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Before you answer this OP, please read all the terms and conditions below. Thank you...
Today I hold an unofficial little contest on brilliant.org. Now, I will hold it here on Math S.E. It's just for fun guys. (>‿◠)✌
Before we start the contest, here are the rules of my little contest that you should obey as a contesta... |
Ring of Polynomial Forms over Integral Domain is Integral Domain Theorem Then $\struct {D \sqbrk X, \oplus, \odot}$ is an integral domain. Proof
From Ring of Polynomial Forms is Commutative Ring with Unity it follows that $\struct {D \sqbrk X, +, \circ}$ is a commutative ring with unity.
Suppose $f, g \in D \sqbrk X$ s... |
Solve over real $a$ $$\sqrt{3a-4}+\sqrt[3]{5-3a}=1.$$
If $p=3a-4$, $$\sqrt{p}+\sqrt[3]{1-p}=1.$$ If $q=5-3a$, $$\sqrt{1-q}+\sqrt[3]{q}=1.$$ Seems useful, but not sure how to proceed.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It on... |
The context of this question is coming up with the parameters for the ElGamal encryption scheme.
One of the requirements for the parameters for ElGamal is that we have primes $p$ and $q$ such that $p = q \cdot k + 1$ for some $k$. For simplicity, let $k=2$. We also need a generator $g$ for $p$ such that $g^q \equiv 1 \... |
This is about simple infinite continued fraction. I don't understand the line '...then $C_0 < x < C_1$'. $C_k$ here refers to $C_k=[a_0;a_1,a_2,...,a_k]$ where $1 \leq k \leq n$. $C_o=a_0$.
Can anyone explain it to me why is the inequality true?
Mathematics Stack Exchange is a question and answer site for people studyi... |
Convergent Sequence is Cauchy Sequence/Normed Division Ring Theorem
Let $\struct {R, \norm {\,\cdot\,}} $ be a normed division ring.
Let $\epsilon > 0$.
Then also $\dfrac \epsilon 2 > 0$.
Because $\sequence {x_n}$ converges to $l$, we have:
$\exists N: \forall n > N: \norm {x_n - l} < \dfrac \epsilon 2$
So if $m > N$ a... |
$\newcommand{\Cof}{\text{cof}}$ Let $d>2$. Let $f \in W^{1,p}(\Omega,\mathbb{R}^d)$ where $\Omega$ is an open subset of $\mathbb{R}^d$. Let $2 \le k \le d-1$ be fixed.
Suppose that $\det df>0$ a.e. and that $\bigwedge^k df$ is smooth. Is $f$ smooth?
Partial answer: If $k,d$ are not both even and $\bigwedge^k df \in \te... |
The derivative of exponential function with respect to a variable is equal to the product of the exponential function and natural logarithm of base of the exponential function. The differentiation of exponential function $a^{\displaystyle x}$ with respect to $x$ can be derived in differential calculus by first principl... |
Film Boiling Analysis in Porous Media From Thermal-FluidsPedia
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Film boiling
+
Film boiling in porous <></>
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Film boiling in porous <math>{T_w} > {T_{sat}}</math> is analyzed (see ). Vapor generated at the liquid-vapor interface flows upward due to buoyancy force... |
Question in the title.
It intuitively seems absurd that $p_N - p_{N-1} \gt p_{N-1} - 3 = $ the largest gap formable from all $p_i = $ odd primes $3, \dots, p_{N-1}$.
Was wondering how difficult the proof is.
$2 p_i$ is the smallest composite divisible by $p_i$. And $p_N + 3$ is certainly a composite. Not sure if that h... |
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Now showing items 1-9 of 9
Production of $K*(892)^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$ =7 TeV
(Springer, 2012-10)
The production of K*(892)$^0$ and $\phi$(1020) in pp collisions at $\sqrt{s}$=7 TeV was measured by the ALICE experiment at the LHC. The yields and the transverse momentum spectra $d^2 ... |
Take a vector error correction (VECM) model:
$$\;\;\;\Delta y_t=\Pi y_{t-1}+\Gamma_1\Delta y_{t-1}+...+\Gamma_{p-1}\Delta y_{t-(p-1)}+\varepsilon_t$$
where $\Pi=\alpha \beta'$ and each row of $\beta'$ (or, equivalently, each column of $\beta$) is a cointegrating vector.
