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When was $\sum$ introduced as the notation for a sum and who was the first person to solve a infinite sum other than 0+0+0+...?
According to Florian Cajori's
History of Mathematical Notations Vol II paragraph 438, the symbol $\displaystyle \sum$ for summation is attributed to Leonard Euler. In Euler's own words, "summa... |
The condition is a bit misleading and incomplete, the gradient of the function will indeed be a linear combination of the gradients of all constraints (equalities as well as inequalities), however there are some additional conditions on this linear combination which might make make things more clear. Assume that $f$ is... |
Chapter 03: General Theorem, Intermediate Forms
Rolle's theorem Geometrical interpretation of Rolle's theorem The mean value theorems Another form of mean value theorem Increasing and decreasing functions Cauchy's mean value theorem Extended mean value theorem Indeterminate form The form $\frac{0}{0}$ The form $\frac{\... |
The internal definition of the
sagesilent environment involves the use of verbatim text, which never can be written in a macro argument. The same kind of problem arises if you try something like
\AtBeginDocument{\begin{verbatim} Some verbatim text\end{verbatim}}
As a workaround, you can move to an auxiliary
tex file al... |
Graphing Quadratic Functions:
Quadratic equations in standard form are represented as \(ax^2~+~bx~+~c~=~0\)
To plot any function \(y~+~f(x)\)
The graph of a quadratic function is a parabola which can be represented in two forms:
Standard Form: \(ax^2~+~bx~+~c\) Vertex Form or \((a~-~h~-~k)\) form: \(f(x)~=~a(x~-~h)^2~+... |
Let V be the universe (the class of all sets), let W(0)=V, W(1) be the class of all singletons whose unique member element is a member set of W(0), and for n>0 let W(n+1) be the class of all singletons whose unique member element is a member set of W(n). Let, for every n>=0 S(n)=W(n+1)/W(n) be the class that is the dif... |
I think the missing link for you is not realizing that $Q$ is actually equal to $q_1 + q_2$: in a duopoly, quantity demanded can only be derived for the two firms in question. With that in mind, we can rewrite the profit functions for both firms in terms of $q_1$ and $q_2$ and then optimize with respect to the $q$'s ac... |
Description
Recently, I have been learning a couse called "
Numerical Analysis". The
fixed point iteration theory was introducted to solve the
the approximate root of the equations in this course.
Fixed point iteration theory: $x=Ψ(x) \Rightarrow x_{k+1}=Ψ(x_k)$ Example
Solving the approximate root of $f(x)=x^3+4x^2-10... |
There are two ways to answer your question. One is direct and has less depth to it, the other is more indirect and has a lot of depth to it. I will begin with the indirect one because it has wide ranging applications beyond finance or economics and because it should serve as a warning to journal editors and so forth. A... |
Higher order Melnikov function for a quartic hamiltonian with cuspidal loop
1.
Department of Mathematics, Sun Yat-sen University, Guangzhou, 510275, China
2.
Department of Mathematics, Zhongshan (Sun Yat-sen) University, 510275, Guangzhou, China
$X_\epsilon=(H_y+\epsilon f(x,y,\epsilon))\frac{\partial}{\partial x}+ (-H... |
Local and global well-posedness results for the Benjamin-Ono-Zakharov-Kuznetsov equation
1.
Université Paris-Est Marne-la-Vallée, Laboratoire d'Analyse et de Mathématiques Appliquées (UMR 8050), 5 Bd Descartes, Champs-sur-Marne, 77454 Marne-la-Vallée Cedex 2, France
2.
Université Paris 13 Sorbonne Paris Cité, LAGA, CNR... |
Equivalence between uniform $L^{2^\star}(\Omega)$ a-priori bounds and uniform $L^{\infty}(\Omega)$ a-priori bounds for subcritical elliptic equations
DOI: http://dx.doi.org/10.12775/TMNA.2018.036
Abstract Keywords References
F.V. Atkinson and L.A. Peletier, Elliptic equations with nearly critical growth, J. Differentia... |
Ok, here's my first attempt. Close scrutiny and comments appreciated!
