying to understand geometrical way of doing it, specifically as... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11997 | # Double-quantitative γ^∗-fuzzy coverings approximation operators
In digital-based information boom, the fuzzy covering rough set model is an important mathematical tool for artificial intelligence, and how to build the bridge between the fuzzy covering rough set theory and Pawlak's model is becoming a hot research to... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11998 | # complex analysis
• March 16th 2010, 11:53 PM
Kat-M
complex analysis
Let $\gamma$: [0,1] $\rightarrow C$ be any $C^1$ curve. Define $f(z)=\oint_{\gamma} \frac{1}{\zeta-z}d\zeta$
Prove that $f$ is holomorphic on $C$\ $\tilde{\gamma}$, where $\tilde{\gamma}=\{ \gamma (t):0\leq t \leq 1\}.$
• September 12th 2010, 09:43 ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11999 | jjuden one year ago What is the sine of a 30° angle?
1. misty1212
HI!!
2. jjuden
$a. \frac{ \sqrt{3} }{ 3 } b. \frac{ \sqrt{3} }{ 2}c. \frac{ 1 }{ 2 }d.\sqrt{3}$
3. jjuden
hi
4. misty1212
you need a unit circle cheat sheet
5. misty1212
find 30 degrees on the unit circle then find the coordinates of that point... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11986 | # 1987 AIME Problems/Problem 4
## Problem
Find the area of the region enclosed by the graph of $|x-60|+|y|=\left|\frac{x}{4}\right|.$
## Solution 1
Since $|y|$ is nonnegative, $\left|\frac{x}{4}\right| \ge |x - 60|$. Solving this gives us two equations: $\frac{x}{4} \ge x - 60\ \mathrm{and} \ -\frac{x}{4} \le x - 6... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11994 | # y-intercept
A simple line graph. The y-intercept in this case is 2.
The y-intercept of a line on a graph is where the line touches (or intercepts) the y-axis (the numbered line going straight up).
The equation for straight lines is ${\displaystyle y=mx+b}$. "${\displaystyle b}$" is the ${\displaystyle y}$-intercep... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_11991 | # Reciprocal grid
The reciprocal lattice (Latin reciprocus , “in relation to one another”, “alternately”) is a construction of crystallography and solid state physics .
In crystallography, the reciprocal lattice describes the X-ray, electron and neutron diffraction on crystals , e.g. B. in the Laue condition . In con... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24513 | # The cost of reliability in decentralized solar power systems in sub-Saharan Africa
## Abstract
Although there is consensus that both grid extensions and decentralized projects are necessary to approach universal electricity access, existing electrification planning models that assess the costs of decentralized sola... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24514 | Would you like to see this cheatsheet in your native language? You can help us translating it on GitHub!
# Reflex-based models with Machine Learning
By Afshine Amidi and Shervine Amidi
## Linear predictors
In this section, we will go through reflex-based models that can improve with experience, by going through sam... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24515 | # The fox population in a certain region has an annual growth rate of 9 percent per year. It is estimated that the population in the year 2010 was 23,900. Find a function for the population and estimate the fox population in the year 2018.
This article aims to find the population growth. Exponential growth is the proc... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24516 | What is $\mathop {\lim }\limits_{n \to \infty } \frac{{\tan (n)}}{n}$? [duplicate]
This question already has an answer here:
What is $\mathop {\lim }\limits_{n \to \infty } \frac{{\tan (n)}}{n}$?
