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Well, the title of the question pretty much says everything. To be more precise: I'd like to know (1) what font would be visually suitable to use with Linux Libertine and/or Linux Biolinum as the main text font (I haven't decided which of the two I'll use) and (2) how to enable it (as a math font) in XeTeX.
A good guid... |
The MVT, Higher Order Partial Derivatives, and Taylor's Formula Review
The Mean Value Theorem, Higher Order Partial Derivatives, and Taylor's Formula Review
We will now review some of the recent material regarding the Mean Value Theorem, higher order partial derivatives of functions, and Taylor's formula for functions ... |
Eigenvalues of the Adjoint of a Linear Map
Eigenvalues of the Adjoint of a Linear Map
In the following proposition we will see that the eigenvalues of $T^*$ are the complex conjugate eigenvalues of $T$.
Proposition 1: Let $V$ be a finite-dimensional nonzero inner product spaces. Then $\lambda$ is an eigenvalue of $T$ i... |
Geometric Series of Real Numbers Examples 1
Recall from Geometric Series of Real Numbers page the following test for convergence/divergence of a geometric series:
We will now look at some examples of applying the test to geometric series.
Example 1 Determine whether the series $\displaystyle{\sum_{n=1}^{\infty} 2 \cdot... |
Question
Repeat Exercise 22.48, but with the loop lying flat on the ground with its current circulating counterclockwise (when viewed from above) in a location where the Earth’s field is north, but at an angle $45.0^\circ$ below the horizontal and with a strength of $6.00 \times 10^{-5} \textrm{ T}$.
Exercise 22.48(a) ... |
\(\quad\)In the following few sections We will often drop the subscript I for convenience, but remember all the computation involves interaction picture fields.
Def:
\(\quad\)Such a term (e.g., \(a_{\boldsymbol{p}}^{\dagger}a_{\boldsymbol{q}}^{\dagger}a_{\boldsymbol{k}a_{\boldsymbol{l}}}\)) is said to in \text{normal o... |
Mazur's Theorem
Theorem 1 (Mazur's Theorem): Let $X$ be a normed linear space and let $K$ be a convex subset of $X$. Then $K$ is norm closed if and only if $K$ is weakly closed.
Mazur's Theorem says that the concept of norm closed and weakly closed is the same for convex subsets of a normed linear space $X$. Since we k... |
Dirichlet's Test for Convergence of Complicated Series of Real Numbers
Recall from the Dirichlet's Test for Convergence of Series of Real Numbers page that if $(a_n)_{n=1}^{\infty}$ and $(b_n)_{n=1}^{\infty}$ are two sequences of real numbers where $(A_n)_{n=1}^{\infty}$ denotes the sequence of partial sums for $(a_n)_... |
The Range and Kernel of Linear Operators
The Range and Kernel of Linear Operators
Definition: Let $X$ and $Y$ be linear spaces and let $T : X \to Y$ be a linear operator. The Range of $T$ denoted $\mathrm{range}(T)$ is the image of $X$ under $T$, that is, $\mathrm{range} (T) = T(X)$. The Kernel of $T$ denoted $\ker (T)... |
In the book
Bayesian Data Analysis by Gelman et al. (3rd edition, 2014), a hierarchical model (or one-way random-effects ANOVA) is presented in section 5.4 as follows,
\begin{equation}\label{eq:lme1} y_{ij} = b_0 + \lambda_i + \varepsilon_{ij}, \end{equation}
where the data $y_{ij}$ come from the $i$th measuring entity... |
I guess this is more a math question than a statistics question. I do not understand how the value of a first derivative can be larger than the range of the original function. I must have a fundamental mistake but I fail to locate it.
The logistic CDF is $$\Lambda(X\beta) \in [0,1]$$ and in this case $$X\beta = \beta_1... |
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Stochastic partial differential equation models for spatially dependent predator-prey equations DCDS-BHome This Issue
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Qualitative analysis on an SIS epidemic reaction-diffusion model with mass action infection mechanism and spontaneous infection in a heterogeneous environment Detailed anal... |
Under the auspices of the Computational Complexity Foundation (CCF)
We describe a new proof of the PCP theorem that is based on a
combinatorial amplification lemma. The *unsat value* of a set of constraints C={c_1,..,c_n}, denoted unsat(C), is the smallest fraction of unsatisfied constraints, ranging over all possible ... |
Under which condition is the largest eigenvalue of a positive semi-definite matrix strictly larger than the largest of the matrix's diagonal entries?
