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A commutative ring $R$ with $1\neq 0$ is called an integral domain if it has no zero divisors.That is, if $ab=0$ for $a, b \in R$, then either $a=0$ or $b=0$.
Proof.
We give two proofs.
Proof 1.
Let $r \in R$ be a nonzero element in $R$.We show that $r$ is a unit.
Consider the map $f: R\to R$ sending $x\in R$ to $f(x)=... |
LaTeX supports many worldwide languages by means of some special packages. In this article is explained how to import and use those packages to create documents in
Portuguese.
Contents
Portuguese language has some accentuated words. For this reason the preamble of your file must be modified accordingly to support these... |
Abbreviation:
BDLat
A
is a structure $\mathbf{L}=\langle L,\vee ,0,\wedge ,1\rangle $ such that bounded distributive lattice
$\langle L,\vee ,\wedge \rangle $ is a distributive lattice
$0$ is the least element: $0\leq x$
$1$ is the greatest element: $x\leq 1$
Let $\mathbf{L}$ and $\mathbf{M}$ be bounded distributive la... |
A
quantum gate or quantum logic gate is a rudimentary quantum circuit operating on a small number of qubits. They are the analogues for quantum computers to classical logic gates for conventional digital computers. Quantum logic gates are reversible, unlike many classical logic gates. Some universal classical logic gat... |
Today, I am presenting the Chapter 3 of the book Probability on Graphs ofGeoffrey Grimmett during a monthly reading seminar at LIAFA. The title ofthe chapter is
Percolation and self-avoiding walks. I did some computationsto improve my intuition on the question. My code is in the following file :bond_percolation.sage. T... |
I am trying to find the amplitude and phase plots of the saw tooth waveform pictured.I have already computed the Fourier series of the waveform but I don't know how to derive the amplitude and phase plots from the sawtooth's Fourier series.
$$ x(t) = \begin{cases} \frac{V}{T}t + V & \text{$-T < t < 0$} \\ \\ \\ \\ \fra... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Keywords density distribution (2) (remove)
296
We show that the occupation measure on the path of a planar Brownian motion run for an arbitrary finite time intervalhas an average density of order three with respect to thegauge function t^2 log(1/t). This is a sur... |
i'm having trouble a bit of trouble with taking the derivatives and collating my results of trig functions in the form of $sin$ $3x$ for example.
The specific problem i'm stuck on is;
Find the derivative of $2\sin3t\cos4t$
I'll show what I have done, but i'm really looking for some explanation of a general case for thi... |
Consider a Dirichlet character, $\chi(n)$, and the partial sum :
$$S(\chi,x)=\bigg |\sum_{n=1}^{x} \chi(n)\bigg|$$
There are many works to bound this sum when $\chi$ is a primitive character, but what can we say if $\chi$ is not primitive ?
More specifically if we fix a primitive Dirichlet character $\chi$ and then def... |
In a university statistics course, we were presented with a "proof" of the Weak Law of Large Numbers (as it applies to population samples) based on Chebyshev's inequality. The steps the professor took are nearly identical to those linked in the following Wikipedia article: https://en.wikipedia.org/wiki/Law_of_large_num... |
I am trying to evaluate $$\lim_{x \to \frac{\pi}{4}} \frac{1-\tan x}{x-\frac{\pi}{4}}$$ without using L'hopital's rule. However, I am not sure what to do. The only thing that came to my mind was to change the tan to sin over cos and get a common denominator but I felt that won't get me anywhere. A hint will be greatly ... |
Using Properties of Inverse Matrices, Simplify the Expression
Problem 694
Let $A, B, C$ be $n\times n$ invertible matrices. When you simplify the expression\[C^{-1}(AB^{-1})^{-1}(CA^{-1})^{-1}C^2,\]which matrix do you get?(a) $A$(b) $C^{-1}A^{-1}BC^{-1}AC^2$(c) $B$(d) $C^2$(e) $C^{-1}BC$(f) $C$
In this problem, we use ... |
Abbreviation:
ComBCK
A
is a structure $\mathbf{A}=\langle A,\cdot ,0\rangle$ of type $\langle 2,0\rangle$ such that commutative BCK-algebra
(1): $((x\cdot y)\cdot (x\cdot z))\cdot (z\cdot y) = 0$
(2): $x\cdot 0 = x$
(3): $0\cdot x = 0$
(4): $x\cdot y=y\cdot x= 0 \Longrightarrow x=y$
(5): $x\cdot (x\cdot y) = y\cdot (y\... |
By definition supersymmetry transformations square to spacetime translations. In a superspace formalism the supersymmetry operator is constructed from the vector field $\partial_\theta$ with respect to the odd coordinates $\theta$. As this operator has to square to the vector field $\partial_x$ with respect to the even... |
The Area Interaction Point Process Model
Creates an instance of the Area Interaction point process model (Widom-Rowlinson penetrable spheres model) which can then be fitted to point pattern data.
