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Created in the early 17th century, the gas laws have been around to assist scientists in finding volumes, amount, pressures and temperature when coming to matters of gas. The gas laws consist of three primary laws: Charles' Law, Boyle's Law and Avogadro's Law (all of which will later combine into the General Gas Equati... |
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 ... |
Regularity of extremal solutions of semilinear elliptic problems with non-convex nonlinearities on general domains
1.
School of Mathematics, Iran University of Science and Technology, Narmak, Tehran, Iran
2.
School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, P.O.Box: 19395-5746, Iran
$... |
Group Generated by Commutators of Two Normal Subgroups is a Normal Subgroup
Problem 129
Let $G$ be a group and $H$ and $K$ be subgroups of $G$.For $h \in H$, and $k \in K$, we define the commutator $[h, k]:=hkh^{-1}k^{-1}$.Let $[H,K]$ be a subgroup of $G$ generated by all such commutators.
Show that if $H$ and $K$ are ... |
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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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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 ... |
I must use each number 2,0,1,9 (only once) to come up with an answer of 76
Please edit the question to limit it to a specific problem with enough detail to identify an adequate answer. Avoid asking multiple distinct questions at once. See the How to Ask page for help clarifying this question. If this question can be re... |
Microscopic Realization of the Kerr/CFT Correspondence Author
Guica, Monica
Published Versionhttps://doi.org/10.1007/JHEP02(2011)010 MetadataShow full item record CitationGuica, Monica, and Andrew Strominger. 2011. Microscopic Realization of the Kerr/CFT Correspondence. Journal of High Energy Physics 2011(2): 1-20. Abs... |
Manual definition of Feynman-Kac models¶
It is not particularly difficult to define manually your own
FeynmanKac classes. Consider the following problem: we would like to approximate the probability that \(X_t \in [a,b]\) for all \(0\leq t < T\), where \((X_t)\) is a random walk: \(X_0\sim N(0,1)\), and
This probabilit... |
Posted in
The web presence of the MPIM has been relaunched, offering a fresh design and a number of new features:
There is a calendar, which can be subscribed with current calendar applications (see the link at the lower right corner). The management of events is improved, e.g. conference programmes are created automat... |
A discrete-time Markov chain (DTMC) is a tuple $M=(S,s_{init},P)$ where $S$ is a finite set of states, $s_{init}\in S$ the initial state, and $P:S\times S\to[0,1]$ the one-step transition probability matrix.
For a subset $S'\subseteq S$ with $s_{init},t\in S'$ we define the induced sub-DTMC $M_{S'}=(S',s_{init},P')$ wi... |
Answer
The displacement amplitude is $2.77\times 10^{-7}~m$ The displacement amplitude is about 92 times larger than the average distance between molecules in a room.
Work Step by Step
We can find the intensity of the sound: $\beta = 10~log\frac{I}{I_0}$ $60.0 = 10~log\frac{I}{I_0}$ $6.0 = log\frac{I}{I_0}$ $10^{6.0} =... |
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Measurement of transverse energy at midrapidity in Pb-Pb collisions at $\sqrt{s_{\rm NN}} = 2.76$ TeV
(American Physical Society, 2016-09)
We report the transverse energy ($E_{\mathrm T}$) measured with ALICE at midrapidity in Pb-Pb collisions at ${\sqrt{s_{\mathrm {NN}}}}$ = 2.76 T... |
Learning Objectives
Explain the Ideal Gas Law
There are a number of chemical reactions that require ammonia. In order to carry out the reaction efficiently, we need to know how much ammonia we have for stoichiometric purposes. Using gas laws, we can determine the number of moles present in the tank if we know the volum... |
Difference between revisions of "Geometry and Topology Seminar"
(→Spring 2014)
(→Spring Abstracts)
Line 302: Line 302:
This talk will describe recent work developing aspects of this picture in the setting of a free-by-cyclic group G. Specifically, I will introduce a polynomial invariant that determines a convex polygon... |
Miloslav Znojil
