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Let $$R(\theta)=\begin{bmatrix} \cos\theta &-\sin\theta \\ \sin\theta & \cos\theta \end{bmatrix}$$
Also, $a$ and $b$ are real numbers. We suppose that $b\neq 0$ and we consider the matrix: $$A=\begin{bmatrix} a &-b \\b &a \end{bmatrix}$$
Show that it exist a unique number $\lambda>0$ and a unique number $\theta \in\ ]0... |
Let $X$ be a locally compact and Hausdorff space, and let $\mu$ be a positive measure on the Borel sets of $X$ (here $\mu$ is
not necessarily regular).
Then the linear map $L : C_c(X) \to \Bbb C$ defined by $L : f \mapsto \int_X f \;d\mu$ can be represented, by Riesz theorem, as$$L(f) = \int_X f \;d\nu$$where $\nu$ is ... |
Edit: This question is about rejecting the null hypothesis.
Last month my evil twin and I were at a game show.
The rules are as follows: There is a sealed booth with two magic boxes.
Box A has a button that generates a real number according to a normal distribution with mean 5 and standard deviation 1. Box B has a butt... |
I have the following expression
$$ \sum_{n=-\infty}^{+\infty} \frac{1}{(1-q^{2n-1})(1-q^{m-2n})}$$ where $m$ is an odd positive integer and $|q|<1$.
Given this, the sum should converge to a finite answer, which I would like to compute.
As $|q|<1$ I can expand the reciprocal factors in power series depending on whether ... |
Let us consider a canonical system of N independent, distingusiable harmonic oscillators in 1D. Its partition function $$Z = (Z_{sp})^N = \left(\sum_{n=0}^{\infty} e^{-\beta E_i}\right)^N$$ where, $Z_{sp}$ is the single particle partition function of a simple harmonic oscillator, $E_i$ is the energy of a simple harmoni... |
LaTeX General LaTeX guidelines
(based on http://www.math.uiuc.edu/~hildebr/tex/)
If you want to learn LaTeX from the beginning, use Grätzer's “Short Course” (part I of his book,
More Math into Latex, 4th ed., Springer, 2007).
If you come across a LaTeX problem, do not try to find an ad hoc solution of your own - check ... |
For the dynamics of open quantum systems, the Kraus operators $K_\kappa$ can be derived from the unitary orbit $U(t)\rho U(t)^\dagger$ for $\rho=\rho_S\otimes\rho_E$ of the composite system given by the time-propagators $U(t)=\exp(-\mathrm{i} tH)$ via tracing over the environmental states $|\mu\rangle$: $$K_\kappa(t)=K... |
What is conservation of flux linkage ?? Please explain with suitable diagram. I understand charge conservation and textbooks usually say that flux linkage conservation is analogous to that, but they rarely explain this in detail.
I wiil try to go through a simple application of flux conservation using an example.
I wil... |
There is known a lot about the use of groups -- they just really appear a lot, and appear naturally. Is there any known nice use of semigroups in Maths to sort of prove they are indeed important in Mathematics? I understand that it is a research question, but may be somebody can hint me the direction to look on so that... |
Evaluating Riemann-Stieltjes Integrals
We will now look at evaluating some Riemann-Stieltjes integrals. Before we do, be sure to recall the results summarized below. Let $f$ and $g$ be Riemann-Stieltjes integrable function with respect to $\alpha$ and $\beta$ on the interval $[a, b]$ and let $c \in \mathbb{R}$.
Additiv... |
Tagged: group Problem 343
Let $G$ be a finite group and let $N$ be a normal abelian subgroup of $G$.
Let $\Aut(N)$ be the group of automorphisms of $G$.
Suppose that the orders of groups $G/N$ and $\Aut(N)$ are relatively prime.