Questions: When VECM is estimated by maximum like... |
Lower attic
From Cantor's Attic
Revision as of 16:52, 28 December 2011 by Jdh
Welcome to the lower attic, where we store the comparatively smaller notions of infinity. Roughly speaking, this is the realm of countable ordinals and their friends.
$\omega_1$, the first uncountable ordinal, and the other uncountable cardin... |
I was working in my project when I was struck by the question of whether it would be necessary, or at least cautious, prevent overflow and underflow in the calculation of these two distances.
I remembered that there is an implementation of the calculation of the hypotenuse to prevent this. Most languages implementers, ... |
Search
Now showing items 1-10 of 34
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... |
I found this SO post which expresses the PDF of a multivariate t-distribution in terms of the gamma and normal distribution in python as follows
$$ G = \Gamma (k = \nu /2 ; \theta = 2 / \nu)\\ Z = N (\mu; \Sigma)\\ PDF_t = \mu + Z / \sqrt{G} $$
where $\mu$ is the mean vector of the distribution, $\nu$ is the degrees of... |
Tool to calculate triple Integral. The calculation of three consecutive integral makes it possible to compute volumes for functions with three variables to integrate over a given interval.
Triple Integral - dCode
Tag(s) : Functions, Symbolic Computation
dCode is free and its tools are a valuable help in games, maths, g... |
Let $F$ be a locally constant sheaf on $X$ and $U$ is an open subset and $F|U$ is a constant sheaf. Let $x\in U$, now let $s,s'$ be two sections from $F(U)$ s.t. $s(x)=s'(x)$, can we say $s=s'$ in a local neighbourhood of $x$?
I think there are two different understandings of "constant"
I know the sections of the const... |
What is a correlation?
A correlation quantifies the linear association between two variables. From one perspective, a correlation has two parts: one part quantifies the association, and the other part sets the scale of that association.
The first part—the covariance, also the correlation numerator—equates to a sort of ... |
The interaction term in the Lagrangian for Yukawa theory is given by
$$ \mathcal{L}_\text{int} = -g\phi\bar{\Psi}\Psi, $$
where $g$ is the coupling constant, $\phi$ some scalar field and $\Psi$ a fermion field. My question might be a little bit naive but I'm trying to understand how you can see that for a given quantum... |
The Annals of Statistics Ann. Statist. Volume 46, Number 3 (2018), 1077-1108. On the systematic and idiosyncratic volatility with large panel high-frequency data Abstract
In this paper, we separate the integrated (spot) volatility of an individual Itô process into integrated (spot) systematic and idiosyncratic volatili... |
Inaccessible cardinal Inaccessible cardinals are the traditional entry-point to the large cardinal hierarchy, although weaker notions such as the worldly cardinals can still be viewed as large cardinals.
A cardinal $\kappa$ being inaccessible implies the following:
$V_\kappa$ is a model of ZFC and so inaccessible cardi... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
Absolutely continuous measures
A concept in measure theory (see also Absolute continuity). If $\mu$ and $\nu$ are two measures on a $\sigma$-algebra $\mathcal{B}$ of subsets of $X$, we say that $\nu$ is absolutely continuous with respect to $\mu$ if $\nu (A) =0$ for any $A\in\mathcal{B}$ such that $\mu (A) =0$. The abs... |
ok, suppose we have the set $U_1=[a,\frac{a+b}{2}) \cup (\frac{a+2}{2},b]$ where $a,b$ are rational. It is easy to see that there exists a countable cover which consists of intervals that converges towards, a,b and $\frac{a+b}{2}$. Therefore $U_1$ is not compact. Now we can construct $U_2$ by taking the midpoint of eac... |
Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Purchase individual online access for 1 year to this journal.
Impact Factor 2019: 1.204 Fundamenta Informaticae is an international journal publishing original research results in a... |
The rule of changing the base of a logarithmic term is called the change of base rule of logarithmic term. In logarithms, the base of any logarithm term can be changed in three ways and they are used as change of base formulas in logarithms.
The change of base logarithm formula in division form.
$\large \log_{b}{m} = \... |
It is a common exercise in algebra to show that there does not exist a field $F$ such that its additive group $F^+$ and multiplicative group $F^*$ are isomorphic. See e.g. this question.
One of the snappiest proofs I know is that, if we suppose for a contradiction they are, then any isomorphism sends solutions of the e... |
Let $(x_n)$ be a bounded but not convergent sequence. Prove that $(x_n)$ has two subsequences converging to different limits.
