text stringlengths 256 16.4k |
|---|
« Page 3 / 3
In Pentagonal Number Theory, I touched on the topic of generating function but now I'll give examples of generating functions being used to find explicit solutions for recurrent relations. I think this was their primary purpose; Abraham de Moivre invented them when he tried to find the exact formula for …
... |
How should one go about solving this problem?
Use identities to find the exact values at $\alpha$ for the remaining five trigonometric functions.
$\cos\alpha = -\sqrt{2}/4$ and $\alpha$ is in quadrant III.
Thanks
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professi... |
Ok, let me see if I can shed light on some of the questions raised.
"What fails if I try the construction with non-smooth stuff?" This question is a bit unspecific, a lot of things can fail, depending on what you want. For instance, if you want higher Chow groups to come out of the construction, you need homotopy invar... |
Many accounts of the history of quantum physics explain how Planck resorted to quantizing energy in an "act of desperation" while attempting to solve blackbody radiation, only to discover by surprise that a nonzero value of $h$ in $E=nh\nu$ reproduced experimental results.
What was Planck's motivation behind the $\nu$ ... |
The description of the movement of bodies by their position, velocity, acceleration (and possibly higher time derivatives, such as, jerk) without concern for the underlying dynamics/forces/causes.
When to Use this Tag
Use kinematics to discuss the movement of a body in terms of position, velocity, acceleration (or, in ... |
There are formulae you can use to calculate the strength of interactions between two molecules, which are derived from first principles. You can find an overview here on Chemistry LibreTexts. The two relevant ones are:
$$U_{\mathrm{dipole}} = -\frac{2}{3kT} \frac{p^4}{(4\pi\varepsilon_0)^2r^6}$$
$$U_{\mathrm{dispersion... |
Newform invariants
Coefficients of the \(q\)-expansion are expressed in terms of \(\beta = \sqrt{2}\). We also show the integral \(q\)-expansion of the trace form.
For each embedding \(\iota_m\) of the coefficient field, the values \(\iota_m(a_n)\) are shown below.
For more information on an embedded modular form you c... |
Our new book (NAT)
Nonabelian algebraic topology: filtered spaces, crossed complexes, cubical homotopy groupoids, EMS Tracts in Mathematics vol 15
uses mainly cubical, rather than simplicial, sets. The reasons are explained in the Introduction: in strict cubical higher categories we can easily express
algebraic inverse... |
I'm trying to follow Andrew Ng's notes on Support Vector Machines and had the following question.
In his notes, Ng, transforms the following optimization problem [using the notion of geometric margin] of the SVM
into the following equivalent problem [using the notion of functional margin]
My question is this: how are t... |
The Schrödinger equation describes the energy and time-evolution of a particle or system of particles, and is one of the fundamental building blocks of modern physics. In it’s general form, the (time-independent) Schrödinger equation looks like this:
1
There are relatively few situations in which the Schrödinger equati... |
Two-graphs¶
A two-graph on \(n\) points is a family \(T \subset \binom {[n]}{3}\)of \(3\)-sets, such that any \(4\)-set \(S\subset [n]\) of size fourcontains an even number of elements of \(T\). Any graph \(([n],E)\)gives rise to a two-graph\(T(E)=\{t \in \binom {[n]}{3} : \left| \binom {t}{2} \cap E \right|\ odd \}\),... |
Semimonomial transformation group¶
The semimonomial transformation group of degree \(n\) over a ring \(R\) is the semidirect product of the monomial transformation group of degree \(n\) (also known as the complete monomial group over the group of units \(R^{\times}\) of \(R\)) and the group of ring automorphisms.
The m... |
Find
$$\lim_{x\to1^-}\log_2(1-x)+x+x^2+x^4+x^8+\cdots$$
I have found $1-\dfrac{1}{\ln2}$ as a lower bound, but not further than that
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this ... |
The Schrödinger equation is the basis to understanding quantum mechanics, but how can one derive it? I asked my instructor but he told me that it came from the experience of Schrödinger and his experiments. My question is,
can one derive the Schrödinger equation mathematically?
The Schrödinger equation is the basis to ... |
The orthogonal group, consisting of all proper and improper rotations, is generated by reflections. Every proper rotation is the composition of two reflections, a special case of the Cartan–Dieudonné theorem.
