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Cardinal characteristics of the continuum The subject known as cardinal characteristics of the continuum explores the rich territory---sometimes hidden from view, depending on the set-theoretic background---between the countably infinite cardinal $\aleph_0$ and the uncountable cardinality of the continuum. The subject ... |
The package
CircuiTikz provides a set of macros for naturally typesetting electrical and electronic networks. This article explains basic usage of this package.
Contents CircuiTikz includes several nodes that can be used with standard tikz syntax.
\documentclass{article} \usepackage[utf8]{inputenc} \usepackage[english]... |
When I studied QM I'm only working with time independent Hamiltonians. In this case the unitary evolution operator has the form $$\hat{U}=e^{-\frac{i}{\hbar}Ht}$$ that follows from this equation $$ i\hbar\frac{d}{dt}\hat{U}=H\hat{U}. $$ And in this case, Hamiltonian in Heisenberg picture ($H_{H}$) is just the same as t... |
this question is giving me some issue because i know sin and cos is the same as $45$ degrees but there is a $2$ on the right side where cosine is.
So how would i get $\theta$?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only take... |
I am having trouble understanding the spectral characterization of Reed-Solomon codes. My script states the following:
An evaluation codes is defined as:
$$C = \{(c_0, \ldots, c_n) : c_l = a(\beta_l) \text{ for some } a(x) \in F[x] \text{ with deg } a(x) < k \text{ and F = some field}\}$$
(($\beta_0, \ldots, \beta_{n-1... |
Noninertial effects on a scalar field in a spacetime with a magnetic screw dislocation Abstract
We investigate rotating effects on a charged scalar field immersed in spacetime with a magnetic screw dislocation. In addition to the hard-wall potential, which we impose to satisfy a boundary condition from the rotating eff... |
The analemmatic sundial is unique with the ability to use a gnomon (the shadow casting element) of any height. This leads to the popular use of the analemmatic sundial as a "human sundial" where people use their own shadow to tell time.
Unlike garden horizontal dials or vertical dials on buildings, the analemmatic sund... |
Rocky Mountain Journal of Mathematics Rocky Mountain J. Math. Volume 48, Number 3 (2018), 905-912. Invariant means and property $T$ of crossed products Abstract
Let $\Gamma $ be a discrete group that acts on a semi-finite measure space $(\Omega , \mu )$ such that there is no $\Gamma $-invariant function in $L^1(\Omega ... |
I looked at the proof of Archimedean Property in several places and, in all of them, it is proven using the following structure (proof by contradiction), without much variation:
If $\space x \in \mathbb{R} \space,\space y \in \mathbb{R},$ and $x > 0$, then there is at least one natural number $n$ such that $nx > y$. $\... |
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Division (mathematics) [math]6/3\,[/math] or [math]\frac 63[/math] or [math]6 \div 3.[/math]
Each, of those three, means "6 divided by 3" giving 2 as the answer. The first number is the
dividend (6), and the second number is the divisor (3). The result (or answer) is th... |
Semilinear nonlocal elliptic equations with critical and supercritical exponents
Department of Mathematics, Indian Institute of Science Education and Research, Dr. Homi Bhaba Road, Pune-411008, India
$\left\{ \begin{align} &{{(-\Delta lta )}^{s}}u={{u}^{p}}-{{u}^{q}}\ \text{in}\ \text{ }{{\mathbb{R}}^{N}}, \\ &u\in {{{... |
Omega, $\omega$
The smallest infinite ordinal, often denoted $\omega$ (omega), has the order type of the natural numbers. As a von Neumann ordinal, $\omega$ is in fact equal to the set of natural numbers. Since $\omega$ is infinite, it is not equinumerous with any smaller ordinal, and so it is an initial ordinal, that ... |
2019-07-18 17:03
Precision measurement of the $\Lambda_c^+$, $\Xi_c^+$ and $\Xi_c^0$ baryon lifetimes / LHCb Collaboration We report measurements of the lifetimes of the $\Lambda_c^+$, $\Xi_c^+$ and $\Xi_c^0$ charm baryons using proton-proton collision data at center-of-mass energies of 7 and 8 TeV, corresponding to an... |
As he described it some time later the situation was as follows.