The Two-Sample Hypotheses If we can frame two-sample one-sided Kolmogorov-Smirnov hypothesis tests, with null and alternate hypotheses along these lines:
H$_{0}\text{: }F_{Y}\left(t\right) \geq F_{X}\left(t\right)$, and
H$_{\text{A}}\text{: }F_{Y}\le... |
It's hard to say just from the sheet music; not having an actual keyboard here. The first line seems difficult, I would guess that second and third are playable. But you would have to ask somebody more experienced.
Having a few experienced users here, do you think that limsup could be an useful tag? I think there are a... |
What does the classical proof of the proposition "there exists irrational numbers a, b such that $a^b$ is rational" want to reveal? I know it has something to do with the difference between classical and constructive mathematics but am not quite clear about it. Materials I found online does not give quite clear explana... |
Entanglement is synonymous to ignorance!
In general, it arises whenever trying to break down a quantum system into subsystems. In more mathematical terms of quantum mechanics, this means to decompose the Hilbert space $\mathcal{H}$ of the full system into a Hilbert space $\mathcal{H}_{A}$ of a subsystem $A$ and a Hilbe... |
This question already has an answer here:
Apparently my question
is different from Lagrangian Mechanics - Commutativity Rule $\frac{d}{dt}δq=δ\frac{dq}{dt}$. I hadn't noticed because the answer given in the comments to this question was satisfactory for my immediate purposes. My question pertains to time-independent va... |
Good Morning!
I am new in signal processing and I am trying to do a work in noise control of an electronic steering lock device (ESL). My aim is to calculate the loudness (Zwicker Method- ISO 532 B) of this device. To do so, first I need to obtain the 1/3 octave spectrum of a time signal that I measure with a microphon... |
Most engineers have seen the moment-to-moment fluctuations that are common with instantaneous measurements of a supposedly steady spectrum. You can see these fluctuations in magnitude and phase for each frequency bin of your spectrogram. Although major variations are certainly reason for concern, recall that we don’t l... |
Current browse context:
math.DG
Change to browse by: References & Citations Bookmark(what is this?) Mathematics > Differential Geometry Title: Convergence of vector bundles with metrics of Sasaki-type
(Submitted on 2 Nov 2010 (v1), last revised 18 Mar 2011 (this version, v2))
Abstract: If a sequence of Riemannian manif... |
A differential equation can be easily converted into an integral equation just by integrating it once or twice or as many times, if needed. Let’s start with an example. Let $$\frac{dy}{dx} + 5y+1=0 \ldots (1)$$ be a simple first order differential equation. We can integrate it one time with respect to $x$ , to obtain $... |
Terms sourced from: http://iupac.org/publications/pac/51/12/2451/
"Quantities and Units in Clinical Chemistry", IUPAC and IFCC,
Pure and Applied Chemistry 1979, 51(12), 2451
base kind of quantity catalysed rate of reaction \(\xi_{\text{cat}}\)derived coherent unit derived kind of quantity derived non-coherent unit mean... |
Fraction & Decimals
Category : 5th Class
FRACTION AND DECIMALS
FUNDAMENTALS
Types of Fraction
Example: \[\frac{1}{3},\frac{2}{3},\frac{4}{5}\]
Example:\[\frac{5}{3},\frac{6}{5},\frac{7}{4},\frac{7}{7}\] etc.
