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Reversing a matrix
Ok I think this should be easy, if I can explain it properly.
Let's say I had a 2*2 matrix = matrix A
And I was multiplying it 2*1 matrix = matrix B
And it would produce a 2*1 matrix = matrix C
Right?
But let's say - I want to go back ways, reverse it...
I have Matrix C and I have Matrix A but I need... |
2.2 Libraries and Clients Each program that you have written consists of Java code that resides in a single
.java file.For large programs, keeping all the code in a single file is restrictive and unnecessary.Fortunately, it is very easy in Java to refer to a method inone file that is defined in another.This ability has... |
If $[$.$]$ denotes the greatest integer function, then find the value of $\lim_{n \to \infty} \frac{[x] + [2x] + [3x] + … + [nx]}{n^2}$
What I did was, I wrote each greatest integer function $[x]$ as $x - \{x\}$, where $\{.\}$ is the fractional part. Hence, you get
$\lim_{n \to \infty} \frac{\frac{n(n+1)}{2}(x-\{x\})}{... |
OpenCV 3.0.0
Open Source Computer Vision
class cv::ConjGradSolver This class is used to perform the non-linear non-constrained minimization of a function with known gradient,. More... class cv::DownhillSolver This class is used to perform the non-linear non-constrained minimization of a function,. More... class cv::Min... |
Answer to the title question:
absolutely not. Experimental Touchstone
Before we explain in detail, let's begin by noticing that the Michelson-Morley interferometric experiment
explicitly tests if orientation affects the clocking behavior of a there-and-back light path. And quite famously the answer is "no". This must b... |
The beth numbers, $\beth_\alpha$
The
beth numbers $\beth_\alpha$ are defined by transfinite recursion: $\beth_0=\aleph_0$ $\beth_{\alpha+1}=2^{\beth_\alpha}$ $\beth_\lambda=\sup_{\alpha\lt\lambda}\beth_\alpha$, for limit ordinals $\lambda$
Thus, the beth numbers are the cardinalities arising from iterating the power se... |
I have been trying to prove that the two definitions of $\limsup$ are equivalent.
I would appreciate it if someone could verify my attempt! Thanks in advance!
Here are the two definitions:
For any bounded sequence $(x_n)$, $\displaystyle \limsup_{n\to\infty} x_n$ is defined to be $\displaystyle\limsup_{n\to\infty}x_n\c... |
Consider the following linear model under classical Gauss-Markov assumtions: $$Y = X\beta + e$$ where $\mathbb{E}X'e = 0$
Consider the following estimator $$\tilde\beta = \left(\sum_{i=1}^{N}x_ix_i' + \lambda I_k\right)^{-1}\left(\sum_{i+1}^Nx_iy_i\right)$$ where $x_i$ is a column vector $k\times1$ from $X$ and $\lambd... |
Foundations (Energy Balance) For the Room
Consider the system shown in the picture below. Air flows through a room volume (area and height) with a residence time. Heat is provided by people inside the room.
The steady state energy balance equation becomes
$$\dot{m}_a\left( \tilde{H}_{a,out} - \tilde{H}_{a,in} \right) =... |
$\textsf{DWCDM+}$: A BBB secure nonce based MAC
1.
Indian Statistical Institute, Kolkata, India
2.
NTT Secure Platform Laboratories, NTT Corporation, Japan
$\textsf{EWCDM}$
$n$
$\textsf{E}$
$n$
$\textsf{H}$
$\textsf{E}_{K_2}\bigl(\textsf{E}_{K_1}(N)\oplus N\oplus \textsf{H}_{K_h}(M)\bigr),$
$N$
$M$
$2n/3$
$\textsf{DWCD... |
In this MathStackExchange post the question in the title was asked without much outcome, I feel.
Edit: As Douglas Zare kindly observes, there is one more answer in MathStackExchange now.