The quantum-catastrophe (QC) benchmark Hamiltonians of paper I (M. Znojil, J. Phys. A: Math. Theor. 45 (2012) 444036) are reconsidered, with the infinitesimal QC distance \(\lambda\) replaced by the total time $\tau$ of the fall into the singularity. Our amended model becomes unique, describing the comp... |
1. Analogy
Generally speaking, a
base is a reference system in which things are expressed. For example, the number $64$ is written
1000 in the base $2$ (binary base). They are in fact the
same number but they are expressed (represented) in different bases :
The natural base for numbers is the base 10. As regards vector... |
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Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
Find eigenvalues and a basis for the eigenspace(2)
Substituting our new $\lambda$ back into our A matrix,(3)
Row reduction here doesn't quite work the way we understand it, but we can notice that each equation in the matrix should have the same nontrivial solution. This was given by the book and I have no justification... |
February 4, 2015
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Ampere's law, antenna, antisymmetric, average power, bivector, complex power, constituative relations, continuity equation, cross product, curl, dB, dBi, decibel, directivity, divergence, divergence theorem, dot product, dual, duality, ece1229, electic source, electric dipole, elect... |
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... |
The Symmetric Group is a Semi-Direct Product of the Alternating Group and a Subgroup $\langle(1,2) \rangle$ Problem 465
Prove that the symmetric group $S_n$, $n\geq 3$ is a semi-direct product of the alternating group $A_n$ and the subgroup $\langle(1,2) \rangle$ generated by the element $(1,2)$.
Add to solve later
Con... |
1. Analogy
In basic algebra, the solution of the following equation is said to be the
multiplicative inverse :
Solution of $(1)$ is $\frac{1}{a}$, which is also written $a^{-1}$.
In linear algebra, the equivalent equation to $(1)$ is :
In $(2)$, $I$ is the so-called
identity matrix. It contains $1$’s in its diagonal an... |
Finitely Generated Torsion Module Over an Integral Domain Has a Nonzero Annihilator Problem 432 (a) Let $R$ be an integral domain and let $M$ be a finitely generated torsion $R$-module. Prove that the module $M$ has a nonzero annihilator. In other words, show that there is a nonzero element $r\in R$ such that $rm=0$ fo... |
№ 8
All Issues Panakhov E. S.
Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1516-1525
We consider the inverse problem for second-order differential operators with regular singularity and show that the potential function can be uniquely determined by the set of values of eigenfunctions at some interior point and parts of two ... |
This example explores the physics of the damped harmonic oscillator by
solving the equations of motion in the case of no driving forces,
investigating the cases of under-, over-, and critical-damping
Derive Equation of Motion
Solve the Equation of Motion (F = 0)
Underdamped Case ()
Overdamped Case ()
Critically Damped ... |
In this post we’re going to cover some basic intuition to work on
logistic regression for Deep Learning algorithms.
Logistic regression is an algorithm for
binary classification, which is basically used when you want to have your model to return 0 or 1. Some examples: is this image a cat? is this email spam? etc.
The b... |
Authors:
Malaj V. P., Ratsa M. F.
Abstract
A system $\Sigma$ of function from the set $K$ is called a chain (completive) system in $K$, if the set of closed systems $K'$, such that $\Sigma \subseteq K'\subseteq K$, forms a chain with respect to the inclusion (is finite). A system $\Sigma \subseteq K$ is precompletive i... |
If $W_1 \cup W_2$ is a subspace, then $W_1 \subset W_2$ or $W_2 \subset W_1$.
$(\implies)$ Suppose that the union $W_1\cup W_2$ is a subspace of $V$.Seeking a contradiction, assume that $W_1 \not \subset W_2$ and $W_2 \not \subset W_1$.This means that there are elements\[x\in W_1\setminus W_2 \text{ and } y \in W_2 \se... |
When my information changes, I alter my conclusions. What do you do, sir?
—attributed to John Maynard Keynes
The last two chapters showed how Bayesians make personal probabilities objective. They can be quantified using betting rates. And they are bound to the laws of probability by Dutch books.
But what about learning... |
(a) Is it true that $A$ must commute with its transpose?
The answer is no.