I doubt that there's a nice necessary and sufficient condition, but a sufficient condition is that at least one off-diagonal entry in the row with the largest diagonal en... |
In what follows $X$ will be a scheme and $G$ a group scheme. In the examples I will take $X=\mathbb{P}^1_k$ and $G=\mathbb{G}_{m}$. When reading about "the torsor..." I found many definitions, not sure which are equivalent and why exactly:
(Principle $G$-bundle) A $G$-torsor $P$ over a scheme $X$ is a scheme $P\to X$ w... |
I''ve been struggeling with this problem for the last couple of days.
The main goal is to use the probabilistic classification output $p(C_k|x)$, from for example a logistic regression, to enhance and make a overall classification performance more robust, over a given set of measurements.
In other words: I want to make... |
In the colloquial sense of the word "justified," it is not justified. I will describe why it is justified mathematically and under what circumstances and in what case it is not justified.
Let me begin with the simplest of equations $$\tilde{w}=R\bar{w}+\epsilon,\epsilon\sim\mathcal{N}(0,\sigma^2).$$ Let us assume that ... |
The set of $2\times 2$ Symmetric Matrices is a Subspace Problem 586
Let $V$ be the vector space over $\R$ of all real $2\times 2$ matrices.
Let $W$ be the subset of $V$ consisting of all symmetric matrices. (a) Prove that $W$ is a subspace of $V$. (b) Find a basis of $W$. (c) Determine the dimension of $W$.
Contents
Pr... |
Direct Sum Theorems
Recall the following definition and lemma regarding the direct sum of a set of subspaces $U_1, U_2, ..., U_m$ of a vector space $V$.
Definition: Let $U_1, U_2, ..., U_m$ all be vector subspaces of the $\mathbb{F}$-vector space $V$. We define the direct sum of these subspaces $\bigoplus_{i=1}^{m} = U... |
Difference between revisions of "Main Page"
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== Proof strategies ==
== Proof strategies ==
−
It is natural to look for strategies based on
+
It is natural to look for strategies based on
* [[Szemerédi's original proof of Szemerédi's theorem]].
* [[Szemerédi's original pro... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
Let $\phi:R \rightarrow S$ be a ring homomorphism and let $J$ be an ideal in $S$, then it is quite easy to prove that $\phi^{-1}(J)$ is an ideal in $R$. But can someone help me with proving the opposite? i.e. if $\phi^{-1}(J)$ is an ideal in $R$ then $J$ is an ideal in $S$. (of course, it could be that the statement I ... |
Suppose we have a positive point charge And we put a positive test charge in in the electric field, how can we keep this charge static, And how external work May keep it static because i think it will continue to repel
closed as unclear what you're asking by Chris♦, ZeroTheHero, user191954, Frobenius, John Rennie Sep 1... |
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1. Combination of inclusive and differential $ \mathrm{t}\overline{\mathrm{t}} $ charge asymmetry measurements using ATLAS and CMS data at $ \sqrt{s}=7 $ and 8 TeV
Journa... |
K-function
Estimates Ripley's reduced second moment function \(K(r)\) from a point pattern in a window of arbitrary shape.
Usage
Kest(X, …, r=NULL, rmax=NULL, breaks=NULL, correction=c("border", "isotropic", "Ripley", "translate"), nlarge=3000, domain=NULL, var.approx=FALSE, ratio=FALSE)
Arguments X
The observed point ... |
Tagged: module theory Problem 434
Let $R$ be a ring with $1$.
A nonzero $R$-module $M$ is called irreducible if $0$ and $M$ are the only submodules of $M$. (It is also called a simple module.) (a) Prove that a nonzero $R$-module $M$ is irreducible if and only if $M$ is a cyclic module with any nonzero element as its ge... |
I can give the expectation but I don't know for the monotonicity.
Let $C \sim \chi^2(d,\theta)$ (where $d$ degrees of freedom, and $\theta$ non-centrality parameter).