I am not used to basic Probability, and I am trying to prepare a class that I need to teach this year. I feel I am unable to motivate... |
Home
Integration by PartsIntegration by Parts
Examples
Integration by Parts with a definite integral
Going in Circles
Tricks of the Trade
Integrals of Trig FunctionsAntiderivatives of Basic Trigonometric Functions
Product of Sines and Cosines (mixed even and odd powers or only odd powers)
Product of Sines and Cosines (... |
We discussed this topic in previous posts:
Graph theory: connections in the market. To understand what a graph is and the elements it has. World connections using financial indexes. In this other post, you can learn how to create a graph using the correlation matrix between financial indexes from different countries of... |
From
Statistical Physics, 2nd Edition by F. Mandl:
Two vessels contain the same number $N$ molecules of the same perfect gas. Initially the two vessels are isolated from each other, the gases being at the same temperature $T$ but at different pressures $P_1$ and $P_2$. The partition separating the two gases is removed.... |
I grasp this answer, except for one identity. To quote: "$\sum_{d\mid n}\left[\Phi_d(X)\right]_{-1} = \left[\prod_{d\mid n} \Phi_d(X)\right]_{-1}$"
It isn't so simple i think because you don't take the coefficients corresponding to the same place/x-power. What is my misunderstanding?
Update: I simply had missed reading... |
Analisi, algebra lineare, topologia, gruppi, anelli, campi, ...
Rispondi
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How do you prove this $\displaystyle z\cot \left(z\right)=1-2\sum _{k=1}^{\infty}\frac{z^2}{k^2\pi ^2-z^2}$ ?
i’ve seen this formula on a document about Bernoulli’s numbers and their relations with Riemann’s zeta function... |
Let's start with the energy-momentum equation:$$E^2=p^2c^2+(m_0c^2)^2\tag{1}$$This can be derived according to the Minkowski metric. This works because the inner product of the four-momentum, $\langle\mathbf{P},\mathbf{P}\rangle$, is equal to $|\mathbf{P}|^2=-(m_0c)^2$. We can also use $$\langle\mathbf{P},\mathbf{P}\ra... |
This post contains the notes taken from reading of the following paper:
I was also helped by the slides of Stanford’s CS231b.
Fast-RCNN was the state-of-the-art algorithm for object detection in 2015; itsobject proposal used Selective Search that itself used Efficient Graph-BasedSegmentation.
The reason this segmentati... |
I'm not the person to understand everything in
Geometric Endoscopy and Mirror Symmetry, but some parts of it are reasonably clear to me.
In particular, one of the main objects, mathematically speaking, is the category of coherent sheaves on an orbifold point $\mathrm{pt}/\Gamma$, where $\Gamma$ is a finite group of aut... |
Suppose that $A$ has discrete spectrum consisting of eigenvalues with finite multiplicities
$$ 0<\lambda_1 < \lambda_2<\cdots $$
with $\lambda_n\to\infty$ as $n\to \infty$. Denote by $(\psi_n)$ an orthonormal basis consisting of e-vectors of $A$. In this basis $A$ is an (infinite) diagonal matrix $\DeclareMathOperator{... |
Home
Integration by PartsIntegration by Parts
Examples
Integration by Parts with a definite integral
Going in Circles
Tricks of the Trade
Integrals of Trig FunctionsAntiderivatives of Basic Trigonometric Functions
Product of Sines and Cosines (mixed even and odd powers or only odd powers)
Product of Sines and Cosines (... |
Research Open Access Published: Optimal control problem for a generalized sixth order Cahn-Hilliard type equation with nonlinear diffusion Boundary Value Problems volume 2015, Article number: 58 (2015) Article metrics
1631 Accesses
Abstract
In this paper, we study the initial-boundary-value problem for a generalized si... |
This has been asked several times already, I am just too bored to look for duplicates.
In general, for $x,y \in \Bbb C$, one defines $x^y$ as $\Bbb e ^{y \ln x}$. Of course, one has to tell what the natural logarithm means for complex numbers. The usual procedure is to eliminate a half-line from the complex plane, in o... |
The question is related to the question: detecting weak equivalences in a simplicial model category
Suppose that we have a simplicial model category $M$ and denote by $M^{f}$ the full simplicial subcategory of fibrant objects. Suppose that $R$ is a subcategory of $M^{f}$ such that for any object $m\in M^{f}$ there exis... |
The object you're talking about is called, in mathematics, a Clifford algebra. The case when the algebra is over the complex field in general has a significantly different structure from the case when the algebra is over the real field, which is important in Physics.