marked as duplicate by leonbloy, Simon S, JimmyK4542, Alex M., user228113 Jun 13 '16 at 22:03
• Have you heard of L'Hôpi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24517 | # Fourier transform of product of Bessel functions
I need help finding the Fourier transform of the function
$$\rho(\vec{r}) = \alpha \delta_{\vec{r},0} \left(\lambda\lambda' J_1 (\beta |\vec{r}|)Y_1(\beta |\vec{r}|) - \pi^2 J_0 (\beta |\vec{r}|)Y_0(\beta |\vec{r}|) \right),$$
where $\alpha,\beta \in \mathcal{R}$ an... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24519 | PL EN
Preferencje
Język
Widoczny [Schowaj] Abstrakt
Liczba wyników
Czasopismo
## Bulletin of the Polish Academy of Sciences. Mathematics
2010 | 58 | 2 | 147-165
Tytuł artykułu
### Optics in Croke-Kleiner Spaces
Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We explore the interior geom... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24520 | # Change of measure
I am looking at the derivation of the Hill estimator. It is $$\bar{F}(x) = 1 - F(x)$$ the right tail of the distribution. In the derivation they use the equation $$\frac{1}{\bar{F}(u)}\int\limits_u^\infty (\log(x)-\log(u))dF(x) = -\frac{1}{\bar{F}(u)}\int\limits_u^\infty (\log\left(\frac{x}{u}\righ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24522 | # Monte Carlo
2021-04-24 | Modified: 2021-04-24
Monte Carlo methods are a class of sampling algorithms to obtain numerical approximations. To do this we rely on the weak law of large numbers:
The weak law of large numbers
A sequence of random variables $$X_1, X_2, \cdots, X_n$$ converges in probability to a random ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24523 | ## Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)
RECALL: (1) The slope of the horizontal line $y=k$ is zero. (2) The slope of the vertical line $x=h$ is undefined. $y=10$ is a horizontal line. Thus, its slope is zero |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24524 | # zbMATH — the first resource for mathematics
On generating functionals for antisymmetric functions and their application in quantum field theory. (English) Zbl 0325.46071
##### MSC:
46N99 Miscellaneous applications of functional analysis 28C20 Set functions and measures and integrals in infinite-dimensional spaces ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24526 | # Determine if (1,3)is a solution to given system of linear equationsy-2x=33x-2y=5
Determine if (1,3)is a solution to given system of linear equations
$$y-2x=3$$
$$3x-2y=5$$
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24527 | Article
Ufa Mathematical Journal
Volume 10, Number 1, pp. 3-13
Some functional equations in Schwartz space and their applications
Baizaev S., Rakhimova M.A.
DOI:10.13108/2018-10-1-3
In the paper we consider functional equations of form $$(B+r^{2}E)u(z)=0,$$ where $B$ is a constant complex $n\times n$ matrix, $E$ i... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24512 | # Combinatorics Probability for a Board Game
There's a board game I recently played called "Welcome to the Dungeon." In it, there is a deck of 13 cards that consists of 8 types of monsters. Each player may draw a new card each turn. Each player can end the game at any point it is their turn.
There is a mechanism in t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24525 | iGCSE (2021 Edition)
# 7.01 Exact values
Lesson
You'll have noticed by now that when you find angles using trigonometric ratios, you often get long decimal answers. If, for example, you put $\cos30^\circ$cos30° into the calculator, you will see an answer of $0.86602$0.86602... which we'd have to round. However, when... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24521 | For l1_ratio = 1 it Release Highlights for scikit-learn 0.23¶, Lasso and Elastic Net for Sparse Signals¶, bool or array-like of shape (n_features, n_features), default=False, ndarray of shape (n_features,) or (n_targets, n_features), sparse matrix of shape (n_features, 1) or (n_targets, n_features), {ndarray, sparse ma... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_24518 | # Random walk
Five eight-step random walks from a central point. Some paths appear shorter than eight steps where the route has doubled back on itself. (animated version)
In mathematics, a random walk is a mathematical object, known as a stochastic or random process, that describes a path that consists of a successio... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1952 | ## A community for students. Sign up today
Here's the question you clicked on:
## sebastiangonzagonza one year ago HI PLEASE SOMEONE HELP ME WITH SOME QUESTIONS FOR GEOMETRY
• This Question is Closed
1. sebastiangonzagonza
@poopsiedoodle Can you please help me?