We give a counterexample. Let\[A=\begin{bmatrix}1 & -1\\0& 2\end{bmatrix}.\]Then the transpose of $A$ is\[A^{\trans}=\begin{bmatrix}1 & 0\\-1& 2\end{bmatrix}.\]We compute\[AA^{\trans}=\begin{bmatrix}1 & -1\\0& 2\end{bmatrix}\begin{bmatrix}1 & 0\... |
Apps for Teaching Mathematical Modeling of Tubular Reactors
The Tubular Reactor application is a tool where students can model a nonideal tubular reactor, including radial and axial variations in temperature and composition, and investigate the impact of different operating conditions. It also exemplifies how teachers ... |
Determinant/Trace and Eigenvalues of a MatrixLet $A$ be an $n\times n$ matrix and let $\lambda_1, \dots, \lambda_n$ be its eigenvalues.Show that(1) $$\det(A)=\prod_{i=1}^n \lambda_i$$(2) $$\tr(A)=\sum_{i=1}^n \lambda_i$$Here $\det(A)$ is the determinant of the matrix $A$ and $\tr(A)$ is the trace of the matrix […]
Nilp... |
The matrix
size, noted $m \times n$, is the number of rows, respectively the number of columns that a matrix contains. A matrix is said to be square when $m=n$. Matrices of example II are of size $2 \times 3$. 1. Multiplication
We have seen in the previous chapter how coefficients and variables are separated from one a... |
It is well-known that the complement of $\{ ww \mid w\in \Sigma^*\}$ is context-free. But what about the complement of $\{ www \mid w\in \Sigma^*\}$?
Still CFL I believe, with an adaptation of the classical proof. Here's a sketch.
Consider $L = \{xyz : |x|=|y|=|z| \land (x \neq y \lor y \neq z)\}$, which is the complem... |
Math General Math Forum - For general math related discussion and news
View Poll Results: Is x/0 infinitesimal? Yes! Completely agree! 0 0% Possibly agree... 0 0% Don't agree. 2 100.00% I have proof against it. 0 0% I don't know. 0 0% Multiple Choice Poll. Voters: 2. You may not vote on this poll
LinkBack Thread Tools ... |
An argument is valid if it is impossible for the premises to be true and the conclusion false.
An argument is sound if it is valid and all the premises are true.
There are three connectives: \(\neg\) (negation), \(\wedge\) (conjunction), and \(\vee\) (disjunction).
Their truth tables are as follows
\(A\) \(B\) \(\neg A... |
Inverse Map of a Bijective Homomorphism is a Group Homomorphism
Problem 445
Let $G$ and $H$ be groups and let $\phi: G \to H$ be a group homomorphism.Suppose that $f:G\to H$ is bijective.Then there exists a map $\psi:H\to G$ such that\[\psi \circ \phi=\id_G \text{ and } \phi \circ \psi=\id_H.\]Then prove that $\psi:H \... |
Define $\Pi_k \text{SAT}$ by 'Given a quantified boolean formula $\varphi = \forall y_1\exists y_2\dots Q_ky_k\mbox{ }\phi(y_1, \dots, y_k)$, where $\phi(y_1, \dots, y_k)$ is boolean predicate with each $y_i$ a vector of variables, $Q_{2j-1} = \forall$ and $Q_{2j} = \exists$ at every $j\in\mathbb N$, is $\varphi$ valid... |
Eigenvector
A vector which has the property that its product with A is the same as its product with a scalar quantity known as its eigenvalue. This follows the form(1)
To find said eigenvector, one must subtract $\lambda\vec{x}$ from both sides after multiplying the right side of the equation by the identity matrix (es... |
proof: pair up people from different sets; no pair from same set
imagine you have people from different groups and you would like to pair them up so that no pair is constituted by people of the same group. i've spent a couple of minutes simulating different possibilities and have come to the conclusion that it is alway... |
Skills to Develop
Predict the acidity of a salt solution. Calculate the pH of a salt solution. Calculate the concentrations of various ions in a salt solution. Explain hydrolysis reactions.
A salt is formed between the reaction of an acid and a base. Usually, a neutral salt is formed when a strong acid and a strong bas... |
Bayesian inference for state-space models¶ Defining a prior distribution¶
We have already seen that module
particles.distributions defines various
ProbDist objects; i.e. objects that represent probability distribution. Such objects have methods to simulate random variates, compute the log-density, and so on.