My attempt is: Since the sequence is bounded , there exists $M>0$ such that $x_n \in [-M,M]$ for all $n \in \mathbb{N}$. Since the sequence does not converge to $x$, there exists $\epsilon_0>0$ ... |
Regularity for Variational Problems in the Heisenberg Group
Speaker
Shirsho Mukherjee, Department of Mathematics and Statistics, University of Jyväkylä
When Jan 12, 2016
from 04:00 PM to 05:00 PM
Where LH006 Add event to calendar vCal
iCal
Abstract: We examine the local interior regularity of minimizers of scalar varia... |
I've been given the following question and solution:
Let $W_t$ be a standard Brownian Motion w.r.t. ($\mathbf{P},\mathcal{F}_t)$. Prove that \begin{align} E[|W_t|] < \infty, \forall \text{ } t \end{align}
Solution: \begin{align} E[|W_t|] < E[1+W_t^{2}] < 1 + E[W_t^2] < 1+t <\infty \end{align}
My question is, what allow... |
It is a special function, which contains algebraic, trigonometric and exponential functions in terms of a variable $x$. So, the limit of the function should be simplified to our known form of exponential and trigonometric limit rules to solve this limit problem.
The numerator contains two exponential functions and a tr... |
→ → → → Browse Dissertations and Theses - Mathematics by Contributor "Erdogan, M. Burak"
Now showing items 1-12 of 12
(2016-08-25)One of the widely studied topics in singular integral operators is T1 theorem. More precisely, it asks if one can extend a Calder\'on-Zygmund operator to a bounded operator on $L^p$. In addi... |
Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Purchase individual online access for 1 year to this journal.
Impact Factor 2019: 0.808
The journal
Asymptotic Analysis fulfills a twofold function. It aims at publishing original m... |
Topological Methods in Nonlinear Analysis Topol. Methods Nonlinear Anal. Volume 33, Number 1 (2009), 51-64. Wecken property for periodic points on the Klein bottle Abstract
Suppose $f\colon M\to M$ on a compact manifold. Let $m$ be a natural number. One of the most important questions in the topological theory of perio... |
Tarski–Grothendieck set theory Tarski–Grothendieck set theory ( TG, named after mathematicians Alfred Tarski and Alexander Grothendieck) is an axiomatic set theory. It is a non-conservative extension of Zermelo–Fraenkel set theory (ZFC) and is distinguished from other axiomatic set theories by the inclusion of Tarski's... |
Given an elliptic curve $(E/\mathbb{K})$ where $char(\mathbb{K}) \ne 2,3$ defined by the Weierstrass equation $y^2=x^3+ax+b$. The $j$-invariant is $j=1728 \frac{4a^3}{4a^3+27b^2}$.
I want to understand very clearly how this j-invariant is constructed and especially from where does the 1728 come.
A rather simple but int... |
Let $A(n)$ be a finite square $n \times n$ matrix with entries $a_{ij}=1$ if $i+j$ is a perfect power; otherwise equals to $0$. Is it true that $${1 \above 1.5 pt n^2}\sum_{i=1}^n \sum_{j=1}^n a_{ij} \leq {1 \above 1.5pt 3}$$ with equality holding if and only if $n=3$ or $n=6$ ? Question:
Let $A(n)$ be a finite square ... |
Exponential Function is Well-Defined/Real/Proof 5 Theorem
Let $x \in \R$ be a real number.
Let $\exp x$ be the exponential of $x$.
Then $\exp x$ is well-defined. Proof
This proof assumes the definition of $\exp$ as the solution to an initial value problem.
That is, suppose $\exp$ solves:
$ (1): \quad \dfrac \d {\d x} y... |
Searching for just a few words should be enough to get started. If you need to make more complex queries, use the tips below to guide you.
Purchase individual online access for 1 year to this journal.
Impact Factor 2019: 0.808
The journal
Asymptotic Analysis fulfills a twofold function. It aims at publishing original m... |
Another one from my assignment:
Assume $$ \tan (\frac{x}{2})=\tan A\tanh B $$
Prove that $$ \tan(x)=\frac{\sin(2A)\sinh(2B)}{1+cos(2A)\cosh(2B)} $$
I manipulated $$ \tan(x)=\tan2(\frac {x}{2})=\frac {2\tan A \tanh B}{1-(\tan A\tanh B)^2} $$ Using the half angle formula for tan. From there I seem to just be going in cir... |
Oct 22nd 2017, 10:46 AM
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Originally Posted by
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I was noticing that there is a lot of similarity between the formula of kinetic energy 1/2 mv2 and Einstein's E=mc2. Was Einstein inspired from this kinetic energy formula when he c... |
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Purchase individual online access for 1 year to this journal.
