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I'm trying to find the power function in the t test of two samples, (the variances are assumed to be equal ($\sigma_1=\sigma_2$ ), in the paper, on page 144 (5), I found that
"The power to detect a difference of $\delta=\mu_1-\mu_2$ with two-sided significance level $\alpha$ is given by:" $$1-\beta =T_v \left(t_{\alpha... |
Let $x_0$ be a fixed vector in a Hilbert space $H$ and suppose $\{x_1,...,x_n\}$ and $\{y_1,...,y_m\}$ are sets of linearly independent vectors in $H$. We seek the vector
$x^* = \operatorname{arg} \min\limits_x \|x-x_0\|$,
subject to
$x \in M=\text{span}(x_1,...,x_n)$ and $\langle x, y_i \rangle=c_i$ for $i=1,...,m$ wh... |
10 1
Hi,
I've had a question ever since my quantum classes that's pretty simple I guess, but still seems to elude me. So here it is:
One text I used for quantum (Liboff's "Introductory Quantum Mechanics") says that in classical mechanics, there is a "vector of the state" of a system, that contains all the information i... |
One can interpret a homomorphic image of an algebraic structure as a "collapsed" or "low-resolution" version of it, since different elements of the original structure get blurred together into becoming the same pixel in the image. Thus if we have a chain of surjective homomorphisms, we are getting higher and higher res... |
Answer:
Let the number of students in the class be \[x\]. Then rupees donated by each student = Rs \[x\]. \[\therefore \] Rupees denoted by \[x\] students \[=\,\text{Rs}\,x\times x\] \[=\text{Rs}\,{{x}^{2}}\] \[\therefore \] The students of class VIII of a school donated Rs 2401 for Prime Minister's National Relief Fun... |
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The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
I'm no graphics expert, but appreciate why square roots are useful. The Pythagorean theorem computes distance between points, and dividing by distance helps normalize vectors. (Normalizing is often just a fancy term for division.)
3D games like Quake divide by distance zillions (yes zillions) of times each second, so "... |
Many functions can be written in terms of a power series
\[ \sum _{k=0}^{\infty} a_k(x-x_0)^k\]
If we assume that a solution of a differential equation is written as a power series, then perhaps we can use a method reminiscent of undetermined coefficients. That is, we will try to solve for the numbers \(a_k\). Before we c... |
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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 ... |
Difference between revisions of "Model"
(→Mantle and large cardinals: -selflink)
(→Mantle and large cardinals: $$)
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If $\kappa$ is [[hyperhuge]], then $V$ has $<\kappa$ many [[ground]]s (so the mantle is a ground itself).<cite>Usuba2017:DDGandVeryLarge</cite>
If $\kappa$ is [[hyperhuge]], then $V$ has ... |
The Triangle Inequality for Inner Product Spaces
We will now look at a very important theorem known as the triangle inequality for inner product spaces. Suppose that $V$ i an inner product space. If we form a triangle with the vectors $u$, $v$, and $u + v$, then the shortest path from the initial point of $u$ to the te... |
Frequently we will want to estimate the empirical probability density function of real-world data and compare it to the theoretical density from one or more probability distributions. The following example shows the empirical and theoretical normal density for EUR/USD high-frequency tick data \(X\) (which has been tran... |
The Method of Integrating Factors Examples 2
The Method of Integrating Factors Examples 2
Recall from The Method of Integrating Factors page that we can solve first order linear differential equations of the form $\frac{dy}{dt} + p(t) y = g(t)$ by multiplying both sides of the equation by the integrating factor $\mu (t... |
This post has been cross-posted on the Quansight LabsBlog.
As of November, 2018, I have been working at Quansight. Quansight is a new startup founded by the same people who started Anaconda, which aims to connect companies and open source communities, and offers consulting, training, support and mentoring services. I w... |
You most likely found this post for one of two reasons:
Either you haven’t heard of Z-Boxes and are interested in if they can somehow help you or you have to learn about Z-Boxes and you have absolutely no idea how to understand the mathematical definitions.
Either way, we’re going to investigate Z-Boxes – not using a b... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
I am trying to solve the following exercise:
Prove that on a surface of constant curvature the geodesic circles have constant curvature.