Example:\[1+\frac{2}{3}\] is written as\[1\frac{2}{3}\],\[2+\frac{1}{5}\] is written as\[2\frac{1}{5}\]
Example:... |
I have done question on frequency response of RLC it is easy to find whether a given circuit is high pass filter or low pass filter. But I am wondering how to determine for band pass or band reject filters. Please help me and I would be obliged if someone explain it by considering an example of a passive filter (contai... |
This is a famous problem of intermediate analysis, also known as ‘Archimedes’ Cattle Problem Puzzle’, sent by Archimedes to Eratosthenes as a challenge to Alexandrian scholars. In it one is required to find the number of bulls and cows of each of four colors, the eight unknown quantities being connected by nine conditi... |
Lengthy post ahead! Look toward the end for a quick recap.
The relationship between energy and temperature is a little more complicated than what you sketched here.
Boltzmann Distribution
The atoms in a gas don't all have the same amount of energy. In fact, their energies greatly vary. It is true that temperature is th... |
To round off our series on round objects (see the first and second posts), let’s compute the sphere’s surface area. We can compute this in the same way we related the area and circumference of a circle two weeks ago. Approximate the surface of the sphere with lots of small triangles, and connect these to the center of ... |
[This is the 6th post in the current series about Wythoff’s game: see posts #1, #2, #3, #4, and #5.
Caveat lector: this post is a bit more difficult than usual. Let me know what you think in the comments!]
Our only remaining task from last week was to prove the mysterious Covering Theorem: we must show that there is ex... |
Answer
$f=64.3249482 \dfrac{\sqrt T}{Ld}$
Work Step by Step
General equation for inverse variation is given by $y=\dfrac{k}{x}$ Here, we have $f=k \dfrac{\sqrt T}{Ld}$ ...(1) Plug the data, we have $262=k \dfrac{\sqrt {670}}{(62)(0.1025)}$ and $K \approx 64.3249482$ Thus, the equation (1) becomes: $f=64.3249482 \dfrac{... |
To round off our series on round objects (see the first and second posts), let’s compute the sphere’s surface area. We can compute this in the same way we related the area and circumference of a circle two weeks ago. Approximate the surface of the sphere with lots of small triangles, and connect these to the center of ... |
I'm a student in electrical engineering in Belgium and I use a multiple feedback bandpass filter in one of my projects.
I tried to find out the transfer function of this filter and this is what I found:
$$ \frac{V_o}{V_i}=-\left( j\omega C+ \frac{2}{R_2}+\frac{R_1+R_3}{R_1R_2R_3}\cdot\frac{1}{j\omega C} \right) ^{-1} $... |
Lasted edited by Andrew Munsey, updated on June 15, 2016 at 2:04 am.
There was an error working with the wiki: Code[12]s and other circular path
There was an error working with the wiki: Code[13]s
There was an error working with the wiki: Code[14]s
There was an error working with the wiki: Code[15]s
There was an error ... |
One shouldn't imagine the T-duality between the two heterotic strings to be a $Z_2$ group, like in the case of type II string theories' T-duality. In type II string theory, there is only one relevant scalar field, the radius of the circle producing T-duality, and it gets reverted $R\to 1/R$ under T-duality.
In the hete... |
I have come across two similar definitions of
primary fields in conformal field theory. Depending on what I am doing each definition has its own usefulness. I expect both definitions to be compatible but I can't seem to be able to show it. By compatible I mean definition 1 $\iff$ definition 2. I will write both definit... |
I have been reviewing general equilibrium models and was trying to find an efficient method for computing the core of a cooperative game. I was taught this topic in a very poor way so I believe I still have some conceptual errors.
Here is a thought I had:
Suppose we are in an economy with three consumers, $A$, $B$, and... |
Search
Now showing items 1-10 of 27
Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
The SImg Wiki bases on a DokuWiki. For editing pages a registration is required.
For every namespace a navigation bar can be generated by creating the page
sidebar in the corresponding namespace.If this page does not exist, the version of the next higher level namespace is used.