Then prove that $N$ is contained in the center of $G$. Problem 332
Let $G=\GL(n, \R)$ be th... |
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Coherent $\rho^0$ photoproduction in ultra-peripheral Pb-Pb collisions at $\mathbf{\sqrt{\textit{s}_{\rm NN}}} = 2.76$ TeV
(Springer, 2015-09)
We report the first measurement at the LHC of coherent photoproduction of $\rho^0$ mesons in ultra-peripheral Pb-Pb collisions. The invarian... |
Linear Maps Examples 3
Recall from the Linear Maps page that a linear map or linear transformation from the vector space $V$ to the vector space $W$ is a function $T : V \to W$ such that for all $u, v \in V$ and for all $a \in \mathbb{F}$ we have that $T(u + v) = T(u) + T(v)$ (additivity property) and $T(av) = aT(v)$ (... |
I. As a background, in Traces of Singular Moduli (p.2), Zagier defines the modular form of weight 3/2,
$$g(\tau) = \frac{\eta^2(\tau)}{\eta(2\tau)}\frac{E_4(4\tau)}{\eta^6(4\tau)}=\vartheta_4(\tau)\, \eta^2(4\tau)\,\sqrt[3]{j(4\tau)}$$
which has the nice
q-expansion (A027652, negated terms),
$$g(\tau) = 1/q - 2 + 248q^... |
Are you sure about the factor of $3$ in Koszul's formula? The computation below does not give such a factor, and it gives a stronger result.
Let $X_i$ be any basis of the left-invariant vector fields (where the indices run from $0$ to $n$), with $[X_i,X_j] = c^k_{ij}X_k$, where, of course, $c^k_{ij}=-c^k_{ji}$ (and whe... |
Let $A \subset \mathbb{C}$ be an topological annulus, i.e. a region of $\mathbb{C}$ bounded by two disjoint Jordan curves.
Let $B \subset \mathbb{C}$ be a quadrilateral, i.e. a topological disc with four distinct marked points $(z_1,z_2,z_3,z_4)$ arranged anticlockwise on the boundary.
Both annuli and quadrilaterals, a... |
860 42
Hello Forum,
A sound wave intensity (pure frequency) is proportional to the square of the wave pressure amplitude, i.e. ##I \approx p_0^2##, where ##p_0## is the pressure wave amplitude: ##p_0 sin(\omega t \pm kx)##. This means that the (gauge) pressure value goes larger (positive) and lower (negative) than the ... |
2018-08-25 06:58
Recent developments of the CERN RD50 collaboration / Menichelli, David (U. Florence (main) ; INFN, Florence)/CERN RD50 The objective of the RD50 collaboration is to develop radiation hard semiconductor detectors for very high luminosity colliders, particularly to face the requirements of the possible u... |
Compare these two results:
Theorem (Scott):$ZFC+V=L\vdash \nexists~\text{Measurable cardinal}$
Theorem (Kunen):$ZFC+AC\vdash \nexists~\text{Reinhardt cardinal}$
Now compare these two chains:
$V=L\rightarrow AC\rightarrow \cdots$
$Con(ZF+ \exists~\text{Measurable cardinal})\leftarrow Con(ZF+\exists~\text{Reinhardt cardi... |
I want to ask for some help with my OR model. What guidance is available to me for doing so?
How to ask for help with your OR model
We love mathematical models and are happy to help you with yours. Before you ask your question, please read these suggestions about how to ask a good question. Doing so will make it easier... |
Pointwise Convergence of Fourier Series Review
Pointwise Convergence of Fourier Series Review
We will now review some of the recent material regarding pointwise convergence of Fourier series.
Recall from the Periodic Functionspage that a function $f$ is said to be $p$-Periodic($p > 0$) if the following equality holds f... |
What is Wave Optics?
Wave optics stands as a witness for a famous standoff between two great scientific communities who dedicated their lives to understand the nature of light. One supports the particle nature of light; the other supports the wave nature. Sir Isaac Newton stands as a prominent figure that supported the... |
first of all, I need to confess my ignorance with respect to any physics since I'm a mathematician. I'm interested in the physical intuition of the Langlands program, therefore I need to understand what physicists think about homological mirror symmetry which comes from S-duality. This question is related to my previou... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Criteria for a Set to be Closed in a Metric Space
Recall from the Adherent, Accumulation and Isolated Points in Metric Spaces page that if $(M, d)$ is a metric space and $S \subseteq M$ then:
A point $x \in M$ is said to be an adherent point of $S$ if every ball centered at $x$ contains points of $S$, that is, for all ... |
Proofs Regarding Functions
We will now look at some proofs regarding functions, direct images, inverse images, etc… Before we look at such proofs, let's first recall some very important definitions:
Definition: A function $f$ is called an injection, injective function, or one-to-one function if for all $m, n \in A$ whe... |
I need help with this problem. Some numerical answers would also be very helpful.
