text stringlengths 256 16.4k |
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In a project we're using a commercial text font. The project is not a math related project but has some math in it here and there. The text font of course does not have a direct math font. But the XITS Math font (which is a part of standard LaTeX, at least TeX Live) seems a good enough match.
I decided to play with
uni... |
Images are essential elements in most of the scientific documents. LaTeX provides several options to handle images and make them look exactly what you need. In this article is explained how to include images in the most common formats, how to shrink, enlarge and rotate them, and how to reference them within your docume... |
Let $G$ be a finite group and $H$ a subgroup such that the interval $[H,G]$ is a boolean lattice.
Let $L_1, \dots , L_n$ be the maximal subgroups of $G$ containing $H$.
Let the alternative sum of the interval $[H,G]$ defined as follows: $$\chi([H,G]):= \sum_{r=0}^n (-1)^{r} \sum_{ \ i_1 < i_2 < \cdots < i_r } [L_{i_1} ... |
This is a follow-up to a different question I asked with more detail.
For $v\in\mathbb{R}^n$, denote $D_v\in\mathbb{R}^n$ as the diagonal matrix with elements in $v$. Given a "tall" matrix $B\in\mathbb{R}^{n\times m}$, I would like to solve the following optimization problem: $$\min_{v\in\mathbb{R}^n} \|X-B^\top D_v B\... |
Difference between revisions of "Geometry and Topology Seminar"
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In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
Yes, assuming you want both $f_1(x)$ and $f_2(x)$ with integer coefficients.
One of the reasons why LLL is so popular is precisely because it gives a polynomial time algorithm to factor polynomials with integer coefficients.
For an excellent introduction, I recommend C. Yap's "Fundamental Problems in Algorithmic Algebr... |
Version 19 (modified by 5 weeks ago) (diff), 'perturbative' and 'real' particles; the perturbative weight 'perturbative' and 'real' particles
(following text is taken - slightly modified - from: O.Buss, PhD thesis, pdf, Appendix B.1)
Reactions which are so violent that they disassemble the whole target nucleus can be t... |
Let
SAT-100 be the following problem: Input: Any boolean logic formula Output: True if there exists a combination of exactly 100 input variables that satisfy the formula.
This is the description of a problem that is apparently in $P$. (old exam question)
I have tried to design an algorithm but I got stuck, so here it g... |
First of all, sorry for this long and maybe not very informative title...
Context:
Let $G=(V,E)$ be a directed graph, let $v_0 \in V$ be the initial node of paths that I will consider in the graph.
Let $\Sigma$ an alphabet and let $T$ (for target) a set of words built from $\Sigma$ (e.g. $T \subset \Sigma^*$). Nodes of... |
IWOTA 2019
International Workshop on
Operator Theory and its Applications
We discuss a kind of spectral theory for bounded linear operators $T$ on a Hilbert space $H$ satisfying\begin{equation}\label{eq}
\alpha(T^*,T) := \sum_{n=0}^{\infty} \alpha_n T^{*n} T^n \ge 0 \quad \text{(convergence in SOT)},\end{equation} wher... |
IWOTA 2019
International Workshop on
Operator Theory and its Applications
We consider truncated moment problems associated with algebraic varieties in the nonnegative quadrant of $\mathbb{R}^2$. We focus our attention on the interactions between two related problems, as follows.
The talk is based on joint work with S. ... |
I learned recently that when an object moves with a velocity comparable to the velocity of light the (relativistic) mass changes. How does this alteration take place?
In relativistic mechanics, there is a conserved quantity, relativistic momentum:
$\vec p = \gamma m \vec v$
$\gamma = \dfrac{1}{\sqrt{1-\frac{v^2}{c^2}}}... |
In their original paper, Storing a sparse table with O(1) worst case access time (Fredman, Kolmos and Szemeredi,
Proc. FOCS '82, IEEE, 1982), the authors show that a perfect hash function must exist, provided that the table is the square of the number of elements in the key space.