"Constant curvature" in case of the surface I take to refer to the Gaussian curvature. Now, the geodesic curvature of a curve parameterized by arc length in orthogonal coordinates is ... |
Suppose $X_1, \dots, X_n \overset{\text{iid}}{\sim}\dfrac{x}{\theta}\exp\left(-\dfrac{x^2}{2\theta}\right)\mathbf{1}_{(0, \infty)}(x)$, $\theta > 0$. At the end of the day, my goal is to calculate $$\max_{\theta > 16}L(\theta)$$ where $L$ is the likelihood function, i.e., $$L(\theta) = \dfrac{\prod_{i=1}^{n}x_i}{\theta... |
Tangential Continuous Displacement and Normal-Normal Continuous Stress Mixed Finite Elements for Linear Elasticity Dipl.-Ing. in Dr. in Astrid Pechstein Jan. 9, 2007, 3:30 p.m. T 1010
Abstract. We consider the mixed formulation of linear elasticity, which contains the displacement $u$ as well as the stress tensor $\sig... |
@user193319 I believe the natural extension to multigraphs is just ensuring that $\#(u,v) = \#(\sigma(u),\sigma(v))$ where $\# : V \times V \rightarrow \mathbb{N}$ counts the number of edges between $u$ and $v$ (which would be zero).
I have this exercise: Consider the ring $R$ of polynomials in $n$ variables with integ... |
Difference between revisions of "Group cohomology of dihedral group:D8"
(→Over an abelian group)
(→Baer invariants)
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group = dihedral group:D8|
group = dihedral group:D8|
connective = of}}
connective = of}}
+ + + + + + + +
==Homology groups for trivi... |
Nope. I like to think of ecological inference as creating confounds between contextual (and spatial) effects and individual level effects (in Sociological speak). So consider a set of equations at the individual level:
$$y_1 = \beta_1(x_1) + \beta_2(\bar{X})$$$$y_2 = \beta_1(x_2) + \beta_2(\bar{X})$$
Where $y_1$ and $x... |
How significant is a value compared to a list of values? In most cases statistical testing involves comparing a sample set to a population. In my case the sample is made by one value and we compare it to the population.
I am a dilettante in statistical hypothesis testing confronted with perhaps the most basic problem. ... |
S-shaped and broken s-shaped bifurcation curves for a multiparameter diffusive logistic problem with holling type-Ⅲ functional response
Department of Applied Mathematics, National University of Tainan, Tainan 700, Taiwan, ROC
${\left\{ {\begin{array}{*{20}{l}} {{u^{\prime \prime }}(x) + \lambda \left[ {ru(1 - \frac{u}{... |
Use the diagram to prove the double angle formula, where $t=\tan\theta$: $$\tan2\theta = {2t\over {1-t^2}},\quad \sin2\theta ={2t\over {1+t^2}},\quad \cos2\theta = {{1-t^2}\over {1+t^2}}$$
The point $P'=(p',q')$ is the image of the point $P=(p,q)$ afterreflection in the line $y=mx$. To find $(p',q')$ use the fact thatt... |
The Existence/Uniqueness of Solutions to Second Order Linear Differential Equations
Recall that from The Existence/Uniqueness of Solutions to First Order Linear Differential Equations page that if $p$ and $g$ are continuous functions on an interval $I = (\alpha, \beta)$ and $t_0 \in I$, then the linear first order diff... |
Tournaments and Rankings Tournaments
Definition: A Tournament is a directed graph $G$ so that for every pair $x, y \in V(G)$, then either $(x, y) \in E(D)$ (a directed edge from $x$ going to $y$) or $(y, x) \in E(D)$ (a directed edge from $y$ going to $x$).