In Physics, in the specific case of 4 dimensions, us... |
Astrid the astronaut is floating in a grid. Each time she pushes off she keeps gliding until she collides with a solid wall, marked by a thicker line. From such a wall she can propel herself either parallel or perpendicular to the wall, but always travelling directly \(\leftarrow, \rightarrow, \uparrow, \downarrow\). F... |
Let's count the number of ways
not to get $7$ heads in a row. We will put together atoms that consist of $0$ to $6$ heads followed by a tail. Any arrangement of heads and tails without $7$ heads in a row, appended with a tail, can be uniquely made up of a number of such atoms.
All arrangements of such atoms appear once... |
Let $\Phi: R^n \to R^n$ satisfy
$\Phi(x)=u+Ax+Q(x)$, with $x=(x_1, x_2,\ldots, x_n) \in R^n$. $u$ is a given positive vector, $A$ non negative matrix, and $Q(x)$ quadratic mapping with
$Q(x)_i=x_i(k_{i1}x_1+k_{i2}x_2+\ldots+k_{in}x_n)$, where all the $k_{ij}$ are nonnegative and at least one $k_{ij}, 1 \leq i, j \leq n... |
I'm afraid that a thorough answer requires the contents of chapters 2 and 3 of Leishman, but here is an outline. The relationship between power and true airspeed from this answer:
Power equals torque times angular velocity of the rotor: $ P = Q * \Omega$. Most helicopters have constant speed rotors, so the relationship... |
Power quality is related to the quality of power being supplied or consumed. It is maintained when:
EB can assure power quality from their side only when its consumers do meet certain power quality standards (such as, IEEE 519-1992 and/or IEEE 519-2014). Recently, several EBs across the globe have started imposing stri... |
With the approaching hurricane, I am curious about what would happen if I go outside, in particular whether the wind gusts might be fast enough to blow me away. How fast would the wind have to be to blow away a person?
Let's do math before we look for information. First, what is the force that keeps you anchored to the... |
The compression of the air outside the cylinder by the $\ce{N2}$ escaping from the cylinder takes place reversibly (as far as the air is concerned), but the process of $\ce{N2}$ leaking out of the cylinder through a valve or small orifice is definitely irreversible because of the Joule–Thompson throttling that takes pl... |
Given matrix $A = \begin{bmatrix} -3 & 2 \\ 0 & -3 \end{bmatrix}$ The eigenvalues of $A$ are $\lambda_{1,2} = -3$ with algebraic multiplicity 2. Now to find the eigenvector, we use Gaussian elimination as follows
$$ \quad (A-\lambda I | 0) \Rightarrow \left( \begin{array}{cc|c} 0 & 2 & 0 \\ 0 & 0 & 0 \end{array} \right... |
Let $u: \Omega\subset \mathbb{R}^N \to \mathbb{R}^M$ be a $BV$ function.
Is the Hausdorff dimension of the graph of $u$ equal to $N$? How can we prove it?
Update.
In an answer to this post, it has been showed that there exist a representative $\tilde u$ of $u$ such that its graph has Hausdorff dimension equal to $N$.
I... |
Research Open Access Published: Stability and Hopf bifurcation of a predator-prey model Boundary Value Problems volume 2019, Article number: 129 (2019) Article metrics
366 Accesses
Abstract
In this paper, we study a class of predator-prey model with Holling-II functional response. Firstly, by using linearization method... |
While I know this question has already been answered, I felt obligated to get around to writing a formal answer. I will not go into detail about irreversible/dissipative systems, as Arnold Neumaier's answer already addressed that issue. Rather, my answer will focus on the mathematics behind ergodicity and mixing.
Note:... |
Let $\mathbb F_q$ be a finite field, $C$ a curve over $\mathbb F_q$ of genus $g\geq 2$, $\rho: \pi_1(C) \to GL_2(\overline{\mathbb Q}_\ell)$ an irreducible local system. The geometric Langlands correspondence constructs a geometrically irreducible Hecke eigensheaf on $Bun_2(C)$ associated to $\rho$, which is a perverse... |
Science Advisor
Homework Helper
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Part 1 of (9)
##\phi: R \to S## is a ring epimorphism. Define ##I:= \phi^{-1}(J)##. It is well known that the inverse image of an ideal is an ideal, thus ##I## is an ideal.