You have a spectrometer. The point of spectrometry is to find the frequency of light (or electromagnetic radiation more generally — but for convenience I’ll just say “light” from now on). Given a light source, spectrometry aims to find which frequencies (... |
Lethbridge Number Theory and Combinatorics Seminar: Nathan Ng Date: 01/29/2018
University of Lethbridge
Mean values of long Dirichlet polynomials
A Dirichlet polynomial is a function of the form $A(t)=\sum_{n \le N} a_n n^{-it}$ where $a_n$ is a complex sequence, $N \in \mathbb{N}$, and $t \in \mathbb{R}$. For $T \ge 1... |
Supercompact cardinal
Supercompact cardinals are best motivated as a generalization of measurable cardinals, particularly the characterization of measurable cardinals in terms of elementary embeddings and strong closure properties. The notion of supercompactness and its consequences was initially developed by Solovay a... |
If I have volatility smile quoted with respect to the delta of an option on the forward, how can I convert this delta into the moneyness or strike of the option?
Is there any bult-in function of Matlab financial toolbox?
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and aca... |
from the POV of sinusoidal modeling or identifying sinusoids, two very good basic reasons why a Gaussian window is good are:
The Fourier Transform of a Gaussian is a Gaussian. (and Gaussians have essentially no side lobes.)
$$ \mathscr{F} \{ e^{-\pi t^2} \} = e^{-\pi f^2} $$
The Gaussian function is just like the linea... |
I am reading about Dihedral Groups and I have following questions:
Elements of $D_n$ act as linear transformations of plane. My thought:I know that $D_n=\{\langle a,b\rangle :a^n=b^2=1,bab=a^{-1}\}$which comprises of rotations and reflections of the n-gon.
But then
How to prove that rotations and reflections are linear... |
Your observation is correct! The issue is one that is regrettably rather commonly left unexplained in physics texts: A single coordinate system on a manifold
does not define the spacetime. Often, the coordinates useful for computations in physics do not even cover the entire space, i.e. they are not defined everywhere ... |
In Griffith's Introduction into Particle Physics (p. 251, eq. 7.125) we derive Casimir's trick
$$ \sum_{s_1,s_2}[\bar{v}(s_1,p_1)\Gamma_1 v(s_2,p_2)][\bar{v}(s_a,p_a)\Gamma_2v(s_b,p_b)]^* = \text{Tr}[\Gamma_1(\gamma_\mu p_b^\mu-m_bc)\gamma^0\Gamma_2^\dagger\gamma^0(\gamma_\nu p_a^\nu-m_ac)] $$
wherein $\bar{v}=v^\dagge... |
Rocky Mountain Journal of Mathematics Rocky Mountain J. Math. Volume 48, Number 3 (2018), 1019-1030. Orthogonal rational functions on the extended real line and analytic on the upper half plane Abstract
Let $\{\alpha _k\}_{k=1}^\infty$ be an arbitrary sequence of complex numbers in the upper half plane. We generalize t... |
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D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
How many power series of the form $1+\sum_{k=1}^{\infty} a_{k}x^{k}$ with $a_{k}\in \{-1,0,1 \}$, that have a double zero $f(x)=f'(x)=0$ in $(0,1)$, are there. Ok, there are many ways to understand the question: set theoretical, topological, measure theoretical. I would be especially interested in the Bernoulli measure... |
In Fluid Mechanics we often see the term inertial force when discussing Reynolds number. The problem is, I didn't really get what's this inertial force. Basically, the notion of inertia I have is that given by Newton's laws where we think of inertia as the resistance of a body to change its state of motion.
This inerti... |
This will be a talk for the CUNY Set Theory Seminar, March 6, 2015.
I shall describe the current state of knowledge concerning the question of whether there can be an embedding of the set-theoretic universe into the constructible universe.