Yeah it does seem unreasonable to expect a finite presentation
Let (V, b) be an n-dimensional, non-degenerate s... |
Is there any reference which studies sets of random variables as independence systems, a type of combinatorial object (see below)?
Motivation:In particular, since independence systems are abstract simplicial complexes, this would allow one to apply homology theory (I think) to study families of random variables. Moreov... |
I'm considering implementing (just for simplicity) the unconstrained implicit optimization based integration for Material Point Method as described in Chenfanfu Jiang's thesis on MPM (the minimization algorithm starts on page 101 – "
A.3.1 Unconstrained minimization").
I have difficulties understanding how would be the... |
I read that every chemical reaction is theoretically in equilibrium in an old textbook. If this is true how can a reaction be one way?
Yes, every chemical reaction can theoretically be in equilibrium. Every reaction is reversible. See my answer to chem.SE question 43258 for more details.
This includes even precipitatio... |
Consider $\mathbb{R}^n$ equipped with the standard dot product $\langle \cdot, \cdot \rangle$ and $m$ vectors there: $v_1, v_2, \ldots, v_m$. We want to build a data structure that allows queries of the following format: given $x \in \mathbb{R}^n$ output $\min_i \langle x, v_i \rangle$.
Is it possible to go beyond the ... |
I'm struggling to understand the reasoning in question $b)$. Basically, I had to write Newton's Second Law and do a change of variables to put the equation of motion of a mass $m$ in a specific form, which will give the driven harmonic oscillator time function once solved.
My Physics assistant was unable to answer my q... |
The relationship between 3d Chern-Simons theory on the product of the disk and the real line ($D\times \mathbb{R}$) and the chiral WZW model on $S^1\times \mathbb{R}$ was shown in Elitzur et al Nucl.Phys. B326 (1989) 108 (the main details can be found in the top answer to this question, whose notation we follow).
The e... |
Rational function \( R(z)= \frac {P(z)}{Q(z)} \) ; where P and Q are polynimials . There are some theory about fixed points .
Theorem:
Let \( \rho \) be the fixed point of the maps R and g be the Mobius map . Then \( gRg^{-1} \) has the same number of fixed points at \( g(\rho) \) as \( R \) has at \( \rho \).
Theorem ... |
Normal Forms
James Murdock (2006), Scholarpedia, 1(10):1902. doi:10.4249/scholarpedia.1902 revision #91592 [link to/cite this article]
A
normal form of a mathematical object, broadly speaking, isa simplified form of the object obtained by applying atransformation (often a change of coordinates) that is consideredto pre... |
This is the final part of this hands-on tutorial. I will assume from now on that you have read Part I, Part II, and Part III of this series.
As promised, this post will deal with:
As promised, this post will deal with:
Some tweaks to the protocol presented in the previous posts. A complexity analysis of the protocol, A... |
I think there are two legitimate sources of complaint. For the first, I will give you the anti-poem that I wrote in complaint against both economists and poets. A poem, of course, packs meaning and emotion into pregnant words and phrases. An anti-poem removes all feeling and sterilizes the words so that they are clear.... |
Problem
I want to convert the general second order linear PDE problem \begin{align} \begin{cases} a(x,y)\frac{\partial^2 u}{\partial x^2}+b(x,y) \frac{\partial^2 u}{\partial y^2} +c(x,y)\frac{\partial^2 u}{\partial x \partial y}\\+d(x,y)\frac{\partial u}{\partial x}+e(x,y)\frac{\partial u}{\partial y}+f(x,y)u=g(x,y) & ... |
I have used the
tcolorbox to highlight my equations, the problem i have i that the indentation does somehow not work properly. If i use regular equations i just have to remove the lines before and after the equation to get no indentation. Nevertheless with tcolorbox this does not seem to work.
Here is an example:
This ... |
I'm doing research in generalised inverse limits, and I'm trying to prove a result about circle-like plane continua.
Definitions
A
continuum is a compact, connected metric space.
A
plane continuum is a continuum that is homeomorphic to a subcontinuum of $\mathbb{R}^2$. This definition can just be interpreted as "a cont... |
Current browse context:
math.KT
Change to browse by: Bookmark(what is this?) Mathematics > Differential Geometry Title: Spectral sections, twisted rho invariants and positive scalar curvature
(Submitted on 23 Sep 2013 (v1), last revised 25 Apr 2014 (this version, v3))
Abstract: We had previously defined the rho invaria... |
Warning: Boring technical stuff that’s only here because I needed it for the model in the Helicopter Money paper, and there are no other good references online.