Usage
AreaInter(r)
Arguments r
The radius of the discs in the area interaction process
Details
This function defines the int... |
skills to develop
To learn how some events are naturally expressible in terms of other events. To learn how to use special formulas for the probability of an event that is expressed in terms of one or more other events.
Some events can be naturally expressed in terms of other, sometimes simpler, events.
Complements
Def... |
Statistics Seminar
Department of Mathematical Sciences
DATE: Thursday, May 05, 2016 TIME: 1:15pm to 2:15pm LOCATION: WH 100E SPEAKER: Aleksey Polunchenko, Binghamton University TITLE: On a Diffusion Process that Arises in Quickest Change-Point Detection Abstract
We consider the diffusion $(R_t)_{t\ge0}$ generated by th... |
This question was originally posted on mathoverflow. Having obtained no answers after one month, I've decided to cross-post it here.
Let $H = ( V, E )$ be a $k$-uniform connected hypergraph, with $n = |V|$ vertices and $m = |E|$ hyperedges. Let $O_w$ be the number of distinct edge induced subgraphs of $H$ having $w$ ve... |
I know it’s taking a while before I use maths to model a mass on a spring, but that will only make sense by fully describing the graphs of sine equations. Hopefully, this development is interesting in its own right.
Now if you were to plot the daylight length at a certain latitude against days, and if you plotted for a... |
First, let me introduce my little story:
I started searching information about the famous Dirichlet Divisor Problem: getting the exact asymptotic behaviour of the sum of the divisor function up to an integer $x$. More specifically, the aim of the problem is to bound $\theta$ in:
$$D(x)=\sum_{n \le x} d(n) = x \log x +x... |
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Now showing items 1-9 of 9
Measurement of $J/\psi$ production as a function of event multiplicity in pp collisions at $\sqrt{s} = 13\,\mathrm{TeV}$ with ALICE
(Elsevier, 2017-11)
The availability at the LHC of the largest collision energy in pp collisions allows a significant advance in the measurement of $J/\ps... |
Anyons are particles which quantum statistics is neither bosonic or fermionic one. They are proved to exist only in 2 dimensions and can have some quantum numbers of fractional values in respect to other elementary particles such as for example electron. An anyon can be charged and the charge can be a fracture of 1e. (... |
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 ... |
Giulio Ciraolo
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When holes or hard elastic inclusions are clos... |
I realize that the solution I'm giving further below is basically the one you mentioned in your question. So let's begin by addressing this:
The solution in question assumes that M° is linear.. if that was the case you can have:
M°(P) = alpha*M°(A) + beta * M°(B) + gamma*M°(C)
But that is not the case (correct me if I'... |
Yesterday, in the short course on model theory I am currently teaching, I gave the following nice application of downward Lowenheim-Skolem which I found in W. Hodges
A Shorter Model Theory:
Thm: Let $G$ be an infinite simple group, and let $\kappa$ be an infinite cardinal with $\kappa \leq |G|$. Then there exists a sim... |
How does one get the frequency response of a filter, given an input signal and the signal output by the filter?
The plant output data is usually generated using Gaussian white-noise excitation, although more informative input signals can be generated by experiment design, if prior information about the plant is known [... |
In the preceding chapter we learned that populations are characterized by descriptive measures called parameters. Inferences about parameters are based on sample statistics. We now want to estimate population parameters and assess the reliability of our estimates based on our knowledge of the sampling distributions of ... |
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 $D_8=D_{2 \cdot 4}$ be the dihedral group on a regular $4$-gon. Suppose that $S$ is a subset of $S_4$, such that S contains the element $( 1 \ 2 \ 3)$. We also know that $D_8$ acts
transitivelyon $S$ via the action: $$ D_8 \times S \mapsto S$$ $$ (\sigma, s) \mapsto \sigma \circ s $$ Task: determine $S$
My approach... |
The argument made by Ben can be supported by computational chemistry. I calculated three conformers of the compound.