Question.(Hamkins) Can there be an embedding $j:V\to L$ of the set-theoretic uni... |
An important consideration in the implementation of any practical numerical algorithm is numerical accuracy: how quickly do floating-point roundoff errors accumulate in the course of the computation? Fortunately, FFT algorithms for the most part have remarkably good accuracy characteristics. In particular, for a DFT of... |
Recall that the category of $\sigma Set$ of
symmetric simplicial sets is the category of presheaves on $\Sigma$, the category of finite nonempy sets and all functions. The inclusion $v: \Delta \to \Sigma$ transfers the Kan-Quillen model structure via a Quillen equivalence with $sSet$. In this "canonical" model structur... |
Question:
For which of the following matrices $A_i$ is there
A complex matrix $B$ such that $B^2 = A_i$; A self-adjoint complex matrix $B$ such that $B^2 = A_i$; A real matrix $B$ such that $B^2 = A_i$?
$A_1 = \begin{pmatrix} 2 & 1\\1 & 2\end{pmatrix}$, $A_2 = \begin{pmatrix} 1 & 2\\2 & 1\end{pmatrix}$, $A_3 = \begin{p... |
I've already found that the fundamental group of the connected sum $P^2\#T$, by the labelling scheme $aabcb^{-1}c^{-1}$, to be $F_3/<aabcb^{-1}c^{-1}>$. How would I find the first homology group? The first homology group is defined to be: $ H_1(X) = \pi_1(X,x_0)/[\pi_1(X,x_0),\pi_1(X,x_0)] $. I believe I have to use th... |
So I want a function that is zero on the reals
only on the prime integers and which doesn't depend on knowing the primes. I construct:
$$f(x) = e^{-x^2} - \sum\limits_{n=2}^\infty e^{-n^2} \frac{ \sin(\pi x)^2 }{ n^2\sin(\pi x/n)^2}$$
Which has zeros on the real line only on the positive and negative prime integers.
( ... |
Let $k$ be a field, and $f:k[x_1,\ldots,x_n]\to k[y_1,\ldots,y_m]$ a $k$-algebra homomorphism. Given $r_1,\ldots,r_k\in k[y_1,\ldots,y_m]$, is there an algorithm for producing a finite generating set for the ideal $f^{-1}((r_1,\ldots,r_k))$?
The answer is yes. The question is asking to compute the kernel of
$$f : k[x_1... |
Codeforces Round #526 (Div. 1) Finished
The Fair Nut is going to travel to the Tree Country, in which there are $$$n$$$ cities. Most of the land of this country is covered by forest. Furthermore, the local road system forms a tree (connected graph without cycles). Nut wants to rent a car in the city $$$u$$$ and go by a... |
Salts, when placed in water, will often react with the water to produce H
3O + or OH -. This is known as a hydrolysis reaction. Based on how strong the ion acts as an acid or base, it will produce varying pH levels. When water and salts react, there are many possibilities due to the varying structures of salts. A salt ... |
3.1: Generalize Construction 3.2.1 to be an
n-out-of- n secret-sharing scheme, and prove that your scheme is correct and secure.
3.2: Prove Theorem 3.2.2.
3.3: Fill in the details of the following alternative proof of Theorem 3.2.1: Starting with \(\mathscr{L}_{\text{tsss-L}}\), apply the first step of the proof as bef... |
What are some conditions that ensure that a function $f(x) : \mathbb{R} \to \mathbb{R}$ which is in $L^1_{loc}$ and almost everywhere differentiable (in the classical sens ) with derivative in $L^1_{loc}$ has its derivative equal to its weak derivative (its derivative in the sens of distributions) ie :
$$ \forall \phi ... |
Nonstandard Constraints and the Power of Weak Contributions
Have you ever wanted to add a certain boundary or domain condition to a physics problem but couldn’t find a built-in feature? Today, we will show you how to implement nonstandard constraints using the so-called weak contributions. Weak contributions are, in fa... |
In some book about continuum mechanics I read that from principle of virtual work follows balance of rotational momentum when $\delta \boldsymbol{r} = \boldsymbol{\delta \varphi} \times \boldsymbol{r}, \; \boldsymbol{\delta \varphi} = \boldsymbol{\mathsf{const}}$ ($\boldsymbol{r}$ is location vector, $\delta \boldsymbo... |
First, note that
isomorphism is a map between two objects which preserves the structure. The more structure, the "less" isomorphisms you might have. Isomorphism is an equivalence relation: the identity map gives us reflexivity; the fact the inverse of an isomorphism is also an isomorphism gives symmetry; and by composi... |
Operator product expansion says that, the product of two primary fields(of same dimension in this case) can be expanded as sum of primaries and their descendants
$$\phi_1(x)\phi_2(0) = {\Large \Sigma_\mathcal{O}}\lambda_\mathcal{O}C_\mathcal{O}(x,\partial_y)\mathcal{O}(y)|_{y=0} $$ where the summation $\Sigma_\mathcal{... |
Definition:Natural Logarithm/Complex Contents Definition
Let $z = r e^{i \theta}$ be a complex number expressed in exponential form such that $z \ne 0$.