I'll augment the correct answers in the comments with the following circuit model. A resistor with noise can be modeled as a noiseless resistor in series with a voltage source representing the Johnson (thermal) noise. More on that here. S... |
Let $C$ be a smooth irreducible (complex) curve of genus $g\geq2$.
The
gonality of $C$ is defined as the minimum degree of surjective morphisms $C\rightarrow\Bbb{P}^1$. So $C$ has gonality $d$ if it has a $g^1_d$ but no $g^1_{d-1}$, where $g^r_d$ denotes a linear system of dimension $r$ and degree $d$ on $C$.
Now my qu... |
I am reading the paper "The category of good modules over a quasi-hereditary algebra has almost split sequences", the link is here:https://pub.uni-bielefeld.de/publication/1780235.
In the paper, $A$ is an artin algebra, and $A$-mod the category of (finitely generated) $A$-modules. Let $\Theta=\{\Theta(1), \dots, \Theta... |
Hollow cylinder in plain strain condition¶ Overview¶
The aim of this test case is to validate the following functions:
distributed pressure symmmetry BC nodal displacements strains and nodal stresses
The simulation results of SimScale were compared to the analytical results in [SSLV04_A] and the numerical results in [S... |
Let $f:[0,1]\to[0,1]$ be a continuous function such that its derivative $f'$ exists on $(0,1)$. My question is:
Q1.If $E\subset[0,1]$ is a nowhere dense closed subset, is $f(E)$ also nowhere dense in $[0,1]$?
If the answer is negative, what will happen when we additionaly assume that $f'\ge 0$ on $(0,1)$?
My question o... |
This is a popular question on this site but I haven't found the answer I'm looking for in other questions. It is often stated that charge conservation in electromagnetism is a consequence of local gauge invariance, or perhaps it is due to some global phase symmetry. Without talking about scalar or spinor fields, the EM... |
If the galaxy is axisymmetric and $\Phi = \Phi(R, z)$ is the potential then
$$v_c^2 = \left.R\frac{\partial \Phi(R, z)}{\partial R}\right|_{z = 0}$$
The trick is now in getting the potential $\Phi$. For the Milky Way you have a bunch of components
$$\Phi = \Phi_{\rm halo, ~DM} + \Phi_{\rm disk} + \Phi_{\rm halo, \star}... |
Algebra and Algebraic Geometry Seminar Spring 2018
The seminar meets on Fridays at 2:25 pm in room B235.
Contents 1 Algebra and Algebraic Geometry Mailing List 2 Fall 2018 Schedule 3 Spring 2018 Schedule 4 Abstracts Algebra and Algebraic Geometry Mailing List Please join the AGS Mailing List to hear about upcoming semi... |
O.D.E. type behavior of blow-up solutions of nonlinear heat equations
1.
Département de Mathématiques, Université de Cergy-Pontoise and IUF, 2 Ave. Adolphe Chauvin, BP 222, Pontoise, 95 302 Cergy-Pontoise cedex, France
2.
Département de Mathématiques et Applications, CNRS École Normale Supérieure, 45 rue d'Ulm, 75 230 ... |
I'm working through different books about financial mathematics and solving some problems I get stuck.
Suppose you define an arbitrary stochastic process, for example
$ X_t := W_t^8-8t $ where $ W_t $ is a Brownian motion.
The question is, how could I deduce that this stochastic process is a martingale or not using Itô... |
The question is as follows:
Let $X_1$ ~ Binomial(3,1/3) and $X_2$ ~ Binomial(4,1/2) be independent random variables. Compute P($X_1$ = $X_2$)
I'm not sure what it means to compute the probability of two
random variables being equal.
