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Theorem
Let $\struct {R, \norm {\,\cdot\,}}$ be a normed division ring.
Let $\sequence {x_n}$ be a sequence in $R$.
Let $\sequence {x_n}$ be convergent in the norm $\norm {\,\cdot\,}$ to the following limit:
$\displaystyle \lim_{n \mathop \to \infty} x_n = l$
Then $\sequence {x_n}$ is bounded.
Proof
Let $d$ be the metr... |
Global Optimization
McCormick-based Algorithm for mixed-integer Nonlinear Global Optimization (MAiNGO) is a deterministic global optimization software for solving mixed-integer nonlinear programs (MINLPs), which is being developed at AVT.SVT.
Any (mixed-integer or continuous) nonlinear program with nonconvex functions ... |
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The ALICE Transition Radiation Detector: Construction, operation, and performance
(Elsevier, 2018-02)
The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron... |
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Now showing items 1-10 of 165
J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed i... |
Gevrey regularity and existence of Navier-Stokes-Nernst-Planck-Poisson system in critical Besov spaces
1.
School of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330032, China
2.
Department of Mathematics, Northwest Normal University, Lanzhou 730070, China
J. Funct. Anal., 87(1989), 359-... |
The difference rule of derivatives is actually derived in differential calculus from first principle. For example, $f{(x)}$ and $g{(x)}$ are two differentiable functions and the difference of them is written as $f{(x)}-g{(x)}$. The derivative of difference of two functions with respect to $x$ is written in the followin... |
A trigonometry identity, derived from Pythagorean Theorem is called Pythagorean identity.
There are three possibilities to form Pythagorean identities in terms of trigonometric functions in trigonometry. They are used as formulas in trigonometry. So, it is very important to remember them to study the trigonometry.
The ... |
Bézout's Lemma/Euclidean Domain Theorem
Let $\nu: D \setminus \set 0 \to \N$ be the Euclidean valuation on $D$.
Let $a, b \in D$ such that $a$ and $b$ are not both equal to $0$.
Let $\gcd \set {a, b}$ be the greatest common divisor of $a$ and $b$.
Then:
$\exists x, y \in D: a \times x + b \times y = \gcd \set {a, b}$
s... |
Let the equations of motion be expressed in a frame with coordinates $q$. We now want to switch over to another (arbitrarily moving) frame, whose corresponding coordinates are $Q$, given by:$$Q = f(q, t)$$For example, if the frame itself is moving with position $x(t)$, we will have:$$Q = q - x(t)$$(where $x$ is not dyn... |
One disadvantage of the fact that you have posted 5 identical answers (1, 2, 3, 4, 5) is that if other users have some comments about the website you created, they will post them in all these place. If you have some place online where you would like to receive feedback, you should probably also add link to that. — Mart... |
Basic Idea
The algorithm essentially counts the number of days that havepassed between a fixed date (this will be 1st January 0 AD) and achosen date (our birthday). By taking this number and finding itsremainder when divided by 7, provided we know what day of the weekit was on 1st January 0 AD we will know what day we ... |
Asymptotics in parameter of solution to elliptic boundary value problem in vicinity of outer touching of characteristics to
limit equation Yu. Z. Shaygardanov Institute of Mathematics, Ufa Scientific Center, RAS,
Chernyshevsky str. 112,
450077, Ufa, Russia Abstract: In a bounded domain $Q\subset\mathbb{R}^3$ with a smo... |
Or Zamir:Faster k-SAT Algorithms Using Biased-PPSZ
Wednesday, September 18, 2019 - 4:00pm to 5:00pm
The PPSZ algorithm, due to Paturi, Pudlak, Saks and Zane, is currently the fastest known algorithm for the k-SAT problem, for every k>3. For 3-SAT, a tiny improvement over PPSZ was obtained by Hertli.
A Swiss-Army Knife ... |
Fréchet space
A Fréchet space is a complete metrizable locally convex topological vector space. Banach spaces furnish examples of Fréchet spaces, but several important function spaces are Fréchet spaces without being Banach spaces. Among these are: the Schwartz space $\mathscr{S}(\R^n)$ of all infinitely-differentiable... |
The course started yesterday with one very concrete example, followed by loads of abstractions. Last night’s lecture began the trip back into things that are a little bit more concrete.