Impact Factor 2019: 0.808
The journal
Asymptotic Analysis fulfills a twofold function. It aims at publishing original m... |
On Wikipedia, the Gibbs measure defines the probability as:
$$ P(X=x) = \frac{1}{Z(\beta)}\exp(-\beta E(x)) $$
Now, the familiar form of the normal distribution is:
$$ P(x) = \frac{1}{\sqrt{2\pi}\sigma}\exp-{\frac{(x-\mu)^{2}}{2\sigma^2}} $$
Now, it seems that the normal distribution is a Gibbs measure and I was wonder... |
Show that the following problem is a convex optimization problem.
$f(x,y,z)=2x^2-y+z^2 \rightarrow min! $
$g_1(x,y,z)=y+x\le1$,
$g_2(x,y,z)=z-y\le1$
Convex optimization problem if:
(1) $f(x)\rightarrow min!$
(2) $f(x)$ is convex
(3) all constraints $g_i$ are convex, $ i=1,..,m$
My idea is to calculate the Hessian matri... |
I would like to "reopen" the previous post regarding Modus ponens because, frankly speaking, I'm not satisfied with some (most of ?) answers by the mathematicians community.
Disclaim: I'm not aiming to "unravel the mystery", but I'm not convincd either that mathematicians and philosophers speaks completely different la... |
The
medium cash bag is an uncommon item won from Treasure Hunter. When opened it will give the player coins based on the player's total level. During the weekend of 1 February 2013, the gold received from the bag was doubled.
The coins received from a medium cash bag is a random number between $ 9X $ and $ 11X $, where... |
I'm trying to find the intermediate fields of the extension $\mathbb Q\big /\mathbb Q(\alpha)$, where $\alpha = \sqrt{7+\sqrt{13}}$. To do so I've tried to use the Galois correspondence. I've already found that $\rm{Gal}\left(\mathbb Q\big /\mathbb Q(\alpha)\right)$ has order $4$ and that is isomorphic to $\mathbb Z\bi... |
In Bourbaki Lie Groups and Lie algebras chapter 6 section 4 excercise 1(c), they have used the word pseudo-discriminant. The reference is given to be Algebra chapter IX which I can't find a English translation of. Here the following definition is given. Since I don't know French I can't understand the definition. Any h... |
The sum of all three interior angles in a triangle is $180^\circ$.
Three interior angles are formed internally by the intersection of every two sides of a triangle. The addition of all three angles is always equal to $180^\circ$ geometrically.
If, $\alpha$, $\beta$ and $\gamma$ are three interior angles in a triangle, ... |
What would be appropriate metaphors to call the
entropy of a question? I was thinking along the lines of "information value," but this would clearly be inappropriate, because it is the answers that contain information, not the question, and an unanswered question has no information value.
Each question has its
entropy,... |
ISSN: 1432-0916
Source: Springer Online Journal Archives 1860-2000
Topics: Mathematics , Physics
Notes: Abstract In ordinary quantum mechanics for finite systems, the time evolution induced by Hamiltonians of the form $$H = \frac{{P^2 }}{{2m}} + V(Q)$$ is studied from the point of view of *-automorphisms of the CCRC*-a... |
Assume, $x$ is a variable. The derivative of a variable $x$ with respect to $x$ is written in mathematical form as follows in differential calculus.
$\dfrac{d}{dx}{\, (x)}$
Use definition of the derivative to express the differentiation of a function $f{(x)}$ with respect to $x$ in limits form. It is useful to prove th... |
Real Number Ordering is Compatible with Multiplication/Negative Factor
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Contents Theorem $\forall a, b, c \in \R: a < b \land c < 0 \implies a c > b c$ where $\R$ is the set of real numbers. Proof
Thus:
\(\displaystyle a\) \(<\) \(\displaystyle b\) \(\displaystyle \leadsto \ \ \) \(\dis... |
The fractional part of common logarithm is called mantissa.
The logarithm of a quantity is expressed as two quantities and they are in fractional and integral forms.
Initially, the fractional part is in the form logarithm of a decimal number but later it’s transformed into another decimal number according to the logari... |
Fred Kline
Contact: fred.kline.98104ATgmailDOTcom
I donate regularly to the The OEIS Foundation.
