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A remark on an eigenvalue condition for the global injectivity of differentiable maps of $R^2$
1.
Instituto de Ciências Matemáticas e de Computa¸cão - USP, Cx. Postal 668, CEP 13560–970, São Carlos, SP, Brazil
2.
Institute of Mathematics, P.O. Box 1078, Hanoi, Vietnam
There does not exist a sequence $R^2$ ∋ $x_i\righta... |
The Hierarchical Strauss Hard Core Point Process Model
Creates an instance of the hierarchical Strauss-hard core point process model which can then be fitted to point pattern data.
Usage
HierStraussHard(iradii, hradii=NULL, types=NULL, archy=NULL)
Arguments iradii
Matrix of interaction radii
hradii
Optional matrix of h... |
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Now showing items 1-9 of 9
Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
Two-parameter homogenization for a Ginzburg-Landau problem in a perforated domain
1.
Department of Mathematics and Materials Research Institute, Penn State University, University Park, PA 16802
2.
Université de Lyon, Université Lyon 1, Institut Camille Jordan CNRS UMR 5208, 43, boulevard du 11 november 1918, F-69622 Vi... |
A field $F$ is said to be algebraically closed if each non-constant polynomial in $F[x]$ has a root in $F$.
Proof.
Let $F$ be a finite field and consider the polynomial\[f(x)=1+\prod_{a\in F}(x-a).\]The coefficients of $f(x)$ lie in the field $F$, and thus $f(x)\in F[x]$. Of course, $f(x)$ is a non-constant polynomial.... |
Given a number of vectors with $n$ elements, i.e., $S=(a_1, \cdots, a_n)$, $T_j=(b_1^j, \cdots, b_n^j)$ for $j=1,\cdots, m$ where each $a_i$ or $b^i_j$ is a natural number.
Question: determine whether, for all subset $I\subseteq \{1, \cdots, n\}$, there is some $T_j$ ($1\leq j\leq m$) such that $\max\{a_i\mid i\in I\}=... |
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To send content items to your Kindle, first ensure no-rep... |
I’m extremely agitated today. I dunno why. Maybe because there was some convulsion in the peaceful tidings of the house I live in, or the fact that I’m kinda hungry at the moment. Anyways, I don’t have time for chitchat. Let’s get to the studying.
The following is taken from
Foundations of Machine Learning by Rostamyar... |
The nLab says the following about closed monoidal functor categories:
Let $C$ be a complete closed monoidal category and $I$ any small category. Then the functor category $[I, C]$ is closed monoidal with the pointwise tensor product, $(F \otimes G)(x) = F(x) \otimes G(x)$.
Now I wonder what the right adjoint of $F \oti... |
And I think people said that reading first chapter of Do Carmo mostly fixed the problems in that regard. The only person I asked about the second pset said that his main difficulty was in solving the ODEs
Yeah here there's the double whammy in grad school that every grad student has to take the full year of algebra/ana... |
Coupling Heat Transfer with Subsurface Porous Media Flow
In the second part of our Geothermal Energy series, we focus on the coupled heat transport and subsurface flow processes that determine the thermal development of the subsurface due to geothermal heat production. The described processes are demonstrated in an exa... |
Any element of the ring $\Z[\sqrt{-5}]$ is of the form $a+b\sqrt{-5}$ for some integers $a, b$.The associated (field) norm $N$ is given by\[N(a+b\sqrt{-5})=(a+b\sqrt{-5})(a-b\sqrt{-5})=a^2+5b^2.\]
Consider the case when $a=2, b=1$.Then we have\begin{align*}(2+\sqrt{-5})(2-\sqrt{-5})=9=3\cdot 3. \tag{*}\end{align*}
We c... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
hide
Free keywords: Mathematics, Number Theory, math.NT,High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
Abstract: We study the correlators of irregular vertex operators in two-dimensional
conformal field theory (CFT) in order to propose an exact analytic for... |
Let A = $\begin{bmatrix} a_1,&a_2,&...,&a_n \end{bmatrix} \text{ and } \vec{x} = \begin{bmatrix} x_1\\x_2\\x_3\\...\\x_n \end{bmatrix}$
$A \vec{x} = x_1a_a + x_2a_2+...+ x_na_n$
Thus,(1)
which is equivalent to(2)
The first way of multiplying takes each row in the first matrix (A) and multiplies it by the corresponding ... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
In
mathematics, the limit comparison test (LCT) (in contrast with the related direct comparison test) is a method of testing for the convergence of an infinite series. Statement [ edit ]
Suppose that we have two series
and Σ n a n {\displaystyle \Sigma _a_} with Σ n b n {\displaystyle \Sigma _b_} for all a n ≥ 0 , b n ... |
Square Space Silo Problem 431
Fred the farmer arranges to have a new storage silo installed on his farm and having an obsession for all things square he is absolutely devastated when he discovers that it is circular. Quentin, the representative from the company that installed the silo, explains that they only manufactu... |
A
perfect number is a positive integer $n$ such that $$\sum_{d|n} d = 2n.$$Put another way, $n$ is the sum of its proper divisors. Check out a a quick intro to perfect numbers that I wrote last November. The first three perfect numbers are $6, 28,$ and $496$. Currently, the largest perfect number, corresponding to the ... |
Smectic-A Order at the Surface of a Nematic Liquid Crystal: Synchrotron X-Ray Diffraction Author
Als-Nielsen, J.