This is a multi-language Wiki written in... |
I am attempting to investigate transformations between two distinct sets of vertices on n-dimensional manifolds with a minimal change in the fundamental shape of the vertices. I will give some background so that when my question is asked it will be fully understood, the introductory explanation describes how the metric... |
FSc Part 1 (KPK Boards)
Notes of FSc Part 1 of “A Textbook of Mathematics For Class XI” published by Khyber Pakhtunkhwa Textbook Board, Peshawar. We are posting the notes chapter-wise. These notes are shared as open educational resources. This page will be continuously updated.
Author: Engr. Majid Amin Type: Solutions ... |
Blatantly ripped off from chem.SE, this post is meant to help people understand how to use MathJax formatting of mathematical expressions here on
Robotics. Getting started with MathJax
On
Robotics Stack Exchange, we use MathJax to format mathematical expressions. MathJax is a tool that lets us display LaTeX expressions... |
Typesetting and Converting Mathematics¶
There are two main uses for MathJax:
Typesetting all the mathematics within a web page, and Converting a string containing mathematics into another form.
In version 2, MathJax could perform the first function very well, but it was much harder to do the second. MathJax version 3 m... |
Mathematically, the intuition is simple. (This is not a formal proof, though it can easily be turned into one. It's just another dimension of intuition -- symbolic intuition.)
The price elasticity of demand at $(P_0, Q_0)$ is the infinitesimal ratio of percentage change in quantity demanded ($dQ/Q_0$) to percentage cha... |
Equivalence of Definitions of Polynomial Function on Subset of Ring Contents Theorem
Let $R$ be a commutative ring with unity.
Let $S \subset R$ be a subset.
A
polynomial function on $S$ is a mapping $f : S \to R$ for which there exist: a natural number $n \in \N$ $a_0, \ldots, a_n \in R$
such that for all $x\in S$:
$\... |
Since I spend a lot of time on solving sparse linear equation systems then I am also a user of sparse matrix reordering methods. My claim to fame is that I have implemented approximate minimum degree myself and it is used in MOSEK.
Below I summarize some interesting link to graph partitioning software:
It is very commo... |
If you take a look at the documentation, Mathematica's symbolic Fourier transform function,
FourierTransform, computes
$$\hat f(k) = \frac{1}{\sqrt{2\pi}}\int_{-\infty}^{\infty}f(x)e^{ikx}\mathrm{d}x$$
You can discretize some piece of this integral by limiting $x$ and $k$ to values $x_1 + (r-1)\Delta x$ and $(s-1)\Delt... |
Roll Your Own Differentiation Filters Introduction
There are many times in digital signal processing that it is necessary to obtain estimates of the derivative of some signal or process from discretely sampled values. Such numerical derivatives are useful in applications such as edge detection, rate of change estimatio... |
Eigenvalue criteria for existence of multiple positive solutions of nonlinear boundary value problems of local and nonlocal type
DOI: http://dx.doi.org/10.12775/TMNA.2006.003
Abstract
New criteria are established for the existence of multiple positive
solutions of a Hammerstein integral equation of the form $$ u(t)= \i... |
I know that if we move a rectangular wire from no magnetic field to through a magnetic field, there would be an induced voltage because there is change in flux (b∆x). However, if we moved a wire/rod in the same situation, it will also induce a voltage but is it due to the change in flux (b∆x) or charge separation?
The ... |
The simplest approach (in terms of programming effort) might be to try using an existing graph layout tool. Those solve a related problem: given a graph with distances on the edges, try to find the best layout to draw the graph on the plane. You can treat your problem as an instance of the graph layout problem: we have... |
The model you referenced in your question is called the "one-way model." It assumes that random row effects are the only systematic source of variance. In the case of inter-rater reliability, rows correspond to objects of measurement (e.g., subjects).
One-way model: $$ x_{ij} = \mu + r_i + w_{ij} $$ where $\mu$ is the ... |
Convergence of measures
$\newcommand{\abs}[1]{\left|#1\right|}$ A concept in measure theory, determined by a certain topology in a space of measures that are defined on a certain $\sigma$-algebra $\mathcal{B}$ of subsets of a space $X$ or, more generally, in a space $\mathcal{M} (X, \mathcal{B})$ of charges, i.e. count... |
Two different documents about how to edit are being combined here. Each starts with the XXXX title. At present the simple outline is first; it should keep users productive for their first few days.