What I Taught
I began the lecture by handing out a few pages from Larry Gonick’s fantastic The Cartoon Guide to Calculus. As I noted y... |
Reference documentation for deal.II version Git 0491297983 2019-09-23 09:31:59 +0200
#include <deal.II/sundials/kinsol.h>
class AdditionalData
KINSOL (const AdditionalData &data=AdditionalData(), const MPI_Comm mpi_comm=MPI_COMM_WORLD) ~KINSOL () unsigned int solve (VectorType &initial_guess_and_solution)
static ::Exce... |
Assume, $x$ is a variable and the natural exponential function is written as $e^{\displaystyle x}$ in mathematics. The indefinite integration of natural exponential function with respect to $x$ is written in the following mathematical form in integral calculus.
$\displaystyle \int{e^{\displaystyle x} \,}dx$
Now, let us... |
Why does Schwarz get credit for proving “Cauchy–Schwarz for integrals”? There is an easy proof of Cauchy–Schwarz that relies only on $\langle \cdot, \cdot \rangle$ being an inner product, whether defined in terms of integrals or not. And proving that $$(f,g) \mapsto \int_X f(x)\overline{g(x)}\,d\mu(x)$$ is an inner pro... |
The biorthogonality relation for discrete wavelets can be formulated as follows:
$$\sum_{n\in \mathbb Z} a_n \tilde a_{n+2m} = 2\cdot \delta_{m,0}$$
for two sequences of numbers $$\{a_{-N},\cdots,a_N\},\{\tilde a_{-N},\cdots,\tilde a_N\}$$
Usually we consider solutions for which $a_k,\tilde a_k \in \mathbb R$.
Now to t... |
If $G$ is a group, the center of G is defined to be $Z(G)=\{ x\in G \mid x*a=a*x$ for all $a\in G \}$. Show that $Z(G)$ is a subgroup of $G$.
Solution:
By the way that $Z(G)$ is defined, all elements in $Z(G)$ must be in $G$, so $Z(G)$ is a subset of $G$.
Let $a,b \in Z(G)$.
Then for every $c\in G, a*c=c*a$ and $b*c=c*... |
By using the polar form of the complex number prove that, $|z_1 z_2| = |z_1| |z_2|$ and $\left|\frac{z_1}{z_2}\right| = \frac{|z_1|}{|z_2|}$
closed as off-topic by Matthew Conroy, Avitus, Michael Albanese, Shailesh, Leucippus Jul 14 '16 at 2:41
This question appears to be off-topic. The users who voted to close gave th... |
Wed, Dec 5, 2018
Disclaimer: the author has a background in Computer Science, the physics, chemistry and biology anecdotes in this article are obtained during research on the topic on the on-demand basis, without a formal training in the respective subjects. Also, this article aims to describe the pipeline to help the ... |
It sounds like all you really care about it is a realistic simulation. For you, this means that you are interested in specifying a force that is "reasonable" for your robot. I say "reasonable" because it's up to you to define, but hopefully I can help you set some guidelines.
Torque, the angular force you apply to a jo... |
Vinogradov method
A new method for estimating trigonometric sums (see Trigonometric sums, method of). By Vinogradov's method one may obtain very accurate estimates of a wide class of trigonometric sums, in which the summation variable runs through a sequence of integers, prime numbers, etc. In this way many classical p... |
1of 1 Tolaso J Kos Administrator Articles:0 Posts:844 Joined:Sat Nov 07, 2015 6:12 pm Location:Larisa Contact:
$$\mathcal{S}= \sum_{n=1}^{\infty} \left(\alpha-\frac{\lfloor n\alpha \rfloor}{n}\right)$$
diverges.
Imagination is much more important than knowledge.
We are focusing on the $\alpha$' s lying in the interval ... |
I'm studying Lie algebras, and I'm struggling to prove the following result:
Let $L$ be a solvable subalgebra of $\mathfrak{gl}(V)$, $dimV = n < \infty$. Then $L$ stabilizes some flags in $V$ (in other words, the matrices of $L$ relative to a suitable basis of $V$ are upper triangular).
The instruction to prove this is... |
ok, suppose we have the set $U_1=[a,\frac{a+b}{2}) \cup (\frac{a+2}{2},b]$ where $a,b$ are rational. It is easy to see that there exists a countable cover which consists of intervals that converges towards, a,b and $\frac{a+b}{2}$. Therefore $U_1$ is not compact. Now we can construct $U_2$ by taking the midpoint of eac... |
Tool for calculating the Hermite normal form (by reducing a matrix to its row echelon form) from a matrix M (with coefficients in Z) the computation yields 2 matrices H and U such that $ H = U . M $.