2. sebastiangonzagonza
@hero
3. mathstudent55
Here... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1953 | # The Discovery That Transformed Pi
For thousands of years, mathematicians were calculating Pi the obvious but numerically inefficient way. Then Newton came along and changed the game. |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1954 | # Lagrangian for a particle in a uniform magnetic field
1. Sep 19, 2009
### mwoerden
1. The problem statement, all variables and given/known data
We know that for a uniform static magnetic field, we may take
V = 0, A = 1/2 B x r (vector potential)
Now, I have to write the Lagrangian L in cylindrical coordinates, bu... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1955 | # Riemann Theta Function On Hyperbolic Riemann Surfaces
The Riemann theta function for a genus $g$ closed Riemann surface with period matrix $\tau=[\tau_{ij}]$ is defined by
$$\theta(\{z_1,\cdots,z_g\}|\tau)=\Sigma_{n\in\mathbb{Z}^g}e^{\pi i(n\cdot\tau\cdot n + 2n\cdot z)}$$
The zeroth of this function is given by t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1956 | Math and Arithmetic
Statistics
Probability
What is a probability of tossing exactly two heads?
Wiki User
Coin tosses are what we call Independent Events, meaning that the results of one toss have no effect on the next toss or any thereafter.
Therefore the probability of each toss is 1/2.
If, however, you want to k... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1957 | Elementary Statistics (12th Edition)
We know that $probability=\frac{number \ of \ good \ outcomes}{number\ of\ all\ outcomes}$, and also $P(A\cup B)=P(A)+P(B)-P(A\cap B)$. Let A=being tested positive, B=being a marijuana user, then $P(A\cup B)=\frac{143}{300}+\frac{122}{300}-\frac{119}{300}=\frac{146}{300}=0.487.$ |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1958 | # Why does it hold true that $\theta_{t} d\overline{X}_{t}$ is a local $Q$ martingale if $\overline{X}$ is a local $Q$ martingale
I am learning from Bernt Oksendal's Stochastic Differential Equations and on page 276 Lemma 12.1.6, it is stated that:
The existence of an equivalent martingale measure $$Q$$ on the discou... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1960 | # How do you factor 121c^4-264c^2+144?
##### 1 Answer
Jul 19, 2016
=${\left(11 {c}^{2} - 12\right)}^{2}$
#### Explanation:
The clues as to what might be happening here lie in the fact that 121 and 144 areboth perfect squares. Checking 264 reveals that it is
$11 \times 12 \times 2$ which means that this is the answ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1962 | # Moderate Number System Solved QuestionAptitude Discussion
Q. If $a$ and $b$ are positive integers, and $x = 2×3×7×a$ , and $y = 2×2×8×b$ , and the values of both $x$ and $y$ lie between 120 and 130 (not including the two), then $a – b =$
✖ A. -2 ✔ B. -1 ✖ C. 1 ✖ D. 2
Solution:
Option(B) is correct
We are given t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1964 | # Strong (topological) mixing and cofinite set
For a topological dynamical system $(X,T)$ (X is a compact Hausdorff space, and T is a continuous map from X to X), it is called strong mixing if For any nonempty open set U and V, $$N(U,V):=\{n\in \mathbb{Z}_+:U\cap T^{-n}V\neq \emptyset\}$$ (Here $\mathbb{Z}_+$ is the s... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1966 | # RS Aggarwal Solutions Class 10 Ex 18C
Q.1: A sector is cut from a circle of radius 21 cm. The angle of the sector is $150^{\circ}$. Find the length of the arc and the area of the sector.
Sol:
Given:
Angle of sector = $150^{\circ}$
Now,
Length of arc = $= \frac{2 \pi r \theta }{360}$
$= \frac{2 \times \frac{22}... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1967 | # Anti-Antigravity Demonstration
This page discusses the May 10, 2011 Fun Physics Facts for the Family Demonstration...