All the existing resources on the internet that I’ve found are either vague or inconsistent with their
σ/ ρ notation (where \(ρ=\frac{σ-1}{σ}\) and σ is the el... |
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... |
The reason is that you want to space the raised-cosine pulses by the symbol interval, $T_p$. Consider the signal you want to create: $$s(t) = \sum_k a_k p(t-kT_p),$$ where $p(t)$ is your prototype raised-cosine pulse, and $a_k$ are the symbols. Notice that pulses are spaced $T_p$ seconds.
To re-create this with a filte... |
Unfortunately, indicator constraints are only supported for
linear constraints. The Cplexdocs say: The constraint must be linear; a quadratic constraint is not allowed to have an indicator constraint. A lazy constraint cannot have an indicator constraint. A user-defined cut cannot have an indicator constraint. Gurobime... |
Group of Tangent-Space Automorphism Fields¶
Given a differentiable manifold \(U\) and a differentiable map\(\Phi: U \rightarrow M\) to a differentiable manifold \(M\) (possibly \(U = M\)and \(\Phi=\mathrm{Id}_M\)), the
group of tangent-space automorphism fieldsassociated with \(U\) and \(\Phi\) is the general linear gr... |
Total invested capital Assets at \(t=0\) Rate of income Rate of expenses Rate of return on invested capital Rate of withdrawal in retirement Saving time Saving rate
The three most harmful addictions are heroin, carbohydrates, and a monthly salary. - Nassim Taleb in The Bed of Procrustes
The acronym FIRE, financial inde... |
IWOTA 2019
International Workshop on
Operator Theory and its Applications
As was discovered by A. Olofsson and O. Giselsson, the shift operator $S_n$ on the standard weighted Bergman space $A_n$ satisfies the identity $$(S_n^*S_n)^{-1}=\sum_{k=0}^{n-1}(-1)^k\left(\begin{array}{c}n \\ k+1\end{array}\right)S_n^kS_n^{*k},... |
Yes, $\vec \jmath(x,y,z)$ should be defined as $e$ times the Schrodinger probability current. \begin{equation*} \vec \jmath = \frac{e\hbar}{2mi}\left(\Psi^* \frac{\partial \Psi }{\partial x}- \left(\frac{\partial \Psi^* }{\partial x}\right)\Psi \right) , \quad e\lt 0. \end{equation*}That's possible to explicitly see in... |
A geometric way of looking at differential equations
In the literature for the h-principle (for example Gromov's
Partial differential relations or Eliashberg and Mishachev's Introduction to the h-principle), we often see the following (all objects smooth):
Give a fibre bundle $\pi:F\to M$ over some manifold $M$, denote... |
It is known that the rational homotopy theory of spaces (e.g. simplicial sets) is equivalent in some sense to the homotopy theory of cdgas over $\mathbb{Q}$. This has been expressed in various forms in the literature. For instance, Felix-Halperin-Thomas show that homotopy classes of maps between simply connected ration... |
The best way to think of this is in terms of maps. A covector is a linear map that turns a vector into a number:
$$ W:\;V^\mu \mapsto W_\mu V^\mu. $$
So if a thing is a linear machine that maps a vector into a scalar we call it a covector. A gradient is an example of such a thing:
$$ \mathrm{d}\phi:\; V^\mu \mapsto \fr... |
View Full Version : Discussion: Fundamental Aspect of the ...
Fraser
2005-Apr-18, 06:53 PM
SUMMARY: Researchers from UC Berkeley have looked into the past to confirm that a fundamental aspect of the Universe - the fine structure constant, or alpha - has remain unchanged for at least 7 billion years. This constant shows... |
Here is a construction of a very broad class of "Lie-like" algebras, and I want to know more about them.
Here is the main definition: Suppose $\mathfrak{g}$ is a complex semsimple Lie algebra and $\Gamma$ is a finite abelian group. Define a "hybrid algebra" over $(\mathfrak{g},\Gamma)$ as a pair $(V,\Phi)$ where $V$ is... |
I've been given this situation
"A surface contains $N$ identical atoms in a fixed position. Every atom can occupy one of two states with energies $E_1$ or $E_2$ and the temperature is $T$."