Hermite Normal Form Matrix - dCode
Tag(s) : Matrix
dCode is free and its tools are a valuable help in games, maths, geoc... |
The lower attic
From Cantor's Attic
Revision as of 07:42, 30 December 2011 by Jdh
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 mid... |
this is a mystery to me, despite having changed computers several times, despite the website rejecting the application, the very first sequence of numbers I entered into it's search window which returned the same prompt to submit them for publication appear every time, I mean ive got hundreds of them now, and it's stil... |
A mathematical equation which contains logarithmic functions as terms is called a logarithmic equation.
The logarithmic terms are formed to express quantities mathematically. The expression of one or more connected log terms represents a quantity and the same quantity can also be expressed by different one or more conn... |
The effect of replacing $x$ in $\cos x$ with $x + a y - a$ is a shear. In particular, this shear can be represented by the (homogeneous matrix)$$ M = \begin{pmatrix} 1 & a & -a \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{pmatrix} $$since $$ \begin{pmatrix} \tilde{x} \\ \tilde{y} \\ 1 \end{pmatrix} = M \cdot \begin{pmatrix} x \\ y \... |
I wonder how to solve the following constrained problem
${\rm Minimize}_{\vec{A}}$ $\parallel Z\vec{A}-Y\parallel^2_2$ , $\quad\vec{A}\in\mathbb{R}^{n^2}$
such that: $A\in\mathbb{R}^{5\times 5}$ is positive definite
where $\vec{A}=vec(A)$. For the unconstrained case, which has a closed form solution, I used MATLAB comm... |
The roots of a quadratic equation are real and also a repeated or double root. It is only possible when the discriminant of a quadratic equation is equal to zero.
$ax^2+bx+c = 0$ is a quadratic equation and its discriminant ($\Delta$) is $b^2-4ac$.
The roots of the quadratic equation in terms of discriminant are $\dfra... |
Dependent Choice (Fixed First Element) Theorem
Suppose that:
$\forall a \in S: \exists b \in S: a \mathrel{\mathcal R} b$
that is, that $\mathcal R$ is a left-total relation (specifically a
serial relation).
Let $s \in S$.
Then there exists a sequence $\left\langle{x_n}\right\rangle_{n \in \N}$ in $S$ such that: $x_0 =... |
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Chemical Society Reviews, ISSN 0306-0012, 07/2010, Volume 39, Issue 7, pp. 2354 - 2371
There has been remarkable progress in the science and technology of semiconducting ... |
(this post requires some rethinking) 7/29/17 -mr
It seems this still does not explain why the mass of the proton is what it is... back to drawing board! $$mr={2h\over \pi c}$$
It seems this still does not explain why the mass of the proton is what it is... back to drawing board!
$$mr={2h\over \pi c}$$
Or, why can't the... |
I am new to any CAS (and Mathematica, for that matter) and new to StackExchange too, so forgive me and correct me on any mistakes.
I have this function: $J_p=\sum_{m,n=1}^{\infty} \epsilon_{mn}f_{mn}\sum_{k=-\infty}^{\infty}\frac{J_k^2(\beta)(m\Omega+k\omega)}{1+(m\Omega+k\omega)^2}$ where $\epsilon_{mn}=-\frac{m n}{4\... |
Closure of Subset in Subspace
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Theorem
Let $T = \struct{S, \tau}$ be a topological space.
Let $H$ be a subset of $S$.
Let $T_H = \struct{H, \tau_H}$ be the topological subspace on $H$.
Let $A$ be a subset of $H$.
Then: $\map {\operatorname{cl}_H} A = H \cap \map {\operatorname{cl}} A$
w... |
I have tried $\gcd(0,8)$ in a lot of online gcd (or hcf) calculators, but some say $\gcd(0,8)=0$, some other gives $\gcd(0,8)=8$ and some others give $\gcd(0,8)=1$. So really which one of these is correct and why there are different conventions?