When I look at the patterns, I can hear the wheels turning.
When I look at the math, I find out the hamsters have died.
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people reached
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Las... |
Question
Is there a closed form for integrals such as
$\int_{-\infty }^{\infty } e^{-y^2} \text{erf}(1-y) \, dy$
The integrant seems simple enough?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign u... |
Cauchy Sequence Is Eventually Bounded Away From Non-Limit Theorem
Let $\struct {R, \norm {\, \cdot \,} }$ be a normed division ring.
Let $\sequence {x_n}$ be a Cauchy sequence in $R$.
Suppose $\sequence {x_n}$ does not converge to $l \in R$, then:
$\exists K \in \N$ and $C \in \R_{\gt 0}: \forall n \gt K: C \lt \norm {... |
Since the explanation was a little more complicated than I initially thought, I figured it would be worth it to combine my comments (and info from Physics SE) into an answer.
Quantum particles satisfy Fermi–Dirac or Bose–Einstein statistics depending on whether they are fermions or bosons. These distributions have the ... |
In geometry, the notion of a
connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner. There are a variety of kinds of connections in modern geometry, depending on what sort of data one wants to transport. For instance, an affine connection, the most e... |
Journal of Symbolic Logic J. Symbolic Logic Volume 49, Issue 4 (1984), 1137-1145. Decidable Subspaces and Recursively Enumerable Subspaces Abstract
A subspace $V$ of an infinite dimensional fully effective vector space $V_\infty$ is called decidable if $V$ is r.e. and there exists an r.e. $W$ such that $V \oplus W = V_... |
What I suggested back then was to sample the parameters of a Dirichlet distribution by sampling
froma Dirichlet distribution and then multiplying that by a magnitude sampled from an exponential distribution. As it turns out, this is a special case of a much nicer general method.
The new method is to sample each paramet... |
Suppose A($\cdot$,$\cdot$) is an efficient randomized algorithm and L is a language such that
$\text{If }x \in L, \text{Pr}_r[(A(x,r) = 1)] = 1$ and if $x \notin L, \text{Pr}_r[A(x, r) = 0] \ge \frac{1}{2}$.
Let $H$ be a hitting set such that for all inputs $x$ of length $n$, if $x \notin L$, then $\exists y \in H, A(x... |
As Wikipedia reports, the fastest currently known algorithm for the gcd of two $n$-bit numbers runs in $O(n f(n))$ time where $f(n)$ is a slow-growing function of $n$ (roughly $\log n \cdot \log \log n$). It is not known whether the gcd of two $n$-bit numbers can be computed in $O(n)$ time.
This means that the iterativ... |
[1101.1650] The cosmological bulk flow: consistency with $\Lambda$CDM and $z\approx 0$ constraints on $\sigma_8$ and $\gamma$
Authors: Adi Nusser, Marc Davis Abstract: We derive estimates for the cosmological bulk flow from the SFI++ catalog of Tully-Fisher (TF) measurements of spiral galaxies. For a sphere of radius $... |
For the following sequence, how do I find if it converges and if so how do I find its limits.
$$a_n = \frac{12−8n}{4n+36}, (n=1,2,3,...)$$
What are the steps that I need to follow to get the answer?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in relat... |
I have the following system: $m\cdot\frac{dx^2}{dt^2}=-k(x-lo)-\frac{dx}{dt}\cdot d+m\cdot g$ It represents a mass with a spring and a damper. It is easy to solve using NDSolve but I'm trying to solve it using matrices. (Because if we represent the system using state equations, we can use some transformations, like dia... |
$\log_{b}{(m \times n)}$ $\,=\,$ $\log_{b}{m}+\log_{b}{n}$
The product rule is a most commonly used logarithmic identity in logarithms. It states that logarithm of product of quantities is equal to sum of their logs. It can be proved mathematically in algebraic form by the relation between logarithms and exponents, and... |
Plugging zero into $x$ gives me infinity-infinity which is indeterminate. I then try to multiply the function by $$\frac{\frac{1}{x^2} + \frac{1}{x\sin(x)}}{\frac1{x^2} + \frac1{x\sin(x)}}$$ which gives me another undeterminate and harder function... I know I need to use L'Hospital's rule, but I can't seem to find the ... |
Research Open Access Published: A posteriori error estimates for fourth order hyperbolic control problems by mixed finite element methods Boundary Value Problems volume 2019, Article number: 90 (2019) Article metrics
285 Accesses
Abstract
In this paper, we consider the a posteriori error estimates of the mixed finite e... |
Holt-Winters Filtering
Computes Holt-Winters Filtering of a given time series. Unknown parameters are determined by minimizing the squared prediction error.
