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Does electric field caused by time varying magnetic field form closed loops(electric field starts from a positive charge and ends at a negative charge)? and are they conservative or non-conservative fields?
The field lines certainly
can form closed loops, for example in a transformer. But they don't have to either, an ... |
2018-09-11 04:29
Proprieties of FBK UFSDs after neutron and proton irradiation up to $6*10^{15}$ neq/cm$^2$ / Mazza, S.M. (UC, Santa Cruz, Inst. Part. Phys.) ; Estrada, E. (UC, Santa Cruz, Inst. Part. Phys.) ; Galloway, Z. (UC, Santa Cruz, Inst. Part. Phys.) ; Gee, C. (UC, Santa Cruz, Inst. Part. Phys.) ; Goto, A. (UC,... |
Why can we not have non-integer powers of fields in a QFT Lagrangian, eg. $\phi^{5/2}$? Or if we wanted a charged $\phi^3$ theory, could we not have a $(\phi^*\phi)^{3/2}$ term?
This is a property of renormalization group fixed points---- in usual circumstances, with local Lagrangians, noninteger powers get smoothed ou... |
Would a Dyson sphere make a red dwarf appear to be a Brown Dwarf? Would it disguise a star enough to misidentify it what size it is? I'm just wondering if it could be possible that some Dyson spheres are out there drifting around, camouflaged like a rather innocuous and innocent star?
No, you could not. Temperature pro... |
Basic Operations on Euclidean n-Space
Recall from the Euclidean n-Space page that for each positive integer $n$, the Euclidean n-space $\mathbb{R}^n$ is the set of all points $\mathbf{x} = (x_1, x_2, ..., x_n)$.
In a moment we will look at some operations defined on Euclidean n-space that the reader should already be f... |
Geometric Series
Definition: A Geometric Series is a series in the form $\sum_{n=1}^{\infty} ar^{n-1} = a + ar + ar^2 + ar^3 + ...$ whose $n^{\mathrm{th}}$ term can be obtained by the formula $a_n = ar^{n-1}$. The value $r$ is called the Common Ratio of the geometric series as $\frac{a_{n+1}}{a_{n}} = \frac{ar^n}{ar^{n... |
Riemann Integrable Functions as Upper Functions
Riemann Integrable Functions as Upper Functions
We will now classify a bunch of very important upper functions. In the following theorem we will see that the set of Riemann integrable functions are also upper functions.
Theorem 1: Let $f$ be a function defined on the clos... |
$ \newcommand{\ra}[1]{\kern-1.5ex\xrightarrow{\ \ #1\ \ }\phantom{}\kern-1.5ex} \newcommand{\ras}[1]{\kern-1.5ex\xrightarrow{\ \ \smash{#1}\ \ }\phantom{}\kern-1.5ex} \newcommand{\da}[1]{\bigg\downarrow\raise.5ex\rlap{\scriptstyle#1}}$ Suppose we have $CW$-complex $X$. All the self-homotopy equivalences form a monoid, ... |
I have been trying to understand a more or less geometric derivation of the Lorentz transformation, and I'm getting stuck at one spot. The wikipedia article for the Lorentz transformation for frames in standard configuration lists the following equations:
$$x^{\prime} = \frac{x-vt}{\sqrt{1-\frac{v^2}{c^2}}}$$
$$y^{\pri... |
The scattering amplitude can be obtained in QFT from the $n$-point Green's function by the LSZ reduction formula. The $n$-point Green's function are a correlation function of a string of fields :
$$G(q_1,..,q_n)=\int dx_1...dx_n\,e^{-iq_1x_1}...e^{-iq_nx_n}\langle 0|\mathcal{T}\{A_1(x_1)...A_n(x_n)\}|0\rangle$$
Now, we... |
In HA, remark 7.4.1.12, Lurie writes that the cotangent complex of $A\to B$ is the fiber of the multiplication map $B\otimes_A B\to B$. The more classical definition of TAQ is given by the indecomposables of the augmentation ideal of $B\otimes_A B$. Lurie's definition seems to bypass the step of taking indecomposables.... |
I've got the opportunity to play with a machine with some premium fonts installed. I ran some experiments with XeTeX and e.g. Palatino Linotype, which worked, but for some reason cyrillic breaks with Garamond Premier Pro. The result may be downloaded here.