This modul... |
NTS ABSTRACTSpring2019
Return to [1]
Contents Jan 23
Yunqing Tang Feb 1
Yunqing Tang The diophantine exponent of the $\mathbb{Z}/q\mathbb{Z}$ points of $S^{d-2}\subset S^d$ Abstract: Assume a polynomial-time algorithm for factoring integers, Conjecture~\ref{conj}, $d\geq 3,$ and $q$ and $p$ prime numbers, where $p\leq ... |
Since $M$ is finitely generated, let $x_1, \dots, x_n$ be generators of $M$.Similarly, let $z_1, \dots, z_m$ be generators of $M^{\prime\prime}$.
The exactness of the sequence (*) yields that the homomorphism $g:M’\to M^{\prime\prime}$ is surjective.Thus, there exist $y_1, \dots, y_m\in M’$ such that\[g(y_i)=z_i\]for $... |
Find an Orthonormal Basis of the Range of a Linear Transformation Problem 478
Let $T:\R^2 \to \R^3$ be a linear transformation given by
\[T\left(\, \begin{bmatrix} x_1 \\ x_2 \end{bmatrix} \,\right) = \begin{bmatrix} x_1-x_2 \\ x_2 \\ x_1+ x_2 \end{bmatrix}.\] Find an orthonormal basis of the range of $T$.
(
The Ohio S... |
Spherical Harmonics are a group of functions used in math and the physical sciences to solve problems in disciplines including geometry, partial differential equations, and group theory. The general, normalized Spherical Harmonic is depicted below:
\[ Y_{l}^{m}(\theta,\phi) = \sqrt{ \dfrac{(2l + 1)(l - |m|)!}{4\pi (l +... |
Conditioning is the soul of statistics.
—Joe Blitzstein
We often need to account for multiple pieces of evidence. More than one witness testifies about the colour of a taxicab; more than one person responds to our poll about an upcoming election; etc.
How do we a calculate conditional probability when there are multipl... |
(1)
Orthogonal Two vectors are orthogonal if their dot product is equal to zero by the relationship
If two vectors are orthogonal (90 degrees or $\frac{\pi}{2}$ rads), $\cos{\theta}=0$.
Unit Vector A vector of magnitude 1. This is often denoted as $\hat{v}$. In fact, in physics, this is where we get the symbols $\hat{i... |
Although machine learning is great for shape classification, for shape recognition, we must still use the old methods. Methods such as Hough Transform, and RANSAC.
In this post, we’ll look into using Hough Transform for recognizing straight lines. The following is taken from E. R. Davies’ book,
Computer Vision: Princip... |
Sylow’s Theorem (Summary)
In this post we review Sylow’s theorem and as an example we solve the following problem.
Problem 64
Show that a group of order $200$ has a normal Sylow $5$-subgroup.
Add to solve later
Contents
Review of Sylow’s Theorem
One of the important theorems in group theory is Sylow’s theorem.
Sylow’s ... |
Since $I_1+I_2=R$, there exists $a \in I_1$ and $b \in I_2$ such that\[a+b=1.\]Then we have\begin{align*}1&=1^{m+n-1}=(a+b)^{m+n-1}\\[6pt]&=\sum_{k=1}^{m+n-1}\begin{pmatrix}m+n-1 \\k\end{pmatrix}a^k b^{m+n-1-k}\\[6pt]&=\sum_{k=1}^{m-1}\begin{pmatrix}m+n-1 \\k\end{pmatrix}a^k b^{m+n-1-k}+\sum_{k=m}^{m+n-1}\begin{pmatrix... |
Authors:
Ashraf Karamzadeh, Hamid Reza Maimani, Ali Zaeembashi
Keywords:
Domination, Signed Italian Dominating Function, Signed Italian Domination Number.
Abstract
A signed Italian dominating function on a graph $G=(V,E)$ is a function $f:V\to \{ -1, 1, 2 \}$ satisfying the condition that for every vertex $u$, $f[u]\ge... |
Measuring distance is an important task for many applications like preprocessing, clustering or classification of data. In general, the distance between two points can be calculated as\begin{equation} \label{eq:EuclideanStandardizationMahalanobis_Distance} \operatorname{d}(\fvec{x}, \fvec{y}) = \sqrt{\left( \fvec{x} - ... |
As Diwali approaches, we have learned to worry about air quality. Over the last few years, several studies have noted the increase in pollution levels during the period of Diwali owing to increase in commercial activity and firework displays. However, as we show in our previous article, there is considerable variation ... |
Problem Set 13
This is to be completed by February 1st, 2018.