If $d > 2$, then$$\mathbb{E}(1/C) = \frac{1}{2}\exp(-\theta/2)\frac{\Gamma(d/2-1)}{\Gamma(d/2)}{}_1\!F_1(d/2-1,d/2,\theta/2).$$(I don't know for $d \leq ... |
Linear Maps Review
Linear Maps Review
We will now review some of the recent content regarding linear maps.
Recall from the Linear Maps that a Linear Mapor Linear Transformationfrom a vector space $V$ to another vector space $W$ is a function $T : V \to W$ with the property that $T(au + bv) = aT(u) + bT(v)$ for all vect... |
4:28 AM
@MartinSleziak Here I am! Thank you for opening this chat room and all your comments on my post, Martin. They are really good feedback to this project.
@MartinSleziak Yeah, using a chat room to exchange ideas and feedback makes a lot of sense compared to leaving comments in my post. BTW. Anyone finds a
\oint\fr... |
4:28 AM
@MartinSleziak Here I am! Thank you for opening this chat room and all your comments on my post, Martin. They are really good feedback to this project.
@MartinSleziak Yeah, using a chat room to exchange ideas and feedback makes a lot of sense compared to leaving comments in my post. BTW. Anyone finds a
\oint\fr... |
A cryptographic hash function $f : \{0,1\}^{*} \to \{0,1\}^n$ has three properties: (1) preimage resistance, (2) second-preimage resistance, and (3) collision resistance. Even further, these properties form a hierarchy where each property implies the one before it, i.e., a collision-resistant function is also second-pr... |
I'm trying to figure out what are the theoretical and practical, implications and limitations, when a high-dimensional chaotic process is modeled as a random process. I understand how low-dimensional chaos (callin' it LD chaos from now on) is different from a stochastic process. However I'm unclear on the pitfalls of a... |
The
amsmath package provides a handful of options for displaying equations. You can choose the layout that better suits your document, even if the equations are really long, or if you have to include several equations in the same line.
Contents
The standard LaTeX tools for equations may lack some flexibility, causing o... |
The definition that you are using is not the most general. If you insist on applying the way you do, it only applies for a uniform flow in between two counter-mooving walls. Then, the velocity profile is indeed linear.
A Newtonian fluid is defined by the approximation that
local stress (or drag) is proportional to loca... |
Search
Now showing items 1-1 of 1
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Abel's Test for Convergence of Series of Real Numbers Examples 1
Recall from Abel's Test for Convergence of Series of Real Numbers page the following test for convergence/divergence of a geometric series:
Let's now look at some examples of using Abel's test.
Example 1 Show that the series $\displaystyle{\sum_{n=1}^{\in... |
I assume this is a thought experiment. Your question is more complicated than you think because of the ill-defined parameters of this situation. For one, the word 'amount' here could be taken to mean mass, volume or number of particles and each would be a different scenario. This question also raises a common myth that... |
Permanent link: https://www.ias.ac.in/article/fulltext/pram/068/01/0043-0049
Parametric dependence of the intensity of 182 Å Balmer-𝛼 line $(C^{5+}; n = 3 \rightarrow 2)$, relevant to xuv soft X-ray lasing schemes, from laser-produced carbon plasma is studied in circular spot focusing geometry using a flat field grati... |
Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of a basis \(1,\beta_1,\beta_2,\beta_3\) for the coefficient ring described below. We also show the integral \(q\)-expansion of the trace form.
Basis of coefficient ring in terms of a root \(\nu\) of \(x^{4}\mathstrut -\mathstrut \) \(x^{3}\m... |
A
myriad (from Ancient Greek μυριάδες, myriades) is technically the number ten thousand; in that sense, the term is used almost exclusively in translations from Greek, Latin, or Chinese, or when talking about ancient Greek numbers. More generally, a myriad may be an indefinitely large number of things. [1] History
The ... |
Probably it's not a good fit for this site, but I'll make a cw answer here (others may add to it). If you want to ask about specific tex issues, better make small example in new questions just asking about one point at a time.