The
complex natural logarithm of $z \in \C_{\ne 0}$ is the multifunction defined as: $\map \ln z := \set {\map \ln r + i \paren {\theta + 2 k \pi}: k \in \Z}$
The
comp... |
You actually do recover the convolution, but as it is discussed in the comments, there is a normalization issue due to discretization.
According to the documentation,
fft is implemented like this:
$$ A_k = \sum_{m=0}^{n-1} a_m \exp \{ - 2\pi i \frac{mk}{n} \} $$
with $A_k$ being the Fourier-coefficients, $a_m$ the $m$-... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
I want to know the hybridization of the central atom in $\ce{(SiH3)3N}$.
I think it should be $\mathrm{sp^3}$, because $\ce{N}$ is attached to three silicon atoms and one lone pair. But actually it is supposedly $\mathrm{sp^2}$.
How is this so?
Chemistry Stack Exchange is a question and answer site for scientists, acad... |
Let me look at the Hamiltonian of a charged particle in a plane in a constant magnetic field ($\vec{B}$) pointing upwards - then in usual notation it is,
$$\hat{H} = \frac{1}{2m}\biggl(\hat{p} + \frac{e}{c}\hat{A}(\hat{r})\biggr)^2$$
To convert this in a Feynman-path-integral language, I pick say a gauge $\vec{A}=(-\fr... |
I am attempting to calculate the unconditional variance of an E-GARCH model: $$\log(h_{t+1}) = \beta_{0} + \beta_{1}\log(h_{t}) + \beta_{2}\left[|\varepsilon_{t} - \lambda| + \gamma(\varepsilon_{t} - \lambda) \right]$$ where $\varepsilon_{t} \sim \mathcal{N}(0,1)$ under the LRNVR measure, $\mathcal{Q}$.
I can calculate... |
Why don't we consider them as linear? I don't understand. You just have to check for factorization up to sqrt of n. So it's even faster than linear. I assume it's not linear only if we compare the number of operations relative to the input in terms of binary representation. But why would we do so? It seems to me wrong.... |
Let $n \in \mathbb{N}$ be a fixed positive integers and $B \in \mathbb{R}_+$ also be fixed. For a fixed $M>0$, let $f:[-B,B]^n \to \mathbb{R}$ be given by $f(x_1,\ldots,x_n)=\sum_{i=1}^n x_i M^i$. My aim is to prove the following:
Prove that one can always find a fixed positive real number $M$ (dependent only on $B$ an... |
We know that $H_A\otimes H_B\neq H_B\otimes H_A$ (in general). Theoretically, we know the formalism and what observables to construct from the two compositions possible, but we never talk about both the possibilities. I wish to know that how experimentally the Measurements or Evolutions are done over such composite sys... |
Given a discrete-time (DT) sequence $g[n]$, I want to represent it as a continuous-time (CT) signal. I can do this by representing this sequence as a weighted sum of Dirac delta impulses. Would it make a difference if I pass the DT signal through a DT filter first and then represent it as a weighted sum of Dirac impuls... |
Background: I have seen lots of people asking whether multiplication and pseudo-random sequences can be approximated by a NN without providing whether the inputs and outputs are bounded or not, and people have answered it (lot of upvotes) based on conventional NN knowledge. without taking into consideration the aforeme... |
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Bored with 2048 ? Try this one 2584.