UPDATE: It turns out the machine had two versions of Garamond P... |
This is kind of an odd thought I had while reviewing some old statistics and for some reason I can't seem to think of the answer.
A continuous PDF tells us the density of observing values in any given range. Namely, if $X \sim N(\mu,\sigma^2)$, for example, then the probability that a realization falls between $a$ and ... |
I'm building a SHA-1 rainbow table to crack basic passwords (i.e. up to 10 character, 0-9,a-z), but I can't seem to calculate that golden ratio that would give me the most coverage. What ration of chain length to number of chains should be chosen?
That choice is not really about coverage, but (mainly) about how much sp... |
A Subgroup of Index a Prime $p$ of a Group of Order $p^n$ is Normal Problem 470
Let $G$ be a finite group of order $p^n$, where $p$ is a prime number and $n$ is a positive integer.
Suppose that $H$ is a subgroup of $G$ with index $[G:P]=p$. Then prove that $H$ is a normal subgroup of $G$.
(
Michigan State University, A... |
A condition for the Holder regularity of strong local minimizers of a nonlinear elastic energy in two dimensions
Bevan, JJ (2017)
A condition for the Holder regularity of strong local minimizers of a nonlinear elastic energy in two dimensions Archive for Rational Mechanics and Analysis.
Text
NLE_holder_submit_arxiv_02_... |
Bancacy is an innovative and decentralized digital asset class that is establishing new form of Money. The ecosystem utilize BNY/XBNY Cryptocurrencies for Asset Solidification, Investments and Passive Income in aspiration to deliver fully independent and immutable Digital Money powerd by the Blockchain. Bancacy derives... |
Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \frac{1}{2}(1 + \sqrt{13})\). We also show the integral \(q\)-expansion of the trace form.
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded ... |
The Adobe Photoshop image manipulation program has a feature called “snap to,” which snaps edges of a selection into alignment with grid lines superimposed over the image as users move the selection around. This feature is an invaluable tool for producing perfectly aligned, professional-quality graphics. An analogous o... |
I am retreating back on this statement, after some explorations and calculationBow to Willie and others who were skeptical on this. Main difficulty can be seen in this reference. But I must mention that my quest for jump discontinuities has not seen a dead end but a new light after this failure. I am very much interest... |
Table of Contents
Continuous Functions on Compact Sets of Metric Spaces
We have looked quite a bit at continuous functions so far, and now we will put out attention on functions that are continuous on compact sets $X$.
The following Theorem tells us that if $(S, d_S)$ and $(T, d_T)$ are metric spaces and $f : S \to T$ ... |
Normal Subgroups
Recall from the Left and Right Cosets of Subgroups page that if $(G, \cdot)$ is a group, $(H, \cdot)$ is a subgroup, and $g \in G$ then the left coset of $H$ with representative $g$ is defined to be the set:(1)
Similarly, the right coset of $H$ with representative $g$ is defined to be the set:(2)
In ge... |
Python is available on any Linux/Unix machine including department machines and Macs.
You can download and install python on your own computer by following instructions at http://www.python.org
You can use the Python interpreter interactively by typing
python at a terminal window.Ipython is a nicer front end to python ... |
Tagged: module 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 generator... |
As I prefer outer parentheses to grow larger in nested expressions, I happen to insert
\bigl and
\bigr and its larger cousins a lot. I have always wondered whether there is a way to do this automagically.
Inserting
\left and
\right prophylacticly before all opening and closing parentheses and hoping that it sorts thing... |
Difference between revisions of "De Bruijn-Newman constant"
(→Threads)
(→Threads)
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* [https://terrytao.wordpress.com/2018/05/04/polymath15-ninth-thread-going-below-0-22/ Polymath15, ninth thread: going below 0.22?], Terence Tao, May 4, 2018.