By the definition above, a tournament on $n$-vertices can be t... |
Yes, but it may not be valid. The extrapolation will be valid for about 0.1 * PBL Height using the Log-Wind Profile
You will need:
PBL Height. A second Wind speed (within 0.1*PBL Height) Surface Sensible Heat Flux Surface Latent Heat Flux Potential Temperature
You can use the last three variables to calculate the Monin... |
The output resistance \$r_a\$ is the parallel combination of \$R_E\$ and the resistance looking into the emitter of the transistor. As shown in the solution drawing, the resistance looking into the emitter of the transistor is \$1/g_m\$ plus some other resistance due to the source resistance \$R_G\$ and the biasing res... |
Start with the unperturbed gravitational potential for a uniform sphere of mass M and radius R, interior and exterior:
$$ \phi^0_\mathrm{in} = {-3M \over 2R} + {M\over 2R^3} (x^2 + y^2 + z^2) $$$$ \phi^0_\mathrm{out} = {- M\over r} $$
Add a quadrupole perturbation, you get
$$ \phi_\mathrm{in} = \phi^0_\mathrm{in} + {\e... |
The Convergence of Newton's Method
Suppose that $f$ is a twice differentiable function on an interval containing the root of interest, $\alpha$ and suppose that $f'(\alpha) \neq 0$. Now consider the first order Taylor polynomial of $f$ about $x_n$ denoted $P_1(x) = f(x_n) + (x - x_n)f'(x_n)$. By Taylor's Theorem, there... |
So let's start by creating a contingency table from the data. The rows will be the counts of females and males, the columns the locations.
$$\begin{bmatrix} 44 & 86 & 110 \\ 56 & 114 & 90 \end{bmatrix} $$
From thus table, we can compute the sum of the rows and the sum of the columns. The expected number cell frequencie... |
Hints will display for most wrong answers; explanations for most right answers. You can attempt a question multiple times; it will only be scored correct if you get it right the first time.
I used the official objectives and sample test to construct these questions, but cannot promise that they accurately reflect what’... |
Bernoulli Bernoulli Volume 9, Number 6 (2003), 1003-1049. A quantization algorithm for solving multidimensional discrete-time optimal stopping problems Abstract
A new grid method for computing the Snell envelope of a function of an $\mathbb{R}^d$-valued simulatable Markov chain $(X_k)_{0\lambda \leq k\lambda \leq n}$ i... |
I'm working through Stancil and Prabhakar's 'Spin Waves', and am stuck with a vector identity which I am not sure how the authors have justified.
On page 34, we adopt the use of a scalar potential $\phi$, and a vector potential, $\vec{A}$. Then we use these to recast the electric and magnetic field in terms of the Coul... |
Take a simple random walk $\gamma$ in the complex plane conditioned to start at point $a$ and end at point $b$. For this random walk, we can define the winding number $W_\gamma(a,b)$ around $b$ in the usual way for complex curves.
If instead we have a 2D Brownian motion $Z=X+iY$, then this definition becomes more compl... |
Fixed Points
So far we have looked at the Bisection Method and Newton's Method for approximating roots of functions. We are about to introduce another root finding method know as the Fixed Point Method, but before we do so, we will need to learn about special types of points on functions known as fixed points which we ... |
Conditioning shows up everywhere in probability theory and statistics. It is, perhaps, one of the most powerful tools from probability theory, since in science we're often interested in how two things are
related. As a simple example, linear regression is, in essence, a question of a conditional expectation.
Typically,... |
Higher Order O.D.E.'s Complex Roots of The Characteristic Equation Examples 1
Consider the following $n^{\mathrm{th}}$ order linear homogenous differential equation:(1)
Recall from the Higher Order Homogenous Differential Equations - Complex Roots of The Characteristic Equation page that sometimes the characteristic eq... |
We start this section by introducing an important number theoretic function. We proceed in defining some convenient symbols that will be used in connection with the growth and behavior of some functions that will be defined in later chapters.
The Function \([x]\)
The function \([x]\) represents the largest integer not ... |
I'm trying to understand Petersen's Theorem as a corollary to Tutte's Theorem.
Corollary 5.4. Every 3-regular graph without cut edges has a perfect matching.
Proof. Let $G$ be a 3-regular graph without cut edges, and let $S$ be a proper subset of $V.$ Denote by $G_1, G_2, ..., G_n$ the odd components of $G - S$ and let... |
Joyal and Tierney's 1984 monograph,
An extension of the Galois theory of Grothendieck, is an example of a substantial piece of mathematics written using informal reasoning in internal logic. The main result is the following:
Theorem. Every open surjection of toposes is an effective descent morphism. In particular, ever... |
Linear Dependence Lemma
We will now look at a very important lemma known as the linear dependence lemma.