The key part of the proof bounds the n... |
Given $a, b, k, n \in \mathbb{N}$, what techniques are available for computing sums of the form:\begin{align}\sum_{i = 1}^{n} (ai^{k} \ \text{mod} \ b ) ?\end{align}
NB: Here, only the summands are reduced modulo $b$, not the overall summation.
I'm specifically interested in the $k = 1$ case. For example, if $a = 2$, $... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
IWOTA 2019
International Workshop on
Operator Theory and its Applications
We establish criteria for boundedness for some classes of integral opearators with logarithmic singularities in weighted Lebesgue spaces for cases $1\lt p \leq q \lt \infty$ and $1\lt q \lt p \lt \infty$. As corollaries some corresponding new Har... |
In a Euclidian world the sum $s$ of two velocities $v$ and $u$ is so such that $s = v + u$. However, in the world of special relativity that's not the case. Instead, the velcity vector sum $s$ is such that $s = \frac{v + u}{1+vu} \; (c=1)$.
I'm trying to deriving it and down below is my work so far. Any hints that woul... |
Fund managers are acting in a highly stochastic environment. What methods do you know to systematically separate skillful fund managers from those that were just lucky?
Every idea, reference, paper is welcome! Thank you!
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and aca... |
So basically my tables work fine under the tabular format, but in some cases I need to use tabularx because they are too large to fit within the normal textwidth.
However, the rows become infinitely long, due to an erroneous extra column it seems?
EDIT: Changed the table to my actual table. Image1 shows the same code u... |
I am interested in the problem of finding a real root of a polynomial equation $f(x)=0$ where $f(x)=\sum_{i=0}^n a_ix^i$. Is it possible to give a reduction, i.e, to compute a different polynomial $g$ in polytime such that $f$ has a real root iff $g$ has a real root in [0,1]$?
Not sure if this is the right SE forum for... |
IWOTA 2019
International Workshop on
Operator Theory and its Applications
This work represents the concept of an $n$-groupoid $ \Gamma^n $ and n-characters $ \chi_n $ on $n$-groupoids as complex-valued maps from spaces of different classes of morphisms satisfying the condition $ \chi_n (\psi \circ_k \varphi) = \chi_n (... |
EDIT: I moved the full code to my github page so the post can be read more easily.
I am writing a script to take the Faber approximation approach outlined in Hassan Fahs paper (free access) and apply it to the Liouville-von-Neumann equation to propagate the density matrix $\rho$ with some inspiration from the scripts f... |
Introduction¶
In my last post I introduced a simple linear time-series model using indicator functions for forecasting. In the meantime, I was experimenting with some other ideas for non-complex models with good predictive power. One approach that has been on my mind for quite long now, is commonly known to Data Scient... |
I tried asking a similar question in SE.Physics, and I got some information regarding the abstract side of this, but I figured I should post here to get more complete information about the numerical benefits of variational formalisms.
Assuming I am able derive a functional representation for
any dynamical system (dissi... |
Question #37681 1 Answer Answer:
242 Hz.
Explanation: Solution : The frequency of the first wire must be Explanation : Solving this problem requires knowing the following concepts, Speed of propagation of a wave in a string: When a string of linear mass density (mass per unit length) #\mu#is held at a tension of #T#, w... |
Please help improve this post. This is intended to be a welcome guide for new users that we can reference in comments to help acclimate then to the Q&A format here at EarthScience.SE. This is a community wiki, which means you can edit this directly to improve it. I have adapted this from Tex.SX and I have cleansed it o... |
Given that $z_1=1+2i$ and $z_2=\frac{3}{5}+\frac{4}{5}i$, write $z_1z_2$ and $\frac{z_1}{z_2}$ in the form $p+iq$, where $p$ and $q \in R$. In an Argand diagram, the origin O and the points representing $z_1z_2$, $\frac{z_1}{z_2}$,$z_3$ are the vertices of a rhombus. Find $z_3$ and sketch the rhombus on this Argand dia... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
I am currently reading Switzer's book "Algebraic Topology: Homotopy and Homology". On page 50, the proof of 3.30 c), he claims that a certian composition is something I can't see how it possibly can be what he states it to be. Let $\beta':S^1 \rightarrow I \vee S^1$ be defined by $(2t,\ast)$ if $t \leq 1/2$ and $(\ast,... |
Let $X:\Omega\to\mathbb{R}$ and $Y:\Omega\to\mathbb{R}$ be univariate random variables with CDF $F_{X,Y}(x,y)$ such that: $$ F_{X,Y}(x,y)=G_1(x)G_2(y),\forall (x,y)\in\mathbb{R}\times\mathbb{R} $$ where $G_1:\mathbb{R}\to\mathbb{R}$, $G_2:\mathbb{R}\to\mathbb{R}$ are known functions.
Question: Is it true that $X$ and $... |
Question
A point particle of mass moves in the region and is reflected elastically at the walls at and .
Calculate the volume of the classical phase space with an energy smaller than . Assume that a particle initially has an energy . Demonstrate that the phase-space volume of this particle remains constant when the wal... |
In this post a simple MIP problem is posted. Basically the problem can be stated as:
\[\boxed{\begin{align} \max & \sum_i Score_i \, x_i \\ & \sum_i x_i = 6 \\ & \sum_i Salary_i \, x_i \le 50000 \\ & x_i \in \{0,1\} \end{align}}\]
We have a database of 153 players, and we want to compose the best team of 6 players with... |
Assume you have poured your distilled water in a 1 liter container.
We write the flux of $n_{\ce{CO2}}$ between air towards your container, as $$J_{\ce{CO2}}=\frac{dn_{\ce{CO2}}}{dt}\times\frac{1}{A}=\frac{d[\ce{H2CO3}]^{*}}{dt}\times\frac{V}{A}$$where $n_{\ce{CO2}}$ is the number of ${\ce{CO2}}$ moles in water, $A$ th... |
I want to model a dynamical system of the form
$\frac{\text{d}x}{\text{d}t} = f(x)+nx\delta(\pi(t-0.2)). $
The problem is that I have a point source which is reoccurring at fixed time steps (say at 0.2,1.2,2.2...). How can I handle this numerically? I have tried to figure out solutions and it seems that there are two "... |
I have no idea for the full generality, but at least I have a complete answer when $g$ is convex.
Proposition. Assume that $g : [a,\infty) \to \Bbb{R}$ is increasing, convex and unbounded. Then
(1) $\int_{a}^{\infty} \sin g(x) \, dx$ does not converge absolutely.
(2) $\int_{a}^{\infty} \sin g(x) \, dx$ converges if and... |
Let $[H,G]$ be a rank $2$ boolean interval of finite groups.
It is true in each of the following cases:
$|G:H| = 2p$ with $p$ prime (see below) $|G:H|<36$ (using GAP and $34=2 \cdot 17$) $G$ simple with $|G| \le 50000$ (by GAP)
For $|G:H| = 2p$ the proof is the following: if $|G:K_i| = 2$ then $K_i$ is a normal subgrou... |
My question will rely on a clarification of a proof, which I simply don't understand.
