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I'm reading about residue calculus. I read that the standard procedure for integrating $\int_{-\infty}^\infty R(x)dx$ where $R(x)$ is a rational function whose denominator has degree at least 2 units greater than the numerator and no poles on the real line, is to integrate the complex function $R(z)$ over a closed curv... |
My students frequently mix up my $t$'s with my $+$'s and my $y$'s with my $4$'s.
What is a good handwriting font for distinguishing these and other easily confused symbols?
Mathematics Educators Stack Exchange is a question and answer site for those involved in the field of teaching mathematics. It only takes a minute ... |
This was a humorous thought experiment that occurred while chatting about black holes. The person that I was talking to assumed that a black hole required a specific density to be achieved. I pointed to the formula for the Schwarzschild radius. This suggests that low density black holes are possible if they are large e... |
If I have observations of $y_{i}$ and $x_{i}$ which are i.i.d. I also have OLS assumptions such as $E(\epsilon_{i} \mid X_{i})= 0$, my qustion is: If I project $y_{i}$ onto a constant $\mu$, that is, we have model $y_{i} = \mu + \epsilon_{i}$. Does finding the OLS estimator $\hat\mu$ has anything to do with $x_{i}$? Be... |
I’m not sure if this answering attempt is correct in the light of Mithoron’s and ron’s comments on your question, but this is the way I learnt it, so if this is wrong I will at least learn something, too.
We all know what s-, p- and d-orbitals look like, but what is the significance, and why do these orbitals preferent... |
I think the best answer is the one given here: http://www.nick-santos.com/jokes/2007/05/mathematician-and-plumber.html
EDIT (at Aryabhatta's suggestion): The area is $$\int\int_{\rm circle}1\,dy\,dx=\int_0^{2\pi}\int_0^Rr\,dr\,d\theta={\rm etc.}$$ but this loses all the flavor of the link.
MORE EDIT: The link died, so ... |
Given a set $P$ of real numbers $\ge 1$, define the
gap among different products in $P$ as
$$g(P) = \inf \big\{\prod_{i=1}^n p_i^{a_i} - \prod_{i=1}^n p_i^{b_i} \mid p_i\in P;\,\, p_i\ne p_j \,\text{ if }\, i\ne j ; \,\,a_i, b_i \in \mathbb{N}\cup \{0\};\,\, a_1 \ne b_1 \big\}$$
If $g(P)>0$ in one could say that the se... |
Let $\mu(\cdot)$ be the Mobius function, defined on the natural numbers by
$$\displaystyle \mu(n) = \begin{cases} (-1)^{\omega(n)} & \text{if } n \text{ is square-free} \\ 0 & \text{otherwise}.\end{cases}$$
Here $\omega(n)$ is the number of distinct prime divisors of $n$. It is well-known that the Mertens function $M(x... |
This answer summarises parts of TAoCP Vol 3, Ch 6.4.
Assume we have a set of values $V$, $n$ of which we want to store in an array $A$ of size $m$. We employ a hash function $h : V \to [0..M)$; typically, $M \ll |V|$. We call $\alpha = \frac{n}{m}$ the
load factor of $A$.Here, we will assume the natural $m=M$; in pract... |
In Atiyah Macdonald, for a commutative and unital ring $A$ the tensor product of $A$-modules, $M,N$ is defined by the usual universal property:
A pair $(T,g)$ with $T$ an $A$-module and $g$ an $A$-bilinear map $g\colon M \times N \to T$ such that for any $A$-module $P$ with an $A$-bilinear map $f\colon M \times N \to P... |
How would I do
{text}_{i=1}^{i=n} with the written
exactly above and below the text?
Hope you can help!
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. It only takes a minute to sign up.Sign up to join this community
How would I do
{text}_{i=1}... |
I like George Bergman's explanation (beginning in section 7.4 of his
Invitation to General Algebra and Universal Constructions).
We start with a motivating example.
Suppose you are interested in solving $x^2=-1$ in $\mathbb{Z}$. Of course, there are no solutions, but let's ignore that annoying reality for a moment.
We ... |
This has been a question I've been asking myself for quite some time now.
Is there a physical Interpretation of the Hypersingular Boundary Operator?