Let's recall the definition of $ $ "$\rm a $ divides $\rm b$" $ $ in a rin... |
Worldly cardinal Every inaccessible cardinal is worldly. Nevertheless, the least worldly cardinal is singular and hence not inaccessible. The least worldly cardinal has cofinality $\omega$. Indeed, the next worldly cardinal above any ordinal, if any exist, has cofinality $\omega$. Any worldly cardinal $\kappa$ of uncou... |
10 Days Of Grad: Deep Learning From The First Principles.
Now that we have seen how neural networks work, we realize that understandingof the gradients flow is essential for survival. Therefore, we will reviseour strategy on the lowest level. However, as neural networks become more complicated,calculation of gradients ... |
Research Open Access Published: Minimal thinness with respect to the Schrödinger operator and its applications on singular Schrödinger-type boundary value problems Boundary Value Problems volume 2019, Article number: 91 (2019) Article metrics
227 Accesses
2 Citations
Abstract
The application of the new criteria for min... |
I'm not sure how to go about this proof. I just need help getting started. Is there a way to prove it algebraically?
Take the prime-power decomposition of $m$ and $n$. We have \begin{array} .m &=&p_1^{a_1}\times p_2^{a_2} \times \ldots \times p_k^{a_k} \\ n &=&p_1^{b_1}\times p_2^{b_2}\times \ldots \times p_k^{b_k} \en... |
The Pythagorean Theorem is derived in algebraic form by the geometric system. Now, it is your time to know how the square of length of hypotenuse is equal to sum of squares of lengths of opposite and adjacent sides in a right triangle.
$a$, $b$ and $c$ are lengths of sides of a right triangle. $\alpha$ and $\beta$ are ... |
Difference between revisions of "Lower attic"
From Cantor's Attic
(the Takeuti-Feferman-Buchholz ordinal)
(19 intermediate revisions by 5 users not shown) Line 1: Line 1:
{{DISPLAYTITLE: The lower attic}}
{{DISPLAYTITLE: The lower attic}}
[[File:SagradaSpiralByDavidNikonvscanon.jpg | thumb | Sagrada Spiral photo by Dav... |
For any given load, a switcher will transfer a given amount of energy thousands of times per second. This is how the buck regulator works.
Let's say your op-amp is switching at 10kHz (because it's a slow sort of device and will have slew rate problems compared to other devices). Let's also say you are aiming to deliver... |
Bernstein inequality
$ \newcommand{\expect}{\mathbb{E}} \newcommand{\prob}{\mathbb{P}} \newcommand{\abs}[1]{\left|#1\right|} $
Bernstein's inequality in probability theory is a more precise formulation of the classical Chebyshev inequality in probability theory, proposed by S.N. Bernshtein [Be2] in 1911; it permits one... |
Bhattacharyya, T and Binding, PA and Seddighi, K (2001)
Multiparameter SturmLiouville Problems with Eigenparameter Dependent Boundary Conditions. In: Journal of Mathematical Analysis and Applications, 264 (2). pp. 560-570.
PDF
sdarticle.pdf
Restricted to Registered users only
Download (135kB) | Request a copy
Abstract
... |
I'm trying to understand why the following proposition is true:
Let $J$ be a small category and $F, G : J \to \textbf{Top}$ functors. If $\tau : F \Rightarrow G$ is a pointwise homotopy equivalence, then $\operatorname{hocolim}_J F \to \operatorname{hocolim}_J G$ is a homotopy equivalence.
This seems to be such a natur... |
In the Art Gallery Problem we are given a polygon P \subset [0,L]^2 on n vertices and a number k. We want to find a guard set G of size k, such that each point in P is seen by a guard in G. Formally, a guard g sees a point p \in P if the line segment pg is fully contained inside the polygon P. The history and practical... |
What is the complexity of the follwoing recurrence? $$T(n) = T(n-1) + 1/n$$I highly suspect the answer to be $O(1)$, because your work reduces by $1$ each time, so by the $n$th time it would be $T(n-...
This is a question about recurrence relation that contains sum inside the recursion.I am totally stuck. Can anyone he... |
Inverse problems for the p-Laplace type equation
Speaker
Dr. Manas Kar, Department of Mathematics and Statistics, University of Jyväskylä
When Jan 06, 2016
from 03:30 PM to 04:30 PM
Where LH 006 Add event to calendar vCal
iCal
Abstract: Inverse problems for non-linear equations have been of great interest recently. We ... |
Your friend meant that all
complex numbers can be represented by such matrices.
$$a+bi = \begin{pmatrix} a & -b \\ b & a \end{pmatrix}$$
Adding complex numbers matches adding such matrices and multiplying complex numbers matches multiplying such matrices.