I didn't look at your class but there are several odd things in the example document. (The fi... |
فهرست مطالب Volume:8 Issue:5, 2011 Special Issue: Fuzzy Mathatics تاریخ انتشار: 1390/09/17 تعداد عناوین: 11
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Page 1The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of ... |
One strength of the human mind is its ability to find patterns and draw connections between disparate concepts, a trait that often enables science, poetry, visual art, and a myriad of other human endeavors. In a more concrete sense, the brain assembles acquired knowledge and links pieces of information into a network. ... |
Orthonormal Basis of Null Space and Row Space Problem 366
Let $A=\begin{bmatrix}
1 & 0 & 1 \\ 0 &1 &0 \end{bmatrix}$. (a) Find an orthonormal basis of the null space of $A$. (b) Find the rank of $A$. (c) Find an orthonormal basis of the row space of $A$.
(
The Ohio State University, Linear Algebra Exam Problem) Add to ... |
This article is cited in scientific papers (total in 2 2 papers) Index sets for $n$-decidable structures categorical relative to $m$-decidable presentations E. B. Fokina , S. S. Goncharov a , V. Harizanov bc , O. V. Kudinov d , D. Turetsky bc e a Vienna University of Technology, Institute of Discrete Mathematics and Ge... |
What is Superposition of Waves?
According to the principle of superposition. The resultant displacement of a number of waves in a medium at a particular point is the vector sum of the individual displacements produced by each of the waves at that point.
Principle of Superposition of Waves
Considering two waves, travell... |
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Now showing items 1-5 of 5
Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV
(Springer, 2015-05-20)
The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement... |
Basic Theorems Regarding the Maximum and Minimum Functions of Two Functions
Recall from The Maximum and Minimum Functions of Two Functions page that if $f$ and $g$ are two functions defined on an interval $I$ then the maximum function of $f$ and $g$ denoted $\max (f, g)$ is defined for all $x \in I$ by:(1)
Similarly, t... |
Subspaces of Linear Spaces
Definition: Let $X$ be a linear space. A subset $S \subseteq X$ is said to be a Subspace of $X$ if $S$ is itself a linear space with the same operations of addition and scalar multiplication defined on $X$.
It can easily be checked that $S \subseteq X$ is a subspace of $X$ if and only if $S$ ... |
Loading the player...
Résumé :
Hermitian complex spaces are a large class of singular spaces that include for instance projective varieties endowed with the metric induced by the Fubini-Study metric. Many of the problems raised by Cheeger, Goresky and MacPherson in the case of complex projective varieties admit a natur... |
Permutations and Inversions
Before we look at the combinatorial definition of a determinant, we will first need to understand some rather simple basic definitions in combinatorics:
Definition: A Permutation of a set $S$ is an ordered arrangement of the elements in this set without omissions or repetitions of elements.
... |
What is Elasticity?
When an external force is applied to a rigid body there is a change in its length, volume (or) shape. When external forces are removed the body tends to regain its original shape and size. Such a property of a body by virtue of which a body tends to regain its original shape (or) size when external ... |
It breaks up into three simple sections that are each relatively easy to explain:
simulate this circuit – Schematic created using CircuitLab
The first part is the diode that provides reverse voltage protection. If for some reason the polarity of the input voltage is wired opposite to what it is supposed to be, then \$D... |
While in class, we were proving a limit problem using the Squeeze Theorem, but when I was reviewing my notes, I came up with a problem,,
The first question was to prove that $$\lim_{n\to \infty}(1+n)^\frac{1}{n}=1$$
Okay, this was easy.
The next question was to use the limit proven above to evaluate the following limit... |
Goldstone's theorem says that if a group, $G$, is broken into its subgroup, $H$, then massless particles will appear. The number of massless particles are given by the dimension of the coset, $G/H$. It is then often said that the Goldstone boson's live in the coset. In what sense is this statement true? The Lagrangian ... |
Result:Average CSMC Regression Regret
For all average constrained CSMC distributions $D$, and all cost-sensitive classifiers $h_g$ derived from a regressor $g$, \[ r_{av} (h_g) \leq \sqrt{2 |K| \epsilon_{L^2} (g)}, \] where $\epsilon_{L^2} (g)$ is the $L^2$ loss on the underlying regression problem.
Proof:See Average A... |
Informally, it is not what you actually know, it is
what the symbols say you should "pretend" to know and not know.