Define ##\psi: R/I \to S/J: [r] \mapsto [\phi(r)]## This is well defined: If ##r \in I##, then ##\phi(r) ... |
Model
A
model of a theory $T$ is a set $M$ together with relations (eg. two: $a$ and $b$) satisfying all axioms of the theory $T$. Symbolically $\langle M, a, b \rangle \models T$. According to the Gödel completeness theorem, in $\mathrm{PA}$ (Peano arithmetic) (so also in $\mathrm{ZFC}$) a theory has models iff it is ... |
The problem is to determine whether the given differential operator $L[y]$, whose domain consists of all functions that have continuous second derivatives on the interval $[0,\pi]$ and satisfy the given boundary conditions, is selfadjoint.
$$L[y]=y''+\lambda y;\;\;\;\;y(0)+y'(\pi)=0,\;\;\;\;y'(0)+y(\pi)=0$$
For an oper... |
You call to someone's house and asked if they have two children. The answer happens to be yes. Then you ask if one of their children's name a William. The answer happens to be yes again.(We assume William is a boy's name, and that it's possible that both children are Williams) What's the probability that the second chi... |
How can the following expression be simplified:
Log[ Sqrt[ (m/(2*Pi*k*T)^3) *4*Pi*v^2 ] * Exp[ -(m*v^2 / (2*k*T)) ]]
I would like to get the result:
Log[ Sqrt[ (m/(2*Pi*k*T)^3) *4*Pi*v^2 ] ] - (m*v^2 / (2*k*T))
Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. It only takes a mi... |
Suppose you are calling someone from another part of the world and the person asks you "how is the weather there?". You answer promptly: "it's really nice today: $75^\circ\textrm{F}$", only to hear the confused reply "wait, what's that in Celsius?". Oops, what should you do now?
If you ever learned to convert temperatu... |
Geometry and Topology Seminar Contents 1 Fall 2013 2 Fall Abstracts 3 Spring 2014 4 Spring Abstracts 5 Archive of past Geometry seminars Fall 2013
date speaker title host(s) September 6 September 13, 10:00 AM in 901! Alex Zupan (Texas) Totally geodesic subgraphs of the pants graph Kent September 20 September 27 October... |
Maybe I misunderstood the question, but what you are describing sounds like a test-retest reliability study on your Q scores. You have a series of experts each going to assess a number of items or questions, at two occasions (presumably fixed in time). So, basically you can assess the temporal stability of the judgment... |
$\exists j:L(V_{\lambda+1})\to L(V_{\lambda+1})$ See first: rank into rank axioms
The axiom
I0, the large cardinal axiom of the title, asserts that some nontrivial elementary embedding $j:V_{\lambda+1}\to V_{\lambda+1}$ extends to a nontrivial elementary embedding $j:L(V_{\lambda+1})\to L(V_{\lambda+1})$, where $L(V_{\... |
Geometry and Topology Seminar Contents 1 Fall 2013 2 Fall Abstracts 3 Spring 2014 4 Spring Abstracts 5 Archive of past Geometry seminars Fall 2013
date speaker title host(s) September 6 September 13, 10:00 AM in 901! Alex Zupan (Texas) Totally geodesic subgraphs of the pants graph Kent September 20 September 27 October... |
Home
Integration by PartsIntegration by Parts
Examples
Integration by Parts with a definite integral
Going in Circles
Tricks of the Trade
Integrals of Trig FunctionsAntiderivatives of Basic Trigonometric Functions
Product of Sines and Cosines (mixed even and odd powers or only odd powers)
Product of Sines and Cosines (... |
Kakeya problem
Define a
Kakeya set to be a subset [math]A\subset{\mathbb F}_3^n[/math] that contains an algebraic line in every direction; that is, for every [math]d\in{\mathbb F}_3^n[/math], there exists [math]a\in{\mathbb F}_3^n[/math] such that [math]a,a+d,a+2d[/math] all lie in [math]A[/math]. Let [math]k_n[/math] ... |
I was wondering if there is a way to write the derivative as an exponential? This might sound crazy at first, but I recently came across this formula for the Taylor expansion in three dimensions:
$$\phi(\vec{x}+\vec{a})=\sum_{n=0}^{\infty}\frac{(\vec{a}\cdotp\vec{\nabla_{x}})^{n}}{n!}\Phi(\vec{x})=e^{\vec{a}\cdotp\vec{... |
I do not think so.