Exercises Datacamp
* Complete the lesson:
a. Python Data Science Toolbox (Part II)
For a logistic regressor (multiclass ending in softmax) write down the update rules for gradient descent.
For a two layer perceptron ending in softmax with intermediate relu n... |
The chances of crashing your car are pretty low, but they’re considerably higher if you’re drunk. Probabilities change depending on the conditions.
We symbolize this idea by writing \(\p(A \given B)\), the probability that \(A\) is true
given that \(B\) is true. And we call this kind of probability . conditional probab... |
Sometimes it is desired to derive attributes for an arbitrary position based on the attributes of some known points. Imagine for example a triangle where each of the three base points has its own colour and you want to derive the colour of any other position in the grid. In such cases, barycentric coordinates are usefu... |
Shortest and straightest geodesics in sub-Riemannian geometry
Starts: 15:00 10 May 2019 Ends: 16:00 10 May 2019 What is it: Seminar Organiser: Department of Mathematics Who is it for: University staff, External researchers, Adults, Alumni, Current University students Speaker: Professor Dmitri Alekseevsky
Join us for th... |
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The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
An eigenvalue semiclassical problem for the Schrödinger operator with an electrostatic field
DOI: http://dx.doi.org/10.12775/TMNA.2006.006
Abstract
We consider the following system of Schrödinger-Maxwell
equations in the unit ball $B_1$ of ${\mathbb R}^3$ $$ -\frac{\hbar^2}{2m}\Delta v+ e\phi v=\omega v, \quad -\Delta\... |
Positive integers $\displaystyle a, b$ are both relatively prime and less than or equal to 2008. $\displaystyle a^2 + b^2$ is a perfect square.$\displaystyle b$ has the same digits as $\displaystyle a$ in the reverse order. The number of such ordered pairs $\displaystyle (a, b)$ is _________ .
I started with 2 digits:L... |
We say that a group $G$ is
residually finite if for each $g\in G$ that is not equal to the identity of $G$, there exists a finite group $F$ and a group homomorphism $$\varphi:G\to F$$ such that $\varphi(g)$ is not the identity of $F$.
The definition does not change if we require that $\varphi$ be surjective. Therefore,... |
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 ... |
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1. Search for heavy ZZ resonances in the ℓ + ℓ - ℓ + ℓ - and ℓ + ℓ - vv - final states using proton–proton collisions at √s=13 TeV with the ATLAS detector
European Physic... |
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The ATLAS detector as installed in its experimental cavern at point 1 at CERN is described in this paper. A brief ... |
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... |
Computational Aerodynamics Questions & Answers
I'm glad to hear that. Because your post may help others, I'll give you 2 points bonus boost.
I corrected it.
Both the integral form and the differential form can be used in CFD. But we can derive the integral form by integrating the differential form over a volume.. We'll... |
From the relation (1), we have\[xy^2x^{-1}=y^3.\]Computing the power of $n$ of this equality yields that\[xy^{2n}x^{-1}= y^{3n} \tag{3}\]for any $n\in \N$.
In particular, we have\[xy^4x^{-1}=y^6 \text{ and } xy^6x^{-1}=y^9.\]Substituting the former into the latter, we obtain\[x^2y^4x^{-2}=y^9. \tag{4}\]Cubing both side... |
Note that since $n>2$, the primitive $n$-th root $\zeta$ is not a real number.Also, we have\begin{align*}\zeta+\zeta^{-1}=2\cos(2\pi /n),\end{align*}which is a real number.
Thus the field $\Q(\zeta+\zeta^{-1})$ is real.Therefore the degree of the extension satisfies\[ [\Q(\zeta):\Q(\zeta+\zeta^{-1})] \geq 2.\]
We actua... |
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 ... |
Let $G$ be a connected (strongly connected) graph (digraph).
Assume that the minimal vertex degree (in/out degrees) of the graph is $\delta$ (are $\delta^-,\delta^+$).