For the solution, I am uncertain what kind of ensemble to use seeing as it is a surface, I would imagine it to be a 2-dimensional ... |
Background information:
I believe we can use Jensen's Inequality here
Show that if the payoff function $V(S_T)$ is a convex function on $S_T$, then the Markovian European contingent claim with payoff $V(S_T)$ has non-negative $\Gamma$, i.e. $V(\tau,S)$ is convex on $S$ for all $\tau$.
Attempted proof: Suppose we have a... |
IWOTA 2019
International Workshop on
Operator Theory and its Applications
We study matrices whose entries are free or exchangeable noncommutative elements in some tracial W*-probability space. We provide quantitative estimates of their convergence to some operator-valued semicircular elements. Many random block matrice... |
You are blindfolded and disoriented, standing exactly 1 mile from the Great Wall of China. How far must you walk to find the wall?
Assume the earth is flat and the Great Wall is infinitely long and straight.
Puzzling Stack Exchange is a question and answer site for those who create, solve, and study puzzles. It only ta... |
4.8. Numerical Stability and Initialization¶
In the past few sections, each model that we implemented required initializing our parameters according to some specified distribution. However, until now, we glossed over the details, taking the initialization hyperparameters for granted. You might even have gotten the impr... |
Introduction¶
While Deep Learning will probably keep its position as the hottest topic in Machine Learning for the nearer future, we also see a rising interest in white-box models whose calculations and outputs can be interpreted by a human being. Although it might look like this interpretability restrictions severely ... |
IWOTA 2019
International Workshop on
Operator Theory and its Applications
A remarkable pair of theorems of Grothendieck say if $p : \mathbb{C}^g \to \mathbb{C}^g$ is an injective polynomial, then $p$ is bijective and its inverse is a polynomial. We prove a free analog of this.
Recall that a free polynomial mapping in $... |
@user193319 I believe the natural extension to multigraphs is just ensuring that $\#(u,v) = \#(\sigma(u),\sigma(v))$ where $\# : V \times V \rightarrow \mathbb{N}$ counts the number of edges between $u$ and $v$ (which would be zero).
I have this exercise: Consider the ring $R$ of polynomials in $n$ variables with integ... |
1. Introduction
Here is the definition of ensemble learning (集成学习).
Given base (weak) learners $\lbrace f_b \rbrace_{b=1}^B$ and their weights $w_b$, $$f(x)=\sum\limits_{b=1}^Bw_bf_b(x).$$ If $w_b$ is uniform, for binary classification, $f(x)=\mathrm{sign}\left(\sum\limits_{b=1}^Bf_b(x)\right);$ for multi-class classif... |
IWOTA 2019
International Workshop on
Operator Theory and its Applications
Let $\mathfrak{S}$ be a subset of the algebra $\mathcal{L}(\mathcal{H})$ of all bounded linear operators on an infinite-dimensional complex Hilbert space $\mathcal{H}$ containing all rank one operators. In this talk, we determine the structures o... |
I was trying to implement the algorithm from the paper "Adapting a Fourier pseudospectral method to Dirichlet boundary conditions for Rayleigh–Benard convection".
I am having a hard time to understand the way the boundary conditions are imposed.
The author rewrites the no-slip (on upper and lower boundaries) boundary c... |
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 ...
... by alerting the driver of possible hazardous situations.Following is the official description of the project:... |
There is a general way to do these sorts of problems. The idea is to consider equilibria of both acid/base and of the water.
When there is solution of a weak acid and it salt, or just the weak acid or just the salt, i.e. pure HA, NaA + HA or pure NaA, then there is no distinction between these types of solution because... |
The thing is that you need to know the coordination environment in the first place as ionic radii are C.N.-dependent. From Shannon's canonical paper "Revised effective ionic radii and systematic studies of interatomic distances in halides and chalcogenides"[1]:\begin{array}{cc}\hline\text{Ion} & \text{C.N.} & \text{C.R... |
(This question has been asked on math.se, with no response.)