Conformation B1 includes an intramolecular hydrogen bond, while in conformation B2 the proton was rotated away from the second hydroxyl group. Conformation C is the staggered one. The displayed structure... |
Suppose {$a_n$}$_{n=1}^{\infty}$ {$b_n$}$_{n=1}^{\infty}$ are sequences such that {$a_n$}$_{n=1}^{\infty}$ and {$a_n + b_n$}$_{n=1}^{\infty}$ converge. Prove that {$b_n$}$_{n=1}^{\infty}$ also converges.
I'm confused on a few parts. Taking what can be assumed, we know that for every $\epsilon$>0, there exists $N_1 \in ... |
Your job is to approximate $\pi$ using the sequence of digits (in order):
1 2 3 4 5 6 7 8 9
with operators inserted between them (permitted operators listed below). You are to find the best approximation to $\pi$ that you can using the allowed operators and the numbers listed in order as they appear above. You must use... |
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The maximum number of isomers for an alkene with molecular formula C4H8
Note by Divyansh Singhal 5 years, 10 months ago
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explana... |
Subspace clustering by (
k, k)-sparse matrix factorization
Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong, China
High-dimensional data often lie in low-dimensional subspaces instead of the whole space. Subspace clustering is a problem to analyze data t... |
Let $M$ be
finite set with $n$ distinct elements. I want to probalistically approximate the relative counts $\frac{|P(Q)|}{|M|}$ of $Q \subseteq M$, where $P(Q) = |P \cap M|$.
An upper-bound for the number of samples need to get an (additive) $\varepsilon$-approximation can be derrived using the Hoeffding bound.
I am i... |
This is the first time I have read about polynomial delay algorithms, so I am not 100% sure of my answer, but I think something like the following should work.
Pick some convention for representing paths that has a natural total ordering $<$ defined on it. (One example would be just to list the vertexes of the path and... |
Skills to Develop
To learn the concept of the probability distribution of a continuous random variable, and how it is used to compute probabilities. To learn basic facts about the family of normally distributed random variables. The Probability Distribution of a Continuous Random Variable
For a discrete random variable... |
Finite Element Analysis - May 2012
Mechanical Engineering (Semester 6)
TOTAL MARKS: 80
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory. (2) Attempt any three from the remaining questions. (3) Assume data if required. (4) Figures to the right indicate full marks. 2(b) Solve the following differential equation using Ray... |
If you know the rolling speed at a given flight speed, you can calculate the aileron effectiveness and use that to calculate the forces. The final rolling speed is reached when roll damping and the aileron-induced rolling moment reach an equilibrium: $$c_{l\xi} \cdot \frac{\xi_l - \xi_r}{2} = -c_{lp} \cdot \frac{\omega... |
So let us start with the "simplest" scheme over $Spec(\mathbf{Z})$ namely $X_0=Spec(\mathbf{Z})$. Then the (reciprocal) Weil zeta function of $X_0$ at a prime $p$ is given by $Z_p(T)=1-T$ (a polynomial of degree $1$). So the Hasse-Weil zeta function of $X_0$ is given by $$ L_{X_0}(s):=\prod_{p}Z_p(p^{-s})^{-1}=\zeta(s)... |
56 0 1. Homework Statement
A large 16.0 kg roll of paper with radius R=18.0 cm rests against the wall and is held in place by a bracket attached to a rod through the center of the roll. The rod turns without friction in the bracket, and the moment of inertia of the paper and rod about the axis is 0.260 kg m^2. The othe... |
I have the following inequation: $\sqrt{t^{2}-t-12}<7-t$. Can I just set both sides of the inequation to the power of two, or is there any condition under which exponentiating is an equivalent operation?
Thanks
Mathematics Stack Exchange is a question and answer site for people studying math at any level and profession... |
"Abstract: We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, insta... |
We are currently in the midst of updating the too-long-unupdated software which underlies Science After Sunclipse. This process has largely gone without incident, though some mathematical formulæ are failing to display properly. Until we get everything sorted, just imagine an early-1990s “This Website Under Constructio... |
Linear Boltzmann equation and fractional diffusion
1.