Observation: Without loss of generality, $p(x)$ can be taken to be monic (constant multiples won't affect either $p(A) = 0$ or boundedness).
Case 1: $p$ is degree $2$.
By the above reduction, $p(x) = (x - \lambda)(x - \mu)$ for some $\lambda$ and $\mu$ in $\mathbb{C}$ (since $A$ clearly commutes with... |
Let $x_{k+1} = \frac{x_k^{d_k}+1}{x_{k-1}}$, $k \in \mathbb{Z}$, where $d_{k+2} = d_k \in \mathbb{Z_{>0}}$. Let $b=d_1$ and $c=d_2$. Define the cluster algebra $A = A(\left( \begin{matrix} 0 & b \\ -c & 0 \end{matrix} \right))$ to be the algebra generated by all $x_k$. Is the following set $B$ a totally positive basis ... |
$3\Rightarrow 2$: Suppose $X$ is a collection of nonempty sets, then $f:P(\bigcup X)\setminus\{\varnothing\}\to\bigcup X$ exists which chooses from every nonempty subset of $\bigcup X$. If we restrict $f$ to the set $X$ then we have a choice function.
$2\Rightarrow 3$: Trivial, if every non-empty collection of non-empt... |
The power law function for gamma-ray burst is defined for amplitude ($A$), energy ($E$), pivot energy ($E_{piv}$) (fixed) and index $\lambda$ as
$ f(E; A, \lambda) = N(E) = A*\left(\dfrac{E}{E_{piv}}\right)^\lambda $
Where we use a range of energy for model fitting of GRB. The fitting gives us a single value for all va... |
A recent video by 3Blue1Brown (previously seen generating Pi from bouncing blocks) introduced me to an interesting problem from the 2011 International Mathematical Olympiad. The problem (described below) describes a windmill process where a line rotates through a cloud of points, switching pivots whenever it hits a new... |
Based on Lorentz factor $\gamma = \frac{1}{\sqrt {1-\frac{v^2}{c^2}}}$ it is easy to see $v < c$ since otherwise $\gamma$ would be either undefined or a complex number, which is non-physical. Also, as far as I understand this equation was known before Einstein's postulates were published. My question is: why didn't Lor... |
Convergence of global and bounded solutions of a two-species chemotaxis model with a logistic source
College of Mathematics and Statistics, Chongqing University, Chongqing University, Chongqing 401331, China
$\left\{\begin{array}{llll}u_t=\Delta u-\chi_1\nabla\cdot( u\nabla w)+\mu_1u(1-u-a_1v),\quad &x\in \Omega,\quad ... |
Morley's Miracle
In 1899, more than a hundred years ago, Frank Morley, then professor of Mathematics at Haverford College, came across a result so surprising that it entered mathematical folklore under the name of
Morley's Miracle. Morley's marvelous theorem states that
The three points of intersection of the adjacent ... |
I just want to add something to the correct @annav answer, with a practical example in basic Quantum Field Theory. Imagine a particle process with $2$ initial particles and $2$ final particles, you have some initial state (say at t= $-\infty$), which is $|i\rangle =|1\rangle |2\rangle$, where $|1\rangle$ and $|2\rangle... |
What Is Area? What Is Area Elementary Introduction into the Concept of Area Equidecomposition of a Triangle and a Rectangle: first variant Pick's Theorem Area of a Circle by Rabbi Abraham bar Hiyya Hanasi Area of a Circle by Leonardo da Vinci Volume and Area of Torricelli's Trumpet Area, as many other mathematical conc... |
I have to admit, I am not familiar with the use of $\mathscr{O}\left[\lambda^{n}\right]$ notation. Apparently it doesn't mean what I thought.
In John L. Friedman's lecture notes on Lie derivatives, forms, densities, and integration
He writes:
A vector field $\mathbf{w}$ is
Lie-derivedby $\mathbf{v}$ if, for small $\lam... |
In the Frobenius Coin problem (or Chicken McNugget theorem) for $n>2$, do the numbers have to be
pairwise relatively prime, or just relatively prime in totality?
They$\let\geq\geqslant\let\leq\leqslant$ need not be
pairwise relatively prime. The reason why is essentially that Bézout's theorem works fine when we are onl... |
I'm curious if there is a known asymptotic scaling for the return-to-origin (i.e. recurrence) probability for a random on $Z^d$ as a function of $d$?