Let us denote by $X$ a pseudo-riemannian symmetric space and define
$$ Z_{\mathrm{Iso}\left(X\right)}G(X) = \{\, f \in \mathrm{Iso}\!\left(X\right) \mid gf = fg \text{ for all } g \in G(X) \,\} $$ as the centralizer of the transvectio... |
The answer to your question is contained in the Authenticity bound (Theorem 5.1). This is because Authenticity implies non-malleability (see e.g. http://eprint.iacr.org/2011/092.pdf). Note that only one term in the bound refers to the length of the tag (referred to by the variable $\tau$):
$$\mathbf{Adv}_{OCB}^{auth}[\... |
I'm asked to plot the frequency response (amplitude) given a specific pole-zero diagram.
$$ H(z) = H_0 \frac{\prod\limits_{m=1}^{M} (z - q_m)}{\prod\limits_{m=1}^{M} (z - p_m)}$$
$$ H(e^{i\omega}) = H_0 \frac{\prod\limits_{m=1}^{M}(e^{i\omega} - q_m)}{\prod\limits_{m=1}^{M}(e^{i\omega} - p_m)}$$
If I understood it corr... |
Some tricks I've seen:
Tricks with notable products
$(a + b)^2 = a^2 + 2ab + b^2$
This formula can be used to compute squares. Say that we want to compute $46^2$. We use $46^2 = (40+6)^2 = 40^2+2\cdot40\cdot6 +6^2 = 1600 + 480 + 36 = 2116$. You can also use this method for negative $b$:$ 197^2 = (200 - 3)^2 = 200^2 - 2... |
Pre-published on: 2019 September 01
Published on: —
Abstract
This proceeding contribution presents a selected number of studies performed by the ATLAS and the CMS experiments on b-hadron spectroscopy. Both collaborations have a rich b-hadron physics program on exploiting the large cross section of b-hadrons at the high... |
17.1. Using Jupyter¶
This section describes how to edit and run the code in the chapters ofthis book using Jupyter Notebooks. Make sure you have Jupyter installedand downloaded the code as described in
chap_installation.If you want to know more about Jupyter see the excellent tutorial in theDocumentation.
17.1.1. Edit ... |
In Section 2.3.3
"Polytopes and LP" of the book "Combinatorial Optimization: Algorithms and Complexity" by Christos H. Papadimitriou, Theorem 2.4 establishes the relation between bfs's (basic feasible solutions) of LP and vertices in polytope (for developing the simplex algorithm). However, I have difficulty in underst... |
I am trying to approximate the exponential of a matrix. I want to use a tolerance but I am confused as to how to compute the error. Any ideas or hints?
First: there is a must read on this topic
Moler, Cleve, and Charles Van Loan. "Nineteen dubious ways to compute the exponential of a matrix, twenty-five years later." S... |
I'll try my hand at this also. In my experience, in courses where the concept of convolution is taught, it's common to see the "flip-and-slide" process diagrammed out as you've alluded to. I don't feel that the graphical illustration itself really gives that much insight, but here's how you might arrive at it starting ... |
Before continuing with my studies, and obtaining a Ph.D in the are of computer vision, I worked for 5 years as an automation engineer, designing, installing and modernizing automation systems. From this ...
Back to the roots! Before obtaining PhD degree in the area of machine vision I designed automation systems. This ... |
IEEE Proceedings Paper on Concensus and Cooperative Control
Consensus and Cooperation in Multi-Agent Networked Systems
The availability of low cost, high bandwidth, wireless communications between independent computing systems has enabled new approaches to cooperation between multi-agent systems performing a common tas... |
I asked this question in mathematics stackexchange and couldn't get an answer.
Let $\phi\in H^{s}$ such that the following energy inequality is true:
$$\|\phi(t,\cdot)\|_s \le\int^t_0 C \| P\phi(t,\cdot)\|_s \, dt $$
where $P$ is the wave operator $\square_{g}$.
Now is the energy inequality true for $-s$?
I have attemp... |
If it helps, this class of problems has a non-existence proof tied to them. Mean-variance finance models have an assumption that all parameters are known built into the proofs. There is an existing proof that shows these models, if true, can never form an estimator for the parameters.