Laboratoire J.-L. Lions, BP 187, 75252 Paris Cedex 05, France
2.
CMLS, École polytechnique, 91128 Palaiseau Cedex, France
3.
DPMMS, University of Cambridge, Wilberforce Road, CB3 0WA Cambridge, United Kingdom
Consider the linear Boltzmann equation of radiative trans... |
I hope nobody cares that i exhume this question, but i found it interesting that it is possible to obtain this integral by a relativly straightforward contour integration method.
Observe that,following the question opener and using parity, that we can rewrite the integral as
$$\frac{1}{2}\int^{\infty}_{-\infty}\frac{1}... |
Torsion Submodule, Integral Domain, and Zero Divisors Problem 409
Let $R$ be a ring with $1$. An element of the $R$-module $M$ is called a
torsion element if $rm=0$ for some nonzero element $r\in R$. The set of torsion elements is denoted \[\Tor(M)=\{m \in M \mid rm=0 \text{ for some nonzero} r\in R\}.\] (a) Prove that... |
Recent CMS results on exclusive processes
Pre-published on: 2019 June 28
Published on: 2019 October 04
Abstract
Exclusive vector meson photoproduction is studied in ultra-peripheral pPb collisions at $\sqrt{s_{NN}} = 5.02$ TeV. The cross sections are measured as a function of the photon-proton centre-of-mass energy, ex... |
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Now showing items 1-10 of 24
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 ... |
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A Dutch variation of this blog post is available.
Astrophysicist Mario Livio has joined the community of people who spread the rumor about a bump that will be presented on Tuesday between 3 pm and 5 pm:
Rumor from #LHC @CERN potential detection of excess at \(700\GeV\) [most recently sometimes said to be \(750... |
This isn't a full answer, just a simple observation that spectral theory gives a partial answer of sorts (as you may already know). See here or any introduction to Banach algebra/C*-algebra theory for supporting details.
A
character of a unital commutative Banach algebra $A$ is a unital algebra homomorphism $\phi: A \t... |
Let $f$ be an entire function (holomorphic over the complex plane). If $f$ has no zero point, then $\text{Log} f$ is also an entire function. How to prove this?
My idea: one branch of $\text{Log}f$ is well-defined on $\mathbb{C}\setminus \gamma$ for any $\gamma:[0,\infty)\longrightarrow \mathbb{C}$ such that $\gamma(\i... |
Dynamic viscosity, abbreviated as \(\mu\) (Greek symbol mu), also called absolute viscosity of simple viscosity, is the force required to move adjacent layers that are parallel to each other at different speeds. The velocity and shear stress are combined to determine the dynamic viscosity.
Dynamic Viscosity Formula
\(\... |
Electronic Journal of Probability Electron. J. Probab. Volume 16 (2011), paper no. 69, 1900-1933. Upper large deviations for Branching Processes in Random Environment with heavy tails Abstract
Branching Processes in Random Environment (BPREs) $(Z_n:n\geq0)$ are the generalization of Galton-Watson processes where 'in ea... |
Let $\phi(n)$ be Euler's totient function. For $n=4m$ what is the smallest $n$ for which
$$\phi(n) \ne \phi(k) \textrm{ for any } k<n \textrm{ ?} \quad (1)$$
When $n=4m+1$ and $n>1$ the smallest is $n=5$ and when $n=4m+3$ it's $n=3.$ However, when $n=4m+2$ the above condition can never be satisfied since
$$\phi(4m+2) =... |
$R$ is taken to be the ring of upper $3 \times 3$ matrices with entries in $\mathbb{R}$.
If I view $R$ as a module over itself, are any of its submodules free?
And how can I prove that its submodules are pojective $R$-modules?
Thanks!