Cross Validated is a question and answer site for people interested in statistics, mach... |
Table of Content: Chemical Equilibrium Ionic Equilibrium – Degree of Ionization and Dissociation Equilibrium Constant – Characteristics and Applications Le Chatelier’s Principle on Equilibrium Solubility and Solubility Product Acid and Base pH Scale and Acidity pH and Solutions Hydrolysis, Salts, and Types Buffer Solut... |
The Partial Summation Formula for Series of Real Numbers
Table of Contents
The Partial Summation Formula for Series of Real Numbers
We will shortly look at two more very useful tests for determining the convergence of series known as Dirichlet's test and Abel's test. Before we look at these two tests though, we will ne... |
De Bruijn-Newman constant
For each real number [math]t[/math], define the entire function [math]H_t: {\mathbf C} \to {\mathbf C}[/math] by the formula
[math]\displaystyle H_t(z) := \int_0^\infty e^{tu^2} \Phi(u) \cos(zu)\ du[/math]
where [math]\Phi[/math] is the super-exponentially decaying function
[math]\displaystyle... |
In a flat toric universe (up connects down, right connects left and front connects back), every points repeats at $size_x$, $size_y$ and $size_z$ intervals.
In such case the Newtonian gravitational acceleration undergone in one point x, y, from a single mass M placed in one corner of a cube, would be undergone from eve... |
Segment of Example from Textbook:
$t=\dots$
More usefully, we have:
$t\sim n\log n$
I recall $\sim$ means "similarity" in geometry, same shape but not same size. How is it interpreted here?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields... |
I am interested in the practical method and I like to discover if it is cheap enough to be done as an experiment in a high school.
Method
The method is based on measuring variations in perceived revolution time of Io around Jupiter. Io is the innermost of the four Galilean moons of Jupiter and it takes around 42.5 hour... |
Main Page The Problem
Let [math][3]^n[/math] be the set of all length [math]n[/math] strings over the alphabet [math]1, 2, 3[/math]. A
combinatorial line is a set of three points in [math][3]^n[/math], formed by taking a string with one or more wildcards [math]x[/math] in it, e.g., [math]112x1xx3\ldots[/math], and repl... |
Constraining Dark Matter with the Long-Term Variability of Quasars Abstract.
By comparing the results of numerical microlensing simulations to the observed longterm variability of quasars, strong upper limits on the cosmological density of compact objects in the mass range \(10^{-2}-10^{-4} M_\odot\) may be imposed. Us... |
Let $H$ be a Hilbert space, $X$ a topological space, and $\{A_t\}_{t\in X}$ a continuous family of bounded, invertible operators on $H$. Continuous here in the sense that the corresponding map $X\rightarrow B(H)$ is continuous (with respect to the uniform topology on $B(H)$). Then the family of inverses $\{A^{-1}_t\}_{... |
Let $k$ be a $p$-adic field, $G$ a connected reductive group over $k$ with minimal parabolic $P_0$ containing a maximal split torus $A_0$. Let $W = N_G(A_0)(k)/Z_G(A_0)(k)$ be the Weyl group, and $S \subset W$ the simple reflections from $P_0$.
For $\theta, \Omega \subset S$, we have the standard parabolic subgroups $P... |
This problem:
I was able to solve it doing this:
But I think i have nowhere " exploited " the equivalence given above. How can this be used in this problem?
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign up.Sign up to join t... |
Suppose I take two independent random samples from a population of size $N$: the first is a simple random sample of size $n$ and the second is a simple random sample of size $m$. Let set $S$ contain all of the records selected from the two samples of size $n$ and $m$ less any duplicates. Thus, $S$ should consist of $n_... |
Here is a beautiful result from numerical analysis. Given any nonsingular $n\times n$ system of linear equations $Ax=b$, an optimal Krylov subspace method like GMRES must necessarily terminate with the exact solution $x=A^{-1}b$ in no more than $n$ iterations (assuming exact arithmetic).