Lemma (Linear Dependence Lemma): Let $\{ v_1, v_2, ..., v_m \}$ be a set of linearly dependent vectors in the vector space $V$ and $v_1 \neq 0$. Then there exists $j \in \{ 2, 3, ..., m \}$ such that: a) $v_j \in \m... |
Notice:
If you happen to see a question you know the answer to, please do chime in and help your fellow community members. We encourage our fourm members to be more involved, jump in and help out your fellow researchers with their questions. GATK forum is a community forum and helping each other with using GATK tools a... |
In Figure 4.1.1 we see that a central angle of \(90^\circ \) cuts off an arc of length \(\tfrac{\pi}{2}\,r \), a central angle of \(180^\circ \) cuts off an arc of length \(\pi\,r \), and a central angle of \(360^\circ \) cuts off an arc of length \(2\pi\,r \), which is the same as the circumference of the circle. So a... |
I wonder if someone knows any general rules of thumb regarding the number of bootstrap samples one should use, based on characteristics of the data (number of observations, etc.) and/or the variables included?
My experience is that statisticians won't take simulations or bootstraps seriously unless the number of iterat... |
Let $f:\mathbb{R}^n\to\mathbb{R}^n$ be analytic and consider the ODE $$x'(t)=f(x(t)).$$ It is well-known that if $(t_{min},t_{max})$ is the maximal domain of a solution $x$ and $t_{max}<\infty$, then $$\lim_{t\to t_{max}}|x(t)|=\infty.$$ Let $t_0\in(t_{min},t_{max})$. What conditions on $f$ (appart from linearity) ensu... |
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Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
I need to draw the derivation tree for $1-2-(3-4)*5*6$ from the grammar below. I want to know how many possible derivation trees are there from this grammar.
$$\begin{align}V_n&=\{expr,term,factor,number\}\\ V_t&= \{(,),-,*,0...9\}\\ P&=\left \{ \begin{aligned} expr&\to expr-expr\;\mid\;term\\ term&\to term*factor\;\mi... |
Solution Spaces to Systems of Linear Equations
We will now begin to look more in-depth into solution spaces for both homogenous and nonhomogenous linear systems of $m$ equations and $n$ unknowns.
Consider the following transformation $T : \mathbb{F}^{n} \to \mathbb{F}^{m}$ defined by:(1)
Homogenous Linear Systems
Suppo... |
Storage of Numbers in IEEE Single-Precision Floating Point Format
For 32 bit storage in computers, a real number $x$ can be stored in which is known as
IEEE Single-Precision Floating Point Format in the following format:
The sign of $x$, $\sigma$ will take up one bit. The significand can be represented in terms of $24$... |
The working principle of a BJT (Bipolar Junction Transistor), which makes it a useful thing, is that it
amplifies current. Throw a small current in, get a larger current out. The amplification factor is an important parameter of the transistor, and is called \$h_{FE}\$. A general purpose transistor may have an \$h_{FE}... |
So far the answers just (cleverly) elaborate on high school tricks and techniques. Therefore, I think it can be interesting to see, instead, how standard modern algorithms work in this special case. I will implement a small version of the Berlekamp-Zassenhaus algorithm. I will try to factor $F(x)=x^5+x+1$ over $\mathbb... |
Let $A \leftarrow C \rightarrow B$ be affinoid $K$-algebras, where $K$ is a non-archimedean field with non-trivial absolute value. Equipping $A$, $B$, $C$ with the supremum seminorms, there is a canonical seminorm $\nu_1$ on $A \otimes_C B$: $$\nu_1(f) = \inf \max_i |a_i|_{\sup} |b_i|_{\sup},$$ the infimum taken over a... |
Apparently the search term I was missing was "Brownian motion". With that, I found several leads. They contradict each other somewhat, but I can at least post a partial answer:
Geisler - Sound to Synapse: Physiology of the Mammalian Ear:
Estimates for the first of these sources, the pressure fluctuations due to the Bro... |
Question : How could I compute the (wave) kernel from the fact I have already found (wave) trace on unit circle?
The definitions are related to the page $25$ of the following pdf.
As the Spectrum$(S^1)=\{n^2 : n\ \in \mathbb{N}^*\}$, the trace (It this relevant for the question?) as distribution is simply $$w(t)=\sum_{... |
The Transpose of a Matrix
Definition: If $A$ is an $m \times n$ matrix, then the Transpose of $A$ denoted $A^T$ is the $n \times m$ matrix resulting from interchanging both the rows and columns of $A$, that is $(A)_{ij} = (A^T)_{ji}$.