Mathworld gives the recurrence probability: http://mathworld.wolfram.com/PolyasRandomWalkConstants.html
$p(d) = 1-\frac{1}{u(d)} = 1- \left(\int_{t=0}^{\infty}I_0(\frac{t... |
[Originally posted on math stackexchage but have not received feedback in over a month, I'm hoping someone here could point me in the right direction].
Consider the eigenvalue equation for the Laplace-Beltrami operator on a manifold with metric $ds^2=|K|^{-1}[d\chi^2+\sin_K^2\chi(d\theta^2+\sin^2\theta\,d\phi^2)]$, whe... |
Brazilian Journal of Probability and Statistics Braz. J. Probab. Stat. Volume 29, Number 4 (2015), 767-777. A note on space–time Hölder regularity of mild solutions to stochastic Cauchy problems in $L^{p}$-spaces Abstract
This paper revisits the Hölder regularity of mild solutions of parabolic stochastic Cauchy problem... |
Riemann-Hilbert problem, integrability and reductions
1.
Department of Applied Mathematics, National Research Nuclear University MEPHI, 31 Kashirskoe Shosse, Moscow 115409, Russian Federation
2.
Institute of Mathematics and Informatics, Bulgarian Academy of Sciences, 8 Acad. G. Bonchev Street, Sofia 1113, Bulgaria
3.
S... |
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If f(x)=(9log2(3−2x)−1)13f(x)=(\dfrac{9}{\log_{2}(3-2x)}-1)^{\frac{1}{3}}f(x)=(log2(3−2x)9−1)31 , then the value of aaa which satisfies f−1(2a−4)=0.5f^{-1}(2a-4)=0.5f−1(2a−4)=0.5 , is given by
Problem Loading...
Note Loading...
Set Loading... |
For many different machine learning problems, finding a solution involves these similar steps.
Firstly, one begins with gathering input data \(x\). Secondly, work out a hypothesis (model) that maps from input to possible output \(h_{\theta}(x) = y\). \(\theta\) is trainable (adjustable) parameters of the model. Next, a... |
Indeed, in non-relativistic quantum mechanics, the equation of evolution of the quantum state is given by Schrödinger's equation and measurement of a state of particle is itself a physical process and thus, should and is indeed be governed by the Schrödinger's equation.
Indeed, people like to predict probabilities usin... |
I couldn't resist putting the sledgehammers to work that Robin Ekman alluded to, and I will try to present their general argumentation in a way one can understand without knowing all the details, but I don't intend to presume that this is in any sense a better answer, it is simply one that shows which things one must k... |
I searched about the difference between state vector and basis vector in Quantum mechanics but couldn't find any clear explanation. Can someone please give a simple and clear explanation of this?
Basis vectors are a special set of vectors that have two properties:
The vectors in the set are linearly independent (meanin... |
I am new to MCMC and reading a intro paper regarding Gibbs sampling. However, there are two parts in the paper I cannot understand and get stuck. The first part is equation 2.3 in page 168. It says that if $X^{'}_{j}$ is drawn from the process of Gibbs sampling, $X^{'}_{j}\sim f(x|Y^{'}_{j}=y^{'}_{j})$. It further clai... |
Consider electromagnetic cylindrical waves. Cylindrical waves can be derived from the plane waves using energy conservation consideration: since the power must be a constant the amplitude of a cylindrical wave must decrease with $\sqrt{r}$. Therefore a cylindrical wave expression must be
$$\mathbf{E}(r,t)=\frac{\mathbf... |
Let $X_1,X_2,...,X_n$ be a random sample from a uniform distribution on $(\mu-\sqrt 3\sigma,\mu+\sqrt3\sigma)$.
Here the unknown parameters are two, namely $\mu$ and $\sigma$, which are the population mean and standard deviation.
Find the point estimator of $\mu$ and $\sigma$.
I have tried to do that by the Method-of-M... |
To calculate an equilibrium concentration from an equilibrium constant, an understanding of the concept of equilibrium and how to write an equilibrium constant is required. Equilibrium is a state of dynamic balance where the ratio of the product and reactant concentrations is constant.