• In the first demonstration (Feb 15, 2011) we examined the principle of Conservation of Angular Momentum, and showed how a body will spin in the same orientation unless some external force is appli... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1961 | Ex6 4
$\def\abs#1{|#1|}\def\i{\mathbf {i}}\def\ket#1{|{#1}\rangle}\def\bra#1{\langle{#1}|}\def\braket#1#2{\langle{#1}|{#2}\rangle}\def\tr{\mathord{\mbox{tr}}}\mathbf{Exercise\ 6.4}$
a) Define a quantum algorithm that computes the maximum of two $n$-qubit registers.
b) Explain why such an algorithm requires one addit... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1965 | # $\int_0^{\infty} \arctan{\left(\frac{n}{\cosh{(x)}}\right)} \mathop{dx}$
$$\int_0^{\infty} \arctan{\left(\frac{n}{\cosh{(x)}}\right)} \mathop{dx}$$ I think the integral evaluates to $$\frac{\pi}{2} \ln{\left(\sqrt{n^2+1}+n\right)}$$ but I dont know how really! I think $$n$$ is any number but I dont know for sure! Th... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1963 | # Finding an oscillating sequence that diverges and whose limit is zero.
1. Mar 10, 2008
### 4zimuth
1. The problem statement, all variables and given/known data
Hi, I need to find an oscillating sequence whose limit of the differences as n approaches infinity is zero but the sequence itself is diverging.
2. Relev... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_1959 | # Has this phenomenon been discovered and named?
If $$x-\frac{x}{2}=\frac{x}{2},$$ and $$\frac{x}{\sqrt{x}}=\sqrt{x},$$ and $$x-\uparrow(x-\uparrow^22)=x-\uparrow^22$$ when $(x\uparrow^n-[A])\uparrow^nA=x$, where $A$ is some constant, and one uses standard Knuth up-arrow notation[where ($\uparrow^{-1}x$)($-\uparrow^{-... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20736 | ### ¿Todavía tienes preguntas de matemáticas?
Pregunte a nuestros tutores expertos
Q:
A recipe for vegetable frittata calls for $$10$$ chard leaves for every $$6$$ eggs. Eggs are available either by the dozen for $$\ 3.20$$ or by the half-dozen for $$\ 1.70$$ . Marissa wants to use $$25$$ chard leaves to make a fritt... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20738 | # Hybrid estimation for ergodic diffusion processes based on noisy discrete observations
We consider parametric estimation for ergodic diffusion processes with noisy sampled data based on the hybrid method, that is, the multi-step estimation with the initial Bayes type estimators. In order to select proper initial val... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20739 | # Open problems in Hopf algebras
I couldn't find a list of open problems in Hopf algebras. So my question is the following:
In the theory of Hopf algebras, what are the (big) open problems?
Any kind of problem/question will be welcome. I am interested in any kind of problem involving Hopf algebras, say going from co... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20740 | # Real polynomials- complex roots occur in conjugate pairs?
According to the theory of real polynomials, if complex roots occur; then they must occur in conjugate pairs. I want to ask if its proof and applicability to odd degree real polynomials, i.e. which definitely have no chance to have all complex roots (provided... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20741 | ## 70.17 Blowing up
Blowing up is an important tool in algebraic geometry.
Definition 70.17.1. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Let $\mathcal{I} \subset \mathcal{O}_ X$ be a quasi-coherent sheaf of ideals, and let $Z \subset X$ be the closed subspace corresponding to $\mathcal{I}$ (Morphis... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20742 | # Is there a “killing” lemma for G-crossed braided fusion categories?
Edit: I found a serious flaw in the question and my answer, and I had to change a lot. The basic question is still there, but the details are a lot different.
## Premodular categories
In braided spherical fusion (=premodular) categories $\mathcal{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20743 | It is currently 21 Apr 2019, 08:52
### 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.
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MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20744 | ## Real Analysis Exchange
### Greedy Approximation in Certain Subsystems of the Schauder System
#### Abstract
Although the sequence of greedy approximants associated with the Schauder expansion of a function, $f$, continuous on $[0,1]$, may fail to converge, there always will be a continuous function, arbitrarily cl... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20745 | Determining wheter point lie on line
1. Oct 13, 2012
salistoun
Hi all,
How do I go about solving the following question?