* [htt... |
Speaker: Affiliation:
Indian Institute of Technology
Department of Computer Science and Engineering Hauz Khas New Delhi 110016 Time: Venue: A-201 (STCS Seminar Room) Organisers:
We develop new techniques for rounding packing integer programs using iterative randomized rounding. It is based on a novel application of mul... |
Under the auspices of the Computational Complexity Foundation (CCF)
We present error-correcting codes that achieve the information-theoretically best possible trade-off between the rate and
error-correction radius. Specifically, for every $0 < R < 1$ and $\eps > 0$, we present an explicit construction of error-correcti... |
Let $\mathcal{C}$ be a small category equipped with a terminal object $1$ and a Grothendieck topology. (Assume $\mathcal{C}$ also has pullbacks, if it is more convenient.) The following is a simplicial version of Verdier's hypercovering theorem:
Let $X$ be a locally fibrant simplicial presheaf on $\mathcal{C}$, let $\h... |
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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 11-20 of 27
Pseudorapidity dependence of the anisotropic flow of charged particles in Pb-Pb collisions at $\sqrt{s_{\rm NN}}=2.76$ TeV
(Elsevier, 2016-11)
We present measurements of the elliptic ($\mathrm{v}_2$), triangular ($\mathrm{v}_3$) and quadrangular ($\mathrm{v}_4$) anisotropic azimutha... |
Properties of Adjoints of Linear Maps
Recall from The Adjoint of a Linear Map page that if $V$ and $W$ are finite-dimensional nonzero inner product spaces and that $T \in \mathcal L (V, W)$ then the adjoint of $T$ is the linear map $T^* \in \mathcal L (W, V)$ defined by considering the linear function $\varphi : V \to ... |
The Zitterbewegung is more of a relic of the early Dirac equation days. It does not exist in the standard position, velocity and acceleration operators of the single particle field, only in alternatively derived versions. These alternative versions were developed because people thought the standard operators were wrong... |
With the growth in the Internet of Things (IoT) products, the number of applications requiring an estimate of range between two wireless nodes in indoor channels is growing very quickly as well. Therefore, localization is becoming a red hot market today and will remain so in the coming years.
One question that is perpl... |
Bipolar disorder (BD) is among the most chronic and severe types of mental illnesses. The disease is a complex neuropsychiatric condition characterized by infrequent but extreme episodes of low (depressed) and elevated (manic) moods. When compared to other mental illnesses, the global health burden of BD is massive: 1-... |
The objective of this project is to validate a coupled heat transfer case including the new ‘Radiation’ feature in the Convection Heat Transfer analysis of SimScale. A project including conduction, convection and radiation has been solved analytically, and using the platform.
The geometry consists of two horizontal con... |
Suppose first that $c_0\neq 0$.Then we have\begin{align*}A^2+c_1A=-c_0I\\\Leftrightarrow A(A+c_1I)=-c_0 I\\\Leftrightarrow A\left(\frac{-1}{c_0}(A+c_1I) \right)=I.\end{align*}It is in the last step that we needed to assume $c_0\neq0$.
Thus, if we put\[B=\frac{-1}{c_0}(A+c_1I),\]then we have proved that\[AB=I.\]
Similar... |
How long can an average aerobatic plane sustain 0g safely?
The longest possible
0g experience is on a parabolic Flight http://www.asc-csa.gc.ca/eng/sciences/parabolic.asp.
As Devil07s great answer explains the time a plane can fly "at 0g" depends on its vertical speed at start of the 0g time.
Lets take a typical air ac... |
also, if you are in the US, the next time anything important publishing-related comes up, you can let your representatives know that you care about this and that you think the existing situation is appalling
@heather well, there's a spectrum
so, there's things like New Journal of Physics and Physical Review X
which are... |
Well, the provided answers are certainly
not correct.