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It is the Fibonacci version of 2048.
Some say it is even more difficult than the regular 2048.
Post your high score here!
Note by Nelvson Shine 5 years, 4 months ago
Easy Math Editor
This discussion board ... |
If \(A\) and \(B\) are numbers such that the polynomial \(x^{2017} + Ax + B\) is divisible by \((x + 1)^2\), what is the value of \(B\)?
This probably isn't how this problem is intended to be done but it's all I can come up with.
\(\text{Let }p(x) = x^{2017}+Ax+B\\ \text{We'll expand }p(x) \text{ as a Taylor series abo... |
In the last post I showed how to use
purrr to perform a simple Monte Carlo simulation.Since simulation studies are usually computationally expensive, it is benifical towrite efficient code and make use of parallelization. The latter even more important when working on a modern computer.
My PC has a Ryzen 3700X CPU with... |
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Description
A technique introduced by Indyk and Woodruff [STOC 2005] has inspired several recent advances in data-stream algorithms. We show that a number of these results follow easily from the application of a si... |
Could you please check my proof to the following exercise:
Consider the topologists's sine curve $X$ defined by: $$X = \{\ \{(0,0)\}\ \cup \ \{(x,\sin(\frac{1}{x})) \in \mathbb{R}^2 \text{ for } x > 0 \}\}$$ We will prove that $X$ is connected. We start by assuming that $X = U_1 \cup V_1$ where $U_1$ and $V_1$ are open... |
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Mathematics Mathematics, sometimes shortened to maths (in England, Australia, New Zealand and France) or math (in the United States, Canada and Germany) is the study of numbers, shapes and patterns. Mathematicians are people who learn about and discover such things in m... |
The beth numbers, $\beth_\alpha$
The
beth numbers $\beth_\alpha$ are defined by transfinite recursion: $\beth_0=\aleph_0$ $\beth_{\alpha+1}=2^{\beth_\alpha}$ $\beth_\lambda=\sup_{\alpha\lt\lambda}\beth_\alpha$, for limit ordinals $\lambda$
Thus, the beth numbers are the cardinalities arising from iterating the power se... |
By Schaefer's dichotomy theorem, this is NP-complete.
Consider the case where all clauses have 2 or 3 literals in them; then we can consider this as a constraint satisfaction problem over a set $\Gamma$ of relations of arity 3. In particular, the relations $R(x,y,z)$ are the following: $x \lor y$, $x \lor \neg y$, $\ne... |
Equivalence of Definitions of Algebraically Closed Field Contents Theorem
Let $K$ be a field.
The only algebraic field extension of $K$ is $K$ itself. Proof Definition $(1)$ implies Definition $(2)$
Let $K$ be algebraically closed by definition 1.
Let $f$ be an irreducible polynomial over $K$.
By Principal Ideal of Pri... |
Infinity The Greeks had already noted that there are two ways of considering infinity. Potential infinity is what we consider when we say that counting never ends. Whatever natural number you can think of, there is a bigger number. Formally
$$(\forall x\in\mathbb{N})(\exists y) (y>x),$$ and this is not really deniable.... |
The Bernstein operator maps $f\in C[0,1]$ to its Bernstein polynomial $B_n f.$ The eigenvalues and eigenfunctions of the Bernstein operator on $C[0,1]$ have been described in [1]. Similar description has been obtained for the $q$-Bernstein polynomials in [2]. The study of $q$-Bernstein polynomials in the case $0<q<1$ l... |
Let $R$ be a ring with identity (not necessarily commutative) and $R[x]$ be a ring of polynomials over $R$. We say that a ring $S$ is an
extension of $R$ if there is a subring $\tilde{R}$ in $S$ isomorphic to $R$.Let $S$ be an extension of $R$, and $$\phi: R\to \tilde{R}\subset S$$be a ring isomorphism.We say that a po... |
The beth numbers, $\beth_\alpha$
The
beth numbers $\beth_\alpha$ are defined by transfinite recursion: $\beth_0=\aleph_0$ $\beth_{\alpha+1}=2^{\beth_\alpha}$ $\beth_\lambda=\sup_{\alpha\lt\lambda}\beth_\alpha$, for limit ordinals $\lambda$
Thus, the beth numbers are the cardinalities arising from iterating the power se... |
2019-09-20 08:41
Search for the $^{73}\mathrm{Ga}$ ground-state doublet splitting in the $\beta$ decay of $^{73}\mathrm{Zn}$ / Vedia, V (UCM, Madrid, Dept. Phys.) ; Paziy, V (UCM, Madrid, Dept. Phys.) ; Fraile, L M (UCM, Madrid, Dept. Phys.) ; Mach, H (UCM, Madrid, Dept. Phys. ; NCBJ, Swierk) ; Walters, W B (Maryland U... |
Suppose $A\subseteq X$. Prove that the boundary $\partial A$ of $A$ is closed in $X$.