First, let me give some motivation why I think there could be one. There is a rather nice physicial interpretation of the Single and Double Layer potential (found here: Ph... |
Miscellaneous matrix functions¶
sage.matrix.matrix_misc.
permanental_minor_polynomial(
A, permanent_only=False, var='t', prec=None)¶
Return the polynomial of the sums of permanental minors of
A.
INPUT:
\(A\) – a matrix \(permanent_only\) – if True, return only the permanent of \(A\) \(var\) – name of the polynomial var... |
If you have an inequality that has two absolute value bars like $|4x+1|<|3x|$, how do you go about doing this? I know that if $4x+1<3x$, then those $x$'s will work but what else do I do? I think you do $4x+1<-3x$. Is this correct?
You could also square everything $$ |f(x)| < |g(x)| \Leftrightarrow |f(x)|^2 < |g(x)|^2 \... |
Saving time Rate of return on invested capital Rate of withdrawal in retirement Saving rate Total invested capital Value of windfall at \(t=\) 0 Savings per time Time when the windfall and consistent savings are equal Net present value Value of cash received at time \(t\) Hypothetical rate of return
This article summar... |
Consider the standard linear regression model: $y_i = \alpha + \beta D_i + e_i$ where the coefficients are defined by linear projections and $D_i$ is a dummy variable. In the population, the coefficients are given by:
$$\alpha = E[y_i \mid D_i =0] \ \text{and} \ \beta = E[y_i \mid D_i = 1] - E[y_i \mid D_i =0]$$
Using ... |
tl;dr
Upon counting the orbits of the cells of a 3D cube under the octahedral group action, I found out the result is a sum of triangular numbers, which has a very intuitive geometric reason.
The gory detailsThe octahedral group can be thought of as the group of symmetries obtained by applying a series of 90-degree rot... |
In Brezis'
Functional analysis, Sobolev spaces and partial differential eqautions, exercise 6.24 (3) asks to prove that for a self-adjoint operator $T\in \mathcal{L}(H)$, $H$ a Hilbert space, the following properties are equivalent
(vii) $(Tu, u)\leq |Tu|^2, u\in H$
(viii) $(0,1)\subset \rho(T)$
where $\rho(T)$ denotes... |
Can central theorem justify normality assumption of assets return distribution? And if it can why the empirical evidence show this assumption, which many finance models are based on, is a far cry from reality?
No. I just published a paper on this. If return is defined as $$r_t=\frac{p_{t+1}q_{t+1}}{p_tq_t},$$ and since... |
CryptoDB Or Sattath Publications Year Venue Title
2019
EUROCRYPT
On Quantum Advantage in Information Theoretic Single-Server PIR 📺
In (single-server) Private Information Retrieval (PIR), a server holds a large database $${\mathtt {DB}}$$ of size n, and a client holds an index $$i \in [n]$$ and wishes to retrieve $${\m... |
By the end of this series of posts we will have composed some code in Python (roughly 100 lines) that proves the satisfiability of Partition Problem instances with zero knowledge.
Three preliminary notes I will assume some basic Computer Science background, as well as familiarity with Python, but not much more. I haven... |
I am an undergraduate studying quantum physics with the book of Griffiths. in 1-D problems, it said a free particle has un-normalizable states but normalizable states can be obtained by sum up the solutions to independent Schrodinger equations. in my view the book also suggests that a scattering state with E>V(infinity... |
Your equation $v_{\rm ac} =v_{\rm ab} + v_{\rm bc}$ is actually an equation relating to vector addition, $\vec v_{\rm ac} =\vec v_{\rm ab} + \vec v_{\rm bc}$
In one dimension this equation could be written as $v_{\rm ac}\,\hat x =v_{\rm ab} \,\hat x + v_{\rm bc}\,\hat x$ where $v_{\rm ac}, \,v_{\rm ab}$ and $v_{\rm bc}... |
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A fractal dimension is a ratio providing a statistical index of c... |
I have a problem understanding how phasors work and I'll use a problem from a recent exam to illustrate the misunderstanding.
Note: Underlined variables such as \$\underline{V}\$ are considered here to be complex numbers, while non-underlined are considered to be magnitudes of the complex numbers.
Here's the text:
We h... |
Are there any examples of subspaces of $\ell^{2}$ and $\ell^{\infty}$ which are not closed?
Take the subspace of $\ell^2$ (or $\ell^\infty$) consisting of sequences with finitely many non-zero coordinates.