I am studying Paz's "Introduction to Probabilistic Automata" and there is an exercise I cannot solve:
Ex. 11, p. 170: Let $\Sigma = \{a\}$. Show that the number of nonregular events of the form $\{x \mid p^A(x) > \lambda\} \subseteq \Sigma^*$, where $A$ is a ... |
IWOTA 2019
International Workshop on
Operator Theory and its Applications
The notion of combinatorial Perron value was introduced in [1]. We continue the study of this parameter and also introduce a new parameter $\pi_e(M)$ which gives a new lower bound on the spectral radius of the bottleneck matrix $M$ of a rooted tr... |
Ok, let's go, one topic at a time:
We model the blackbody radiation as the one escaping by a small hole on the wall of a metal made object manteined at temperature T (such hole connects the interior cavity to the outside). Because the walls of the cavity are made of a conducting material (metal), the electric field van... |
Electronic Journal of Probability Electron. J. Probab. Volume 23 (2018), paper no. 66, 24 pp. Chordal SLE$_6$ explorations of a quantum disk Abstract
We consider a particular type of $\sqrt{8/3} $-Liouville quantum gravity surface called a doubly marked quantum disk (equivalently, a Brownian disk) decorated by an indep... |
Schließen Ja, ich möchte sie behalten Rückgängig es später erneut. how http://grid4apps.com/standard-error/solved-formula-for-the-estimated-standard-error-of-the-mean.php calculate Standard Error Of Proportion Calculator SE, SEM (for standard error of measurement or mean), or SE. In fact, data organizations often set r... |
Forgive me if this question is too elementary however, I haven't found an answer. If $\mathfrak{g}$ is a Lie algebra one can define its Lie algebra cohomology: the definition is quite similar to the way in which de Rham cohomology is defined. For such theory we can consider coefficients in arbitrary $\mathfrak{g}$-modu... |
Quasiperiodic oscillations
Anatoly M. Samoilenko (2007), Scholarpedia, 2(5):1783. doi:10.4249/scholarpedia.1783 revision #91689 [link to/cite this article] Quasiperiodic oscillation is an oscillation that can be described by a quasiperiodic function, i.e., a function \(F\) of real variable \(t\) such that \[F(t)= f(\om... |
For integer $n \ge 1$, let $[n]$ be a short hand for the interval of integers $\{ 1, 2,\ldots, n \}$.
Let $\{ s_1, s_2, \ldots, s_p \}$ be the set of sides of a bunch of squares that cover a rectangle of dimension $w \times h$.
Since $\mathbb{R}$ is a vector space over $\mathbb{Q}$, there is a hamel basis $E$ of $\math... |
You are given $$$n$$$ integers $$$a_1, a_2, \ldots, a_n$$$. Each of $$$a_i$$$ has between $$$3$$$ and $$$5$$$ divisors. Consider $$$a = \prod a_i$$$ — the product of all input integers. Find the number of divisors of $$$a$$$. As this number may be very large, print it modulo prime number $$$998244353$$$.
The first line... |
What Is Stereo Disparity?
Stereopsis is a term that refers to perception of depth, and thus 3D structure, based on observing a scene from two different vantage points. The way this works in nature is that humans, and quite a few other animals, have two eyes located so that these observe the scene from two different pos... |
Given a language L defined by a Turing Machine that decides it, is it possible to determine algorithmically whether L lies in NP?
No. First, by Rice's Theorem, this is a property of TMs that depends only on the language they compute, so it cannot be computable.
But, more than that, it is known that the index set of $NP... |
There is nothing wrong with using the squared distance.
You converted the problem into a one-parameter minimization problem.You are looking for the minimum of a smooth function on the interval $[-\sqrt{262090/6},\sqrt{262090/6}]$.The minimum value is obtained at a zero of the derivative (a critical point)
or at one of ... |
Consider a system of PDEs $$ \begin{cases} u_t = \nabla \cdot (D(u)\nabla u) + \frac{c}{K_U+c}u-ku\\ c_t = d_c\Delta c -\frac{\nu_U c}{K_U + c}u \end{cases} $$ with some boundary conditions. Here, $D(u)$ is a diffusion coefficient which depends on $u$; $K_U$, $\nu_U$ and $k$ are some constants. $D(u)$ can be defined as... |
I'm using
pgfkeys, and a fairly adventurous syntax in which the values for some keys contain additional key/value pairs. (For instance, the value of the
nodes key is a list of pairs, and the second component of each pair is a key-value list.)