The Cayley-Hamilton theorem pro... |
How do we know that dark matter is dark, in the sense that it doesn't give out any light or absorb any? It is impossible for humans to be watching every single wavelength. For example, what about wavelengths that are too big to detect on Earth?
If dark matter emitted very long wave lengths of electromagnetic radiation ... |
This is at least feasible if you allow a one-time setup where related keys are distributed among the $n$ devices and the master device. There is a primitive known as aggregated encryption which has the following properties:
The $n$ devices $(D_0, \cdots, D_{n-1})$ each receive a secret key $(s_0, \cdots, s_{n-1})$. The... |
The question is the same as asking when are the solutions to the Schrodinger equation of the form $\psi(x)=A\sin(kx)$ or $\psi(x)=Ae^{\kappa x}$.
Assume $\psi(x)=A\sin(kx)$ is your solution with $k$ constant but an unknown $V(x)$ and plug into the Schrodinger equation\begin{align}-\frac{\hbar^2}{2m}\frac{d^2}{dx^2}A\si... |
In Yang-Mills theory the field strength tensor $F_{\mu \nu}$ can be calculated as $$ \begin{equation} F_{\mu\nu} \equiv \frac{i}{g} [D_\mu,D_\nu] = \partial_\mu A_\nu - \partial_\nu A_\mu -ig[A_\mu,A_\nu], \end{equation} $$ where covariant derivative is defined as $$ D_\mu = \partial_\mu -ig A_\mu. $$ Can Yang-Mills fi... |
Left-Hand and Right-Hand Limits
Definition: Let $f : A \to \mathbb{R}$ be a function and let $c$ be a cluster point of $A$. Then the left-hand limit of $f$ at $c$ denoted $\lim_{x \to c^-} f(x) = L_1$ if $\forall \epsilon > 0$ $\exists \delta > 0$ such that if $x \in A$ and $x < c$ then $\mid f(x) - L_1 \mid < \epsilon... |
The expected number of picks needed equals the sum of the probabilities that at least $t$ picks are needed, which means that $t-1$ subsets left at least one value uncovered. We can use inclusion-exclusion to get the probability that at least one value is uncovered.
The probability that a particular set of $k$ values is... |
Can someone please tell me how I get vertical lines in the columns of a matrix like it is shown in the picture?
I started with
... = \begin{pmatrix} \lambda A' & \mu B' & \tau C' \end{pmatrix} ...
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems.... |
Every Diagonalizable Nilpotent Matrix is the Zero Matrix Problem 504
Prove that if $A$ is a diagonalizable nilpotent matrix, then $A$ is the zero matrix $O$.
Contents
Definition (Nilpotent Matrix)
A square matrix $A$ is called
nilpotent if there exists a positive integer $k$ such that $A^k=O$. Proof. Main Part
Since $A... |
Difference between revisions of "De Bruijn-Newman constant"
(→t>0)
(→Threads)
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* [https://terrytao.wordpress.com/2018/03/18/polymath15-sixth-thread-the-test-problem-and-beyond/ Polymath15, sixth thread: the test problem and beyond], Terence Tao, Mar... |
Prove the identity:
$$n(n-1)2^{n-2}=\sum_{k=1}^n {k(k-1) {n \choose k}}$$
I tried using the binomial coefficients identity $2^n = \sum_{k=1}^n {n \choose k}$ but got stuck along the way.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. I... |
Table of Contents
The Alternating Series Test for Alternating Series of Real Numbers
Recall from the Alternating Series of Real Numbers page that if $(a_n)_{n=1}^{\infty}$ is a strictly positive sequence then the corresponding alternating sequence is given by $((-1)^{n+1}a_n)_{n=1}^{\infty}$.
We will now look at a very... |
I tried to prove that if $A$ is the disk algebra then the Gelfand transform is the identity map. The statement can be found here in Theorem 4.4 but it is given without proof. Please can someone check my proof?