Consider the intertemporal budget ... |
Current browse context:
cond-mat.dis-nn
Change to browse by: References & Citations Bookmark(what is this?) Condensed Matter > Disordered Systems and Neural Networks Title: $T \to 0$ mean-field population dynamics approach for the random 3-satisfiability problem
(Submitted on 31 Dec 2007 (v1), last revised 25 Sep 2008 ... |
Solutions2tma@gmail.com
Whatsapp: 08155572788 Question This combined force law \(\widetilde{F}= q(\widetilde{E}+\frac{\widetilde V}{C} \times \widetilde{B})\) is known as Answer Lorentz Question How would you describein continous medium mechanics,the response of a linear elastic medium to strain. Answer Hookes law Ques... |
I believe you can, if you try to follow the path of finding representations of the $SO(n)$ group over a given Hilbert space.
I really haven't done the calculation, but if it is the same, you would have something like this:
$H=L_2(\mathbb R^n,\mathbb C)$ would be the Hilbert Space that would correspond to spin 0 particl... |
@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 ... |
In a very natural sense, you can! If $\lim_{x \to \infty} f(x) = \lim_{x \to -\infty} f(x) = L$ is some real number, then it makes sense to define $f(\infty) = L$, where we identify $\infty$ and $-\infty$ in something called the one-point compactification of the real numbers (making it look like a circle).
In that case... |
How would you match the lines between two
cases within the same
equation environment? What I'm having is:
\begin{equation}\begin{rcases} \sum_{I=1}^{NP} K_h (x - x_I; x) \Delta x_I &= 1 \\ \sum_{I=1}^{NP} \left(\frac{x - x_I}{h}\right) K_h (x - x_I; x) \Delta x_I &= 0 \\ &\;\;\vdots \notag \\q \sum_{I=1}^{NP} \left(\fr... |
Not for the faint-hearted: There is an excellent, but very mathsy, article here:
J. Chem. Educ. 2014, 91, 386 describing the difference. The Gibbs free energy change, $\Delta G$
You are quite right in saying that $\Delta G$ represents a change in a system over a time interval. The notation $\Delta G$ itself implies tha... |
In Chapter II of Dirac's book
Principles of Quantum Mechanics, Dirac explains that in general it is very difficult to know whether, for a given real linear operator, that any eigenvalues/eigenvectors exist and (if they do) how to find them.
He then goes on to state that a special tractable case can be found in the even... |
When this identity was posted, it struck me as something that ought to have a combinatorial explanation. I have now found one, using a decomposition of NSEW lattice paths: paths in $\mathbb{Z}^2$ consisting of unit steps in the direction N, S, E or W. Many of the ideas here may be found in [GKS], though not the decompo... |
The production function is:$$q = (l^\rho + k^\rho)^\frac{1}{\rho}$$The MPL and MPK are respectively:$$q_l = \frac{\partial q}{\partial l} = \frac{1}{\rho} \cdot (l^\rho + k^\rho)^{\frac{1}{\rho}-1} \cdot \rho\cdot l^{\rho-1}$$$$q_k = \frac{\partial q}{\partial k} = \frac{1}{\rho} \cdot (l^\rho + k^\rho)^{\frac{1}{\rho}... |
I have to test the series for
absolute and conditional convergence $\sum_{n=2}^{\infty}$ $\frac{(-1)^{n-1}}{n^2+(-1)^n}$
$Notes :$ For absolute convergence def. I have $\vert \frac{(-1)^{n-1}}{n^2+(-1)^n} \vert$ If this convergence then the original series should be convergence.
$proof:$ $\vert \frac{(-1)^{n-1}}{n^2+(-... |
Technical Report
Show 1 to 6 of 6
Issue 6 Generating Highly Accurate Machine Models Indispensable to Model Based Design (MBD)
Elaborate Modeling TechnologyIdeal MBD and Its ChallengesModel based design (MBD) has been around the field of circuits/controls for motors for a long time, but has not been at th…
Issue 5 Versa... |
The NCO is a cyclical counter that can go on indefinitely but is otherwise similar to what you suggest in that you are increment n to set the output rate. It basically is a look up table of all the values in one complete cycle, and "wraps" on an overflow so that it will output continuous cycles with no discontinuity.
