text stringlengths 256 16.4k |
|---|
kernel Spectral Clustering for Community Detection in Complex Networks --This paper proposes a kernel spectral clustering approach for community detection in unweighted networks. The authors employ the primal-dual framework and make use of out-of-sample extension. They also propose a method to extract from a network a ... |
Oscillations and Waves Transverse and longitudinal waves Transverse wave: A wave in which the particles of the medium vibrate at right angles to the direction of propagation of wave is called a transverse wave.This wave travel in the form of crests and troughs.
Longitudinal wave: A wave in which the particles of the me... |
In principle, the Hamiltonian represents the energy of a system. Whether or not you want to model your system to have kinetic energy is up to you and what you need. For example: consider an atom with an electron that can be approximated as a two level system (i.e. it as only its ground state and an excited state).
The ... |
Tagged: symmetric matrix Problem 572
The following problems are Midterm 1 problems of Linear Algebra (Math 2568) at the Ohio State University in Autumn 2017.
There were 9 problems that covered Chapter 1 of our textbook (Johnson, Riess, Arnold). The time limit was 55 minutes. Problem 7. Let $A=\begin{bmatrix} -3 & -4\\ ... |
Search
Now showing items 1-10 of 192
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 i... |
Animation Nodes Version
Animation Nodes
v2.1 includes a very fast and efficient noise functions and so I will be using this version in my answer. However, I also provided an alternative using older versions of Animation Nodes, though it is not as efficient as I stated above.
The Theory
The image you posted above is a
t... |
I found an interesting infinite sequence recently in the form of a 'two storey continued fraction' with natural number entries:
$$\frac{e^2-3}{e^2+1}=\cfrac{2-\cfrac{3-\cfrac{4-\cdots}{4+\cdots}}{3+\cfrac{4-\cdots}{4+\cdots}}}{2+\cfrac{3-\cfrac{4-\cdots}{4+\cdots}}{3+\cfrac{4-\cdots}{4+\cdots}}}$$
The numerical computa... |
Let $U_n=\sum_{i=1}^n X_i,V_n=\sum_{i=1}^n Y_i$, $n\geq 1$, be a two-dimensional random walk with i.i.d. increments $(X_n, Y_n)$, where $X_n, Y_n$ are discrete random variables with joint pmf $P_{X,Y}$. $X_n,Y_n$ have the following properties: \begin{align} 0 < \mathbb{E}[X_n]=\mu_X, \quad 0 < \mathbb{E}[Y_n]=\mu_Y,\qu... |
Tagged: kernel of a matrix Problem 270
Let
\[A=\begin{bmatrix} 4 & 1\\ 3& 2 \end{bmatrix}\] and consider the following subset $V$ of the 2-dimensional vector space $\R^2$. \[V=\{\mathbf{x}\in \R^2 \mid A\mathbf{x}=5\mathbf{x}\}.\] (a) Prove that the subset $V$ is a subspace of $\R^2$.
Add to solve later
(b) Find a basi... |
(a) If $AB=B$, then $B$ is the identity matrix. (b) If the coefficient matrix $A$ of the system $A\mathbf{x}=\mathbf{b}$ is invertible, then the system has infinitely many solutions. (c) If $A$ is invertible, then $ABA^{-1}=B$. (d) If $A$ is an idempotent nonsingular matrix, then $A$ must be the identity matrix. (e) If... |
Effective January 2014, Psychological Science recommends the use of the "new statistics" - effect sizes, confidence intervals, and meta-analysis - to avoid problems associated with null-hypothesis significance testing (NHST).