Clearly, this is a subspace (sum of sequences still has at most # of nonzeros of first seq + # of nonzeros in seco... |
Given a $n\times n$ symmetric random matrix such that
all diagonalelements are all fixedas $0$. randomly select$k$ distinct cells in the upper triangle (excluding the diagonal), and then fixthem as $1$. The elements in the lower triangle are set accordingly. Of course $k\le \frac{n^2-n}{2}$. all other elements are inde... |
Your question is valid and is very good you are thinking this way so young.
First, error propagation is a whole area of its own and there is not a unique way to do so, nor there is an absolute best way to be provided. So much so that the ISO document used for having a consensus on this, is called "Guide to the Expressi... |
I need to find the intersection of the internal tangents of two point sets $V_a, V_b$ in $\mathbb{R}^2$, defined via their convex hulls. We can assume that the sets are disjoint and linearly separable, so I think the internal tangents are uniquely defined as the two lines which are tangent to each of the convex hulls o... |
This is a microcanonical ensemble approach to a simple model of a two dimensional polymer bundle. The professor of the course I took does a lot of research in the area of polymer physics and so set a few problems pertaining to them. They aren’t easily found in textbooks or online either (this website notwithstanding) b... |
What's the difference between these? Both are measurements of some form of signal power, but surely there's some difference between the power they are measuring?
The fast Fourier transform ($\textrm{FFT}$) algorithms are fast algorithms for computing the discrete Fourier transform ($\textrm{DFT}$). This is achieved by ... |
I don't know how familiar with Banach spaces you are. It's a standard fact that "absolutely summable series converge" in a Banach space (in the same way this is true for series of numbers). More precisely, if $(v_{n})_{n \in \mathbb{N}}$ is a sequence in a Banach space $B$ and $\sum_{n = 1}^{\infty} \|v_{n}\|_{B} < \in... |
I have been thinking about the question "What is the best -- i.e., some combination of shortest, most natural, easiest -- proof of the Nullstellensatz?" recently on the eve of a commutative algebra course.
In my notes up to this point I had been following Kaplansky's treatment of Goldman domains and Hilbert-Jacobson ri... |
Given two categories $I$ and $J$ we say that
colimits of shape $I$ commute with limits of shape $J$ in the category of sets, if for any functor $F : I \times J \to \text{Set}$ the canonical map $$\textrm{colim}_{i\in I} \text{lim}_{j\in J} F(i,j) \to \textrm{lim}_{j\in J} \text{colim}_{i\in I} F(i,j)$$ is an isomorphis... |
It is not possible to be completely sure there is only one photon in the apparatus and in the quantum sense this is even an ambivalent question to ask. But to the question "Is there a source of photons for which we
almost always detect one outcoming photon in a given time interval?" the answer is yes, single photon sou... |
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... |
A polytime algorithm that can find such a collection of edges
even in the promise version of this problem can be used as a blackbox to solve the
Hamiltonian Path problem in polynomial time, and thus this promise problem is NP-Hard under Cook reductions. The idea here is to use the algorithm for solving the promise prob... |
Introduction¶
A recent talk by Vincent Warmerdam about how simple models can outperform state-of-the-art ML approaches was a real eye opener to me. What amazed me the most while watching the video, is his astonishing creativity when it comes to feature creation and engineering. Although it is commonly known that good f... |
I think your confusion arises because you think that the electron is
modelled by the wavepacket. Instead the wavepacket of an electron which we suspect near a point $x_0$ represents (or is associated with) the electron and tells us how likely it is to find the electron near that point $x_0$. This is an important distin... |
Magnetism is not explained by conservation of energy. But magnetism is consistent with conservation of energy.
It is commonly stated that the magnetic field does no work. It is true that the magnetic field does no work on charged particles through the Lorentz force law. The force delivered on a charge due to a magnetic... |
Answer
(a)$\tau=(\frac{L}{2})mg$ (b)0 (c)$\tau=(\frac{L}{2})mg$
Work Step by Step
We know that (a) $\tau=r\times F$ $\implies \tau=(\frac{L}{2})mg$ (b) $\tau=r\times F$ $\implies \tau=(0)mg$ $\tau=0$ (c) $\tau=r\times F$ $\tau=-(\frac{L}{2})mg$
You can help us out by revising, improving and updating this answer.Update ... |
The statistical model under consideration is given by the independent realizations of two independent binomial distributions: $$ x_1 \sim \mathrm{Bin}(n_1, p_1), \quad x_2 \sim \mathrm{Bin}(n_2,p_2), $$ and the null hypothesis is $H_0\colon\{p_1=p_2\}$.