Christensen, F.
Published Versionhttps://doi.org/10.1103/PhysRevLett.48.1107 MetadataShow full item record CitationAls-Nielsen, J., F. Christensen, and Peter S. Pershan. 1982. Smectic-A order at the surface ... |
Any Automorphism of the Field of Real Numbers Must be the Identity Map Problem 507
Prove that any field automorphism of the field of real numbers $\R$ must be the identity automorphism.
Contents
Problem 507 Proof. Claim 1. For any positive real number $x$, we have $\phi(x)>0$. Claim 2. For any $x, y\in \R$ such that $x... |
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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... |
Shortcut keys for inserting Greek symbols into the equation \+: name of the symbol
\alpha \kappa \varrho \beta \lambda \sigma \chi \mu \varsigma \delta \nu \tau \epsilon \o \upsilon \varepsilon \pi \omega \phi \varpi \xi \varphi \theta \psi \gamma \vartheta \zeta \eta \rho
See Shortcut keys for inserting symbols and te... |
Hybrid Interaction Point Process Model
Creates an instance of a hybrid point process model which can then be fitted to point pattern data.
Usage
Hybrid(...)
Arguments …
Two or more interactions (objects of class
"interact") or objects which can be converted to interactions. See Details.
Details
A
hybrid (Baddeley, Turn... |
Let $( \mathbb{R}^n, \| \cdot \|_P)$ be the $n$-dimensional Euclidean space equipped with $\ell_p$-norm $\| \cdot \|_p$ for some $p\in [1, + \infty]$. Let $A$ be a convex set in $\mathbb{R}^n$ and define \begin{align} A^{\epsilon} = \{ y \in \mathbb{R}^n \colon \exists x \in A~\text{such that}~\| x -y \| _{p} \leq \eps... |
Intermediate Thermodynamics Questions & Answers
If all molecules would always have a velocity vector pointing in the positive $x$ direction, then the average velocity in the positive $x$ direction would be $\overline{q}$ (with $\overline{q}$ the molecular speed). But, molecules move in all directions randomly, not just... |
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A method is disclosed whereby a semiconductor silicon substrate wafer is diffused with a P or N type dopant or "im... |
Let $\mathbf{x}$ be an eigenvector corresponding to the eigenvalue $\lambda$. Then we have\[A\mathbf{x}=\lambda \mathbf{x}.\]Taking the conjugate of both sides, we have\[\overline{A\mathbf{x}}=\overline{\lambda \mathbf{x}}.\]
Since $A$ is a real matrix, it yields that\[A\bar{\mathbf{x}}=\bar{\lambda}\bar{\mathbf{x}}. \... |
Difference between revisions of "Algebra and Algebraic Geometry Seminar Spring 2018"
Line 1: Line 1:
The seminar meets on Fridays at 2:25 pm in room B113.
The seminar meets on Fridays at 2:25 pm in room B113.