Confidence interval provides an alternative method to NHST, which some have argued provides mo... |
When the switch is closed in the
RLC circuit of Figure(a), the capacitor begins to discharge and electromagnetic energy is dissipated by the resistor at a rate \(i^2 R\). With U given by [link], we have
\[\frac{dU}{dt} = \frac{q}{C} \frac{dq}{dt} + Li \frac{di}{dt} = -i^2 R\]
where
i and q are time-dependent functions.... |
I have some trouble in understanding properly the concept of abelianization in the case of the symmetric group $S_n$. More specifically, it is known that the commutator group of $S_n$ is $A_n$, the group of all even permutations in $S_n$. Now, assume that we are given two elements $[\rho_1], [\rho_2] \in S_n / A_n$ suc... |
I'm working through a homework sheet for a Fluid Mechanics module. The question is given:
Consider the flow described by the complex potential $$w=4z+\frac{8}{z}.$$
Determine $\psi$, $\phi$, $u$ and $v$ in plane polar coordinates $(r,\theta)$. Determine the location of the stagnation points. Show that this complex pote... |
Suppose $F$ is a field s.t $\left|F\right|=q$. Take $p$ to be some prime. How many monic irreducible polynomials of degree $p$ do exist over $F$?
Thanks!
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.... |
The operation of differentiation or finding the derivative of a function has the fundamental property of linearity. This property makes taking the derivative easier for functions constructed from the basic elementary functions using the operations of addition and multiplication by a constant number. The basic different... |
Can someone give me suggestions how can I construct a 2-tape Turing machine which simulates PDA ?
closed as unclear what you're asking by Evil, David Richerby, Rick Decker, Juho, hengxin Jul 9 '17 at 13:00
Please clarify your specific problem or add additional details to highlight exactly what you need. As it's current... |
Given this definition of weak bisimilarity:
A configuration relation $\mathcal{R}$ is a weak bisimulation provided that whenever $P\ \mathcal{R}\ Q$ and $\alpha$ is $\mu$ or $\tau$ action then:
$P \to^\alpha P'$ then $Q \Rightarrow^\widehat{\alpha} Q'$ for some $Q'$ s.t. $P'\ \mathcal{R}\ Q'$
$Q \to^\alpha Q'$ then $P ... |
Theorem. $\int_0^\infty \sin x \phantom. dx/x = \pi/2$.
Poof. For $x>0$ write $1/x = \int_0^\infty e^{-xt} \phantom. dt$,and deduce that $\int_0^\infty \sin x \phantom. dx/x$ is$$\int_0^\infty \sin x \int_0^\infty e^{-xt} \phantom. dt \phantom. dx= \int_0^\infty \left( \int_0^\infty e^{-tx} \sin x \phantom. dx \right)\... |
6.11.1
I think the first thing that I would do, would be to convert the coordinates to degrees and decimals (or maybe even radians and decimals, though I do it below in
degrees and decimals):
Antares: \(α = 247.375 \quad δ = -26.433\)
Deneb \(α = 309.400 \quad δ = +45.283\)
We already did a similar problem in Chapter 3... |
Mathematics - Functional Analysis and Mathematics - Metric Geometry
Abstract
The following strengthening of the Elton-Odell theorem on the existence of a $(1+\epsilon)-$separated sequences in the unit sphere $S_X$ of an infinite dimensional Banach space $X$ is proved: There exists an infinite subset $S\subseteq S_X$ an... |
Difference between revisions of "stat946w18/Implicit Causal Models for Genome-wide Association Studies"
(→Implicit causal model in Edward)
(→Implicit causal model in Edward)
Line 203: Line 203:
== Implicit causal model in Edward ==
== Implicit causal model in Edward ==
−
[[File: coddde.png|600px
+
[[File: coddde.png|60... |
Sound, like all waves, travels at a certain speed and has the properties of frequency and wavelength. You can observe direct evidence of the speed of sound while watching a fireworks display. The flash of an explosion is seen well before its sound is heard, implying both that sound travels at a finite speed and that it... |
Difference between revisions of "stat946w18/Implicit Causal Models for Genome-wide Association Studies"
(→Implicit causal model in Edward)
(→Implicit causal model in Edward)
Line 203: Line 203:
== Implicit causal model in Edward ==
== Implicit causal model in Edward ==
+
[[File: coddde.png|600px]]
[[File: coddde.png|60... |
The function $f(x)$ is continuous and differentiable in $[0,1]$ if $f'(x)\le 10$ for all $x\in[0,1]$ and $f(0)=0$,
What is the maximum possible value of $f(x)$ for $x\in [0,1]$ ?