I get a compilation error whenever I put anything too fancy into the
label ke... |
This is a microcanonical approach to the problem of the mixture of two ideal gases. It involves a somewhat tricky integral over the surface of an N-dimensional hypersphere, and as far as I can tell is an example beloved of professors for exam questions. It might be a good one to become familiar with if you’re taking a ... |
Let $R$ be a ring (associative with unit, but not necessarily commutative, and definitely not necessarily Noetherian.) Then the category $\operatorname{GP}(R)$ consists of those $R$-modules having a complete projective resolution, i.e. that are expressible as the image of the map $P_{-1}\to P_0$ in some sequence
$$\cdo... |
Set forcing works over models of ${\rm NBG}$. Suppose ${\mathbb P}$ is a set partial order. Set $\mathbb P$-names are defined as usual. A class $\mathbb P$-name is defined to be a collection of pairs $(\tau,p)$ where $\tau$ is a set $\mathbb P$-name and $p\in\mathbb P$. All the usual properties of the set forcing const... |
An eigenvalue problem for a quasilinear elliptic field equation on $\mathbb R^n$
DOI: http://dx.doi.org/10.12775/TMNA.2001.013
Abstract
We study the field equation
$$-\Delta u+V(x)u+\varepsilon^r(-\Delta_pu+W'(u))=\mu u$$ on $\mathbb R^n$, with $\varepsilon$ positive parameter. The function $W$ is singular in a point a... |
Finite lattice posets¶ class
sage.categories.finite_lattice_posets.
FiniteLatticePosets(
base_category)¶
The category of finite lattices, i.e. finite partially ordered sets which are also lattices.
EXAMPLES:
sage: FiniteLatticePosets() Category of finite lattice posets sage: FiniteLatticePosets().super_categories() [Ca... |
Search
Now showing items 1-10 of 24
Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
The Hadamard gate might be your first encounter with superposition creation. When you say you can relate the usefulness of the Pauli $X$ gate (a.k.a.
NOT) to its classical counterpart – well, Hadamard is exactly where you leave the realm of classical analogue, then. It is useful for
exactly the same reason, however, na... |
This question already has an answer here:
How can I place several equations side by side inside the gather environment with the line breaking working to avoid this equations to exceed the page size. Here goes one example:
\documentclass[12pt,oneside]{report}\usepackage{geometry}\geometry{a4paper,total={170mm,257mm},lef... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
For the reversible isothermal expansion of an ideal gas: $${∆H}={∆U}=0 \tag1$$ This is obvious for the case of internal energy because $${∆U} = \frac {3}{2} n R {∆T} = 0 \tag2$$ and $${∆U} = -C_P n {∆T} = 0 \tag3$$ For the case of enthalpy it is easy to see that $${∆H} = -C_v n {∆T} = 0 \tag4$$ I've also seen $${∆H} = ... |
Loan balance vs time Loan balance after the ith payment Principal or loan balance at Fraction of payment to interest during the ith payment Fraction of payment to interest Interest rate Loan term Number of loan payments Time between loan payments Loan product, important parameter which fully specifies a loan Helpful co... |
Search
Now showing items 1-1 of 1
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 ... |
According to Wikipedia caesium’s density is $1.90\ \mathrm{g/cm^3}$ at $\Theta =20\ \mathrm{^\circ C}$. How does this change when $T$ changes? E.g. will it expand when melting?
Looking at the wikipedia page you can see that the density is $\rho=1.93$ kg/l at room temperature and $\rho=1.843 kg/l$ at it's melting point.... |
I'm trying to understand the derivation of the zero order hold discretization method, and I have a couple of questions about some of the steps.I think I understand the first part, this is just the ...
I have found a problem in applying Laplace Transform to $-e^{-at}u(-t)$I am doing these steps:$$ = - \int_{-\infty}^{+\... |
Codeforces Round #484 (Div. 2) Finished
Petr is a detective in Braginsk. Somebody stole a huge amount of money from a bank and Petr is to catch him. Somebody told Petr that some luxurious car moves along the roads without stopping.
Petr knows that it is the robbers who drive the car. The roads in Braginsk are one-direc... |
I have a set of numbers, and want to calculate the maximum subset such that the sum of any two of it's elements is not divisible by an integer $K$.I tried to solve this problem, but I have found the quadratic solution, which is not efficient response.
$K < 100, N < 10000$, where $N$ is the number of elements and $K$ is... |
Finite monoids¶ class
sage.categories.finite_monoids.
FiniteMonoids(
base_category)¶
The category of finite (multiplicative)
monoids.