−
Here is the schedule for [[Algebraic Geometry Seminar Spring 2017 | the previous semester]]
+
Here is the sch... |
Prefixes
concept
When dealing with the values in electrical circuits we often have to use numbers from 0.0000001 to 1000000. Sometimes we use numbers of both extremes in the same circuit for different things. This becomes tedious and difficult to use. It's also error prone since so many zeros makes leaving one off or a... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
I think -- and hope -- that every computer science student is confronted with this problem which feels like a paradoxon. It is a very good example for the difference of computable in TCS sense and computable in a practical sense.
My thoughts back then were: "Yea, if I
knew the answer, it would obviously be computable. ... |
In mathematics, a theory like the theory of probability is developed axiomatically. That means we begin with fundamental laws or principles called
axioms, which are the assumptions the theory rests on. Then we derive the consequences of these axioms via proofs: deductive arguments which establish additional principles ... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
Difference between revisions of "Geometry and Topology Seminar"
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(→Fall 2016)
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Revision as of 22:00, 8 November 2016 Contents 1 Fall 2016 2 Spring 2017 3 Fall Abstracts 4 Spring Abstracts 5 A... |
Recall that a complex matrix $M$ is said to be Hermitian if $M^*=M$.Here $A^*$ is the conjugate transpose matrix $M^*=\bar{M}^*$.
Proof.
Let\[B=\frac{A+A^*}{2} \text{ and } C=\frac{A-A^*}{2i}.\]We claim that $B$ and $C$ are Hermitian matrices.Using the fact that $(A^*)^*=A$, we compute\begin{align*}B^*&=\left(\, \frac{... |
2014 Heat Transfer Midterm Exam
May 2nd 2014
19:00 — 21:00
NO NOTES OR BOOKS; USE HEAT TRANSFER TABLES THAT WERE DISTRIBUTED; ANSWER ALL 4 QUESTIONS; ALL QUESTIONS HAVE EQUAL VALUE.
$c_{\rm c}=900$ J/kg$^\circ$C, $\rho_{\rm c}=2000$ kg/m$^3$, $k_{\rm c}=0.3$ W/m$^\circ$C
that the earth has properties of:
$c_{\rm e}=100... |
Exponential Functions Form a Basis of a Vector Space Problem 590
Let $C[-1, 1]$ be the vector space over $\R$ of all continuous functions defined on the interval $[-1, 1]$. Let
\[V:=\{f(x)\in C[-1,1] \mid f(x)=a e^x+b e^{2x}+c e^{3x}, a, b, c\in \R\}\] be a subset in $C[-1, 1]$. (a) Prove that $V$ is a subspace of $C[-... |
Chemical Equations (YAY!)
Given the combustion reaction $x_1CH_4 + x_2O_2 \rightarrow x_3CO_2 +x_4H_2O$, what are the values of $\vec{x}$?
Using Linear Algebra and assigning each element to a ROW we can redefine this apparently difficult problem to a simple matrix(1)
Therefore, the $\vec{x} = x_3 \begin{bmatrix} 1\\0\\... |
Take: $M$ a Riemannian manifold, ${X_0}\in M$, $N_{X_0}$ a submanifold of $M$ going through ${X_0}$, and $Z \in N_{X_0}$ in a neighborhood of ${X_0}$.
At ${X_0} \in N_{X_0}$, we consider the orthogonal splitting of the tangent space: $T_{X_0} M=T_{X_0} N_{X_0} \oplus H$. The coordinates of $Z$ can be written $(z,F(z))$... |
Is there any way to theoretically, by the use of mathematics, to calculate the time taken to brute-force RSA keys?
Even classically, this is not so easy as you seem to imply.
RSA is based on the hardness of the integer factorization problem. The fastest classical algorithm known that solves this problem is the General ... |
Note that the polynomial $x^3-2$ is irreducible over $\Q$ by Eisenstein’s criterion (with prime $p=2$).This implies that if $\alpha$ is any root of $x^3-2$, then the degree of the field extension $\Q(\alpha)$ over $\Q$ is $3$:\[[\Q(\alpha) : \Q]=3. \tag{*}\]
Seeking a contradiction, assume that $x^3-2$ is reducible ove... |
This article is all about the basics of probability. There are two interpretations of a probability, but the difference only matters when we will consider inference.
Frequency The degree of belief Axioms of Probability
A function \(P\) which assigns a value \(P(A)\) to every event \(A\) is a
probability measure or prob... |
1.