Any help would be greatly appreciated, thanks.
Mathematics Stack Exchange is a question and answer site for people studying math at any level... |
We imagine a slippery (no friction) bar of soap slithering around in a conical basin. An isolated bar of soap in intergalactic space would require three coordinates to specify its position at any time, but, if it is subject to the holonomic constraint that it is to be in contact at all times with a conical basin, its p... |
Since $I_1+I_2=R$, there exists $a \in I_1$ and $b \in I_2$ such that\[a+b=1.\]Then we have\begin{align*}1&=1^{m+n-1}=(a+b)^{m+n-1}\\[6pt]&=\sum_{k=1}^{m+n-1}\begin{pmatrix}m+n-1 \\k\end{pmatrix}a^k b^{m+n-1-k}\\[6pt]&=\sum_{k=1}^{m-1}\begin{pmatrix}m+n-1 \\k\end{pmatrix}a^k b^{m+n-1-k}+\sum_{k=m}^{m+n-1}\begin{pmatrix... |
A few times I have been told to not to turn the titles to Latex only as that stops them from being indexed by search engines.
I see two problems with that :
1.What seems natural humans behaviour needs to be modified in order to accommodate machines. a latex of an integral is far more descriptive. e.g. compare $\int \ln... |
Structure of Atom Quantum Mechanical Model of Atom and Concept of Atomic Orbitals Calculation of no.of waves in an orbit : \tt no.of \ waves = \frac{Circumference}{wavelength} =\frac{3.33 \times \left(\frac{n^{2}}{Z}\right)Å}{3.33\left(\frac{n}{z}\right)Å} n = orbit number Total no.of revolutions per second : \tt = \fr... |
My question is about quantum algorithms for QED (quantum electrodynamics) computations related to the fine structure constants. Such computations (as explained to me) amounts to computing Taylor-like series $$\sum c_k\alpha^k,$$ where $\alpha$ is the fine structure constant (around 1/137) and $c_k$ is the contribution ... |
In one dimension, if I have a Riemann-integrable derivative $f'$ of a function $f$ which I don't know, I can (almost) recover $f$ from integrating $f'$.
A simple example would be $f'(x)=2x$, then by the Fundamental Theorem of Calculus, I get that $f(x)=x^2 + const,$ where the constant does not depend on $x$. I said 'al... |
Forgot password? New user? Sign up
Existing user? Log in
∫0∞ln1+x111+x3(1+x2)lnx dx= ?\large \int_0^\infty\frac{\ln\frac{1+x^{11}}{1+x^3}}{(1+x^2)\ln x}\, \mathrm dx = \, ?∫0∞(1+x2)lnxln1+x31+x11dx=?
The integral above has a closed form. Evaluate this integral and give your answer to three decimal places.
Problem Loadi... |
This is a very common fallacy, yes!
So when we say that "fluid flows faster as the pipe gets narrower" we mean
within the same pipe. We do not mean across all circumstances. The cause of the increased fluid flow is that water is a highly incompressible fluid. Because of this, any mass that flows into a box must also fl... |
This question already has an answer here:
Dummies instead of the Chow test 1 answer
I am sitting on a pile of data concerning wages at a local company and other information, such as the gender, whether the person in question belongs to a minority group etc. What I would like to investigate is whether an additional year... |
Calculating the Heat Transfer Coefficient for Flat and Corrugated Plates
In many engineering applications involving conjugate heat transfer, such as designing heat exchangers and heat sinks, it’s important to calculate the heat transfer coefficient. Often determined with the aid of correlations and empirical relations,... |
Search
Now showing items 1-2 of 2
D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
Search
Now showing items 1-10 of 27
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 ... |
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 ... |
Possible Duplicate: Series converges implies $\lim{n a_n} = 0$
Someone can help me? If $(a_n)$ is a decreasing sequence and $\sum a_n$ converges. Then $\lim {(n.a_n)} = 0$.