Proof:
$\Omega (A)=$ character space of $A$
$\sigma (a) = $ spectrum of $a$
If $A$ is the disk algebra then it... |
Just another variant that is somewhat simplistic but I think deliver the message without explicitly using the library
boot that may confuse some people with the syntax it uses.
We have a linear model: $y = X \beta + \epsilon$, $\quad \epsilon \sim N(0,\sigma^2)$
The following is a
parametric bootstrap for that linear m... |
The Annals of Mathematical Statistics Ann. Math. Statist. Volume 27, Number 3 (1956), 854-855. On Minimum Variance Among Certain Linear Functions of Order Statistics Abstract
Suppose there are $n$ normal populations $N(\mu_i, 1), i = 1, \cdots, n$ and that one random observation from each of these $n$ populations is gi... |
Elementary Matrices
Definition: A square $n \times n$ matrix is an Elementary Matrix $E$ if it can be obtained by performing exactly one elementary row operation on the identity matrix $I_n$.
The following three matrices are all considered elementary matrices:(1)
$E_1$ is obtained by taking $I_3$ and multiplying row 2 ... |
Is there something similar to the Magnus effect for electromagnetism? Would a spinning particle generate a centripetal force moving through something like a circular accelerator? And how would you calculate this?
Electron spin contributes to the centrifugal force on an electron.
Compare the wave function of the hydroge... |
I am attempting to work through "Shahverdiev, Sivaprakasam, and Shore (2002) Lag synchronization in time-delayed systems", but I'm missing something basic up front.
The problem is to take a unidirectionally coupled dynamical system,
$\dot{x} =-\alpha x + (m_1+m_3) \sin x_{\tau_1}$
$\dot{y} =-\alpha y + m_2 \sin y_{\tau... |
Table of Contents
Indeterminate Forms
We are now going to look a little more thoroughly into evaluating limits before moving forward with calculus. We will soon learn an important limit rule known as L'Hospital's Rule, but before we do, we must first look at some indeterminate forms that may arise in determining the li... |
Difference between revisions of "Main Page"
(→IP-Szemeredi (a weaker problem than DHJ))
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High-dimensional Sperner
+
High-dimensional Sperner
Kalai.29: There is an analogous for Sperner but with high dimensional combinatorial spaces instead of "lines" but I do not remember the ... |
Difference between revisions of "Main Page"
(Added reference to cheatsheet)
(Fixing location.)
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== The Problem ==
== The Problem ==
−
Let <math>[3]^n</math> be the set of all length <math>n</math> strings over the alphabet <math>1, 2, 3</math>. A ''combinatorial line'' is a set of three points in <math>[... |
In
mathematics, is a Steinhaus– Moser notation notation for expressing certain extremely large numbers. It is an extension of Steinhaus's polygon notation. [1] Definitions [ edit ] a number in a n triangle means . n n a number in a n square is equivalent to "the number inside n triangles, which are all nested." n a num... |
Let G be a nontrivial finite group. Does there exist an irreducible representation of G of dimension greater than or equal to the cardinality of G?
[Edited for clarity. -- PLC]
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up.Sign up to join this community
Le... |
I think this is a bit odd but I am juggling since hours with $\sin$, $\cos$, $\tan$ and other stuff to proof a formula, but I can't do it. Slowly I am thinking that this formula is wrong. Maybe there is some expert who could tell me if I am right. I have the following problem:
In the end I want to reach the form:
$$ L_... |
My favourite one: $[0, 1]$ is compact, i.e. every open cover of $[0, 1]$ has a finite subcover.
Proof: Suppose for a contradiction that there is an open cover $\mathcal{U}$ which does not admit any finite subcover. Thus, either $\left[ 0, \frac{1}{2} \right]$ or $\left[ \frac{1}{2}, 1 \right]$ cannot be covered with a ... |
@HarryGindi So the $n$-simplices of $N(D^{op})$ are $Hom_{sCat}(\mathfrak{C}[n],D^{op})$. Are you using the fact that the whole simplicial set is the mapping simplicial object between cosimplicial simplicial categories, and taking the constant cosimplicial simplicial category in the right coordinate?