So $E(X)$ says that you should calculate the expected value of $X$ in a situation where you don't know anything abut any event having happened or not having happened. $E(X\mid A)$ on the other hand says t... |
However, the sample standard deviation, time series: Correcting for autocorrelation. See unbiased estimation of what effect rust infestation has on flower initiation of strawberry. spread because it is less susceptible to sampling fluctuation than (semi-)interquartile range.Compute the sample mean and standard deviatio... |
After reading Cohen and Voronov's notes on string topology, one can find the following construction: Suppose we have a topological space $X$ with continuous action of $S^1$. This means we have a map $\rho: S^1 \times X \to X$. If we choose a fundamental class $[S^1]$ of the circle, we can form the operator $\Delta: H_\... |
You can. By using partitioned-regression results (F-W-L theorem), if the model includes a constant term,
$$y = \alpha + \mathbf x' \beta + u$$
then the "slope coefficients" are in practice calculated by OLS as
$$\hat{\beta}_{OLS} = (\hat {\tilde X}'\hat {\tilde X})^{-1}\hat {\tilde X}'\hat {\tilde y}= \beta + (\hat {\t... |
Difference between revisions of "De Bruijn-Newman constant"
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* [https://terrytao.wordpress.com/2018/04/17/polymath15-eighth-thread-going-below-0-28/ Polymath15, eighth thread: going below 0.28], Terence Tao, Apr 17, 2018.
* [https://terrytao.wordpress.com/2018/04/17/polymath15-eig... |
The $\delta$ function is not continuous, so it's a priori not differentiable. In fact, it's not even well-defined as an ordinary real-valued function, but can be made so in terms of distributions - linear maps on a space of test functions given by $f\mapsto\int\delta f=f(a)$.
It's possible to sensibly
define derivative... |
Properly Divergent Sequences
Properly Divergent Sequences
Recall that a sequence $(a_n)$ of real numbers is said to be
convergent to the real number $A$ if $\forall \epsilon > 0$ there exists an $N \in \mathbb{N}$ such that if $n ≥ N$ then $\mid a_n - A \mid < \epsilon$.
If we negate this statement we have that a seque... |
Recall that when a matrix is diagonalizable, the algebraic multiplicity of each eigenvalue is the same as the geometric multiplicity.
The geometric multiplicity of an eigenvalue $\lambda$ is the dimension of the eigenspace $E_{\lambda}=\calN(A-\lambda I)$ corresponding to $\lambda$.
The nullity of $A$ is the dimension ... |
Difference between revisions of "Development/Architecture/KDE3/Low-level Graphics"
m (Development/Architecture/KDE 3 Architecture/Low-level Graphics moved to Development/Architecture/KDE3/Low-level Graphics)
m (Text replace - "<code cppqt3>" to "<syntaxhighlight lang="cpp-qt">")
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So, it is possible to ... |
Matthew Lake
Title: The black hole - uncertainty principle correspondence from extended de Broglie relations
Abstract: The Compton wavelength, which gives the minimum radius within which the mass of a particle may be localized due to quantum mechanical effects, and the Schwarzschild radius, which gives the maximum regi... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
Journal of Symbolic Logic J. Symbolic Logic Volume 55, Issue 3 (1990), 1022-1036. Set Theoretic Properties of Loeb Measure Abstract
In this paper we ask the question: to what extent do basic set theoretic properties of Loeb measure depend on the nonstandard universe and on properties of the model of set theory in which... |
(Wikipedia page for background info: https://en.wikipedia.org/wiki/Principle_of_transformation_groups )
I'm reading Edwin Jaynes's paper, "Prior Probabilities":
and on page 17 he describes the principle of transformation groups, wherein he provides a method to derive objective prior distributions for different paramete... |
According to this site the general form of the Gravitational Potential Energy of mass $m$ is
$$U=-\frac{GMm}{r}\tag{1}$$ where $G$ is the gravitation constant, $M$ is the mass of the attracting body, and $r$ is the distance between their centre's.
However, I am learning Astrophysics at the moment and in the derivation ... |
2018-09-02 17:21
Measurement of $P_T$-weighted Sivers asymmetries in leptoproduction of hadrons / COMPASS Collaboration The transverse spin asymmetries measured in semi-inclusive leptoproduction of hadrons, when weighted with the hadron transverse momentum $P_T$, allow for the extraction of important transverse-momentu... |
First: Lemma 1 says that $||\mathbf{x}|| \leq \alpha q \sqrt{n}$ with overwhelming probability if $\mathbf{x}$ is drawn from the discrete Gaussian since $\frac{1}{2^n}$ is negligible.