I don't have idea how to solve this.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professiona... |
As the title mentioned, I've not known exactly about Fourier series and when I was reading an digital communication textbook, I wondered about below equation derivation of Fourier series like $$\alpha(f)=\frac1T\sum^{\infty}_{m=-\infty}\delta\left(f-\frac mT\right)$$ which is periodic with period $\frac1T$ and $\delta$... |
The action of $GL_6$ on $P(\wedge^3 \mathbb{C}^6)=P^{19}$ has 4 orbits (of dim 19, 18, 14, 9). Can you describe how the springer resolution applies to each of these orbits? It should have positive dimensonal fibers over the 14 and 9 dimensional orbits (probably some flag variety?).
A representative of the quartic orbit... |
In section 9.2 on oscillator strengths, we first defined what we meant by absorption oscillator strength \(f_{12}\). We then showed that the equivalent width of a line is proportional to \(ϖ_1f_{12}\). We followed this by defining an emission oscillator strength \(f_{21}\) by the equation \(ϖ_2f_{21} = ϖ_1f_{12}\). The... |
I can only offer a partial answer here. I don't really know how resurgence is used in QFT, so I am going to talk about the general principles.
First thing first. The definition of an asymptotic series does not need complex analysis. However an asyptotic series in a real setting is much less useful. Lets say that a func... |
Consider the language $L_{k-distinct}$ consisting of all $k$-letter strings over $\Sigma$ such that no two letters are equal:
$$ L_{k-distinct} :=\{w = \sigma_1\sigma_2...\sigma_k \mid \forall i\in[k]: \sigma_i\in\Sigma ~\text{ and }~ \forall j\ne i: \sigma_j\ne\sigma_i \}$$
This language is finite and therefore regula... |
''Diamond Paradox'' by Diamond (1971)
This is a "less-known paradox," usually put as a counter to famous Bertrand paradox. It is a starting point in the literature on informational frictions in consumer markets, and the scientists in the field agree on its significance.
Its idea is diametrically opposite to that of Ber... |
The second order equation
$\frac{d^2\vec{x}}{dt^2} = A\vec{x}\ + \vec{g}(t)$
models an earthquake's effect on a 7-story building. Let $x_j(t)$ be the displacement of the $j$th floor with respect to its equilibrium position. The ground moves with displacement $g(t)$.
Here
$\vec{x} = \begin{pmatrix} x_1\\ x_2\\ \vdots\\ ... |
In the Subset Sum problem can some of the given numbers $a_1,a_2,a_3,\dots,a_n$ be the same? For example, we might have $[1,1,1,2,3,4]$ and the target is $5$? Can I assume that I have a specific solution with numbers $2$ and $3$ and $1,1,1$ and $2$ is not?
One question we could ask is "Can we reduce this back to the su... |
In a complex methods course I am taking, we were given an equation for a particular driven harmonic oscillator where the driving force is trigonometric. I have worked out the math and obtained an equation that tells me that the driving frequency at resonance is the natural frequency multiplied by i. My tutor tells me t... |
This question combines two aspects:
what do we mean by the relativity of simultaneity, and does it always hold? what is a good way to understand the constantly accelerating reference frame (in flat spacetime)
1. Relativity of simultaneity
In special relativity, the relativity of simultaneity is the fact that if in one ... |
The Lie algebra of $ \mathfrak{so(3)} $ and $ \mathfrak{su(2)} $ are respectively
$$ [L_i,L_j] = i\epsilon_{ij}^{\;\;k}L_k $$ $$ [\frac{\sigma_i}{2},\frac{\sigma_j}{2}] = i\epsilon_{ij}^{\;\;k}\frac{\sigma_k}{2} $$
And of course, there is an isomorphism between these two algebras, $$ \Lambda : \mathfrak{su(2)} \rightar... |
I would like to argue that the result follows if one demands that energy is differentiable in k space. To be precise, one would need $E = E\,(k_x, k_y)$ such that $\nabla_{\mathbf{k}}E$ always exists (I have reduced the dimensionality for ease of visualisation).