Introduction
An equilibrium const... |
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Inside an equilateral △ABC\triangle ABC △ABC lies a point OOO. It is known that ∠AOB=113∘\angle AOB=113^{\circ} ∠AOB=113∘ and ∠BOC=123∘\angle BOC=123^{\circ} ∠BOC=123∘. Find the angles of the triangle whose sides are equal to segments OA,OB,OCOA,OB,OCOA,OB,OC.
No... |
I’m going to make some assumptions in this answer:
Two moons have masses $m_1$ and $m_2$ and orbit a planet of mass $m_p$, where $m_1, m_2\ll m_p$.The planet is far enough away from the star that any gravitational/tidal effects from that star are negligible.There are no other planets capable of destabilizing any moons ... |
Let $F_0 \subset F_1 \subset F_2 \subset \cdots$ and $K_0 \subset K_1 \subset K_2 \subset \cdots$ be two towers of fields. Also, let $F = \cup_{i=0}^\infty F_i$ and $K = \cup_{i=0}^\infty K_i$.
Now suppose for each $i$ we have injective homomorphisms from $F_i$ to $K_{\sigma(i)}$ and from $K_i$ to $F_{\mu(i)}$ where $i... |
Geometry and Topology Seminar Contents 1 Fall 2013 2 Fall Abstracts 3 Spring 2014 4 Spring Abstracts 5 Archive of past Geometry seminars Fall 2013
date speaker title host(s) September 6 September 13, 10:00 AM in 901! Alex Zupan (Texas) Totally geodesic subgraphs of the pants graph Kent September 20 September 27 October... |
Epsilon naught, $\epsilon_0$ The ordinal $\epsilon_0$, commonly given the British pronunciation "epsilon naught," is the smallest ordinal $\alpha$ for which $\alpha=\omega^\alpha$ and can be equivalently characterized as the supremum
$$\epsilon_0=\sup\{\omega,\omega^\omega,\omega^{\omega^\omega},\ldots\}$$
The ordinals... |
In particle physics, scalar potentials have to be bounded from below in order for the physics to make sense. The precise expressions of checking lower bound of scalar potentials are essential, which is an analytical expression of checking copositivity and positive definiteness of tensors given by such scalar potentials... |
Although we find currency risk particularly interesting, it is not often the case with many investors for whom it is no more than a necessary inconvenience. As such, they tend to neglect it, accepting undesirable non-remunerated risks and missing potential opportunities. To prevent this, in this post we will try to pro... |
Why doesn't amplitude increase when the frequency of external periodic force increases above the natural frequency of the vibrating object?
In one sense this is a consequence of the meaning of resonance. Resonance is identified by a maximum in amplitude. If amplitude increased above (or below) the resonant frequency th... |
Assume $$X\sim \frac{e^{-\beta Nf(x)}}{Z_{\beta}}$$ where $$ f(x) = -hx -x^2 + \frac{1}{\beta N}(1-x)\ln(1-x) + (1+x)\ln(1+x) $$ and $Z_{\beta}$ is the appropriate normalization factor. The support of $X$ is the lattice $\Gamma_N = \{-1,-1+2/N,\ldots,1-2/N,1\}$ and $N$ is some large positive integer and $\beta>1$.
I wo... |
I'm reading "Microelectronics" by Millman, Grabel.
Premise:
The book developed, for a pn step-graded junction, the contact potential as $$ V_0 = V_T \text{ln} \frac{p_{p0}}{p_{n0}} = - V_T \text{ln} \frac{n_{p0}}{n_{n0}} \qquad (1) $$ where $p_{p0}$ is the hole concentration in the p-side, $p_{n0}$ is the hole concentr... |
For the full list: https://meta.stackexchange.com/a/216607/360277
Possible uses
1) Elliptic curves: I know $dG$, how can I find $d$
2) Amounts paid: Alice has $5$ dollars
3) Tables
4) Selfish mining formulae: $\sum_{k=0}^\infty\frac{\lambda^k e^{-\lambda}}{k!}\cdot\begin{cases}(q/p)^{z-k} & k \leq z\1 & k >z\end{cases}... |
I searched about the difference between state vector and basis vector in Quantum mechanics but couldn't find any clear explanation. Can someone please give a simple and clear explanation of this?
Basis vectors are a special set of vectors that have two properties:
The vectors in the set are linearly independent (meanin... |
DefinitionLet $K$ be a quadratic number field.Let $\mathcal{O}_K$ be the ring of algebraic integers in $K$.By Lemma 4 in my answer to this question, there exists a unique square-free integer $m$ such that $K = \mathbb{Q}(\sqrt m)$.