Next, from properties of absolute values, $|a + b| \leq |a| + |b|$. So, leaving the $2$ out for now and writing $\mathbf{s_A}^T\mathbf{e... |
Let $X$ be an $n-$dim Alexandrov space with curvature $\geq k$. Does $X$ satisfy a reverse doubling condition? That is, does there exist a constant $C>1$, s.t., for any $x\in X$, $0<r<\mathrm{diam}(X)/2$, $\mathrm{vol}(B_x(2r))\geq C\cdot\mathrm{vol}(B_x(r))$?
The answer is no. In fact, it is not even true for Riemanni... |
I'm trying to align an equation in two points, my code is the following:
\documentclass{article}\usepackage{amsmath}\begin{document}\begin{equation} \begin{cases} \omega_W \geq \omega_{W0} \hspace{2mm} &\Leftrightarrow \hspace{2mm} S_x \rightarrow \infty & \longrightarrow \text{Wheel is spinning} \\ \omega_W > \omega_{... |
A fairly random example of a great pedagogical technique for mathematics -
examples first.
For example, suppose I was trying to explain to you what a
ring is in algebra. I could start by telling you that a ring is a set $R$ together with two binary operations $+$ and $.$ such that: $r+s=s+r$ and $(r+s)+t$=$r+(s+t)$ for... |
On Aug 3, 2009, at 8:59 AM, marlene marchena wrote:
> Dear R users,>> I'm running a SVR in package e1071 but I did not able to calculate the> parameters w and b of the regression. I don't know how to do that> and if it> is possible to do it with this package.>> Someone have some idea. Any help would be much appreciated... |
I want to use a slanted
\sum symbol denoting a different meaning from summation. How do I get a slanted
\sum symbol?
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. It only takes a minute to sign up.Sign up to join this community
If you are usi... |
Background:
I notice that there is quite a bit of similarity between the standard heat equation and the energy equation (from the navier stokes equations). The heat equation is given as
$$\frac{\partial\left(\rho h\right)}{\partial t} + \nabla\cdot\left(u\rho h \right) - \nabla\cdot\left(k\nabla T \right)=0$$
with $\rh... |
Mean, mode, median and range of the data set
When you get a set of data there are some terms to describe the data. The terms mean, median, and mode are different types of averages. Together with range, they describe our data set.
Mean - basic average of our data set, which is calculated by adding all data numbers and d... |
Write down
the significance level. samples or a normal population? is called the standard error of the difference between independent means. Standard Error of the Difference Between the Means of Two Samples The logic andat the 5% level of significance.We will discuss this in more details and quantify what is "close" st... |
$F$ ${\hat f_{{\rm{r}}1}}$ 余数理论值 ${\hat f_{{\rm{r}}2}}$ 余数理论值 ${\hat f_{{\rm{r}}3}}$ 余数理论值 $\Delta F$ ${\rm{5}}{\rm{.5122}} \times {\rm{1}}{{\rm{0}}^{\rm{3}}}$ ${\rm{512}}{\rm{.60}}$ $512$ ${\rm{5512}}{\rm{.65}}$ $5512$ ${\rm{5512}}{\rm{.90}}$ $5512$ ${\rm{1}}.57 \times {\rm{1}}{{\rm{0}}^{{\rm{ - 1}}}}$ $512.58$ $5512.... |
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Now showing items 1-1 of 1
Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Orthonormal Bases of Vector Spaces Examples 1
Recall from the Orthonormal Bases of Vector Spaces page that if $V$ is a finite-dimensional inner product space, then a basis $\{ e_1, e_2, ..., e_n \}$ is said to be an orthonormal basis of $V$ if $<e_i, e_j> = 0$ if $i \neq j$ for $i, j = 1, 2, ..., n$ and $<e_i, e_i> = 1... |
Time: Venue: A-201 (STCS Seminar Room) Organisers:
Given a boolean function $f : \{0, 1\}^n \rightarrow \{0, 1\}$ define the function $f \circ \mathsf{XOR}$ on $2n$ bits by $f \circ \mathsf{XOR} (x_1, \dots, x_n, y_1, \dots, y_n) = f(x_1 \oplus y_1, \dots, x_n \oplus y_n)$. Such a function is called an $\mathsf{XOR}$ f... |
I'm attempting to numerically solve the following in order to get a function of 2 variables, just looking at the real part of
$$\psi(x,t)=\frac{1}{\pi\sqrt{2}}\int_{-100}^{100}\frac{\sin{(k)}}{k}e^{i\left[kx-\frac{k^2}{2}t\right]}\,dk$$
where I have specific values for $t=0,2,4$ and I'd like to plot the function from $... |
Given natural numbers $m,n$ such that $m^2 + n^2 - m \equiv 0 \pmod{mn}$ and $p$ a prime dividing $m$, then I want to show that $p^2$ divides $m$.