I... |
Given a continuous time LTI system with impulse response $h(t)$ and determined with the transform $\mathcal{T}\{\cdot\}$, we define an input/output relationship as follows:
$$ y(t) = \mathcal{T}\{ x(t) \} $$ which can be evaluated based on the convolution integral as: $$y(t) = \mathcal{T}\{ x(t) \} = x(t) \star h(t) = ... |
The first or third option below may be close to what you're looking for. Or, switch from Newton-style to Leibniz-style notation for the derivative, as shown by the fourth option (newly fixed to incorporated @marmot's comment). A separate comment: to make the
\frac{1}{2} term less visually dominant, consider using
\tfra... |
Current browse context:
cond-mat.stat-mech
Change to browse by: Bookmark(what is this?) Condensed Matter > Statistical Mechanics Title: One-Dimensional Impenetrable Anyons in Thermal Equilibrium. I. Anyonic Generalization of Lenard's Formula
(Submitted on 28 Jan 2008 (v1), last revised 30 Apr 2008 (this version, v2))
A... |
Given a 2D lattice with coordinates $1 \leq x \leq c$ and $1 \leq y \leq d$, we define $f(x, y) = xy$.
We wish to find a boolean function $I(x,y)$ that determines in $O(1)$ time whether or not $(x,y)$ belongs to the set of points $S$ of size $k$ such that the sum $Z(S) = \sum_{(x,y) \in S} f(x,y)$ is smaller or equal t... |
I've noted, that the following fact can be proven in a few lines using $C^*$-algebra theory. I wonder if it has a simple elementary proof or not. Probably you can give me a reference.
Suppose $X$ is a compact Hausdorff space, $V\subset X$ is a closed subset, $f\colon V\to \mathbb{R}$ is a continuous function. Then ther... |
Given the ionization reaction $2H^0 <=> H^+ + H^-$ where:
$H^+$ is the ionized state with electron occupancy n = 0 and energy 0
$H^0$ is the doubly degenerate neutral hydrogen atom with electron occupancy n = 1 and energy $-\Delta$.
$H^-$ is the ionized state with electron occupancy n = 2 and energy $-(\epsilon + \delt... |
From an advanced perspective, this follows from a variant of semistable reduction which Harris and Morrison call Nodal Reduction. I quote from their textbook Moduli of Curves, Proposition 3.49.
Let $B$ be a smooth curve, $0$ a point of $B$ and $B^{\ast} = B \setminus \{ 0 \}$. Let $X \to B^{\ast}$ be a flat family of n... |
It is known that the Kitaev Hamiltonian and its spin-liquid ground state both break the $SU(2)$ spin-rotation symmetry. So what's the spin-rotation-symmetry group for the Kitaev model?
It's obvious that the Kitaev Hamiltonian is invariant under $\pi$ rotation about the three spin axes, and in some recent papers, the au... |
Cutwidth¶
This module implements several algorithms to compute the cutwidth of a graph and the corresponding ordering of the vertices. It also implements tests functions for evaluation the width of a linear ordering (or layout).
Given an ordering\(v_1,\cdots, v_n\) of the vertices of \(V(G)\), its
cost is defined as:
W... |
I have trouble with finding the eigenstates of a spherical pendulum (length $l$, mass $m$) under the small angle approximation. My intuition is that the final result should be some sort of combinations of a harmonic oscillator in $\theta$ and a free particle in $\phi$, but it's not obvious to see this from the Schrodin... |
Problem statement
Given \(n\) points with their distances \(d_{i,j}\), select \(k\) points such that the sum of the distances between the selected points is
maximized[1].