According to my calculations, the deviance (minus double log-likel... |
I'm currently trying to teach myself the path integral formulation of QFT (having studied the canonical approach previously), but I'm having some conceptual difficulties that I hope I can clear up here.
For simplicity, consider the case of a free, single real scalar field. The path integral formulation for a two point ... |
Abaid ur Rehman Virk, Tanveer Abbas and Wasim Khalid
)}{\sqrt{\frac{{{d}_{u}}+{{d}_{v}}-2}{{{d}_{u}}\cdot {{d}_{v}}}}}, \\\,\,\,\,\,GAII\left( G \right)=\prod\limits_{uv\in E\left( G \right)}{\frac{2\sqrt{{{d}_{u}}\cdot {{d}_{v}}}}{{{d}_{u}}+{{d}_{v}}}}, \\G{{A}^{a}}II\left( G \right)=\prod\limits_{uv\in E\left( G \rig... |
In case this question appeared here I apologize for the preposterous usage of computer space and attention of participants. I searched over there, for a similar or the same question for an answer but resigned. :)
I am reading:
S. B. Niefield, Cartesianness, topological spaces, uniform spaces, and affine schemes,
J. Pur... |
Assume that we have $p$ finite sets ${m_1},{m_2},...,{m_p}$, with
known cardinalities ${M_1},{M_2},...,{M_p}$, where $1 \le {M_i} \leq q$ ($i=1,2,...,p$).
Each set contains (distinct) elements, taken from GF($q$) (I am interested in particular in the case where $q$ is a power of $2$). Now, we consider all possible assi... |
awhich has not been declared. For the first error the macro %x%causes the cursor to point to parameterb. >I decided to have a go at the challenge set in this paper - hope you don't mind.>
See also: http://people.sabanciuniv.edu/ertekg/papers/2006/alp_et_al_ims2006.pdf.
I can find a better solution using the column gene... |
Bayesian performance bounds are supposed to benchmark Bayesian estimators and detectors, which infer random parameters of interest from noisy measurements. These parameters are usually physical values as temperature, position, etc.
Consider a
measurement model
\[\boldsymbol{y} = C(\boldsymbol{x})~,\]
where a sensor mod... |
As other answers explained, the key idea is that $\left|\frac{x^2e^{-x}}{x^2+1}\sin(xe^{x^2})\right|\le e^{-x}$ from which it easily follows, using the squeeze theorem, that the limit is 0.
I'd like to also address your question about the ε−δ definition.
It is always "possible" to prove limits directly using the ε−δ de... |
I am doing my first semester of Quantum Mechanics and we're using Griffith's Introduction to Quantum Mechanics. As he is introducing the Dirac delta function potential he explains bound and scattering states, and I understand that a system is considered bound if the energy of the system is less than the potential at in... |
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
Spanish.
Contents
Spanish language has some special characters, such as the
ñ and some accentuated words. For this reason the preamble of your document must... |
Sequential Bayesian estimation and detection [VB07] inferes temporal evolving
states in contrast to non-evolving parameters. The sequential Weiss-Weinstein bound is a lower bound on the mean-square-error matrix of any Bayesian estimator. This article is based on Bayesian Cramer-Rao Bounds and Weiss-Weinstein Bounds abo... |
Introduction¶
A somewhat neglected model in the Data Science/Machine Learning community are
Multivariate Adaptive Regression Splines (MARS). Despite being less popular than Neural Networks or Trees, I find the concept of MARS pretty interesting, especially because it comes as a fully linear model and thus can preserve ... |
Every now and again I hear something about Tsallis entropy, $$ S_q(\{p_i\}) = \frac{1}{q-1}\left( 1- \sum_i p_i^q \right), \tag{1} $$ and I decided to finally get around to investigating it. I haven't got very deep into the literature (I've just lightly skimmed Wikipedia and a few introductory texts), but I'm completel... |
Problem
The problem (from [1]) is to determine where to pump gasoline (and how much) during a trip, where prices between gas stations fluctuate.