This is perhaps essential on physical grounds, since the ... |
The Annals of Mathematical Statistics Ann. Math. Statist. Volume 42, Number 5 (1971), 1671-1680. Limit Theorems for Some Occupancy and Sequential Occupancy Problems Abstract
Consider a situation in which balls are falling into $N$ cells with arbitrary probabilities. A limiting distribution for the number of occupied ce... |
I want to show that $(L^\infty,\|\cdot\|_\infty)$ is a normed vector space. I understand that there are two things to show; firstly, that $L^\infty(X,\mu)$ is a linear space and secondly that $\|\cdot\|_\infty$ defines a norm on this space.
I don't have solutions to check whether what I have done here is correct or not... |
Thrust is the wrong measurement to use for this comparison, as is thrust to weight. What matters is the Specific Impluse $I_{\text{sp}}$, which is a measure of the ability to change momentum per unit of propellent.
The RL10C has a specific impulse of 450s, while the Dawn engine is over 3,000, in other words, the Dawn e... |
Tagged: abelian group
Abelian Group Problems and Solutions.
The other popular topics in Group Theory are:
Problem 616
Suppose that $p$ is a prime number greater than $3$.
Consider the multiplicative group $G=(\Zmod{p})^*$ of order $p-1$. (a) Prove that the set of squares $S=\{x^2\mid x\in G\}$ is a subgroup of the mult... |
Tagged: subspace Problem 709
Let $S=\{\mathbf{v}_{1},\mathbf{v}_{2},\mathbf{v}_{3},\mathbf{v}_{4},\mathbf{v}_{5}\}$ where
\[ \mathbf{v}_{1}= \begin{bmatrix} 1 \\ 2 \\ 2 \\ -1 \end{bmatrix} ,\;\mathbf{v}_{2}= \begin{bmatrix} 1 \\ 3 \\ 1 \\ 1 \end{bmatrix} ,\;\mathbf{v}_{3}= \begin{bmatrix} 1 \\ 5 \\ -1 \\ 5 \end{bmatrix... |
Let $C=\Omega \times (0,\infty)$. We want to find a solution $v \in H^1(C)$ such that given $u \in H^{\frac 12}(\Omega)$, $$\int_0^\infty\int_\Omega \nabla v \nabla \varphi + v_y\varphi_y = 0\quad\forall \eta \in H^1(C), \quad\eta(x,0) \equiv 0$$ $$v(x,0) = u(x)$$ where eg. the $n(x,0) = 0$ means in the sense of trace,... |
If we are connected to the internet via one single ISP, it is most likely that we will have a default route set up to one of their access routers. However, if we want to multi-home, either for reliability or load-balancing reasons, the most straightforward way is to set up BGP peering with our upstream providers. For e... |
Update: see below for an update on the incorrectness of this join operation
Here is a very rough sketch of a possible solution:
I think I may have a solution to this problem using a type of randomly-balanced B+-tree.Like treaps, these trees have a unique representation.Unlike treaps, they store some keys multiple times... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Year of publication 1996 (22) (remove) Has Fulltext yes (22) (remove)
284
A polynomial function \(f : L \to L\) of a lattice \(\mathcal{L}\) = \((L; \land, \lor)\) is generated by the identity function id \(id(x)=x\) and the constant functions \(c_a (x) = a\) (fo... |
For a language $L$ over the finite alphabet $\Sigma$, let $L_n$ denote the set of words in $L$ of length $n$. The word $u$ is a
subword of $w$ if $u$ can be obtained from $w$ by deleting letters. The language $L$ is subword-closed if whenever $w\in L$ and $u$ is a subword of $w$ then $u\in L$. It can be shown (see belo... |
And yet another question to discuss the assumptions in PRIIPs. It is remarkable that in these legal documents a Cornish-Fisher expansion including skewness and kurtosis is used.