A simple MIQP (Mixed-Integer Quadratic Programming) model is:
Non-convex MIQP Model \[\begin{align} \max & \sum_{i \lt j} \color{darkblue} d_{i,j} \c... |
Let $V$ be an $n$-dimensional vector space over a field $F$ equipped with a symmetric bilinear map $B:V\times V\rightarrow F$ and associated quadratic map $Q(v):=B(v,v).$ The pair $(V,Q)$ is a quadratic space. Fixing a basis, $\{v_1,...,v_n\}$ for $V$, the space $(V,Q)$ has an associated quadratic form, that is, a homo... |
@egreg It does this "I just need to make use of the standard hyphenation function of LaTeX, except "behind the scenes", without actually typesetting anything." (if not typesetting includes typesetting in a hidden box) it doesn't address the use case that he said he wanted that for
@JosephWright ah yes, unlike the hyphe... |
LaTeX uses internal counters that provide numbering of pages, sections, tables, figures, etc. This article explains how to access and modify those counters and how to create new ones.
Contents
A counter can be easily set to any arbitrary value with
\setcounter. See the example below:
\section{Introduction} This documen... |
The Baker-Campbell-Hausdorff formula¶
AUTHORS:
Eero Hakavuori (2018-09-23): initial version
sage.algebras.lie_algebras.bch.
bch_iterator(
X=None, Y=None)¶
A generator function which returns successive terms of the Baker-Campbell-Hausdorff formula.
INPUT:
X– (optional) an element of a Lie algebra
Y– (optional) an elemen... |
I'm new to
LaTeX so you're going to have to bear with me. I am trying to write a project report using it and I have got this so far for a certain section:
Then,
\documentclass[a4paper,12pt]{article}\usepackage{amsmath,graphicx,hyperref,parskip,gensymb} % In case you are wondering what these packages are for: % amsmath ... |
View Answer
question_answer1) If \[x=-\frac{1}{2},\] is a solution of the quadratic equation \[3{{x}^{2}}+2kx-3=0\]find the value of k.
View Answer
question_answer2) The tops of two towers of height x and y, standing on level ground, subtend angles of \[30{}^\circ \] and \[60{}^\circ \] respectively at the centre of th... |
Transformation means changing some graphics into something else by applying rules. We can have various types of transformations such as translation, scaling up or down, rotation, shearing, etc. When a transformation takes place on a 2D plane, it is called 2D transformation.
Transformations play an important role in com... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
Water, as simple as it might appear, has quite a few extraordinary things to offer. Most does not seem to be as it appears.
Before diving deeper, a few cautionary words about hybridisation. Hybridisation is an often misconceived concept. It only is a mathematical interpretation, which explains a certain bonding situati... |
Let $G$ be a quasisplit connected, reductive group over a field $F$. Let $A_0$ be a maximal $F$-split torus, and $P$ a maximal $F$-parabolic subgroup containing $A_0$. Let $W = N_G(A_0)/Z_G(A_0)$ be the Weyl group of $A_0$, and let $w \in W$. I think that $G$ is the disjoint union of the double cosets $$G = \bigcup\lim... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
Wikipedia also says that Troelstra said in 1988 that there were no satisfactory foundations for ultrafinitism. Is this still true? Even if so, are there any aspects of ultrafinitism that you can get your hands on coming from a purely classical perspective?
There are no foundations for ultrafinitism as satisfactory for ... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
For example, the rate of a chemical reaction can be expressed in $\mathrm{mol}/\mathrm{L}^{-1}/\mathrm{sec}^{-1}$. Why is it ‘−1’ and not, say, ‘−2’? Does it change the meaning if the minus is removed and we simply express the rate in $\mathrm{mol}/\mathrm{L}/\mathrm{sec}$?
The -1 means "per" unit. So your first exampl... |
So I was looking through related questions on this site and the book "Proper and Improper Forcing" by Shelah kept popping up. So I checked it out and the appendix actually resolves the question. I rephrase the proof there because I think this way it's simpler and also because it suggests an interesting question (see th... |
Many thanks to Bart Andrews for this contribution!