We consider some different objectives:
Minimize Cost. This results in an LP model. Minimize Number of Stops. This makes the model a MIP. Minimize Number of Stopsfollowed by Mi... |
Consider a multivariate polynomial $f(x) = f(x_1, \ldots, x_n)$ with maximum degree $d$. Following the linear symbolic perturbation scheme described in Seidel 1998, I want to evaluate the limit
$$\lim_{\epsilon \to 0^+} \textrm{sign}~ f(x + \epsilon y)$$
for some $x,y \in \mathbb{R}^n$. This limit is given by the lowes... |
A random survey of 68 adults finds that the way... If it isn't, do it can also be smaller than the significance level. Please tryreject the null hypothesis.At the 5% level of significance, how the standard deviation and standard error.
sample mean t test.Five Step Hypothesis Testing Procedure1. Test standard dig this -... |
This example shows how to update an RUL prediction as new data arrives from a machine under test. In the example, you use an ensemble of training data to train an RUL model. You then loop through a sequence of test data from a single machine, updating the RUL prediction for each new data point. The example shows the ev... |
How to find the average value of several measurement results if we know their statistical and systematics uncertainties? There might be that there is no such thing as best way to do it, but it would be helpful to know how is this done in different areas of physics/science.
If all of your measurements are completely ind... |
I get regularly the feedback in comments to use Latex or MathJax. Also I would write beautiful formulas what I can do only on pen & paper. Where can I get info about these?
While this seems like a well-intentioned thread, there is already a comprehensive tutorial over on the Mathematics Meta Stack Exchange site, at
and... |
Quick question: is there a difference between credit VaR and VaR or are they the same thing?
They are different metrics.
As I understand it:
Market risk VaR is a not a coherent risk measure, because it is not subadditive.
Market returns are generally considered on a shorter time horizon relative to credit returns, whic... |
@Secret et al hows this for a video game? OE Cake! fluid dynamics simulator! have been looking for something like this for yrs! just discovered it wanna try it out! anyone heard of it? anyone else wanna do some serious research on it? think it could be used to experiment with solitons=D
OE-Cake, OE-CAKE! or OE Cake is ... |
10.3. Gradient Descent¶
In this section we are going to introduce the basic concepts underlying gradient descent. This is brief by necessity. See e.g. [Boyd.Vandenberghe.2004] for an in-depth introduction to convex optimization. Although the latter is rarely used directly in deep learning, an understanding of gradient ... |
I was wondering whether it is possible to derive the model of a thermodynamical system by combining thermodynamic equations and Lagrangian mechanics. Let's consider the following closed system. A mass $m$ is glued to the top of cylinder full of air. Inside of the cylinder we have an electrical resistance $R$ that can b... |
I am using an equation in IEEE style confrence paper. The pages are two column and I cannot place the following equation in the page. How I can make the equation be placed in one column ?
\begin{equation}\label{eq:3} min \left| \sum_{\substack{x,y\in b_{ij}}} I(x,y,t) - \sum_{\substack{x,y\in b^{'}_ {ij}}} I(x,y, t+\De... |
In this post, we will develop a framework for always-valid inference based on the paper Always Valid Inference: Continuous Monitoring of A/B Tests (2019 Johari, Pekelis, Walsh). Using an always-valid p-value allows us to continuously monitor A/B tests, and potentially stop the test early in a valid way
1.
In section 5 ... |
13.6. Word Embedding with Global Vectors (GloVe)¶
First, we should review the skip-gram model in word2vec. The conditional probability \(\mathbb{P}(w_j\mid w_i)\) expressed in the skip-gram model using the softmax operation will be recorded as \(q_{ij}\), that is:
where \(\mathbf{v}_i\) and \(\mathbf{u}_i\) are the vec... |
I am trying to create a presentation in latex and have the following
\documentclass[11pt]{beamer}\usetheme{Madrid}\usepackage[utf8]{inputenc}\usepackage[T1]{fontenc}\usepackage[english]{babel}\usepackage{graphicx}\author{Anthony Robinson}\title{Irrational and Transcendental Numbers}\subtitle{Mathematics Project}%\logo{... |
This question already has an answer here:
Our model is $Y=\beta_0+\beta_1X+U$.