I guess I'm just v... |
Determine the Dimension of a Mysterious Vector Space From Coordinate Vectors Problem 606
Let $V$ be a vector space and $B$ be a basis for $V$.
Let $\mathbf{w}_1, \mathbf{w}_2, \mathbf{w}_3, \mathbf{w}_4, \mathbf{w}_5$ be vectors in $V$. Suppose that $A$ is the matrix whose columns are the coordinate vectors of $\mathbf... |
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... |
Inside the whale: the structure and dynamics of the isolated Cetus dwarf spheroidal Date2007-02-05 Author
Lewis, G. F.
Ibata, R. A.
Chapman, S. C.
McConnachie, A.
Irwin, M. J.
Tolstoy, E.
Tanvir, N. R.
MetadataShow full item record Abstract
This paper presents a study of the Cetus dwarf, an isolated dwarf galaxy within... |
In this kind of questions, I believe that most of the attention should be focused on the general approach and the philosophy of attacking. Afterwards, each individual may proceed by writing its own equations and solving them in its prefer way.In our particular case, I guess you examined the whole structure, realized th... |
Upon reading about the principal bundle picture of (quantum) field theory I encountered two different definitions of the gauge group:
Local gauge group $G$. Corresponds to the fibers of the $G$-bundle. Local gauge transformations correspond to the change of coordinates in which fields and form are written in trivializa... |
In the theory of relativistic wave equations, we derive the Dirac equation and the Klein-Gordon equation by using representation theory of the Poincare algebra.
For example, in this paper
http://arxiv.org/abs/0809.4942
the Dirac equation in momentum space (equation [52], [57] and [58]) can be derived from the 1-particl... |
Limits of Functions on Metric Spaces Review
Limits of Functions on Metric Spaces Review
We will now review some of the recent material regarding limits of functions on metric spaces.
Let $(S, d_S)$ and $(T, d_T)$ be metric spaces with $A \subseteq S$.
On the Limits of Functions on Metric Spacespage we that a Functionfr... |
I honestly don't recall learning the inverse function theorem until first year uni to be fair (and basically never used it from 2nd year and later) , so I doubt the majority of the high-school students would even consider it.Please share some more rants pls this is hilarious.
Wow this is definitely harder than the prev... |
Sreedhar, K and Ganguly, P (1990)
Evolution and the concomitant disappearance of high-$T_c$ superconductivity with carrier concentration in the $La_{2-x}Sr_xCuO_{4-\delta}$ system $(0.0\leq x \leq 1.2)$: Crossover from a Mott insulator to a band metal. In: Physical Review B, 41 (1). 371 - 382.
PDF
Evolution_and_the_con... |
You are currently browsing the tag archive for the ‘springer’ 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... |
Evaluating Double Integrals in Polar Coordinates
So we have looked at evaluating double integrals over general domains, however, sometimes it may be rather difficult to compute double integrals over certain domains due to the nature of integrating with the rectangular coordinate system. For example, computing a double ... |
I am reading the following paper by Slater:
https://journals.aps.org/pr/pdf/10.1103/PhysRev.81.385
On page 5 they write above equation (12) the following:
"If we now average over all wave functions, we find that the properly weighted average of $F(\eta)$ is 3/4."
Now, $F(\eta)=1/2 + \frac{1-\eta^2}{4\eta}\ln((1+\eta)/(... |
Sign-changing solutions for some nonhomogeneous nonlocal critical elliptic problems
Departamento de Matemática, Universidad Técnica Federico Santa María, Avenida España 1680, Valparaíso, Chile
$ (-\Delta_{\Omega})^{s} u = \left| u\right| ^{\frac{4}{N-2s}}u +\varepsilon f(x)\quad \mbox{in }\Omega, $
$ \Omega $
$ \mathbb... |
I have to solve the differential equation for radial disks, and therefore I need the shear force distribution. The disk is rotationally symmetric.
I want to use the superpositions principle and set 3 areas.