Determine whether the points (5 , -6 , 10) and (3, 3 , 8) are on the line
x = 2 + t; y = 3 - 3t, z = 4 + 2t
Stephen
2. Oct 13, 2012
DonAntonio
Just find out whether there exists a value $\,t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20746 | # Math Help - Evaluating Limits
1. ## Evaluating Limits
Hi, I'm new here and this is my first post but I'm having trouble with one of my homework problems. I have the function:
g(x) = (a(x+b)(x-c)(x+d)) / (e(x-f)(x-b)(x-c)), where a, b, c, d, e, and f are all unique, positive real numbers.
a) At what values of x=h ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20747 | # Lesson 10
Here Comes the Sum
## Warm-up: Number Talk: Adding Fractions (10 minutes)
### Narrative
The purpose of this Number Talk is for students to demonstrate strategies they have for adding fractions with unlike denominators. These understandings help students develop fluency and will be helpful later in this ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20749 | Thread: the area of the triangles
1. the area of the triangles
Hello,
I have a small problem, so I decide to ask You for a help.
I don't know how improve that area AEF is equal to area of ABE and ADF triangels (together)
Have a nice day
2. Re: the area of the triangles
Originally Posted by rudzielica
Hello,
I hav... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20750 | ## Kyoto Journal of Mathematics
### Contact structures on plumbed 3-manifolds
Çağrı Karakurt
#### Abstract
We show that the Ozsváth–Szabó contact invariant $c^{+}(\xi)\inHF^{+}(-Y)$ of a contact $3$-manifold $(Y,\xi)$ can be calculated combinatorially if $Y$ is the boundary of a certain type of plumbing $X$ and if ... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20751 | # Monomial basis
In mathematics the monomial basis of a polynomial ring is its basis (as vector space or free module over the field or ring of coefficients) that consists in the set of all monomials. In fact, a polynomial may be uniquely written as a linear combination of monomials.
Univariate polynomials expressed o... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20748 | +0
# What is i?
0
79
2
Hhhhhhhheeeeeeellllllllllllppppppppppp!?!?!!!?!?
Guest May 24, 2017
Sort:
#1
+78
0
What is i?
ummm.... what?
mathguardian23 May 24, 2017
#2
+6765
0
"i" is the imaginary unit. :)
It has a definition of $$i = \sqrt{-1}$$
Because sqrt(-1) cannot be evaluated(What squared = -1??), so math... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_20737 | Statistics - Kurtosis (Distribution Tail extremity)
kurtosis is seen as measure of the “peakedness” of a distribution but it seems that it is not.
Kurtosis tells you virtually nothing about the shape of the peak - its only unambiguous interpretation is in terms of tail extremity; i.e., either existing outliers (for t... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12672 | # Using the energy conservation, derive the expressions for the minimum speeds at different locations along a
more_vert
Using the energy conservation, derive the expressions for the minimum speeds at different locations along a vertical circular motion controlled by gravity. Is zero speed possible at the uppermost poi... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12673 | # Coefficients of potential
Jump to: navigation, search
In electrostatics, the coefficients of potential determine the relationship between the charge and electrostatic potential (electrical potential), which is purely geometric:
${\displaystyle {\begin{matrix}\phi _{1}=p_{11}Q_{1}+\cdots +p_{1n}Q_{n}\\\phi _{2}=p_{... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12675 | # Subsequence – Serlo
Zur Navigation springen Zur Suche springen
## Introductory Example
Sometimes its necessary to speak about the "subsequence" of a sequence. Much like a subset is a "part" of a set, a subsequence is some part of a sequence -- all elements of a subsequence are also elements of the original sequenc... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12676 | # Atkinson index
The Atkinson index (also known as the Atkinson measure or Atkinson inequality measure) is a measure of income inequality developed by British economist Anthony Barnes Atkinson. The measure is useful in determining which end of the distribution contributed most to the observed inequality.[1]
## Defini... |
MathCode-Pile_decontaminated_orig_math-related_devided_processed_train-00003-of-00114-e7fc257ef044bc03_doc_12677 | It is currently 19 Feb 2019, 16:45
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