We know that $$\hat{\beta_0} = \beta_0 + \sum\limits_{n=1}^N c_nu_n \quad \text{ and }\quad \hat{\beta_1} = \beta_1 + \sum\limits_{n=1}^N k_nu_n \,,$$ where $$k_n = \frac{(x_n-\bar{X})}{D}\,, \quad D = \sum_{n=1}^N (x_n-\bar{X})^2\,,\quad\te... |
My question is why in the delayed choice quantum eraser experiment we don't see interference pattern at D0? While it looks like it is similar to the normal double slit experiments. The following image is from Wikipedia:
In the usual double-slit experiment the photon is in the superposition of states corresponding to ho... |
This is a Test of Mathematics Solution Subjective 81 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta
Find all possible rea... |
16.2. Basics¶
This section summarizes basic tools from linear algebra, differentiation, and probability required to understand the contents in this book. We avoid details beyond the bare minimum to keep things streamlined and easily accessible. In some cases we simplify things to keep them easily accessible. For more b... |
Finally, I felt I had something about Physics that I wanted to write about. The i \epsilon terms sitting in the propagator of a QFT, in the Lippmann-Schwinger equation and in Chapter 4 of Peskin and Schroeder have been bothering a couple students including me at the department for a while now. I am not qualified enough... |
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1. Measurement of the branching fractions of the decays D + → K − K + K + , D + → π − π + K + and D s + → π − K + K
Journal of High Energy Physics, ISSN 1126-6708, 03/201... |
Algebra and Algebraic Geometry Seminar Spring 2018
The seminar meets on Fridays at 2:25 pm in room B113.
Here is the schedule for the previous semester.
Contents 1 Algebra and Algebraic Geometry Mailing List 2 Spring 2018 Schedule 3 Abstracts Algebra and Algebraic Geometry Mailing List Please join the AGS Mailing List ... |
$$ \sigma_{E/K}=\frac{\log{|N_{K/Q}\Delta_{E/K}|}}{\log{|N_{K/Q} f_{E/K}}|}$$
Given $ \varepsilon >0$ there are only finitely many $ E/K$ with $ \sigma_{E/K}\geq 6+\varepsilon $. In particular, $ \sigma_{E/K}$ is bounded.
$\Delta_{E/K}$ is the minimal discriminant.
Szpiro's conjecture implies abc with a bit higher expo... |
I'm very confused by the account on fluctuations near the equilibrium in chapter 12 of Landau's book on statistical physics. To be brief, the kernel of my doubt is that he states that if you have a observable $X$ such that equilibrium is attained at $X=0,$ then the probability of having a fluctuation of size $x$ is giv... |
For finding potential at a point due to a +ve charge $(q)$, we find work done to move a unit +ve charge $(q_o)$ from infinity to that point in the presence of +ve charge $(q)$
Since both charges being +ve, the force would be repulsive and hence while bringing unit +ve charge $(q_o)$ from infinity to that position, the ... |
I am new to finance so I apologize if my question is really basic (which it probably is). If this is not the right "stackexchange" group for this, kindly refer me to the right one.
Let's say you own an asset and you want to cross-hedge using futures on a related asset. I'm going to establish a terminology here:
$S,F$ i... |
In my computer science education, I increasingly notice that most discrete problems are NP-complete (at least), whereas optimizing continuous problems is almost always easily achievable, usually through gradient techniques. Are there exceptions to this?
An example that I love is the problem where, given distinct $a_1, ... |
I am currently reading about binary cubic forms and cubic number fields (mainly about using binary cubic forms with integer coefficients to parametrize orders in the cubic field) and I thought it might be good to do some computations to understand how this theory works by taking a concrete example.
Given a cubic field ... |
The optimization toolbox of Matlab does not contain an MIQP (Mixed Integer Quadratic Programming) solver. So when they discuss a cardinality constrained portfolio problem (this means only a certain number of assets can be in the portfolio), an interesting cutting plane technique is used instead. This method will solve ... |
I will introduce my problem with an example. Say you are designing an exam, which consists of a certain set of $n$ independent questions (that the candidates can get either right or wrong). You want to decide on a score to give to each of the questions, with the rule being that candidates with total score above a certa... |
You may notice that subtraction can be seen as a special case of addition, i.e.$$a-b=a+(-b)$$Thus by commutative law,$$a-b=a+(-b)=(-b)+a=-b+a$$It is certainly not $b-a$.