Introduction to bearings
2.
Bearings and direction word problems
3.
Angle of elevation and depression
Back to Course Index
Theorems that are useful:
Pythagorean Theorem: a2+b2=c2a^{2} + b^{2} = c^{2}a2+b2=c2
Trig ratio: sinθ=OH\sin \theta = \frac{O}{H}sinθ=HO
cosθ=AH\cos \theta = \frac{A}{H}cosθ=HA
tanθ=OA\tan \thet... |
April 27th, 2014, 11:02 AM
# 1
Newbie
Joined: Apr 2014
From: zagreb
Posts: 5
Thanks: 0
Set Theory
I'm reading Jech's book. Can someone solve exercises
1.6.
1.7.
2.12
help me to understand lemmae 3.6.-3.10. and 5.2.
theorem
3.11.
4.5.
4.8.-Baire category theorem
April 28th, 2014, 11:00 AM
# 2
Newbie
Joined: Apr 2014
Fro... |
Yes:
imho geometrically the most interesting one is obtained as a quotient $SO(5)/SO(4)$ where the Poisson stucture on $SO(5)$ is not the so-called standard one, but one determined by an element in the maximal torus (sometimes they are called twisted). This is the Poisson analogue of what is mentioned in Quantum symmet... |
Here is the answer to Question 2. It may be probably simplified.
Denote $y=3-x$, then we rewrite your identity as $$\binom{y+K-2}K=\frac{(y-1)y(y+1)\dots (y+K-2)}{K!}=c_0\binom{y}0+c_1\binom{y}1+\dots+c_K\binom{y}K,$$where $$c_p=p!\sum_{n=p}^K(-K)^{n-p}\frac1{n!}\sum\limits_{ \begin{subarray}{c} k_1+\dotsb+k_{n}=K \\ k... |
Advanced Tutorial (geared toward state-space models)¶
This tutorial covers more or less the same topics as the basic tutorial (filtering, smoothing, and parameter estimation of state-space models), but in greater detail.
Defining state-space models¶
We consider a state-space model of the form:
where function \(f\) is d... |
The equation $M \mathbf{x} = \mathbf{0}$ then yields a system of linear equations with $n$ equations and $n$ variables.To find a solution, consider the augmented matrix $ \begin{bmatrix}[c|c] M & \mathbf{0} \end{bmatrix}$.
Because $M$ is upper-triangular, we can use back-substitution to solve. The bottom row of the aug... |
It is known that the arguments of prime elements of $\mathbb{Z}[i]$ are equidistributed in $(0,2π)$ (by Theorem 5.36 of Iwaniec and Kowalski, or one of Kubilius' papers cited below). This theorem extends to any imaginary quadratic number ring $\mathcal{O}$ if one uses prime ideal numbers (especially for those number ri... |
Meshing Considerations for Linear Static Problems
In this blog entry, we introduce meshing considerations for linear static finite element problems. This is the first in a series of postings on meshing techniques that is meant to provide guidance on how to approach the meshing of your finite element model with confiden... |
Let $P=(p_1,\ldots,p_d)$ be a distribution on $[d]$. Given $n$ iid draws from $P$, we construct some empirical estimate $\hat P_n=(\hat p_{n,1},\ldots,\hat p_{n,d})$. Let us define the $r$-risk by $$ J_n^r = \sum_{i=1}^d |p_i-\hat p_{n,i}|^r. $$
It is known (see, e.g., Lemma 2.4 here) that when $\hat P_n$ is the maximu... |
If a Sylow Subgroup is Normal in a Normal Subgroup, it is a Normal Subgroup
Problem 226
Let $G$ be a finite group. Suppose that $p$ is a prime number that divides the order of $G$.Let $N$ be a normal subgroup of $G$ and let $P$ be a $p$-Sylow subgroup of $G$.Show that if $P$ is normal in $N$, then $P$ is a normal subgr... |
The Order of a Conjugacy Class Divides the Order of the Group Problem 455
Let $G$ be a finite group.
The centralizer of an element $a$ of $G$ is defined to be \[C_G(a)=\{g\in G \mid ga=ag\}.\]
A
conjugacy class is a set of the form \[\Cl(a)=\{bab^{-1} \mid b\in G\}\] for some $a\in G$. (a)Prove that the centralizer of ... |
1. Analogy
Let’s assume that we’d like do a numerical processing in the best suited base on this purpose.