What is the maximal diameter possible for such graph?
For example, if $\delta \geq \frac {n}{2}$ ($\delta^- + \delta^+ \geq n-1)$, then the graph is of ... |
Global weak solution to the quantum Navier-Stokes-Landau-Lifshitz equations with density-dependent viscosity
1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China
2.
Institute of Applied Physics and Computational Mathematics, China Academy of Engineering Physics, Beijing, 1000... |
In this article, we will learn about successive percentage change, it deals with two or more percentage changes in a quantity consecutively.
Therefore, she must visit outlet offering a discount of 60% + 40%. Why this isn’t the simple addition of two percentage changes? Successive Percentage Change:If there are percenta... |
Prove that $\F_3[x]/(x^2+1)$ is a Field and Find the Inverse Elements Problem 529
Let $\F_3=\Zmod{3}$ be the finite field of order $3$.
Consider the ring $\F_3[x]$ of polynomial over $\F_3$ and its ideal $I=(x^2+1)$ generated by $x^2+1\in \F_3[x]$. (a) Prove that the quotient ring $\F_3[x]/(x^2+1)$ is a field. How many... |
Suppose that we have\[\phi(m)=0.\]Then we have $2m=0$, and hence $m=0$.It follows that the group homomorphism $\phi$ is injective.
(c) Prove that there does not exist a group homomorphism $\psi:B \to A$ such that $\psi \circ \phi=\id_A$.
Seeking a contradiction, assume that there exists a group homomorphism $\psi:B \to... |
Self-focusing Multibump Standing Waves in Expanding Waveguides
Article
First Online:
93 Downloads Citations Abstract
Let
Mbe a smooth k-dimensional closed submanifold of \({\mathbb{R}^N, N \geq 2}\), and let Ω be the open tubular neighborhood of radius 1 of the expanded manifold \({M_R := \{R_x : x \in M\}}\). For R Rs... |
Let $ p(t) = \Sigma_{k=1}^n c_k e^{i \lambda_k t}$ be an exponential polynomial.
In the paper "Local estimates for exponential polynomials and their applications to inequalities of the uncertainty principle type" http://www.math.msu.edu/~fedja/Published/paper.ps Nazarov proves an estimate on the maximum value attained ... |
Although machine learning is great for shape classification, for shape recognition, we must still use the old methods. Methods such as Hough Transform, and RANSAC.
In this post, we’ll look into using Hough Transform for recognizing straight lines. The following is taken from E. R. Davies’ book,
Computer Vision: Princip... |
Article Higher order concentration of measure
We study sharpened forms of the concentration of measure phenomenon typically centered at stochastic expansions of order d-1 for any d \in N. The bounds are based on dth order derivatives or difference operators. In particular, we consider deviations of functions of indepen... |
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Search for top squark pair production in final states with one isolated lepton, jets, and missing transverse momentum in √s = 8 TeV pp collisions with the ATLAS detector
(Springer, 2014-11)
The results of a search for top squark (stop) pair production in final states with one isolate... |
The Annals of Statistics Ann. Statist. Volume 11, Number 1 (1983), 104-113. The Generalised Problem of the Nile: Robust Confidence Sets for Parametric Functions Abstract
The pivotal model is described and applied to the estimation of parametric functions $\phi(\theta)$. This leads to equations of the form $H(x; \theta)... |
Illinois Journal of Mathematics Illinois J. Math. Volume 59, Number 3 (2015), 801-817. A note on reduced and von Neumann algebraic free wreath products Abstract
We study operator algebraic properties of the reduced and von Neumann algebraic versions of the free wreath products $\mathbb{G}\wr_{*}S_{N}^{+}$, where $\math... |
Recall that a group $G$ is said to be solvable if $G$ has a subnormal series\[\{e\}=G_0 \triangleleft G_1 \triangleleft G_2 \triangleleft \cdots \triangleleft G_n=G\]such that the factor groups $G_i/G_{i-1}$ are all abelian groups for $i=1,2,\dots, n$.
Proof.