I have tried multiple approaches: Euclidean division gives that $m = qp^2 + r$ for some $q, r \in \mathbb{N}$ where $0 \leq r < p^2$ and filling this in to show that $r = 0$... |
Adding or subtracting a multiple of $2\pi$ from $k_j$ does not affect the values of the sum $\sum_{j=0}^N f(k_j)\exp (-ix_n k_j)$ at the points $x_n$. Thus, either form could be used if all we ever going to plug for $x_n$ are integers. (Or we could randomly add $10\pi$ to all the $k_j$.)
Aliasing is the term used for t... |
Q1: In layman terms (hopefully still accurate/correct), and in the light of my attempt below, what is RSM? Q2: Same question as above, but without " in the light of my attempt below". You are free to explain RSM in layman terms in the perspective that you think is most healthy. Q3: Can I say that Artificial Neural Netw... |
Time: Venue: A-201 (STCS Seminar Room) Organisers:
We consider the following three problems in the areas of Algorithms, Complexity theory and Streaming algorithms respectively.
1) Given a graph $G=(V,E)$, the Sparsest Cut problem asks for a partition of the vertices (i.e. a cut) $S \subseteq V$ with minimum
sparsity: $... |
If an observer travels away from our sun, at what distance would our sun occupy 7 arc seconds of space?
From us, the Sun is visible around a half grad, which is $\approx$ 30 arc min = 1800 arc seconds.
To get to 7 arc seconds, you need to go 1800/7 times farther away, so the result is around 250 AU.
While this might se... |
Geometric progression – Introduction:
If in a sequence of terms each term is constant multiple of the preceding term, then the sequence is called a geometric progression.(G.P), whereas the constant multiplier is called the common ratio.
In an A.P, the difference between \(n^{th}\) term and \((n-1)^{th}\) term will be a... |
Integration by Parts of Indefinite Integrals
We are now going to learn another method apart from U-Substitution in order to integrate functions. First recall the product rule for a function in the form $f(x) = u(x)v(x)$:(1)
Now suppose that we integrate both sides of the product rule. By the The Fundamental Theorem of ... |
Projection Operators
Definition: For any vector $\vec{x} \in \mathbb{R}^2$, a projection operator $T: \mathbb{R}^2 \to \mathbb{R}^2$ projects every vector $\vec{x}$ onto some axis. For any vector $\vec{x} \in \mathbb{R}^3$, a projection operator projects every vector $\vec{x}$ onto some plane. Projection Transformation... |
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Now showing items 1-10 of 24
Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
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Now showing items 1-10 of 18
J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
Finding a Matrix's Inverse with Elementary Matrices
Recall that an elementary matrix $E$ performs an a single row operation on a matrix $A$ when multiplied together as a product $EA$. If $A$ is an $n \times n$ matrix, then we can say that $A$ is constructed from applying a finite set of elementary row operations on $I_... |
To show that $H$ is a normal subgroup of $G$, we prove that\[ghg^{-1}\in H\]for any $g\in G$ and $h\in H$.
For any $g\in G$ and $h\in H$ we have\begin{align*}&ghg^{-1}\\&=g^2g^{-1}hg^{-1} &&\text{since $g=g^2g^{-1}$}\\&=g^2g^{-1}hg^{-1}hh^{-1} &&\text{since $e=hh^{-1}$}\\&=g^2(g^{-1}h)^2h^{-1}. \tag{*}\end{align*}
It f... |
It's not that hard. If you have just planar or angular light sources, you can think of them as one light source split into multiple chunks and the only thing to deal with is how to sample this multi-light and how to compute the PDF of the resulting samples.
Picking probability
First, you need to setup the picking proba... |
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