Mathematics Stack Exchange is a question and answer site for people studying math at ... |
The best model is not always the most complicated. Sometimes including variables that are not evidently important can actually reduce the accuracy of predictions. In this section we discuss model selection strategies, which will help us eliminate from the model variables that are less important. In this section, and in... |
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Networks & Heterogeneous Media
June 2006 , Volume 1 , Issue 2
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Abstract:
This work is concerned with some aspects of the social life of the amoebae
Dictyostelium discoideum(Dd). In particular, we shall focus on the early stages of the star... |
I'm trying to solve the following partial differential equations: $$ u_t + \frac{1}{3}{u_x}^3 = 0 \tag{a} $$ $$ u_t + \frac{1}{3}{u_x}^3 = -cu \tag{b} $$ with the initial value problem $$ u(x,0)=h(x)= \left\lbrace \begin{aligned} &e^{x}-1 & &\text{for}\quad x<0\\ &e^{-x}-1 & &\text{for}\quad x>0 \end{aligned} \right. $... |
Votes cast (9)
all time by type 9 up 7 question 0 down 2 answer
4
$\sum x_n$ and $\sum y_n$ converge, show $\sum (x_n + y_n)$ converges
2
Prove that the translation of an integrable function is also integrable.
2
Prove Lipschitz function $f$ with constant $K$ is integrable on $[0, 1].$
1
If a function $f(x)$ is Riemann... |
This question was inspired by the Homotopy Type Theory Book.
Might we define a weak $\omega$-category as described below?
Is any similar approach already considered in the literature?
Let $\def\Ob{{\rm Ob}\,} \Ob\mathcal C$ be a set [class] with partial functions $\def\dom{\rm dom} \def\cod{\rm cod} \dom,\cod$ defined ... |
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We consider the conductivity problem in an array structure with square closely spaced absolutely conductive inclusions of the high concentration, i.e. the concen... |
So how do you convert percentages to fractions and decimals and vice versa? This post will show examples of each.
Convert a percentage to a fraction:
This one is easy as if you remember, a percentage is already a fraction where the numerator is displayed and the denominator is 100. So you just create the fraction and s... |
I want to expand Einstein-Hilbert action for the metric
$$ g_{\mu \nu} = \eta_{\mu \nu} + h_{\mu \nu} $$
up to quadratic order in $h_{\mu \nu}$. For this purpose I need to calculate the Ricci tensor at some stage. There is no problem in linear terms of the metric perturbation but there happens to be a problem when I in... |
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December 2006 , Volume 1 , Issue 4
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The launching meeting of Networks and Heterogeneous Media took place on June 21-23 2006 in Maiori (Salerno, Italy). The meeting was sponsored by the American Inst... |
Is there any theoretical or practical limit to the maximum number of passengers - and therefore size - one can build an airplane for?
Yes, there is an upper limit, but that upper limit might change with technological innovation.
An airplane flies because of the lift coefficient $L=\frac12\rho v^2 A C_L$, with $v$ the a... |
Let $X,Y\in\mathbb{R}^{n\times n}$ be symmetric matrices. You may assume that $X$ is positive semidefinite and $Y$ negative semidefinite, if needed, but not that they are invertible.
I would like to find a way to factor the $2n\times 2n$ block matrix $$ \begin{bmatrix} X & I\\\\ I & Y \end{bmatrix} $$ into some form of... |
Abbreviation:
Frm
A
is a structure $\mathbf{A}=\langle A, \bigvee, \wedge, e, 0\rangle$ of type $\langle\infty, 2, 0, 0\rangle$ such that frame
$\langle A, \bigvee, 0\rangle$ is a complete semilattice with $0=\bigvee\emptyset$,
$\langle A, \wedge, e\rangle$ is a meet semilattice with identity, and
$\wedge$ distributes ... |
If $f,g$ are uniformly continuous, then is $\alpha f+\beta g$ uniformly continuous?
So far, I looked at here If $f,g$ are uniformly continuous prove $f+g$ is uniformly continuous, but I didn't understand something. I know that from what I've been told,: 1. $\forall\epsilon >0$ $\exists\delta_1 >0$, if $|x-y|<\delta_1$ ... |
The Riemann zeta function is $$\zeta(s) = \sum_{n=1}^\infty \frac{1}{n^s}$$ Now let's say that our input $r \in \mathbb{N}$ and $r > 1$. That way we can create the parametric function $$f_r(x) = \frac{1}{x^r}$$
Now my theory was that $\zeta(s)$ could be calculated by $$\zeta(r) \approx \int_{1}^{\infty}f_r(x)dx = \lim_... |
For an integer $n > 0$, let $\mathrm{P}_n$ denote the vector space of polynomials with real coefficients of degree $2$ or less. Define the map $T : \mathrm{P}_2 \rightarrow \mathrm{P}_4$ by\[ T(f)(x) = f(x^2).\]
Determine if $T$ is a linear transformation.