I see that for both of the you added some parentheses to help disambiguate, which is good. Some books use a 'priority' system to say that something like $P \land Q \to R$ will always mean $(P \land Q) \to R$ (so we can't really 'fault' the book on that one), but I t... |
Orthogonal Projection Operators
Recall from the Orthogonal Complements page that if $U$ is a subset of an inner product space $V$, then the orthogonal complement of $U$ denoted $U^{\perp}$ is the set of vectors $v \in V$ such that $v$ is orthogonal to every vector $u \in U$, that is $U^{\perp} = \{ v \in V : <v, u> = 0... |
Table of Contents:
We know already that a capacitor is used to store energy. In this module we shall discuss how much energy can be stored in a capacitor, the parameters that the energy stored depends upon and their relations.
How to Calculate the Energy Stored in Capacitor?
Work has to be done to transfer charges onto... |
You are currently browsing the tag archive for the ‘pdf’ tag.
This happens a lot: I am reading a paper, as usual going directly to the results and skipping the introduction, related literature, discussion, preliminaries, formal model etc. And then there is some which I have no idea what it stands for. I would like to s... |
Generated Sun, 16 Oct 2016 - μx) / [ s/sqrt(n) ]. The larger your sample Number of observations. Scholarship Page to apply!Correlation Coefficient of between proportions.
Von OehsenList Price: $49.95Buy Used: $0.71Buy New: $57.27Statistics for while standard deviations use parameters. All standard http://grid4apps.com/... |
The matrix norm for an n-by-n matrix A is defined as |A|=max(|Ax|) where x ranges over all vectors with |x|=1, and the norm on the vectors in R^n is the usual Euclidean one. This is also called the induced (matrix) norm, the operator norm, or the spectral norm. The unit ball of matrices under this norm can be considere... |
In addition to what’s in Anaconda, this lecture will need the following libraries:
!pip install --upgrade quantecon!pip install interpolation
Overview¶
Next, we study an optimal savings problem for an infinitely lived consumer—the “common ancestor” described in [LS18], section 1.3.
This is an essential sub-problem for ... |
By O.L.V. Costa and M.D. Fragoso
When associated with unexpected events that cause losses, abrupt changes are extremely undesirable. Such changes can be due, for instance, to environmental disturbances, component failures or repairs, changes in subsystem interconnections, changes in the operation point of a nonlinear p... |
2019-10-11 14:20
TURBO stream animation /LHCb Collaboration An animation illustrating the TURBO stream is provided. It shows events discarded by the trigger in quick sequence, followed by an event that is kept but stripped of all data except four tracks [...] LHCB-FIGURE-2019-010.- Geneva : CERN, 2019 - 3. Rekord szcze... |
The Squares of Riemann-Stieltjes Integrable Functions with Increasing Integrators
Recall from The Absolute Value of Riemann-Stieltjes Integrals with Increasing Integrators page that if $f$ is a function defined on $[a, b]$ and $\alpha$ is an increasing function on $[a, b]$ then if $f$ is Riemann-Stieltjes integrable wi... |
Criteria for a Subgroup to be Normal
Recall from the Normal Subgroups page that if $(G, \cdot)$ is a group and $(H, \cdot)$ is a subgroup then $(H, \cdot)$ is said to be a normal subgroup of $G$ if $gH = Hg$ for all $g \in G$, that is, the left and right cosets of $H$ with representative $g$ are equal for all $g \in G$... |
Table of Contents
Directional Derivatives of Functions from Rn to Rm and Continuity
Recall that if $f : S \to \mathbb{R}$ where $S \subseteq \mathbb{R}$ is open, then $f$ being differentiable at a point $x_0 \in S$ implies that $f$ is continuous at $x_0$ (the converse being false).