A finite monoid is a
finite setsendowed with an associative unital binary operation \(*\).
EXAMPLES:
sage: FiniteMonoids() Category of finite monoids sage: FiniteMonoids().super_categori... |
I cannot see how Willie Wong's example of the Bernstein-Robinson result supports his conclusion. It seems to me to do the opposite, and I am not alone here. Halmos admits himself in his autobiography: "The Bernstein-Robinson proof uses non-standard models of higher order predicate languages, and when Abby [Robinson] se... |
I have that $R$ is the $k$-algebra ($k$ is a field) finitely generated by $S=\{f_1, ..., f_m \}\subset k[x_1, \cdots, x_n]$ and this set of polynomials is minimal with respect to inclusion (i.e., e dont have redundant elements). However, I know that the $f_i$'s are algebraically dependent. Can be the number $m=|S|$ uni... |
10.7. Adagrad¶
In the optimization algorithms we introduced previously, each element of the objective function’s independent variables uses the same learning rate at the same time step for self-iteration. For example, if we assume that the objective function is \(f\) and the independent variable is a two-dimensional ve... |
Given a list of intervals $[s_1, e_1], [s_2, e_2], \ldots$, what's the most efficient way to determine if an interval $[a, b]$ can be covered by the intervals in the list?
closed as unclear what you're asking by Raphael♦ Feb 25 '14 at 20:19
Please clarify your specific problem or add additional details to highlight exa... |
The impatient reader can skip my attempt at motivation and go straight my "Question formulations for the impatient."
In a failed(?) attempt at discovering something new, some years ago I toyed with the idea of dualizing the notion of a compact topological space. So starting from the "open covers have finite subcovers" ... |
I'm following the methodology outlined in Developing High-Frequency Equities Trading Models. On page 27, the author outlines an OLS regression model to obtain beta coefficients. The model is defined as:
$$r_{t+1} + ... + r_{t+H} = \beta_1\sum_{i=0}^HD_{t-i,1}+...+\beta_{k}\sum_{i=0}^HD_{t-i,k}+\eta_{t+H,H}$$
Where $r_{... |
When doing multiple linear regression,
$\boldsymbol{Y} = X\boldsymbol{\beta}+\boldsymbol{\epsilon}$
where
$\boldsymbol{\epsilon} \sim N(0, \Sigma)$
The best estimates of the coefficients can be found using the generalised least squares formula:
$\boldsymbol{\hat{\beta}} = (X'\Sigma^{-1}X)^{-1}X'\Sigma^{-1}\boldsymbol{Y... |
I think the work of Dr. Paul Garabedian (and Dr. Schiffer)[1], and Dr. Mel'nikov (who built on Dr. Garabedian's result) are important theorems that were
almost forgotten. I'll share the main theorem from Dr. Mel'nikov's work[2] as it incorporates the main result from Dr Garabedian's:
Given complex numbers $z_1,\ldots,z... |
Current browse context:
astro-ph.CO
Change to browse by: Bookmark(what is this?) Astrophysics > Cosmology and Nongalactic Astrophysics Title: Effect of Template Uncertainties on the WMAP and Planck Measures of the Optical Depth Due To Reionization
(Submitted on 4 Jan 2018 (v1), last revised 8 Jan 2019 (this version, v3... |
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:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
I don’t think we’re clear on what simulation is NOT. RANDOMNESS IS NOT NECESSARY, for the simple reason randomness is merely a state of knowledge. Hence this classic post from 12 June 2017.
“Let me get this straight. You said
what makes your car go?”
“You heard me. Gremlins.”
“Grelims make your car go.”
“Look, it’s obv... |
@user193319 I believe the natural extension to multigraphs is just ensuring that $\#(u,v) = \#(\sigma(u),\sigma(v))$ where $\# : V \times V \rightarrow \mathbb{N}$ counts the number of edges between $u$ and $v$ (which would be zero).
I have this exercise: Consider the ring $R$ of polynomials in $n$ variables with integ... |
Let $\mathcal A = (X, Q, \delta, q_0, F)$ be a deterministic finite automata with the following acceptance condition on infinite words:
The automata accepts $\xi \in X^{\omega}$ with respect to $F$ iff $$ \forall i : \delta(q_0, \xi[0...i]) \in F. $$ Meaning that every prefix $\xi[0...i]$ of $\xi$ goes to an acceptance... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.