XXXXXXXXXEdit The basicsEdit
The
bare essential points of editing are: Type in the edit box, much the same as in any wordp... |
Expected Index of Coincidence usually refers to a language's expected index of coincidence (1.73 for English, or 0.067 if you're not normalising).
The formula in question is usually used to determine the length of the key ($t$) given the (measured) $IC$ of received cipher-text. $IC$ is the probability that two randomly... |
I am reading about Riemann-Stieltjes Integrals in Carother's Real Analysis. I am trying to prove the following Theorem:
Theorem: $14.9$
Let $\alpha$ be continuous and increasing. Given $f$ $\in$ $R_{\alpha}([a,b])$ and $\epsilon >0 $.
There exists a step function $h$ on $[a,b]$ with $||h||_{\infty}$ $\leq$ $||f||_{\inf... |
A tl;dr of the below is basically what was echoed in the comments: it's not even remotely close to Graham's number, nor even close to the "building block" of it that is $3 \uparrow \uparrow \uparrow \uparrow 3$. Truthfully, pretty much any analogy grounded in reality would only serve to show "yeah Graham's number is wa... |
I'm trying to learn how to apply WKB. I asked a similar question already, but that question was related to finding the energies. Here, I would like to understand how to find the wave functions using WKB.
An electron, say, in the nuclear potential$$U(r)=\begin{cases} & -U_{0} \;\;\;\;\;\;\text{ if } r < r_{0} \\ & k/r \... |
Sandbox From AbInitio
Revision as of 03:37, 9 January 2008 (edit)
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(→Scribble below)
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X F Wang
Articles written in Pramana – Journal of Physics
Volume 71 Issue 1 July 2008 pp 167-173 Research Articles
The EPR 𝑔 factors $g_{i}$ $(i = x, y, z)$ for the interstitial Ti
3+ in rutile are theoretically studied from the perturbation formulas of these parameters for a 3d 1 ion in rhombically compressed octahed... |
I am working on a cryptographic scheme and I need to rely on the following problem, which I have nicknamed the
"Hybrid Decisional Bilinear Diffie Hellman (hDBDH)" problem:
Let $e: \mathbb G_1 \times \mathbb G_1 \rightarrow \mathbb G_T$ be an efficient bilinear pairing. Given the tuple $(g,g^x,e(g,g)^y,Q)$ as input, the... |
Generally speaking functions of operators are defined as
spectral functions, making use of the spectral theorem machinery.
The approaches based of power series usually have not a rigorous basis: Even identities like $$e^A = \sum_n \frac{1}{n!}A^n$$ are generally false if $A$ is an
unbounded operator.
Nevertheless in mo... |
Valter Moretti's answer is very nice, and I learned some things from reading it. This answer is meant to be a lower-level explanation of the basics of this topic, giving a treatment in the same style that is found when most GR texts introduce this topic.
Definition of a Killing vector
A Killing vector $\xi$ is vector f... |
No laws are broken, but Planck's constant is higher than in our world.
I would say that no physical laws are broken, it's just that the double jump is performed in a universe where Planck's constant has a (much) higher value.
Looking at the uncertainty principle for energy:$$\Delta E \Delta t \geq \frac{\hbar}{2}$$Just... |
2018-08-25 06:58
Recent developments of the CERN RD50 collaboration / Menichelli, David (U. Florence (main) ; INFN, Florence)/CERN RD50 The objective of the RD50 collaboration is to develop radiation hard semiconductor detectors for very high luminosity colliders, particularly to face the requirements of the possible u... |
While vertical asymptotes describe the behavior of a graph as the
output gets very large or very small, horizontal asymptotes help describe the behavior of a graph as the input gets very large or very small. Recall that a polynomial’s end behavior will mirror that of the leading term. Likewise, a rational function’s en... |
Injection iff Left Cancellable Theorem Proof $\forall X: \forall g_1: X \to Y, g_2: X \to Y: f \circ g_1 = f \circ g_2 \implies g_1 = g_2$
Let $f: Y \to Z$ be an injection.