We would like to develop a derivative... |
The Figure 2 of this paper
http://arxiv.org/pdf/hep-ph/0611148v1.pdf
doesn't show a factor-of-ten difference at all! Extract the ratio properly on the log scale and you will see it is less than four, just slightly greater than 1/2 of the height corresponding to the decade. Note that 1/2 of the weight corresponds to the... |
I consider a riemannian manifold $(M,g)$ with a fiber bundle $E$ equipped by one parameter family of connections $\nabla^t$. The curvature of $\nabla^t$ is $R(\nabla^t)$ and the codifferential is $\delta_{\nabla^t} = * \circ d_{\nabla^t} \circ *$, with $*$ the Hodge operator and $d_{\nabla^t}$ the differential of the c... |
The Integral Remainder
We recently saw from Taylor's Theorem and The Lagrange Remainder page that if $f$ is $n + 1$ time differentiable on some interval containing the center of convergence $c$ and $x$ and if $P_n(x)$ is the $n^{\mathrm{th}}$ order Taylor polynomial of $f$ centered at $c$ then for $f(x) + P_n(x) + E_n(... |
Frequent Links Rec. 709 ITU-R Recommendation BT.709, more commonly known by the abbreviations Rec. 709 or BT.709, standardizes the format of high-definition television, having 16:9 (widescreen) aspect ratio. The first edition of the standard was approved in 1990. Contents Technical details Pixel count
Rec. 709 refers t... |
Hey guys! I built the voltage multiplier with alternating square wave from a 555 timer as a source (which is measured 4.5V by my multimeter) but the voltage multiplier doesn't seem to work. I tried first making a voltage doubler and it showed 9V (which is correct I suppose) but when I try a quadrupler for example and t... |
The Baire Category Theorem Review
The Baire Category Theorem Review
We will now review some of the recent material regarding the Baire Category theorem.
On The Cantor Intersection Theorem for Complete Metric Spacespage we looked at the Cantor intersection theorem which states the following. If $X$ is a complete metric ... |
Giải hệ phương trình: (Editor's note: This translates to "Solve a system of equations:") $$ \begin{cases}\sqrt[4]{x}\left(\dfrac{1}{4}+\dfrac{2\sqrt{x}+\sqrt{y}}{x+y}\right)=2 \\[8pt] \sqrt[4]{y}\left(\dfrac{1}{4}-\dfrac{2\sqrt{x}+\sqrt{y}}{x+y}\right) =1\end{cases} $$
Divide the first equation by $\sqrt[4]{x}$ and the... |
ddid2.Rmd
We are interested in estimating Conditional Quantile Treatment Effects on the Treated (QTT) with two periods of panel data (or repeated cross sections) under a Difference in Differences Assumption. These are defined by
\[ CQTT_x(\tau) = F^{-1}_{Y_{1t}|X=x,D=1}(\tau) - F^{-1}_{Y_{0t}|X=x,D=1}(\tau) \]
for \(\t... |
The Completion of a Normed Algebra
The Completion of a Normed Algebra
Definition: Let $\mathfrak{A}$ be a normed algebra. A Banach algebra $\mathfrak{B}$ is said to be a Completion of $\mathfrak{A}$ if there exists an isometric isomorphism $T$ from $\mathfrak{A}$ onto a dense subalgebra of $\mathfrak{B}$.
The following... |
Since $a$ and $b$ are relatively prime, at least one of them is relatively prime to $p$.Without loss of generality let us assume that $b$ and $p$ are relatively prime.
Then the given equality becomes\begin{align*}a^{2^n}\equiv -b^{2^n} \pmod{p} \\\iff \left( \frac{a}{b}\right)^{2^n} \equiv -1 \pmod{p}.\end{align*}Takin... |
The Union and Intersection of Collections of Closed Sets
The Union and Intersection of Collections of Closed Sets
Recall from The Union and Intersection of Collections of Open Sets page that if $\mathcal F$ is an arbitrary collection of open sets then $\displaystyle{\bigcup_{A \in \mathcal F} A}$ is an open set, and if... |
The whole problem is really about knowing what the words mean.
An
event is a time and a place together as single object. For instance the event where a light sends its first, last, or only pulse. Or the event where a beam or particle touches something and bounces.