My knowledge:
$A^{\circ}$ is the interior $A^{\circ}\subseteq A \subseteq \overline{A}\subseteq X$
My proof was as follows:
To show $\partial A = \overline{A} \setminus A^{\circ}$ is closed, we have to show that the complement $( \par... |
If $A\subseteq B$ are affine domains over an algebraically closed field $k$ of characteristic zero, such that $Q(A)$ is algebraically closed in $Q(B)$, how can one show that $Q(A)$ is also algebraically closed in the field of fractions of $Q(A)\otimes_kB$?
The history behind this problem:
Starting from the fact that $Q... |
The lower attic
From Cantor's Attic
Welcome to the lower attic, where the countably infinite ordinals climb ever higher, one upon another, in an eternal self-similar reflecting ascent.
$\omega_1$, the first uncountable ordinal, and the other uncountable cardinals of the middle attic stable ordinals The ordinals of infi... |
Let $u$ be an element of $\mathbb{Z}[\sqrt 5]$ of norm 1, i.e. $u = r + s \sqrt 5$ with $r^2-5s^2 = 1$.
The multiplication by $u$ in $\mathbb{Z}[\sqrt 5]$ turns any element $y$ of norm $44$ into another element $uy$ of norm $44$.View this multiplication operation on $\mathbb{Z}[\sqrt 5]$ as the transformation of the pl... |
Answer
The value of $y$ here is $$y=\frac{5\pi}{6}$$
Work Step by Step
$\DeclareMathOperator{\arccot}{arccot}$ $$y=\arccot (-\sqrt 3)$$ First, we see that the domain of inverse cotangent function is $(-\infty,\infty)$. Therefore, in fact when we deal with inverse cotangent function, we do not need to do this checking s... |
The Dirac’s theorem states that: “For a Graph G with N vertices, if the degree of each vertex is atleast N/2 then, the Graph has a Hamilton Circuit.” Can the same be said if a graph has a Hamilton Circuit then the degree of each vertex is atleast N/2 ?
Given a natural number $ n \geq 1$ , I am looking for a Boolean cir... |
Disclaimer
In the process of typing up this question, I determine its solution. Since I went through the trouble of typing up the question in its entirety, I will post its answer as well. It may help out others who find themselves in the same predicament. Think of this as a sort of blog-post, if you will.
The Goal
Cons... |
The Feferman-Schütte ordinal, $\Gamma_0$ The Feferman-Schütte ordinal, denoted $\Gamma_0$ ("gamma naught"), is the first ordinal fixed point of the Veblen function. It figures prominently in the ordinal-analysis of the proof-theoretic strength of several mathematical theories.
This page needs additional information.
Ve... |
We can multiply $a$ and $n$ by adding $a$ a total of $n$ times.
$$ n \times a = a + a + a + \cdots +a$$
Can we define division similarly using only addition or subtraction?
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... |
Your problems are with algebraic manipulation. You have a linear equation to solve for $\frac{dy}{dx}$. If you were trying to solve $3(5+T)=7$ for $T$, you could divide by $3$ to get $5+T=\frac{7}{3}$, then subtract $5$ to get $T=\frac{7}{3}-5$ (which you might rewrite as $T=-\frac{8}{3}$). Or, you could distribute the... |
Analysis.