Looking at the very recent version of the document we find on page 27 the following formula for the moderate scenario (Which is, if I read it ... |
stat946w18/Implicit Causal Models for Genome-wide Association Studies Contents 1 Introduction and Motivation 2 Implicit Causal Models 3 Implicit Causal Models with Latent Confounders 4 Likelihood-free Variational Inference 5 Empirical Study 6 Conclusion 7 Critique 8 References 9 Implicit causal model in Edward Introduc... |
Naime Ekici
Articles written in Proceedings – Mathematical Sciences
Volume 121 Issue 3 August 2011 pp 291-300
Let 𝐹 be a free Lie algebra of rank $n\geq 2$ and 𝐴 be a free abelian Lie algebra of rank $m\geq 2$. We prove that the test rank of the abelian product $F\times A$ is 𝑚. Morever we compute the test rank of t... |
The general purpose of multiple regression (the term was first used by Pearson, 1908), as a generalization of simple linear regression, is to learn about how several independent variables or predictors (IVs) together predict a dependent variable (DV). Multiple regression analysis often focuses on understanding (1) how ... |
Not related to this old question of mine, but takes the question from a different perspective.
Let $\mathcal V$ be a monoidal model category (following the def of Hovey, for example). Then there is a bicategory $\text{Prof}(\mathcal V)$ of $\cal V$-valued profunctors, which has the following interesting property:
every... |
The key here is the
antimagnetic strip, quite aside from whether or not such a device can be built.
When you insert the anti-magnetic strip, you must change the shape of the magnetic field. You must force the magnetic field to "leave" the high permeability ball. The same magnetic induction $|\vec{B}|$ in a high permeab... |
It is often explained that renormalization arises in QFT because QFT is a low-energy effective theory that needs to be replaced by a more fundamental theory at higher energies/smaller distances. While we don't have a more fundamental theory that's accepted by everyone, candidates do exist. Can string theory for example... |
Search
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... |
Let’s start by recalling some background about
modules.
Suppose that \(R\) is a ring and \(1_R\) is its multiplicative identity. A left
\(R\)-module \(M\) consists of an abelian group \((M, +)\) and an operation \(R \times M \rightarrow M\) such that for all \(r, s \in R\) and \(x, y \in M\), we have: \(r \cdot (x+y)= ... |
Published February 2011.
The most ancient device found in all early civilisations, is a "shadow stick". The shadow cast from a shadow stick was used to observe the motion of the Sun and thus to tell time. Today we call this instrument a Gnomon. The name gnomon comes from the Greek and refers to any L-shaped instrument,... |
Search
Now showing items 1-2 of 2
Search for new resonances in $W\gamma$ and $Z\gamma$ Final States in $pp$ Collisions at $\sqrt{s}=8\,\mathrm{TeV}$ with the ATLAS Detector
(Elsevier, 2014-11-10)
This letter presents a search for new resonances decaying to final states with a vector boson produced in association with a... |
Search
Now showing items 1-1 of 1
Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
Motion in a Straight Line General Kinematics of a Moving Body A particle is there which is having negligible dimension A body in that which is having countable dimension. Distance is the actual path covered by the body where as displacement is change in the initial and final position with direction. Distance is a scala... |
I am looking for a list of classifying spaces $BG$ of groups $G$ (discrete and/or topological) along with associated covers $EG$; there does not seem to be such cataloging on the web. Or if not a list, just some further fundamental examples. For instance, here are the ones I have off the top of my head:
$B\mathbb{Z}_n=... |
I was trying to understand why the equation $y_i = \left( \frac{n}{w} \right) + (i \pmod w) $ describes the step property in a balancing network?