For example, suppose that we have the following $3 \times 4$ matrix $A = \begin{bmatr... |
Feynman diagrams provide a very compact and intuitive way of representing interactions between particles. These diagrams can be included into LaTeX documents thanks to a few packages. One of the older packages is
feynmf which uses MetaPost in order to generate the diagrams. More recently, a new package called Ti
kZ-Fey... |
My question is that when we want to find the Lorentz force acted on a particle moving in an electric and magnetic field , the equation is invariant in any two inertial relativistic frames. Why is that so ? And only the electric and magnetic fields transform ?
The force f also transforms. In one frame you see f,E,v, and... |
Urysohn metrization theorem says that every regular and second countable topological space is metrizable. My question, is the converse of this theorem ture ? If not, what are the counter examples?
Any reply kindly appreciated. Thanks.
Mathematics Stack Exchange is a question and answer site for people studying math at ... |
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What is the rate of change of y=sinθ y = \sin \theta y=sinθ when θ=sin−1144180? \theta = \sin^{-1} \frac { 144}{180}? θ=sin−1180144?
What is the derivative of the function y=5cosx?y=5\cos x?y=5cosx?
What is the derivative of the function y=cotx?y=\cot x?y=cotx?
W... |
EDIT: Thanks to hryghr I see that the starting assumptions were incorrect. The transfer function magnitude can't be found that simply.It is more than ten years since I considered my skills sharp on thistopic, and knives don't get sharper in the drawer! But I can't havethat I posted something formally incorrect, so here... |
The ensuing development relies on the elementary inequality for the logarithm function
$$\log(x)\le x-1 \tag 1$$
for all $x>0$.
Let $f(t,h)$ be the function given by
$$f(t,h)=\frac{t^h-1}{h}\tag 2$$
for $h\ne 0$. Note that $f(t,h)>0$ for $t>1$ and $f(t,h)<0$ for $t<1$.
We seek to find a function $g(t)$ such that (i) $|... |
Ab initio calculation of the $$np \to d ³$$ radiative capture process Abstract
In this study, lattice QCD calculations of two-nucleon systems are used to isolate the short-distance two-body electromagnetic contributions to the radiative capture process $$np \to d\gamma$$, and the photo-disintegration processes $$\gamma... |
Before answering the question more or less directly, I'd like to point out that this is a good question that provides an object lesson and opens a foray into the topics of
singular integral equations, analytic continuation and dispersion relations. Here are some references of these more advanced topics: Muskhelishvili,... |
Let $Y^3$ be a handlebody with boundary $\Sigma$. By definition, there is some associated vector $v_{WRT}(Y^3)\in Z(\Sigma)$, the (finite dimensional) Hilbert space associated to $\Sigma$ by the Witten-Reshetikhin-Turaev TQFT. I'd like to understand what this vector is.
In short, $Z(\Sigma)$ is a space of sections of a... |
For example, in this paper on page 21 the authors write the vev that breaks $SO(10)$ to $SU(4)\times SU(2) \times SU(2)$
$$ <54>= 1/5 \cdot diag( -2,-2,-2,-2,-2,-2,3,3,3,3) \omega_s$$
where $\omega_s$ denotes the scale.
What do the authors mean by this?
The Higgs field or Higgs fields that develop a vev are elements of... |
On the variational representation of monotone operators
Dipartimento di Matematica, dell'Università degli Studi di Trento, via Sommarive 14,38050 Povo di Trento, Italy
$V$
$z'\in V'$
$\alpha: V\to {\mathcal P}(V')$
$\alpha(u) \ni z'$
$D_tu + \alpha(u) \ni z'$ representative function
$f_\alpha: V \!\times\! V'\to \mathb... |
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Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
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Now showing items 1-6 of 6
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... |
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Now showing items 1-1 of 1
Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
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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... |
Repeated Roots of The Characteristic Equation
Recall that if $a\frac{d^2y}{dt^2} + b \frac{dy}{dt} + c = 0$ is a second order linear homogenous differential equation, then the characteristic equation for this differential equation is $ar^2 + br + c = 0$. We saw that if the roots of this equation, call them $r_1$ and $r... |
section 3.8 exercise
For each function, find a domain on which the function is one-to-one and non-decreasing, then find an inverse of the function on this domain.