Anything you can describe with a time and place togethe... |
Table of Contents
Criterion for a Set to be Closed in a Metric Subspace
Recall from the Criterion for a Set to be Open in a Metric Subspace page that if $(M, d)$ is a metric space and $S \subseteq M$ such that $(S, d)$ is a metric subspace of $(M, d)$ then a set $X$ in the metric subspace, i.e., $X \subseteq S$ is open... |
The Annals of Statistics Ann. Statist. Volume 5, Number 5 (1977), 842-865. Estimation for Autoregressive Moving Average Models in the Time and Frequency Domains Abstract
The autoregressive moving average model is a stationary stochastic process $\{y_t\}$ satisfying $\sum^p_{k=0} \beta_ky_{t-k} = \sum^q_{g=0} \alpha_g\n... |
Consider a spherical triangle with 3 angles: $\pi/2$, $\pi/3$, $\pi/3$. All sides are geodesics of course. The sphere has radius $r=1$.
Context: I want to know whether a given point in polar coordinates ($\phi$, $\theta$, $r$) where $r=1$, is in my triangle. (My convention for polar coordinates is: $\phi$ is the rotati... |
Yes, there are generalizations of Rainich conditions to many others fields, including scalar fields, perfect fluids and
null electromagnetic fields. (Indeed! The original form of the Rainich conditions were not conveniently formulated for electromagnetic fields \(F\in \bigwedge ^2M\) whose both Poincaré invariant vanis... |
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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 ... |
In Big Rudin, theorem 2.7, Rudin states that if there is a compact set $K\subset U$ where $U$ is an open set in a locally compact Hausdorff space $X$, then there is an open set $V$ with compact closure such that:
$K\subset V\subset \overline{V}\subset U$.
In theorem 2.13, he states that if we have $K\subset V_1\cup\ldo... |
The basic Weyl ordering property generating all the Weyl ordering identities for polynomial functions is:
$((sq+tp)^n)_W = (sQ+tP)^n$
$(q, p)$ are the commuting phase space variables, $(Q, P)$ are the corresponding noncommuting operators (satisfying $[Q,P] = i\hbar $).
For example for n = 2, the identity coming from th... |
Children usually ask questions like “How many hours have passed?” And they have no idea about the start time to be taken as a reference.
Just like the zero of a measuring tape, a zero reference for time plays a crucial role in analyzing the signal behaviour in time and frequency domains. Until now, we assumed that refe... |
I'm doing some classical field theory exercises with the Lagrangian $$\mathscr{L} = -\frac{1}{4}F_{\mu \nu}F^{\mu \nu}$$ where $F_{\mu \nu} = \partial_\mu A_\nu - \partial_\nu A_\mu$. To find the conjugate momenta $\pi^\mu_{\ \ \ \nu} = \partial \mathscr{L} / \partial(\partial_\mu A^\nu)$, I can use two methods.
First ... |
Table of Contents
The Uniqueness of Limits of Sequences in Metric Spaces
Recall from the Limits of Sequences in Metric Spaces that if $(M, d)$ is a metric space then a sequence of elements from $M$ is of the form $(x_n)_{n=1}^{\infty}$ where $x_k \in M$ for all $k \in \{ 1, 2, ... \}$.
We will now show that if the sequ... |
Concentration of ground state solutions for quasilinear Schrödinger systems with critical exponents
1.
School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China
2.
Department of Mathematics, Tsinghua University, Beijing, 100084, China
$ {\Bbb R}^N: $
$ \left\{\begin{array}{ll}-\Delta w+(\lambda... |
One of the properties of Fourier Transform is that the derivative of a signal in time domain gets translated to multiplication of the signal spectrum by $j2\pi f$ in frequency domain. This property is usually derived as follows.
For a signal $s(t)$ with Fourier Transform $S(f)$
\begin{equation*} s(t) = \frac{1}{2\pi}\i... |
(a) Prove that every finitely generated subgroup of $(\Q, +)$ is cyclic.
Let $G$ be a finitely generated subgroup of $(\Q, +)$ and let $r_1, \dots, r_n$ be nonzero generators of $G$.Let us express\[r_i=\frac{a_i}{b_i},\]where $a_i, b_i$ are integers.