$0 \le r \le D_i / 2$
$D_i / 2 < r \le k / 2$
$k/2 < r \le D / 2$
The shear forces are for area 1
$\sum F_z = 0$
... |
I came across the following statement in my course notes:
Consider $R = \left\{f \in \mathbb{Q}[X] \mid f(\mathbb{Z}) \subset \mathbb{Z}\right\}$ the
ring of integer-valued polynomials. Then the ideal generated by $X$ is nota prime ideal.
Isn't this incorrect? I'd argue that $R/(X)$ (where $(X)$ denotes the ideal gener... |
Journal of Symbolic Logic J. Symbolic Logic Volume 57, Issue 1 (1992), 172-178. Lusin-Sierpinski Index for the Internal Sets Abstract
We prove that there exists a function $f$ which reduces a given $\Pi^1_1$ subset $P$ of an internal set $X$ of an $\omega_1$-saturated nonstandard universe to the set $\mathbf{WF}$ of we... |
I am reading the following paper by Slater:
https://journals.aps.org/pr/pdf/10.1103/PhysRev.81.385
On page 5 they write above equation (12) the following:
"If we now average over all wave functions, we find that the properly weighted average of $F(\eta)$ is 3/4."
Now, $F(\eta)=1/2 + \frac{1-\eta^2}{4\eta}\ln((1+\eta)/(... |
Difference between revisions of "Main Page"
(Fixing location.)
(Collected background materials)
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'''<math>k=3</math> Density Hales-Jewett (DHJ(3)) theorem:''' <math>\lim_{n \rightarrow \infty} c_n/3^n = 0</math>
'''<math>k=3</math> Density Hales-Jewett (DHJ(3)) theorem:''' <math>\lim_{n \rightarrow \inft... |
4:28 AM
@MartinSleziak Here I am! Thank you for opening this chat room and all your comments on my post, Martin. They are really good feedback to this project.
@MartinSleziak Yeah, using a chat room to exchange ideas and feedback makes a lot of sense compared to leaving comments in my post. BTW. Anyone finds a
\oint\fr... |
I am reading the following paper by Slater:
https://journals.aps.org/pr/pdf/10.1103/PhysRev.81.385
On page 5 they write above equation (12) the following:
"If we now average over all wave functions, we find that the properly weighted average of $F(\eta)$ is 3/4."
Now, $F(\eta)=1/2 + \frac{1-\eta^2}{4\eta}\ln((1+\eta)/(... |
This Lecture summarizes some well known facts about $\#P$ completeness of permanent.
Given a CNF formula $\phi$ on $n$ variables, they construct matrix $A$ such that:
$$perm(A)=4^{3m} \#SAT(\phi)$$
This gives easy upper bound on $perm(A)$.
$\phi$ is unsatisfiable iff $perm(A)=0$, so the decision problem "Is the permane... |
Let's assume that we have measured the height of each member in our population below:
Figure 1 - The heights (at the shoulders) are: 600mm, 470mm, 170mm, 430mm and 300mm. Images taken from http://www.mathsisfun.com/data/standard-deviation.html
We'll put these in a numpy array so we can use them later on:
import numpy a... |
We write the group operation multiplicatively.Let $x, y\in T(A)$. Then $x, y$ have finite order, hence there exists positive integers $m, n$ such that $x^m=e, y^n=e$, where $e$ is the identity element of $A$. Then we have\begin{align*}(xy)^{mn}&=x^{mn}y^{mn} \qquad \text{ (since $A$ is abelian)}\\&=(x^m)^n(y^m)^n=e^me^... |
Table of Contents
Internal Direct Products Isomorphic To External Direct Products
Recall from The Internal Direct Product of Two Groups page that if $(G, *)$ is a group and $(H, *)$, $(K, *)$ are two subgroups of $(G, *)$ then we say that $(G, *)$ is the internal direct product of $(H, *)$ and $(K, *)$ if the following... |
How big of an engine would I need, if the original is 65hp? What would be the weight of the up-scaled plane? Simply twice the weight? What would be the stall speed? How fast would it go? 75mph? Is there a software program to test aircraft design?
Unfortunately a simple scale-up would fall victim to the square-cube law:... |
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