Since $18=2\cdot 3^2$, the number $n_3$ of Sylow $3$-subgrou... |
Quiz 12. Find Eigenvalues and their Algebraic and Geometric Multiplicities Problem 376 (a) Let \[A=\begin{bmatrix} 0 & 0 & 0 & 0 \\ 1 &1 & 1 & 1 \\ 0 & 0 & 0 & 0 \\ 1 & 1 & 1 & 1 \end{bmatrix}.\] Find the eigenvalues of the matrix $A$. Also give the algebraic multiplicity of each eigenvalue. (b) Let \[A=\begin{bmatrix}... |
Computational Aerodynamics Questions & Answers
I'm glad to hear that. Because your post may help others, I'll give you 2 points bonus boost.
I corrected it.
Both the integral form and the differential form can be used in CFD. But we can derive the integral form by integrating the differential form over a volume.. We'll... |
Hello all,
I have a multi-stage stochastic problem and I am employing multi-cut Benders decomposition to solve it. The objective function is that of a typical planning problem, essentially the summation of expected investment and operation cost across all scenario tree nodes. A node-variable formulation of the non-deco... |
Simulation Tools for Solving Wave Electromagnetics Problems
When solving wave electromagnetics problems with either the RF or Wave Optics modules, we use the finite element method to solve the governing Maxwell’s equations. In this blog post, we will look at the various modeling, meshing, solving, and postprocessing op... |
In this chapter we’ll introduce the last few concepts we need from deductive logic, and we’ll learn a useful technique in the process: truth tables.
Complex propositions can be built up out of other, simpler propositions:
Notice, we call
it’s not true that a connective even though it doesn’t actually connect two propos... |
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... |
Ground states of nonlinear Schrödinger systems with periodic or non-periodic potentials
1.
School of Mathematics and Statistics, Central South University, Changsha, 410083 Hunan, China
2.
School of Traffic and Transportation Engineering, Central South University, Changsha, 410075 Hunan, China
In this paper we study a c... |
Mathematics About the Number 2017
Happy New Year 2017!!
Here is the list of mathematical facts about
the number 2017 that you can brag about to your friends or family as a math geek.
Contents
2017 is a prime number
Of course, I start with the fact that
the number 2017 is a prime number.
The previous prime year was
2011... |
Difference between revisions of "Algebra and Algebraic Geometry Seminar Spring 2018"
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[[Algebra and Algebraic Geometry Seminar Fall 2018 | Fall 2018 schedule]]
[[Algebra and Algebraic Geometry Seminar Fall 2018 | Fall 2018 schedule]]
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[[
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[[Spring 2018 ]]
== Spring 2018 Sche... |
A commutative ring $R$ is called a principal ideal domain (PID) if every ideal of $R$ can be generated by a single element. If $R$ is a principal ideal domain, is every subring of $R$ a principal ideal domain? No, definitely not. That is because you can take any integral domain that is not a […]
An associative ring $R$... |
Matching Digit Sums Problem 676
Let $d(i,b)$ be the
digit sum of the number $i$ in base $b$. For example $d(9,2)=2$, since $9=1001_2$.When using different bases, the respective digit sums most of the time deviate from each other, for example $d(9,4)=3 \ne d(9,2)$.
However, for some numbers $i$ there will be a match, li... |
We give an example of a group of infinite order each of whose elements has a finite order.Consider the group of rational numbers $\Q$ and its subgroup $\Z$.The quotient group $\Q/\Z$ will serve as an example as we verify below.
Note that each element of $\Q/\Z$ is of the form\[\frac{m}{n}+\Z,\]where $m$ and $n$ are int... |
This is a very quick introduction to Galois descent for schemes defined over fields. It is a very special case of faithfully flat descent and other topos-descent theorems, which I won't go into at all. Typically, if you look up descent in an algebraic geometry text you will quickly run into all sorts of diagrams […]
Th... |
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... |
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... |
שלח תגובה
3 הודעות • דף
1מתוך 1
\(\langle M \rangle = \beta N m^2 H\)
\(\sigma = N\ln 2 -\frac{1}{2}N\left(\beta m H\right)^2\) \(d\sigma = 0\Rightarrow \sigma = \text{const}\) In \(\sigma\) - \(N,m\) and \(2\) are constants trivially. So if \(\sigma\) is constant (adiabatic), it means that \(\beta H\) is too. But also... |
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