Since both factors are very close in value, we can place a lower bound on $M$ with the square root of the smallest 6-digit valid number. $\sqrt[]{123456} \approx 351.36$ results to $M \ge 3$.
From $D * N = M$ we know all 3 numbers must be different. This means that neither $D$ nor $N$ can be in $\{0, 1, 5\}$.... |
I saw this question, but was unable to answer because of my inexistant knowledge of Rust, so I decided to try and write an algorithm on my own and put it for review.
There is the casual way to compute factorials:
\$n! = \prod\limits_{k=1}^n k\$
public static BigInteger fact(BigInteger n) => n == 0 ? 1 : n*fact(n - 1);
... |
I do not understand completely how do rotating pulleys with ropes (that do not slip) work. Besides the equations of motions, which are clear to me, some
conditions on the accelerations are needed to solve the system with the equations. I'm having troubles in finding these conditions. Consider the following situations.
... |
Electrochemical Impedance Spectroscopy: Experiment, Model, and App
Electrochemical impedance spectroscopy is a versatile experimental technique that provides information about an electrochemical cell’s different physical and chemical phenomena. By modeling the physical processes involved, we can constructively interpre... |
Abstract: The Xe isotopes are located at a possible phase change in the collective structure from vibrational to rotational. The Xe isotopes therefore were considered as potential candidates for \(\gamma\)-soft nuclei or \(O(6)\) symmetry limit within the IBM. However, testing of the O(6) symmetry in Xe reveals that in... |
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Now showing items 1-10 of 15
A free-floating planet candidate from the OGLE and KMTNet surveys
(2017)
Current microlensing surveys are sensitive to free-floating planets down to Earth-mass objects. All published microlensing events attributed to unbound planets were identified based on their short timescale (bel... |
Below I've addressed your specific questions. However, based on your multiple questions about this I think it might be more useful to give a list of good sources, so I'll do that first.
On "gaps" in the constructible universe: Marek/Srebrny, Gaps in the constructible universe. The introduction is very readable and will... |
7
Share Simplification Quiz for SSC CGL Railways
4 years ago .
Here is Simplification Quiz for SSC CGL Railways. This quiz contains important questions matching the exact pattern and syllabus of upcoming exams. Make sure you attempt today’s Quant Quiz for Upcoming Exams to check your preparation level.
The fourth root ... |
Let $\mathbb{T}$ be the $1$-torus and define: $$H^1(\mathbb{T}):=\{f\in L^1(\mathbb{T})\ | \ \forall n<0, \hat{f}(n)=0\},$$ where if $f\in L^1(\mathbb{T})$ we have denoted by $\hat{f}$ the Fourier transform of $f$.
By the linearity of the Fourier transform, it is clear that $H^1(\mathbb{T})$ is a subspace of $L^1(\math... |
The aleph numbers, $\aleph_\alpha$
The aleph function, denoted $\aleph$, provides a 1 to 1 correspondence between the ordinal and the cardinal numbers. In fact, it is the only order-isomorphism between the ordinals and cardinals, with respect to membership. It is a strictly monotone ordinal function which can be define... |
Limit ordinal Properties
All limit ordinals are equal to their union.
All limit ordinals contain an ordinal $\alpha$ if and only if they contain $\alpha + 1$.
$\omega$ is the smallest nonzero limit ordinal, and the smallest ordinal of infinite cardinal number.
$(\omega + \omega)$, also written $( \omega \cdot 2 )$, is ... |
I have a question about functions satisfying a condition.
Let $D \subset \mathbb{R}^d$ be a Lipschitz domain. That is, for each $x \in \partial D$, there exists an open neighborhood $U$ of $x$ in $\mathbb{R}^d$ and a bi-Lipschitz function $\psi_{x}:B(1) \to U$ such that $\psi(0)=x$ and $\psi_{x}(B_{+}(1))=U \cap D$. He... |
I would like to apply the known version of the conjectural formula (11) page !0 of the paper Number theory and dynamical Lefschetz trace formula.