Similarly, division is as a special case of multiplication, i.e.$$\frac{a}{b}=a\cdot(\frac{1}{b})$$Where $\frac{1}{b}$ means the inverse element of $b... |
A while ago I asked about versions of Vopenka's principle for logics other than first order. Unfortunately, there doesn't seem to be much there; most logics yield the same notion, while "big" logics like $\mathcal{L}_{\infty\omega}$ yield versions of VP which are easily disprovable.
However, going back I noticed that t... |
As my question states, I want to calculate the Fourier transform $F(q)$ of a radial function $f(r)$ (defined on $[0,\infty)$ and which decays like an exponential $\exp(-Ar+b)$ at large $r$) as accurately as possible in Fortran. The function values come from a data file (which I can easily interpolate through cubic inte... |
I'm stuck on a few Vector homework problems. I don't quite understand how to write vectors A+B and A-B for questions 1b and 2b. I tried starting with calculating the magnitude for vector A+B on question 1b and then followed by finding theta, but I'm not sure if that's what I'm supposed to do...
I have a 4D array of dim... |
I have been trying to solve an exercise on nuclear chemistry, but I was not sure whether I should ask this on physics or chemistry but I think that if chemistry had an exercise based on this then chemistry experts might be having the way to overcome this problem. So here is what my nuclear chemistry question says:
One ... |
I'm now making a documentation of a small LaTeX package with
documentation library from the
tcolorbox package, and having difficulty in printing sample codes without any syntax highlighting.
According to G. Poore's answer, we can set the language as
text to turn off the coloring, which can be specified via
/tcb/minted ... |
This is a Test of Mathematics Solution Subjective 69 (from ISI Entrance). The book, Test of Mathematics at 10+2 Level is Published by East West Press. This problem book is indispensable for the preparation of I.S.I. B.Stat and B.Math Entrance.
Also visit: I.S.I. & C.M.I. Entrance Course of Cheenta
Suppose that the thre... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
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Production of 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 ... |
Let's say that a map $f: V \rightarrow W$ between finite-dimensional real vector spaces is
convex-linear if $f(\lambda x + (1-\lambda)y) = \lambda f(x) + (1-\lambda)f(y)$ for all $\lambda \in [0,1]$.
Let's say that a map $f: V \rightarrow W$ between finite-dimensional real vector spaces is
affine if $f(\lambda x + (1-\... |
I have a distance on the space of probability measures on $[0,2]$. It is defined as such for two probability measures $\mu_1$ and $\mu_2$ :
$d_p(\mu_1,\mu_2) := \sum_{k=0}^p ( \mathbb{E}[X_1 ^k]- \mathbb{E}[X_1 ^k] ) ^2$ where $X_1$ and $X_2$ are random variables whose laws are $\mu_1$ and $\mu_2$ respectively.
Let $d_... |
And I think people said that reading first chapter of Do Carmo mostly fixed the problems in that regard. The only person I asked about the second pset said that his main difficulty was in solving the ODEs
Yeah here there's the double whammy in grad school that every grad student has to take the full year of algebra/ana... |
What is the mathematical notation for rounding a given number to the nearest integer? So like a mix between the floor and the ceiling function.
I have seen $\lfloor x \rceil$. It must have been in the context of math olympiads, so I can't point to a book that uses it. Wikipedia suggest this notation, among others: near... |
Whats the use of representing rotation with quaternions compared to normal axis angle representation? I've been trying to learn quaternions and they make enough sense but as far as I can tell quaternions are just axis angle with a transformed axis and angle of rotation. How exactly does transforming the axis and angle ... |
Pete's excellent notes have correctly explained that there is no set containing sets of unboundedly large size in the infinite cardinalities, because from any proposed such family, we can produce a set of strictly larger size than any in that family.
This observation by itself, however, doesn't actually prove that ther... |
To expand on my comment, your equation holds only if $A$ and $B$ are uncorrelated. More generally, if $F$ is a function of uncorrelated variables $A$ and $B$, then
$$(\delta F)^2 = \left(\frac{\partial F}{\partial A}\delta A\right)^2 + \left(\frac{\partial F}{\partial B} \delta B\right)^2$$
If you plug in $F=AB$, then ... |
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