Keywords ts Usage
HoltWinters(x, alpha = NULL, beta = NULL, gamma = NULL, seasonal = c("additive", "multiplicative"), start.periods = 2, l.start = NULL, b.start = ... |
PFA
A cardinal $\kappa$ is a
PFA cardinal if $\kappa$ is not zero and the canonical forcing of the PFA of length $\kappa$, which is the countable support iteration that at each stage $\gamma$ forces with the lottery sum of all minimal-rank proper partial orders $\mathbb{Q}$ for which there is a family $\cal{D}$ of $\om... |
Fermat's Last Theorem Theorem $\forall a, b, c, n \in \Z_{>0}, \; n > 2$, the equation $a^n + b^n = c^n$ has no solutions. Proof
The proof of this theorem is beyond the current scope of $\mathsf{Pr} \infty \mathsf{fWiki}$, and indeed, is beyond the understanding of many high level mathematicians.
For the curious reader... |
So, I know I'm missing something simple, but I can't find a way to solve the Laplacian with the boundary conditions I've got down.
The Problem:
"Consider the semi-infinite plate sketched below with thickness 2b. The temperature at the base (x = 0) is constant at $T_0$. Heat is transferred on both sides of the plate to ... |
I've always used the method of Lagrange multipliers with blind confidence that it will give the correct results when optimizing problems with constraints. But I would like to know if anyone can provide or recommend a derivation of the method at physics undergraduate level that can highlight its limitations, if any.
Lag... |
It is known that every non-constant polynomial with real coefficients admits a factorization in terms of real and quadratic factors. The proof normally uses the Fundamental Theorem of Algebra. Is there an elementary proof of the above which does not involve complex numbers at all?
I published such a proof (see my artic... |
This is a great question! It's totally reasonable to expect - assuming GCH - that $A^B=A$ when the base $A$ is larger than the exponent $B$ since that's true in all the "simply-imaginable" situations. However, that's not the whole picture. As you've noticed, limit cardinals pose an odd difficulty, and it turns out that... |
I know how to work with the triple integral of the divergence of F part of the theorem, but in many textbooks, they don't explain the surface integral component. I don't understand how they go from here: $$\iint_{\delta W} F\boldsymbol{\cdot}kdS = \iint_{S_1} F\boldsymbol{\cdot}kdS_1 + \iint_{S_2} F\boldsymbol{\cdot}kd... |
Let $A$ be an orthogonal matrix with $\det (A)=1$. Show that there exists an orthogonal matrix $B$ such that $B^2=A$.
Thank you very much.
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join... |
I have never read or otherwise studied the Principia; however, I think the general distinction to which Russell is alluding is still very much a recognized principle in modern (formalized) mathematics. Its basically the difference between a sentence $\varphi,$ versus the metasentence $\vdash \varphi$.
Conceptually, the... |
Supposed that the derivative of $f:X\to Y$ is an isomorphism whenever $x$ lies in the sub-manifold $Z \subset X$, and assume that $f$ maps $Z$ diffeomorphically onto a $f(Z)$ . Prove that $f$ map a neighborhood of $Z$ diffeomorphically on to a neighborhood of $f(Z)$
Here is what I got so far
Since the derivative of $f:... |
To find limits of exponential functions, it is essential to study some properties and standards results in calculus and they are used as formulas in evaluating the limits of functions in which exponential functions are involved.
There are four basic properties in limits, which are used as formulas in evaluating the lim... |
[Note: if you are using smartphone or portable device to browser this post, some math formula might not appear properly. To see the math in correct form, scroll down to the bottom and click " View web version"]
Raspberry Pi has a Broadcom BCM2835 chip, which controls 26 GPIO (general purpose input/output) pins. There a... |
As I am working on a problem with 3 linear equations with 2 unknowns I discover when I use any two of the equations it seems I always find a solution ok. But when I plug it into the third equation with the same two variables , the third may or may not cause a contradiction depending if it is a solution and I am OK with... |
The lower attic
From Cantor's Attic
Revision as of 11:31, 31 May 2013 by Austinmohr (removing superfluous bullet points)
Welcome to the lower attic, where the countably infinite ordinals climb ever higher, one upon another, in an eternal self-similar reflecting ascent.