If it is, find the matrix representation for $T$ relative to th... |
LaTeX supports many worldwide languages by means of some special packages. In this article is explained how to import and use those packages to create documents in
Italian.
Contents
Italian language has some accentuated words. For this reason the preamble of your document must be modified accordingly to support these c... |
Establishing the type of distribution, sample size, and known or unknown standard deviation can help you figure out how to go about a hypothesis test. However, there are several other factors you should consider when working out a hypothesis test.
Rare Events
Suppose you make an assumption about a property of the popul... |
First for some notation $$ l(\lambda) = \text{ number of parts in a partition } \lambda \vdash n$$
$$ f_{\lambda} = \text{number of standard Young tableau of shape } \lambda\vdash n$$
The number $f_{\lambda}$ is given by the hook length formula and might not acquire a "nice form". Given an integer $k$ consider the prob... |
Problem 676
Let $V$ be the vector space of $2 \times 2$ matrices with real entries, and $\mathrm{P}_3$ the vector space of real polynomials of degree 3 or less. Define the linear transformation $T : V \rightarrow \mathrm{P}_3$ by
\[T \left( \begin{bmatrix} a & b \\ c & d \end{bmatrix} \right) = 2a + (b-d)x – (a+c)x^2 +... |
We have recently discovered the densest known crystalline packing of congruent ellipsoids, which are periodic packings with two particles in the fundemantal cell. The resutls was published in the letter entitled
Unusually Dense Crystal Ellipsoid Packings ( Phys. Rev. Lett. 92 , 255506 (2004)) by A. Donev, F. H. Stillin... |
I am currently working with Earl Hammon Jr's Presentation PBR Diffuse Lighting for GGX+Smith Microsurfaces (now mentioned as [PBR, p.XYZ] and have read through (among others) Brent Burley's Physically-Based Shading at Disney (now mentioned as [DIS, p. XYZ] to get a good diffuse BRDF component. I am stuck at combining t... |
The weekend before last, I overcame my reluctance to travel and went to a mathematics conference, the American Mathematical Society’s Spring Central Sectional Meeting. I gave a talk in the “Recent Advances in Packing” session, spreading the word about SICs. My talk followed those by Steve Flammia and Marcus Appleby, wh... |
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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 ... |
If we are given
$u=\cot^{-1}\sqrt{\cos 2m} - \arctan \sqrt{\cos2m}$
Then we have to prove $\sin u = \tan^2m$
I tried and it as $\tan u = \frac{(1+\cos2m)}{2\sqrt{\cos2m})}$
But got stuck after that .
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in rela... |
Imhotep-SMT A novel SMT-based solver for secure state estimation Tutorial: Securing an Unmanned Ground Vehicle
In this tutorial, we are going to demonstrate how to use Imhotep-SMT to secure the control of an unmanned ground vehicle (UGV) against attacks to its sensors. The UGV has two state variables: the position $x(t... |
Wave Optics Polarisation Polarisation is the property of obstructing the vibration of particle. Polarisation Establishes the transverse nature of Light waves If the Electric vector vibrates in all directions in a plane perpendicular to the direction of propagation is called unpolarised light. If the Electric field vect... |
Image Dimensions Contents Describing the fields of the Canvas Properties Dialog
The user access the image dimensions in the Canvas Properties Dialog.