Let $X$ be a set
Let $g_1: X \to Y, g_2: X \to Y$ be mappings such that:
$f \circ g_1 = f \circ g_2$ Then $\forall x \in X$:
\(\displaystyle \map f... |
Now we know how to do some math with vectors, and the question arises, “If we can add and subtract vectors, can we also multiply them?” The answer is yes and no. It turns out that there is not one unique way to define a product of two vectors, but instead there are two…
Scalar Product
Soon we will be looking at how we ... |
Faddeeva Package From AbInitio
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Line 26: Line 26: :<math>\mathrm{erfi}(x) = -i\mathrm{erf}(ix) = -i[e^{x^2} w(x) - 1]</math> (imagina... |
I would say because of the way you efficiently solve problems as well as pedagogy. Both are used in both cases though.
The Hamiltonian operator approach emphasises the spectrum aspects of quantum mechanics, which the student is introduced to at this point $-$ but here is a Lagrangian
$$\mathcal{L}\left(\psi, \mathbf{\n... |
ROOT 6.19/01
Reference Guide
These examples show the functionalities of the VecOps utilities.
file vo001_AdoptOrOwnMemory.C In this tutorial we learn how the RVec class can be used to adopt existing memory or allocate some. file vo001_AdoptOrOwnMemory.py In this tutorial we learn how the RVec class can be used to adopt... |
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... |
It looks like you're new here. If you want to get involved, click one of these buttons!
I'd like to tell you about two kinds of logic. In both, we start with a set \( X \) of "states of the world" and build a set of statements about the world, also known as "propositions". In the first, propositions correspond to subse... |
[This is the 6th post in the current series about Wythoff’s game: see posts #1, #2, #3, #4, and #5.
Caveat lector: this post is a bit more difficult than usual. Let me know what you think in the comments!]
Our only remaining task from last week was to prove the mysterious Covering Theorem: we must show that there is ex... |
On spherical cycles in the complement to complex hypersurfaces Natalia A. Bushueva Institute of Mathematics, Siberian Federal University, Krasnoyarsk, Russia Abstract: It is known due to S. Yu. Nemirovski, that for $n\geq3$ and generic hypersurface $V\subset\mathbb C^n$ of degree $d\geq3$ there exists a sum of the Whit... |
I did some algebra...
In Planck unit, if make $\mu_0 = 4\pi$ and $\epsilon_0 = \frac{1}{4\pi}$ you get:
$$\mu_0 = 4\pi \cdot \frac{m_p l_p}{t_p^2 I_p^2} = 1.2566368452237765 \cdot 10^{-6} N \cdot A^{-2} $$
(where $4\pi$ is the supposed value of $\mu_0$, $m_p$ is Planck mass, $l_p$ is Planck length, $t_p$ is Planck time... |
Looping Directions and Integrals of Eigenfunctions over Submanifolds
Article
First Online:
57 Downloads Abstract
Let \((M,\,g)\) be a compact
n-dimensional Riemannian manifold without boundary and \(e_\lambda \) be an \(L^2\)-normalized eigenfunction of the Laplace–Beltrami operator with respect to the metric g, i.e.,
... |
Hom-set adjunction Collection
context ${\bf C},{\bf D}$ … small category context $F$ in ${\bf D}\longrightarrow{\bf C}$ context $G$ in ${\bf C}\longrightarrow{\bf D}$ definiendum $\Phi$ in $\mathrm{it}$ postulate $\Phi$ in $\mathrm{Hom}_{\bf C}(F-,=)\cong\mathrm{Hom}_{\bf D}(-,G=)$ Discussion
Here $\mathrm{Hom}_{\bf C}... |
Writing Mathematics for MathJax¶ Putting mathematics in a web page¶
To put mathematics in your web page, you can use TeX and LaTeX notation, MathML notation, AsciiMath notation, or a combination of all three within the same page; the MathJax configuration tells MathJax which you want to use, and how you plan to indicat... |
Mahalanobis distance is unperturbed by inclusion of highly correlated additional variable, unlike Euclidean distance (Dasgupta 2008). With an application of law of iterated logarithm, an almost sure result is proved in this direction for convergence of sample
$$D^2$$
statistic to
$$\Delta ^2,$$
the population Mahalanob... |
In my current research, I'm confronted with the justification of some facts, and I don't know how to proceed in proving them, so I need to know if there exist some theorems (precisely three theorems) which allow me to do so.