Let\[s:=\frac{1}{\prod_{j=1}^n b_j} \in \Q.\]Then we can write each $... |
Calculations of Strings Downforce on the Bridge:
$T\small(kg_{F})\normalsize = T\small(lb_{F})\normalsize \times 0.45359$
$\cos\alpha + \cos\beta = 2\cos(\frac{\alpha + \beta}{2})\cos(\frac{\alpha - \beta}{2})$
$F_{d}\small(kg_{F})\normalsize = T\small(kg_{F})\normalsize \times 2\cos(\frac{\alpha + \beta}{2})\cos(\frac... |
Scattering in the weighted $ L^2 $-space for a 2D nonlinear Schrödinger equation with inhomogeneous exponential nonlinearity
1.
Laboratoire Paul Painlevé UMR 8524, Université Lille CNRS, 59655 Villeneuve d'Ascq Cedex, France
2.
Laboratoire Paul Painlevé UMR 8524, Université de Lille CNRS, 59655 Villeneuve d'Ascq Cedex,... |
Consider the following $2\times 2$ matrix $$ A = \begin{pmatrix} a_{11} & a_{12} \\ a_{21} & a_{22} \end{pmatrix}. $$
Let $\Delta = a_{11}a_{22}-a_{21}a_{12}$ be its determinant.
Then $A$ has full rank iff $\Delta \ne 0.$
I noticed that it holds that $$ A \begin{pmatrix} a_{22} \\ -a_{21} \end{pmatrix} = \begin{pmatrix... |
Consider the well-known fact that correlation is bounded between $-1$ and $1$:
$$ -1 \le \text{corr}(X,Y) = \frac{E[(X - E[X])(Y - E[Y])]}{\sigma_X \sigma_Y} \le 1. $$
I've been trying to wrap my mind intuitively around why this is so.
Question: Is this because (or is it true that)
$$ \frac{E[(|X - E[X]|)(|Y - E[Y]|)]}... |
It looks like a voronoi diagram with a non-Euclidean distance metric. Probably not Manhattan L1 but something close related, but maybe Mahalanobis with some kind of restriction on seed point generation and movement.A similar result may be calculated with Weight-proportional Space Partitioning Using Adaptive Voronoi Dia... |
see title.
An algorithm is 'good' if it is able to distinguish between zero Eigenvalues and nonzero Eigenvalues.
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.Sign up to join this community
One method is to reduce the computation to that of computing matri... |
Determine Whether Given Subsets in $\R^4$ are Subspaces or Not Problem 480 (a) Let $S$ be the subset of $\R^4$ consisting of vectors $\begin{bmatrix} x \\ y \\ z \\ w \end{bmatrix}$ satisfying \[2x+4y+3z+7w+1=0.\] Determine whether $S$ is a subspace of $\R^4$. If so prove it. If not, explain why it is not a subspace. (... |
Some quick electoral prediction math Matthew Martin10/20/2015 12:17:00 PM
Tweetable
Do the prediction market numbers make sense? A little probability analysis:
Let [$]A[$] denote the event where Clinton wins the nomination, and [$]B[$] denote that a democratic nominee wins the presidency. Tankersley then provides the f... |
Transpose of a Matrix and Eigenvalues and Related Questions Problem 12
Let $A$ be an $n \times n$ real matrix. Prove the followings.
(a) The matrix $AA^{\trans}$ is a symmetric matrix. (b) The set of eigenvalues of $A$ and the set of eigenvalues of $A^{\trans}$ are equal. (c) The matrix $AA^{\trans}$ is non-negative de... |
Hyperplane Through Origin is Subspace of 4-Dimensional Vector Space Problem 371
Let $S$ be the subset of $\R^4$ consisting of vectors $\begin{bmatrix}
x \\ y \\ z \\ w \end{bmatrix}$ satisfying \[2x+3y+5z+7w=0.\] Then prove that the set $S$ is a subspace of $\R^4$.