Let’s have an example : we’d like to divide an even number by $2$. It turns out that the base 2 is the best suited base for doing that. Indeed a simple shift from left to right does that processing.
We have the thr... |
Tagged: skew-symmetric matrix Problem 593
We fix a nonzero vector $\mathbf{a}$ in $\R^3$ and define a map $T:\R^3\to \R^3$ by
\[T(\mathbf{v})=\mathbf{a}\times \mathbf{v}\] for all $\mathbf{v}\in \R^3$. Here the right-hand side is the cross product of $\mathbf{a}$ and $\mathbf{v}$. (a) Prove that $T:\R^3\to \R^3$ is a l... |
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,... |
Let \( A \) be any real square matrix (not necessarily symmetric). Prove that: $$ (x'A x)^2 \leq (x'A A'x)(x'x) $$
The key point in proving this inequality is to recognize that \( x'A A'x \) can be expressed as vector norm of \( A'x \).
Proof:
If \( x=0 \), then the inequality is trival.
Suppose \( x \neq 0 \).
\( \fra... |
PDE Geometric Analysis seminar
The seminar will be held in room 901 of Van Vleck Hall on Mondays from 3:30pm - 4:30pm, unless indicated otherwise.
Contents Seminar Schedule Spring 2016
date speaker title host(s) January 25 Tianling Jin (HKUST and Caltech) Holder gradient estimates for parabolic homogeneous p-Laplacian ... |
CDS 212, Homework 7, Fall 2010
From MurrayWiki
J. Doyle Issued: 9 Nov 2010 CDS 212, Fall 2010 Due: 18 Nov 2010 Problems Show that <amsmath>E(s) = D+C(sI-A)^{-1}B</amsmath> has <amsmath>H_\infty</amsmath> norm <amsmath>< \gamma</amsmath> if the following LMI is satisfied: <amsmath> \left[\begin{array}{ccccccc} A^TP+PA& ... |
Tagged: matrix Problem 250
Let $\mathbf{u}$ and $\mathbf{v}$ be vectors in $\R^n$, and let $I$ be the $n \times n$ identity matrix. Suppose that the inner product of $\mathbf{u}$ and $\mathbf{v}$ satisfies
\[\mathbf{v}^{\trans}\mathbf{u}\neq -1.\] Define the matrix \[A=I+\mathbf{u}\mathbf{v}^{\trans}.\]
Prove that $A$ ... |
Recall that the extension degree of the cyclotomic field of $n$-th roots of unity is given by $\phi(n)$, the Euler totient function.Thus we have\[[\Q(\zeta_8):\Q]=\phi(8)=4.\]
Without loss of generality, we may assume that\[\zeta_8=e^{2 \pi i/8}=\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}i.\]
Then $i=\zeta_8^2 \in \Q(\zeta_8... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
I have a (classical) scheduling problem using completion date variables, with a constraint like
$$ c_j = s_j + p_j $$
where \(s_j\) and \(c_j\) are variables representing the start date and the completion date of job \(j\), respectively, and \(p_j\) is a parameter representing the duration of job \(j\) (I skip the othe... |
An electrolyte solution is a solution that generally contains ions, atoms or molecules that have lost or gained electrons, and is electrically conductive. For this reason they are often called ionic solutions, however there are some cases where the electrolytes are not ions. For this discussion we will only consider so... |
Separable ODEs
concept
Separable ODEs are some of the simplest to solve for and don't require any new skills you haven't used before. As such they are a perfect, gentle introduction into the world of ODE solving.