The problem I am investigating is the following: I have an explicit real valued function $f$, D... |
It might help to have an example of each of the three types of statement. So to be concrete, let $F(\vec{v})$ be the probability that a given particle has speed $\vec{v}\in[\vec{v},\vec{v}+d\vec{v}]$ and thus the differential particle flux is given by your expression:
$$ d\vec{\phi}(\vec{v}) = n\vec{v}F(\vec{v})|d\vec{... |
In QFT, a representation of the Lorentz group is specified as follows:$$U^\dagger(\Lambda)\phi(x) U(\Lambda)= R(\Lambda)~\phi(\Lambda^{-1}x)$$Where $\Lambda$ is an element of the Lorentz group, $\phi(x)$ is a quantum field with possibly many components, $U$ is unitary, and $R$ an element in a representation of the Lore... |
In Mas-Colell microeconomics textbook I have found that profit maximization problem (as well as many further optimization tasks) could be represented with application of some transformation function (p.135):
$\begin{cases}Max\text{ }p*y\\s.t.\text{ }F(y)\leq0\end{cases}$
Where y is production vector and
F(.) is a trans... |
As I've already mentioned in my previous answer, the method of using the QZ algorithm for matrix pencils on the Frobenius companion linearization of the polynomial eigenproblem is not always the most efficient approach. To illustrate this, I'll outline a general method for solving a
hyperbolic quadratic eigenvalue prob... |
On well-posedness of vector-valued fractional differential-difference equations
1.
Departamento de Matemáticas, Instituto Universitario de Matemáticas y Aplicaciones, Universidad de Zaragoza, 50009 Zaragoza, Spain
2.
Departamento de Matemática y Ciencia de la Computación, Universidad de Santiago de Chile, Las Sophoras ... |
Let $X$, $Y$ be i.i.d. random variables with distribuition $\mathcal{N}(0,1/2)$ and $Z = X^2 + Y^2$. I'd like to prove based on $X$ and $Y$ pdf's that $Z$ has exponential distribuition.
First use the joint pdf of $X$ and $Y$ and switch to polar coordinates, then $$ \mathbb{P}(Z\leq z)=\mathbb{P}(X^2+Y^2\leq z)=\frac{1}... |
Quick recap’ of April on the Micro blog.
2019-04-01: Arno,
Human Incognito. 2019-04-01: > You are being watched. Private and state-sponsored organizations are monitoring> and recording your online activities. privacytools.io provides knowledge and> tools to protect your privacy against global mass surveillance. 2019-04... |
What's different in MultiMarkdown 3.0? What's different in MultiMarkdown 3.0? Why create another version of MultiMarkdown?