First, recall $x_i$ to be the number of tokens a network gets as input and similarly $y_i$ to be the number of output tokens. Recall that a balancing network is just a networ... |
1 Easy
Proposition Let $f:X\to Y$ be a continuous map of topological spaces, $\mathscr F$ a sheaf of abelian groups on $X$ such that $R^jf_*\mathscr F=0$ for $j>0$. Then for all $i\geq 0$ there exists a natural isomorphism $$H^i(Y, f_*\mathscr F)\simeq H^i(X,\mathscr F)$$
ProofApply the composition rule for the derived... |
\(LS\)-coupling is in practice a good approximation in light atoms, but there are appreciable departures from \(LS\)-coupling in the heavier atoms. Generally the several lines in a multiplet in \(LS\)-coupling are fairly close together in wavelength for \(LS\)-coupling, but, as departures from \(LS\)-coupling become mo... |
I should say that you have 3 related questions, namely 1) To what extent can we trust the approximations based on HP and Jw transformations, 2) The nature of the low excitation spectrum and 3) The relation with Goldstone modes.
We shall look first at the Holstein-Primakoff method. The spin ladder operators for at a sit... |
Consider a family of convex sets $\{K_n\}$ such that $K_n \subset \mathbb{R}^n$ for each $n$. The kinds of sets one might be considering could be, for instance,
$K_n$ is the cube of side $2A$, i.e., $K_n = [-A, A]^n$.
$K_n$ is the $n$ dimensional ball of radius $\sqrt{\lambda n}$.
Suppose we are interested in the rate ... |
For a given finite alphabet $\Sigma$, my goal is to write an algorithm that receives as input a sequence $V=V_{1}V_{2}\dots V_{n}$ of subsets ($V_{i}\subseteq\Sigma$), and returns a weighted deterministic finite-state automaton with the following property: for every input string $s$, the automaton penalizes each substr... |
I apologize if this question is not a good fit for CSTheory. I'm a PhD student who has just started out and I'm working on a game-theory problem in one of my classes. Although my professor hasn't explicitly required it, I'd like to prove the NP-hardness or completeness of the problem since it's something I'd like to le... |
If $y(t) = x(t)*h(t)$, then what is the expression for $y(t+a)$?
Is it $x(t+a)*h(t+a)$ or $x(t+a)*h(t)$?
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and video processing. It only takes a minute to sign up.Sign up to join this community
If $y(t... |
What is a proof by contradiction? This is actually quite difficult to answer in a satisfactory way, but usually what people mean is something like this: given a statement $\phi$, a proof of $\phi$ by contradiction is a derivation of a contradiction from the assumption $\lnot \phi$. In order to analyse this, it is very ... |
The probability
<math>P</math> of some event
<math>E</math> (denoted <math>P(E)</math>) is defined with respect to a "universe" or sample space
<math>S</math> of all possible elementary events
in such a way that <math>P</math> must satisfy the Kolmogorov axioms.
Alternatively, a probability can be interpreted as a meas... |
To show two sets are equivalent, you should show that $A\subseteq B$ and $B\subseteq A$. This implies that $A=B$. If $A=\varnothing$ and $B=\varnothing$, then try an element-chasing proof to show that $A=B$.
($\to$): If $x\in A$, then $x\in B$. Thus, $A\subseteq B$. $\qquad$[ Vacuously true]
($\leftarrow$): If $x\in B$... |
Topology Seminar: Soren Galatius (Stanford) Date: 10/13/2010
University of British Columbia
Homology of moduli spaces of manifolds
We study the space M_g of isometry classes (or conformal equivalence classes) of smooth manifolds, diffeomorphic to #^g(S^d \times S^d), the connected sum of g copies of S^d \times S^d. For... |
I have encountered different notions of isotropy of radiation and I would like to know if they are the same and what the exact definition of isotropy is, if one exists.