The Other tab
Here some properties can simply be locked (such that they can't be changed) and linked (so that changes in one entry simultaneously change other entries as ... |
-- Sorry for the long post, but I prefer to do that way because "
Devil is in the details." :)
I am writing a path tracer from the scratch and it is working nicely for perfectly diffuse (Lambertian) surfaces (
i.e. the furnace test indicates - at least visually - that it is energy conserving, and rendered images match ... |
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Now showing items 1-10 of 24
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 ... |
During Sage Days 31, I worked on theticket #11459 to implement
rst to
sws conversion. This post intends to give some documentationabout this new feature. Here is an example of a ReStructuredText file
calculus.rst:
******** Calculus ******** Let's do some calculus using Sage. Differentiation =============== The derivati... |
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We present a novel class of functions that can describe the stable and unstable manifolds of the Hénon map. We propose an algorithm to construct these functions by using the Bor... |
I just began the new Coursera MOOC on probability, given by UPenn Dr. Santosh S. Venkatesh, and at the very first lecture, my interest was piqued by this intriguing idea, called the Chevalier de Méré's Paradox.. If I ask you which is more likely:
Getting a "6" four times in four throws of a die Getting a "double 6" twe... |
Let's assume the basic nouns of our language to describe the physical world are the members of Lie groups. Okay, this is a pompous-sounding statement and somewhat arbitrary, but my justification is that these objects describe all the
continuous symmetries there can be, and almost every clarification of physics using ma... |
In the Green-Schwarz formalism, for F1 strings, we have the action
$$S=S_1+S_2$$
Where
$${S_1} = - T\int_{}^{} {\sqrt { - \det \left( {{\Pi _{\alpha \mu }}\Pi _\beta ^\mu } \right)} {{\text{d}}^2}\sigma } $$
and $S_2$ is the additional action term that arises through Kappa Symmetry.
The transformations of kappa symmetr... |
Skills to Develop
To learn what the observed significance of a test is. To learn how to compute the observed significance of a test. To learn how to apply the \(p\)-value approach to hypothesis testing. The Observed Significance
The conceptual basis of our testing procedure is that we reject \(H_0\) only if the data th... |
Class "Gammad"
The Gammad distribution with parameters
shape \(=\alpha\), by default
= 1, and
scale \(=\sigma\), by default
= 1, has density $$ d(x)= \frac{1}{{\sigma}^{\alpha}\Gamma(\alpha)} {x}^{\alpha-1} e^{-x/\sigma}% $$ for \(x > 0\), \(\alpha > 0\) and \(\sigma > 0\). The mean and variance are \(E(X) = \alpha\sig... |
I have been asked to solve this exercise.
An environment of $V=1500$ $m^3$, it is considered a reverberated field acoustic pressure level of $70$ $dB$ when an acoustic source of $80$ $dB$ is activated. Compute the total absorption (in $m^2$) in order to obtain a reverberation time of $4$ seconds.
Let me show you my ide... |
I'm looking for some general insight on preconditioning. In particular, relevant references/resources/comments would be greatly appreciated. Note, I have been through some of the literature, but am having trouble finding a reference for a problem similar to the one I am solving.
The system I'm solving takes the form
$Q... |
My reference is L. Simon's
Lectures on Geometric Measure Theory. He defines a measure on a set $X$ as a countably subadditive function $\mu:2^X\to[0,\infty]$ with $\mu(\emptyset)=0.$
When $X$ is a locally compact and separable topological space, he defines a measure $\mu$ on $X$ to be Radon if it is Borel regular (i.e.... |
Proof following statement with interference rules ( without truth table) that$$ (\neg C \wedge B \wedge (A \rightarrow C) \wedge (B \rightarrow D ) )\implies (\neg A \wedge D ) $$Attempt to proof$B$ (premise)$B \rightarrow D$ (premise)$D$ (Modus ponens 1,2)$A \rightarrow C $ (premise)...
Gallian says: In PID, any stric... |
While reading up on quadratic reciprocity, I learned that if $p = 4k+1$ then $-1$ has a square root in $\mathbb{Z} / p \mathbb{Z}$.
Let $r_p$ be an integer with $0\leq r_p < p$ and $r_p^2 \equiv -1 \mod p$. How then is $\frac{r_p}{p} \in \mathbb{Q}$ distributed in $[0,1]$? Naively I would guess this is uniform distribu... |
I have a question regarding the treatment of Robin boundary conditions in a multigrid solver. I am solving the Poisson equation in $\Omega=(0,1)^2$ with Robin boundary conditions on the boundary, $$- \Delta u = f \text{ in } \Omega$$ and $$\frac{\partial u}{\partial n} - au= g \text{ on } \partial \Omega.$$ I use a fin... |
"Abstract: We prove, once and for all, that people who don't use superspace are really out of it. This includes QCDers, who always either wave their hands or gamble with lettuce (Monte Zuma calculations). Besides, all nonsupersymmetric theories have divergences which lead to problems with things like renormalons, insta... |
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