fact
A separable ODE is one where it can be written in the following form: $$f(x)dx = g(y)dy$$ In other wor... |
Do you ever get the feeling that mathematics uses the word dimension a lot? Well, that's for good reason. The concept of dimension is fundamental in mathematics. What is dimension? You can think of dimension as a numerical invariant characterizing the number of parameters required to do a certain thing. For example, fo... |
The Finite Element Method is a powerful numerical technique for solving ordinary and partial differential equations in a range of complex science and engineering applications, such as multi-domain analysis and structural engineering. It involves decomposing the analysis domain into a discrete mesh before constructing a... |
The Annals of Probability Ann. Probab. Volume 25, Number 4 (1997), 1545-1587. Limit theorems for products of positive random matrices Abstract
Let $S$ be the set of $q \times q$ matrices with positive entries, such that each column and each row contains a strictly positive element, and denote by $S^\circ$ the subset of... |
Geometry and Topology Seminar Contents 1 Fall 2016 2 Spring 2017 3 Fall Abstracts 4 Spring Abstracts 5 Archive of past Geometry seminars Fall 2016 Spring 2017
date speaker title host(s) Jan 20 Carmen Rovi (University of Indiana Bloomington) "The mod 8 signature of a fiber bundle" Maxim Jan 27 Feb 3 Rafael Montezuma (Un... |
I had originally contacted Frank Harrell with this issue and he suggested I post here for some discussion. While reviewing a JAMA article (doi:10.100/jama.2018.14276) attempting to understand the application of a Bayesian analysis of existing RCT data, I happened to run across this NEJM article (doi/10.1056/NEJMoa19009... |
AKS primality testing solves whether a given integer is prime in $P$. AKS algorithm is following:
Input: integer n > 1.
Check if $n$ is a perfect power: if $n = a^b$ for integers $a > 1$ and $b > 1$, output composite.
Find the smallest $r$ such that $ord_r(n) > (\log_2 n)^2$ (if $r$ and $n$ are not coprime, then skip t... |
Chemical stoichiometry
Category : JEE Main & Advanced
Chemical stoichiometry
Stoichiometry (pronounced “stoy-key om-e-tree”) is the calculation of the quantities of reactants and products involved in a chemical reaction. That means quantitative calculations of chemical composition and reaction are referred to as stoich... |
Consider a scenario-tree, with 4 stages. The first stage is the root node. This root node has two children. So the second stage has 2 nodes. Each node of the scenario tree has 2 children. So in total we have: 15 nodes.
How many nodes will the deterministic equivalent of this have?
asked
spyimp
I'm not sure I understand... |
Introduction to AC Circuits
concept
All through DC we dealt with voltage and current sources that were constant. We analysed our circuits and figured out what the one, single value for a voltage somewhere or a current somewhere else. In AC we'll be dealing with voltage and current sources that not only change their val... |
The classic “Lockean” thesis about full and partial belief says full belief is rational iff strong partial belief is rational. Hannes Leitgeb’s “Humean” thesis proposes a subtler connection. $ \newcommand\p{Pr} \newcommand{\B}{\mathbf{B}} \newcommand{\given}{\mid} $
The Humean Thesis
For a rational agent whose full bel... |
Powers of a Matrix Cannot be a Basis of the Vector Space of Matrices
Problem 375
Let $n>1$ be a positive integer. Let $V=M_{n\times n}(\C)$ be the vector space over the complex numbers $\C$ consisting of all complex $n\times n$ matrices. The dimension of $V$ is $n^2$.Let $A \in V$ and consider the set\[S_A=\{I=A^0, A, ... |
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Now showing items 1-10 of 19
Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c w... |
1. Matrix
A
matrix is a grid of $m$ rows and $n$ columns. It contains the coefficients of a linear system. These are the so-called elements of the matrix.
Example I shows how a linear system is turned into a matricial equation in the form $A\vec{x} = \vec{y}$.
Example I
Index notation is used to specify a matrix elemen... |
A (quasi)variety $\mathcal{K}$ of algebraic structures has
(EDP(R)C) ifthere is a finite conjunction of atomic formulas $\phi(u,v,x,y)$ such that for allalgebraic structures $\mathbf{A}\in\mathcal{K}$ we have$\langle x,y\rangle\in\mbox{Cg}_{\mathcal{K}}(u,v)\iff \mathbf{A}\models \phi(u,v,x,y)$. Here$\theta=\mbox{Cg}_{... |
Use Sylow’s theorem and determine the number of $5$-Sylow subgroup of the group $G$.Check out the post Sylow’s Theorem (summary) for a review of Sylow’s theorem.
Proof.
(a) When $|G|=100$.