1. \(f\left(x\right)=\left(x-4\right)^{2}\)
2. \(f\left(x\right)=\left(x+2\right)^{2}\)
3. \(f\left(x\right)=12-x^{2}\)
4. \(f\left(x\right)=9-x^{2}\)
5. \(f... |
February 13th, 2018, 02:49 PM
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Posterior Distribution from Beta Density with Exponential Prior
Let $X_1,...,X_n$ be iid random variables with a common density function given by:
$f(x|\theta)=\theta x^{\theta-1}$
for $x\in[0,1]$ and $\theta>0$.
Put ... |
In the previous section, we derived two important properties of logarithms, which allowed us to solve some basic exponential and logarithmic equations.
properties of logs
Inverse Properties :
\(\log _{b} \left(b^{x} \right)=x\)
\(b^{\log _{b} x} =x\)
Exponential Property :
\(\log _{b} \left(A^{r} \right)=r\log _{b} \le... |
Determining Whether a Set is a Vector Space
We have looked at a variety of different vector spaces so far including:
The Vector Space of n-Component Vectors The Vector Space of m x n Matrices The Vector Space of Lines Through the Origin of R2 The Zero Vector Space The Vector Space of Polynomials of Arbitrary Degree The... |
I assume that you are working over the complex numbers. Let $v_j = \frac{1}{\sqrt{n}}(1, \omega_j, \ldots, \omega_j^{n-1})^T$ for $1 \leq j \leq n$ where $\omega_j = e^{\frac{2\pi i j}{n}}$. The vectors $v_j$ form a basis of $\mathbb{C}^n$ and are eigenvectors of
all circulant matrices. If build a matrix $U$ whose colu... |
Let me come back to your question for more practical purposes. In my former theoretical approach (I keep all my previous notations), I gave a necessary and sufficient condition for an element $\alpha\in K^*$ to be a global $m$-th power, but in practice this criterion works well only to give a negative answer, i.e. to s... |
Problem.
Let $\{\lambda_n\}_{n\in\mathbb N}$ be a sequence of complex numbers . Let's call a family of exponential functions $\{\exp (\lambda_n s)\}_{n\in\mathbb N}$ $F$-independent (where $F$ is either $\mathbb C$ or $\mathbb R$) iff whenever the series with complex coefficients
$$f(s)=\sum\limits_{n=1}^{\infty}a_n e^... |
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Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
Lephenixnoir af424d1baa update documentation after writing the wiki 3 mesi fa config 4 mesi fa include/TeX 3 mesi fa src 3 mesi fa .gitignore 3 mesi fa Makefile 4 mesi fa README.md 3 mesi fa TODO.md 3 mesi fa configure 3 mesi fa font5x7.bmp 4 mesi fa font8x9.bmp 4 mesi fa font10x12.bmp 4 mesi fa
This library is a custo... |
I understand that in general if we're adding more planes of atoms (increasing thickness of sample) then the intensity would increase because we have more constructive interference. But isn't there a breaking point for this? Shouldn't there be a finite thickness past which the intensity decreases?
Each layer contributes... |
I recently gave a tutorial at CMU about spectral learning for NLP. This tutorial was based on a tutorial I had given last year with Michael Collins, Dean Foster, Karl Stratos and Lyle Ungar at NAACL.
One of the algorithms I explained there was the spectral learning algorithm for HMMs by Hsu, Kakade and Zhang (2009). Th... |
In my post Trigonometry Yoga, I discussed how defining sine and cosine as lengths of segments in a unit circle helps develop intuition for these functions.
I learned the circle definitions of sine and cosine in my junior year of high school, in the class that would now be called pre-calculus (it was called “Trig Senior... |
What are the advantages/disadvantages of using the arithmetic Sharpe Ratio vs the geometric Sharpe Ratio? Is one more correct? Or is one better in certain circumstances?