If $m \equiv 1$ (mod $4$), let $\omega = (1 + \sqrt m)/2$.
If $m \equiv 2, 3$ (mod $4$),... |
Journal of Symbolic Logic J. Symbolic Logic Volume 55, Issue 3 (1990), 1059-1089. The Interpretability Logic of Peano Arithmetic Abstract
PA is Peano arithmetic. The formula $\operatorname{Interp}_\mathrm{PA}(\alpha, \beta)$ is a formalization of the assertion that the theory $\mathrm{PA} + \alpha$ interprets the theor... |
Difference between revisions of "Group cohomology of elementary abelian group of prime-square order"
(→Over an abelian group)
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Suppose <math>p</math> is a [[prime number]]. We are interested in the [[elementary abelian ... |
You are quite right, there is no objective reason why we should restrict ourselves to canonical transformations. As a matter of fact, the Hamilton equations can be formulated in a coordinate-independent way (by coordinates I mean the coordinates on phase space, i.e. the configuration variables and conjugate momenta), s... |
Club sets and stationary sets Closed and unbounded subsets of ordinals, more commonly referred to as club sets, play a prominent role in modern set theory. We intuitively think of clubs as the "large" subsets of $\kappa$ and the stationary subsets as the "not small" subsets of $\kappa$, though this is sort of a boring ... |
7.Product and Process Comparisons
7.2. Comparisons based on data from one process
Testing proportion defective is based on the binomialdistribution The proportion of defective items in a manufacturing processcan be monitored using statistics based on the observed number ofdefectives in a random sample of size \(N\)from... |
5. Classical Reasoning¶
If we take all the rules of propositional logic we have seen so far and exclude
reductio ad absurdum, or proof by contradiction, we have what is known as intuitionistic logic. In intuitionistic logic, it is possible to view proofs in computational terms: a proof of \(A \wedge B\) is a proof of \... |
I'm trying to find the expectationvalue for $p^2$ where $p = i\sqrt{\frac{hmw}{2}}(a_{+} - a_{-})$ and i end up with the following result \begin{align*} \langle \psi_0|p^2|\psi_0\rangle &= -\frac{\hbar mw}{2}\langle\psi_0|(a_{+} - a_{-})^2|\psi_0\rangle\\ &= -\frac{\hbar mw}{2}\langle\psi_0|a_{+}^2 - a_{+}a_{-} - a_{-}... |
The "universe" is a sphere with a radius of $10^{25}$ m the medium temperature is 3K, how many photons there are in the universe?
$$n_\gamma = \int_{0}^{\infty} \frac{8h\pi\nu^3} {{c^3}{}} \frac{1} {{e^\frac{h\nu} {KT} -1}{}}d\nu = 2.4\frac{8\pi} {c^3} (\frac{KT} {h})^3 \simeq 1.64* 10^{17} photons$$
but according to p... |
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Integration by PartsIntegration by Parts
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Going in Circles
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Integrals of Trig FunctionsAntiderivatives of Basic Trigonometric Functions
Product of Sines and Cosines (mixed even and odd powers or only odd powers)
Product of Sines and Cosines (... |
Bhattacharyya, T and Mohandas, JP (2005)
Two-Parameter Uniformaly Elliptic Sturm–Liovviville Problems With Eigenparameter-Dependent Boundary Conditions. In: Proceedings of the Edinburgh Mathematical Society, 48 (3). pp. 531-547. Abstract
We consider the two-parameter Sturm–Liouville system $-y_1" + q_1y_1 = (\lambda r_... |
Complex number
A complex number is an ordered pair of real numbers. (A real number may take any value from -infinity to +infinity. Real numbers are commonly represented as points on the "real number line", i.e., a straight line of infinite length.)
The two components of a complex number (a,b) are the real part (a) and ... |
Suppose you need to generate all possible bitmasks of length $n$ with $m$ bits set, i.e., all bitmasks with $n$ bits of length having $m$ bits equal to $1$ and $(n-m)$ bits equal to $0$. For small values of $n$, the desired bitmasks can be easily hard-coded, but for general values of $n$ and $m$, this ceases to be a pr... |
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