The prime factorization of $100$ is $2^2\cdot 5^2$. Let us determine the number $n_5$ of $5$-Sylow subgroup of $G$.By Sylow’s theor... |
Let $X$ be a smooth complex quasi-projective variety. We can find good compactification: a smooth proper variety $\bar{X}$ such that ${\bar X} \setminus X$ is a divisor with normal crossing. The variety $\bar{X}$ is then stratified by the singulartities of the divisor. And one can compute the mixed Hodge structure on $... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
I am a new aviation student and I was reading about induced drag the other day. I know that it is produced as a result of the tip vortices and that the greater the aspect ratio of an airplane the less the induced drag force. But when it came to the equation of the force, it is equal to:
$D_i = \frac{1}{2}\rho V^2 S \fr... |
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Lake Titicaca An issue that I was not aware of at all before this class was the drying out of many lakes around the world. It is a huge problem for the communities that surround the lake, as well as … Continue reading
To start off, what... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
The most important thing you need to know about LaTex Wikidots is that any "mathy" writing needs to be inside either the math tag [[math]] Math goes here [[/math]] or the inline math tag [[$ math goes here $]]. Every symbol should be done in LaTex for consistency of font throughout your portfolio.
Here are some of the ... |
A
perfect number is a positive integer $n$ such that $n$ is the sum of its proper divisors. For example $6 = 1 + 2 + 3$. The symbol $\sigma(n)$ is usally used for the sum of all the divisors of a positive integer $n$, so that a number is perfect if and only if $\sigma(n) = 2n$. All known perfect numbers are even, and t... |
A
linear equation in the variables $x_1, x_2, ... , x_n$ is an equation that can be written in the form
A
system of linear equations is a collection of linear equations involving the same variables.
A
solution of the system is a list of numbers that makes each equation true. If the matrix has a solution, it is consider... |
November 6th, 2017, 01:06 AM
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Simplification of a formula
We consider a fixed parameter $\theta>0$.
For all $t>0$ we note:
$$u(t)=\frac{\sinh\big(\frac{t}{2}\cosh(\theta)\bi g)}{\cosh(\theta)}$$
$$A(t)=\frac{\sqrt{\cosh^2(\theta)u^2(t)+1}-1}{\cosh^2(\thet... |
In mathematical logic,
satisfiability and validity are elementary concepts of semantics. A formula is satisfiable if it is possible to find an interpretation (model) that makes the formula true. [1] A formula is valid if all interpretations make the formula true. The opposites of these concepts are unsatisfiability and... |
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Get a MarkDown cheatsheet with Ctrl+M.
# This is a heading!A sentence or two. This is in plain text, and this is *italic text*.We need some **bold** text:- You can also make lists quite easily- Wit... |
Global attractor for a Klein-Gordon-Schrodinger type system
1.
Department of Mathematics, National Technical University, Zografou Campus 157 80, Athens, Greece
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Department of Mathematics, National Technical University, Zografou Campus 157 80, Athens, Hellas, Greece
$i\psi_t + k\psi_(xx) + i\alpha\psi$ = $\phi\psi + f... |
This is a short list of books to get you started on learning automorphic representations. Before I talk about them, I will first define automorphic representation, which will take a few paragraphs.
To start, we need an affine algebraic $F$-group scheme $G$ where $F$ is a number field or function field. We let $\A_F$ be... |
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Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
L-function
Calculates an estimate of the inhomogeneous version of the \(L\)-function (Besag's transformation of Ripley's \(K\)-function) for a spatial point pattern.
Usage
Linhom(...)
Arguments …
Arguments passed to
Kinhomto estimate the inhomogeneous K-function.
Details
This command computes an estimate of the inhomog... |
Difference between revisions of "Geometry and Topology Seminar"
Line 240: Line 240:
"TBA"
"TBA"
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===Rafael Montezuma===
===Rafael Montezuma===
Revision as of 23:13, 27 January 2017 Contents 1 Fall 2016 2 Spring 2017 3 Fall Abstracts 4 Spring Abstracts 5 Archive of past Geometry seminars Fall 2016 Spring 2017
date sp... |
Let's try to generalize the $VC$-dimension (of the class of hyperplanes) to include accuracy/error. Let $S$ be a set of points in $R^d$ and $t$ in $[0,1]$. We say that the class of hyperplanes $t$-shatters $S$ if for every binary labeling of the points in $S$, there exists some hyperplane which separates $S$ with accur... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
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Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
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