Disclaimer: I do not have a complete understanding of this formula but I can get an sketch of it. I just know that both sides of the formula are not number but distribution. ... |
A group $G$ by itself is
not a group of linear transformations, it is an abstract algebraic object. Only its representations map its elements (injectively if the representation is faithful) to elements $\mathrm{Aut}(V)$ of some vector space $V$.
Now, physics seems to have no need of such abstract language at first. Our... |
As anticlimactic as this may be, I'm going to answer my own question here..I found this article that shows the connections between the two models..http://epublications.bond.edu.au/cgi/viewcontent.cgi?article=1126&context=ejsie(mirror) that showsthat prices do converge as N Periods increases. Also they provide all the E... |
Answer
$s(1.3)\approx4$ After $t=1.3$ seconds, the weight is about 4 inches above the equilibrium position.
Work Step by Step
We calculate $s(1.3)$ by substituting $t=1.3$ into the equation and solving: $s(t)=-5\cos 4\pi t$ $s(1.3)=-5\cos (4\pi\times1.3)$ $s(1.3)=-5\cos (16.34)$ $s(1.3)=-5(-0.81)$ $s(1.3)\approx4$ We k... |
When solving equations like
$$\begin{align} 4x-4 &=\frac{(2x)^2}{x} \\ -4 &= \frac{4x^2}{x} -4x \\ -4 &= 4x -4x \\[0.2em] -4 &= 0\end{align}$$
using the equality-symbol feels like abuse of notation, since you'll end up with $-4=0$, which is not an equality. For instance I feel it would be better to write
$$\begin{align... |
Euclidean Geometry • Equitable Distributing • Linear Programming • Set Theory • Nonstandard Analysis • Advice • Topology • Number Theory • Computation of Time (Previous | Next)
Definition: Two distinct
points \(x\) and \(z\) in a Euclidean space (simply called a space in the following) viewed as a subspace of \(\mathbb... |
We defined in the class branched covering as follows.
Let $\Sigma_1, \Sigma_2$ be two surfaces, $f: \Sigma_1 \longrightarrow \Sigma_2$ is a branched covering if $\forall y \in \Sigma_2 $ there exist $V\subset \Sigma_1$ containing y so that $f^{-1}(V)= U_1 \cup U_2 \cup ... \cup U_n $ so that $f: U_j \longrightarrow V$ ... |
If I interpret the request a bit differently, I would say that the Steenrod operations in the cohomology of a spectrum tell you about the attachments of the cells. If $Sq^1 x = y$, then a cell dual to $y$ is attached by a map of degree 2 mod 4 to a cell dual to $x$. Similarly, $Sq^2 x = y$ tells us the attaching map is... |
Let me first answer your question in general. The SVM is not a probabilistic model. One reason is that it does not correspond to a normalizable likelihood. For example in regularized least squares you have the loss function $\sum_i \|y_i - \langle w, x_i\rangle - b\|_2^2$ and the regularizer $\|w\|_2^2$. The weight vec... |
Taiwanese Journal of Mathematics Taiwanese J. Math. Volume 19, Number 2 (2015), 505-517. THE (NORMALIZED) LAPLACIAN EIGENVALUE OF SIGNED GRAPHS Abstract
A signed graph $\Gamma=(G, \sigma)$ consists of an unsigned graph $G=(V, E)$ and a mapping $\sigma: E \rightarrow \{+, -\}$. Let $\Gamma$ be a connected signed graph a... |
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 was wondering if anyone had recommendations for papers or resources on bayesian analysis of frequentist hypothesis testing and use of p-values?
Brad Efron has this quote
One definition is says that a frequentist is a a Bayesian trying to do well, or at least not too badly, against any possible prior distribution
It's... |
The Annals of Mathematical Statistics Ann. Math. Statist. Volume 28, Number 1 (1957), 242-246. Consistency of Certain Two-Sample Tests Abstract
Let $X_1, \cdots, X_m; Y_1, \cdots, Y_n$ be independently distributed on the unit interval. Assume that the $X$'s are uniformly distributed and that the $Y$'s have an absolutel... |
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