(
Linear Algebra Exam Problem, The Ohio State Universi... |
The Archimedean Property
We will now look at a very important property known as the Archimedean property which tells us that for any real number $x$ there exists a natural number $n_x$ that is greater or equal to $x$. This is formalized in the following theorem:
Theorem 1 (The Archimedean Property): For every element $... |
The Annals of Statistics Ann. Statist. Volume 39, Number 1 (2011), 82-130. ℓ 1-penalized quantile regression in high-dimensional sparse models Abstract
We consider median regression and, more generally, a possibly infinite collection of quantile regressions in high-dimensional sparse models. In these models, the number... |
\usepackage{mathtools, amssymb, amsthm}\begin{align}\label{eq1}\sum_{n}\lambda^{n}(i)-\sum_{n}\lambda^{n}(j) \nonumber\\=\begin{cases} \lambda_{n}, &\text{if } n = i\\ -\lambda_{n}, &\text{if } n = i\\ 0, &\text{otherwise} \end{cases} \text{ }\forall i, j\end{align}
First line of the equation must be left aligned (or a... |
Injective and Surjective Linear Maps Examples 3
Recall from the Injective and Surjective Linear Maps page that a linear map $T : V \to W$ is said to be
injective if: $T(u) = T(v)$ implies that $u = v$. $\mathrm{null} (T) = \{ 0 \}$.
Furthermore, the linear map $T : V \to W$ is said to be surjective if:
If for every $w ... |
Image shows a typical layer somewhere in a feed forward network:
$a_i^{(k)}$ is the activation value of the $i^{th}$ neuron in the $k^{th}$ layer.
$W_{ij}^{(k)}$ is the weight connecting $i^{th}$ neuron in the $k^{th}$ layer to the $j^{th}$ neuron in the $(k+1)^{th}$ layer.
$z_j^{(k+1)}$ is the pre-activation function ... |
Sorry for sparse updation due to the mid-term exmamination of Genaral Relativity and Statistical Mechanics……( 我不会说早上才考完广义相对论期中。。)
\(\quad\)We are going to deduce the Einstein’s equation in two ways, one is based on physics analysis, anther one utilizing the variational methods.
Sec 1.1 Energy-Momentum Tensor Def:
\(\qu... |
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 \(x^{4}\mathstrut -\mathstrut \) \(2\) \(x... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Year of publication 1998 (5) (remove) Keywords
319
The Kallianpur-Robbins law describes the long term asymptotic behaviour of the distribution of the occupation measure of a Brownian motion in the plane. In this paper we show that this behaviour can be seen at ev... |
I have been trying to understand why one should look into $c=9, N=2$ superconformal models like the Gepner models or the Kazama-suzuki models, and I am quite confused..
This is what I understood from the arguments I've seen: (mainly from [1])
The usual way to deal with the $6$ spacetime dimensions which we do not obser... |
$165=(3) (5) (11)$
$\sigma (p^a)$=$p^{a+1}-1 \over {p-1}$=$3$
$p^{a+1}-1$=$3p-3$
$p^{a+1}=3p-2$
Got stuck here. How do I proceed?
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.Sign up to join this com... |
The reasoning of your proof follows: "if the limit $\lim_{n \to \infty}na_n$ exists and is equal to some $a$, then $a = 0$. This tells us nothing of the truth of the statement because you need to prove that the first part is true i.e. the limit actually exists.
To prove that $\lim_{n \to \infty}na_n$ exists, we will ha... |
The goal of this case study is to validate the
Conjugate Heat Transfer analysis type on SimScale platform, particularly focusing on applications with volumetric heat generation, i.e. assignment of heat sources to solid regions. Validation is performed against experiments data and analytical calculations of Ventola et a... |
A Group Homomorphism that Factors though Another Group
Problem 490
Let $G, H, K$ be groups. Let $f:G\to K$ be a group homomorphism and let $\pi:G\to H$ be a surjective group homomorphism such that the kernel of $\pi$ is included in the kernel of $f$: $\ker(\pi) \subset \ker(f)$.
Define a map $\bar{f}:H\to K$ as follows... |
Integrals of Step Functions on General Intervals
Recall from the Step Functions on General Intervals page that a function $f$ is said to be a step function on the general interval $I$ if there exists a closed and bounded interval $[a, b] \subseteq I$ such that $f$ is a step function in the usual sense on $[a, b]$ and s... |
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