Question
Consider two systems \(I\) and \(II\) in contact with a common heat bath with temperature T and suppose that a mechanism exists which allows both systems to exchange particles. The probability that the composed system \(I + II\) is in a state for which system ... |
In Thompson's
Modern Particle Physics, in section 6 about electron-positron annihilation, it is stated (p. 152) that
"If the final-state fermion mass is also neglected, (6.63) reduces to the expression for the spin-averaged matrix element squared of (6.25), which was obtained from the helicity amplitudes."
Here:
$$\beg... |
Let $X_i$ be the result, where $X_i=1$ implies heads and $X_i=0$ as tails.
Let $\theta_j\in\{0.5,1\}$, where $\theta_j$ is the bias for heads.
$\theta_1=.5$ and $\theta_2=1$.
$$\Pr(\theta_1|X_{1\dots{10}}=1)\propto{\left(\frac{1}{2}\right)^{10}}\frac{999}{1000}=\frac{999}{1000\times{1024}}.$$
$$\Pr(\theta_2|X_{1\dots{1... |
10.9. Adadelta¶
In addition to RMSProp, Adadelta is another common optimization algorithm that helps improve the chances of finding useful solutions at later stages of iteration, which is difficult to do when using the Adagrad algorithm for the same purpose [Zeiler.2012]. The interesting thing is that there is no learn... |
I am trying to visualize a Hamiltonian H=$\hat{\sigma_x}$ $$ \hat{\sigma}_{x} = \left( \begin{array}{cc} 0 & 1 \\ 1 & 0 \end{array} \right) $$ acting on the state $| 1 \rangle$.
I can write the state of the qubit at time $t$ by Schrodinger's equation as: $$e^{-iHt} = e^{-i\hat{\sigma_x}t} \, .$$
By Euler's formula, sin... |
Variational methods for approximating disparity and optical flow are quite similar. Basically the same model that can be used for approximating optical flow with big displacements (late linearisation with warping) can also be used for approximating disparity. The only difference is that we don't expect vertical movemen... |
I am trying to prove some theorem by using proof environment, but somehow the result is different when I use article as my document class and aip-cp document class.
Is there a way to use aip-cp document class but when I use proof environment it does not add some horizontal space between the proof and the first text of ... |
There are quite a few models that use the ‘
all-different’ constraint, i.e. a set of integer variables \(x_i\), \(i=\{1,...,n\}\) is feasible only if they are all different, i.e. \(x_i\ne x_j\) for \(i\ne j\). We can probably say that most of these models are of the “educational” type and are not practical production m... |
What is the worst case running time to search for an element in a balanced binary search tree with $n 2^n$ elements?
The answer is $\Theta(n)$.
My answer:
To search an element in BST is $\log (n)$ so $$ \begin{align*} \log(n 2^n ) &= \log(n) + \log(2^n) \\ &= \log(n) + n\log 2 & \text{(base is 2)} \\ &= \log(n) + n \en... |
A proof that uses closure properties:
DCF languages are not closed under union, so take, $L_1, L_2 \in DCF$ s.t. $L = L_1 \cup L_2 \notin DCF$
Add three new symbols $\{\alpha, \beta, \#\}$ to the original alphabet $\Sigma$ and build the languages:
$L'_1 = \{ \alpha \# w \mid w \in L_1\}$
$L'_2 = \{ \beta \# w \mid w \i... |
From Artin:
When $d$ is congruent $2$ or $3$ modulo $4$, an integer prime $p$ remains prime in the ring of integers of $\Bbb{Q}[$$\sqrt{d}]$ if the polynomial $x^2-d$ is irreducible modulo $p$.
a) Prove that this is also true when $d \equiv 1$ modulo $4$ and $p\neq 2$
b) What happens to $p=2$ when $d \equiv 1$ modulo $... |
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