$\omega_1$, the first uncountable ordinal, and the... |
Little explorations with HP calculators (no Prime)
03-23-2017, 01:23 PM (This post was last modified: 03-23-2017 01:23 PM by pier4r.)
Post: #21
RE: Little explorations with the HP calculators
(03-23-2017 12:19 PM)Joe Horn Wrote: I see no bug here. Variables which are assigned values should never be used where formal va... |
Statement:
Every permutation $\sigma$ of a finite set is a product of disjoint cycles.
Proof:
Let $B_{1},B_{2},...,B_{r}$ be the orbits of $\sigma$, and let $\mu_{i}$ be the cycle defined by:
$\mu_{i}(x) = \begin{cases}\sigma(x) \text{ for } x \in B_{i}\\\ x \text{ otherwise }\\ \end{cases}$
Clearly $\sigma = \mu_{1}\m... |
You seem to have had the right idea of fixing the scale by arbitrarily choosing the value of one coefficient, and then solving for the rest. Apparently, you just got stuck at some point, presumably either because you couldn't solve for $b$ just with simple substitutions, or because your initial choice of $a = 1$ gave y... |
Let $f(x)$ be a function in a variable $x$. In differential calculus, the differentiation of the function $f(x)$ with respect to $x$ is written in the following mathematical form.
$\dfrac{d}{dx}{\, f(x)}$
For deriving the derivative of a constant multiple function with respect to a variable, we must know the fundamenta... |
Diagonalization
Diagonalization is a process that helps to directly compute values of hierarchies without having to go from the bottom. Each ordinal that is not a sucsessor has a fundemental sequence that helps. When we say some ordinal diagonalized to some finite number, we use: some ordinal[number] to express. You ca... |
Can you explain me, please, what does it mean the transpose of a matrix ? I know the definition in the context of matrix theory and its generalization to adjoint operators (transpose of a linear application). What is the fundamental idea behind transpose ? and why it is introduced and considered in today's mathematics ... |
I have a fixed number $a$. Now using $a$ I need to construct a number $b$ such that $0.99\leq b\leq 1$. Is there any mathematical formulation of such a construction that looks random. The generation of such a number should be deterministic. can somebody hint at any algorithms
For example $\,b=0.99 + \dfrac{\sin^2(\lamb... |
Exam-Style Questions on Sequences Problems on Sequences adapted from questions set in previous Mathematics exams.
1. GCSE Higher
Here is a picture of four models. Some of the cubes are hidden behind other cubes.
Model one consists of one cube. Model two consists of four cubes and so on.
(a) How many cubes are in the th... |
First off, the fact that the board actually blocks the sun light going into the house may have cooled down the house itself (same effect as a solar screen). Since this question is about how the pressure and temperature will be changed after installing the Eco-Cooler air conditioner (the bottle board solely), I will giv... |
I was reviewing RSA by hand.
I picked 53 and 59 as my primes. For e I picked 5. When I solved for d using extended euclid, I got 1 which obviously doesn't decrypt anything. I checked my answers online using calculators and got the same result. Did I pick e or a prime wrong? How do I make sure I don't get 1 as d?
I was ... |
broall wrote:
EgmatQuantExpert wrote:
What is the product of all values of x that satisfies the equation: \(\sqrt{5x} + 1= \sqrt{(7x - 3)}\) ?
A. 9 B. 11 C. 49 D. 99 E. None of the above
First, make sure that \(\sqrt{5x}\) and \(\sqrt{7x-3}\) have real value so \(x \geq 0\) and \(x \geq \frac{3}{7}\). Hence \(x \geq \f... |
I'm trying to approximate $\sqrt{101}$ using the Taylor series for the function $f(x)=\sqrt{x}$ centered at the point $x=100$. I need to obtain an approximation that is within $0.01$ of the correct answer. The Taylor series is given by
$$ f(x) = \sum_{k=0}^{n-1} \frac{f^{(k)}(100)}{k!}(x-100)^k + R_n(x) $$
where $R_n(x... |
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What is Shamir’s Trick used for?
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No, Sha... |
No one of the expressions is correct or wrong. Definitions are not correct or wrong. Definitions are consensus that we take about elements in a formalism.
We can define anything as we want in a formalism, simply we have to respect basic logic rules, such as using always the same definition, once we chose one. Moreover ... |
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