Let's take black body radiation inside a cavity at thermal equilibrium for an example. It's a fact, that in this case the radiation is isotropic, but w... |
I have a normal random variable $X$ with mean $\mu$ and variance $\sigma^2$. Any advice on how to compute the conditional expectation $E[\frac{1}{X}|X \leq T]$ where $T$ is a positive constant?
Comment: Simulation for $T = 10,$ which avoids taking reciprocals of values
anywhere near $0.$ Then $E(\frac 1 X\, |\, X > 10)... |
Laws of Motion Third Law of Motion For every action there is an equal and opposite reaction. Action and reaction never act on same body. Velocity of rocket at any time \tt V = v_o + u \log_{e}\left(\frac{m_{0}}{m}\right) When initial velocity is zero. \tt V = u \log \left(\frac{m_{0}}{m}\right) Thrust acting on rocket ... |
Electronic Devices Classification of Metals, Conductors and Semiconductors The band formed by a series of energy levels containing the valence electrons is known as VALENCE BAND. Valence Band may be partially or completely filled with electrons depending on the nature of crystal. Valence Bond is the highest filled ener... |
Edited:
My question is related to a tutorial I was reading.
The covariance matrix is a block matrix where $C_{xx}$ and $C_{yy}$ are within-set covariance matrices and $C_{xy} = C_{yx}^T$ are between-sets covariance matrices.
$$ \left[\begin{array}{r r} C_{xx} & C_{xy}\\ C_{yx} & C_{yy} \end{array}\right] $$
The tutoria... |
Two questions (more details below):
Let $G$ be a compact Lie group and $X$ a $G$-space such that all stabilizer subgroups are conjugate to a fixed $H \leq G$. Denote by $\pi: X \to X/G$ the quotient map. Under which conditions on $X$ is $\pi$ a Serre fibration?
Let $G$ be as above and $F$ a
free$G$-space. Under which c... |
The previous part brought forth the different tools for reasoning, proofing and problem solving. In this part, we will study the discrete structures that form the basis of formulating many a real-life problem.
The two discrete structures that we will cover are graphs and trees. A graph is a set of points, called nodes ... |
Naturally, a rotating object has kinetic energy - its parts are moving after all (even if they’re just rotating around a fixed axis). The total kinetic energy of rotation is simply the sum of the kinetic energies of all rotating parts, just like the total translational kinetic energy was the sum of the individual kinet... |
A sequence of numbers \(\left\{ {{a_n}} \right\}\) is called a geometric sequence if the quotient of successive terms is a constant, called the common ratio. Thus \({\large\frac{{{a_{n + 1}}}}{{{a_n}}}\normalsize} = q\) or \({a_{n + 1}} = q{a_n}\) for all terms of the sequence. It’s supposed that \(q \ne 0\) and \(q \n... |
Let $E$ be the event that a smartphone of this model is defective. Let $F_A$ be the event that a smartphone is manufactured by factory A. Similarly for $F_B$ and $F_C$.
Then the overall fraction of defective smartphones of this model can be found as follows.\begin{align*}P(E) &= P(F_A \cap E) + P(F_B \cap E) + P(F_C \c... |
(a) If $AB=B$, then $B$ is the identity matrix. (b) If the coefficient matrix $A$ of the system $A\mathbf{x}=\mathbf{b}$ is invertible, then the system has infinitely many solutions. (c) If $A$ is invertible, then $ABA^{-1}=B$. (d) If $A$ is an idempotent nonsingular matrix, then $A$ must be the identity matrix. (e) If... |
Warning: the following may not be considered as a proper answer in that it does not provide a closed form solution to the question, esp. when compared with the previous answers. I however found the approach sufficiently interesting to work out the conditional distribution.
Consider the preliminary question of getting a... |
Newton’s second law of motion tells us what a force does: it causes a change in momentum of any particle it acts upon. It does not tell us where the force comes from, nor does it care - which is a very useful feature, as it means that the law applies to all forces. However, we do of course need to know what to put down... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.