In addition to John's answer and just to make things clear:
The arithmetic mean is given by
$$\mu_a = \frac{1}{n} \sum_{i=1}^n x_i$$
The geometric mea... |
Suppose $C$ is a 3-form, and $G$ is a 4-form defined by $G = dC$. Also, $M_{11}$ is an 11-dimensional manifold (without a boundary), $W_{6}$ is a 6-dimensional submanifold of $M_{11}$ and $D_{\epsilon}W_6 = -S_{\epsilon}W_{6}$ is the 4-sphere bundle over $W_6$.
Further, suppose $\rho$ is a 0-form and $e_{2}^{1}$ is a 2... |
One disadvantage of the fact that you have posted 5 identical answers (1, 2, 3, 4, 5) is that if other users have some comments about the website you created, they will post them in all these place. If you have some place online where you would like to receive feedback, you should probably also add link to that. — Mart... |
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let ai≻0a_i\succ0ai≻0 .Prove that∏i=1nai=1⇒∑i=1n1ai+1≥1\prod_{i=1}^{n}... |
This is a high pass T filter:
According to me, if input voltage is \$V_{\text{in}}\$, then voltage across the inductor \$L\$ should be $$V_x=\frac{j\omega L}{j\omega L + \frac{1}{2j\omega C}}V_{\text{in}}$$
Now, I think \$V_{\text{out}} = V_x\$ since we can only measure the EMF across the output terminals unless there'... |
Exercise \(\PageIndex{1}\): Euler number
Consider the function \(f(x)=\left(1+\dfrac{1}{x}\right)^x\). Make a table showing \(f(x)\) for \(x=1,2,3, .....\) . Round your solutions to five decimal places. What can you say about the value of the function \(f(x)\) as \(x\) increases indefinitely?
Answer
\(\lim_{x \to \inft... |
Evaluate the limit \[\lim_{h\rightarrow 0}\frac{2(-3+h)^{2}-18}{h}\] a) 12 b) 8 c) 14 d) 6
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Evaluate the limit \[\lim_{h\rightarrow 0}\frac{2(-3+h)^{2}-18}{h}\] a) 12 b) ... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
A posteriori error estimates space-time in Isogeometric Analysis of parabolic problems Dr. Svetlana Matculevich Nov. 4, 2016, 10:15 a.m. S2 054
We are concern with guaranteed error control of space-time Isogeometric Analysis (IgA) numerical approximations of parabolic evolution equations in fixed and moving spatial com... |
This question is based on a special case of the Coparaso Harris formula, as described in Counting curves on rational surfaces - R. Vakil.
Let $E$ be a non-singular planar conic.
Then every degree $d$ curve intersects it in $2d$ points (with mult.). Let us focus only on rational irreducible curves that have only simple ... |
Accumulation Points of a Set in a Topological Space
Recall from the The Open Neighbourhoods of Points in a Topological Space page that if $(X, \tau)$ is a topological space and $x \in X$ then a open set $U \in \tau$ is called an open neighbourhood of $x$ if $x \in U$.
We will now define a very important type of point o... |
Homotopically Equivalent Topological Spaces
Definition: Let $X$ and $Y$ be topological spaces. Then $X$ and $Y$ are said to be Homotopically Equivalent if there exists continuous functions $f : X \to Y$ and $g : Y \to X$ such that $g \circ f = \mathrm{id}_X$ and $f \circ g = \mathrm{id}_Y$.
For example, let $D^2$ denot... |
Table of Contents
Isotopic and Non-Isotopic Embeddings on the Bounded Cone
Recall from the Isotopic Embeddings on Topological Spaces page that if $X$ and $Y$ are topological spaces and $f, g : X \to Y$ are embeddings then $f$ and $g$ are said to be isotopic if there exists a continuous function $H : X \times I \to Y$ s... |
Polynomials Review
Polynomials Review Recall that a Polynomialif a function of the form $p(x) = a_0 + a_1x + a_2x^2 + .... + a_nx^n$ where $a_0, a_1, ..., a_n$ are coefficients from the field $\mathbb{F}$. If $a_n \neq 0$, then the Degreeof the polynomial $p$ is $\mathrm{deg} (p) = n$, that is, the largest exponent att... |
When we are working with a new function, it is useful to know as much as we can about the function: its graph, where the function is zero, and any other special behaviors of the function. We will begin this exploration of linear functions with a look at graphs.
When graphing a linear function, there are three basic way... |
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