Maintaining a growing collection of nested regular expressions was going to become increasingly difficult. I don't plan on adding much (if any) in the way of new syntax features, but it was a mess.... |
Correlation vs Regression
I am still confused as to how correlation differs to regression,
technically. I understand that one is a measure of association and one a measure of causation
This is incorrect, the difference between correlation and regression is not causal. Both measures are
associational measures. I will el... |
One of the basic concepts of calculus is the correspondence between sums and integrals, which is easily evaluated with the help of Faulhaber’s formula. The Euler–Maclaurin formula is considered as a powerful connection between integrals. It is mostly used to approximate integrals by finite sums, or conversely to calcul... |
№ 9
All Issues Volume 64, № 10, 2012
Ukr. Mat. Zh. - 2012. - 64, № 10. - pp. 1299-1313
We propose a version of the Gauss - Ostrogradskii formula for a Banach manifold with uniform atlas.
Ukr. Mat. Zh. - 2012. - 64, № 10. - pp. 1314-1329
We study the asymptotic behavior of the eigenvalues and eigenfunctions of a singula... |
Mott effect and \(J/\psi\) dissociation at the quark-hadron phase transition 25 Downloads Citations Abstract.
We investigate the in-medium modification of pseudoscalar and vector mesons in a QCD-motivated chiral quark model by solving the Dyson-Schwinger equations for quarks and mesons at finite temperature for a wide ... |
Some degenerate parabolic problems: Existence and decay properties
1.
Dipartimento di Matematica, Sapienza Universitá di Roma, Piazzale A. Moro 5, 00185 Roma, Italy, Italy
Keywords:unbounded solutions, 1}(\Omega))$-solutions, T;W_0^{1, $L^1(0, Nonlinear parabolic problems, decay estimates, degenerate parabolic equation... |
We often use Ricker wavelets to model seismic, for example when making a synthetic seismogram with which to help tie a well. One simple way to guesstimate the peak or central frequency of the wavelet that will model a particlar seismic section is to count the peaks per unit time in the seismic. But this tends to overes... |
Is it correct to represent Higgs VEV as the coherent state?
I mean, suppose translational invariant coherent state
$$
|\alpha\rangle = Ne^{\alpha \hat{a}^{\dagger}_{\mathbf p =0}}|\alpha =0\rangle, \quad N: \quad \langle \alpha|\alpha\rangle = 1 $$
of massless particles with zero dispersion relation. In principle, it i... |
The functional derivative $\frac{\delta}{\delta \phi}$ acts on
functionals, things that map functions to real numbers. That is, they act on actions $S$, not lagrangians $L$. I don't know where you got your original question, but there indeed should be a minus sign! Altogether, I think what you're asking is why:$$\frac{... |
Unit 02: Differentiation
Notes (Solutions) of Unit 02: Differentiation, Calculus and Analytic Geometry, MATHEMATICS 12 (Mathematics FSc Part 2 or HSSC-II), Punjab Text Book Board Lahore. You can view online or download PDF. To view PDF, you must have PDF Reader installed on your system and it can be downloaded from Sof... |
Is it possible to partition $\mathbb R^3$ into unit circles?
The construction is based on a well ordering of $R^3$ into the least ordinal of cardinality continuum. Let $\phi$ be that ordinal and let $R^3=\{p_\alpha:\alpha<\phi\}$ be an enumeration of the points of space. We define a unit circle $C_\alpha$ containing $p... |
2 Methods for Simulating Radiated Fields in COMSOL Multiphysics®
In Part 2 of our blog series on multiscale modeling in high-frequency electromagnetics, we discuss a practical implementation of multiscale techniques in the COMSOL Multiphysics® software. We will simulate radiated fields using two different techniques an... |
This is a comment on a post by Andreas Blass here.
I have not read Kripke's statement, apart from Andreas's sketch above, but it sounds familiar from elsewhere, so let me comment a bit on the family of results and the many discussions about a family of unprovable statements of the form "for every $n$ there is a finite ... |
The qualifier "natural" is meant to exclude examples like "PA + P=NP" or "PA + True $\Pi_1$".
For concreteness, let's say that "natural" = sound, computably enumerable, with a feasible proof-checker. Context of the question.
A naive way to approach the P vs NP problem, from the logical point of view, could go like this... |
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