This means that the collection of matrices:
$$R = \left\{ \begin... |
1. Because negation is applied to formulas, and $x, y, z$ are not formulas.
$x$, $y$ and $z$ are variables. Variables are
terms. Terms are those strings of symbols of the langauge which stand for . Here, the objects for which $x, y, z$ stand are numbers, so we can do $<$ etc. between them. objects By definition, terms ... |
In general if you have a bijective map $f$ of a ring $S$ to itself then you can define two new operations
$x+_fy:=f^{-1}(f(x)+f(y))$
$x*_fy:=f^{-1}(f(x)f(y))$
In this case $(S,+_f, *_f)$ is a ring, where the neutral element with respect to $+_f$ is $f^{-1}(0)$ and the neutral element with respect to $*_f$ is $f^{-1}(1)... |
$f(x) = 8 \cos^4 x + 6 \sin (2x + 3 \pi/4) \sin(2x - \pi/4)$.
How can I simplify into a linear combination of simple sine functions?
Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. It only takes a minute to sign up.Sign up to join this community
$f(x) = 8 \cos^4 x + 6 \sin (2x... |
Quantity and/or base quantity of logarithmic terms can be expressed in exponential form to find the values of logarithm of quantities. Due to the involvement of exponents in logarithms, the logarithmic identities are simply called as power rules of logarithms.
There are three power rules in logarithms and they are used... |
Connected Subset of Union of Disjoint Open Sets Theorem
Let $T = \struct{S, \tau}$ be a topological space.
Let $A$ be a connected set of $T$.
Let $A \subseteq U \cup V$.
Then either $A \subseteq U$ or $A \subseteq V$. Proof
Let $U’ = A \cap U$ and $V’ = A \cap V$.
From Intersection is Empty Implies Intersection of Subs... |
$x^2+y^2+z^2$ is an algebraic expression. It is given that the values of all three literals are expressed in three equations as follows.
$(1) \,\,\,\,\,\,$ $x = r\cos{\alpha}\cos{\beta}$
$(2) \,\,\,\,\,\,$ $y = r\cos{\alpha}\sin{\beta}$
$(3) \,\,\,\,\,\,$ $z = r\sin{\alpha}$
It is asked us to find the value $x^2+y^2+z^... |
Synchronization of positive solutions for coupled Schrödinger equations
1.
School of Mathematics and Statistics and Hubei Key Laboratory of Mathematical Sciences, Central China Normal University, Luo-Yu Road 152, Wuhan 430079, China
2.
Center for Applied Mathematics, Tianjin University, Tianjin 300072, China
3.
Departm... |
In MSEtool, assessment models are of class
Assess. This appendix provides a brief description and references for the
Assess objects. Further details regarding parameterization, e.g., fixing parameters, and tuning, e.g., adjusting start parameters, are provided in the function documentation.
For LaTeX equation rendering... |
Difference between revisions of "Inertia"
(→Derivation)
Line 41: Line 41:
where <math>I = mr^{2}</math> is called the '''[https://en.wikipedia.org/wiki/Moment_of_inertia moment of inertia]''' (kg.m<sup>2</sup>)
where <math>I = mr^{2}</math> is called the '''[https://en.wikipedia.org/wiki/Moment_of_inertia moment of ine... |
Let $\alpha \geq 1$ and $X_n$ be independent random variables such that $P(X_n=2)=P(X_n=-2)=\frac 1{2n^\alpha}$ and $P(X_n=0)=1-\frac 1{n^\alpha}$. Let $S_n=\sum_{k=1}^n X_k$.
Depending on the value of $\alpha$, what are the properties of $S_n$ (convergence, asymptotic behaviour)?
$S_n$ is clearly a Markov chain on the... |
Help:Formatting
You can format your text by using wiki markup. This consists of normal characters like asterisks, apostrophes or equal signs which have a special function in the wiki, sometimes depending on their position. For example, to format a word in
italic, you include it in two pairs of apostrophes like
''this''... |
[1003.0299] The local B-polarization of the CMB: a very sensitive probe of cosmic defects
Authors: Juan Garcia-Bellido, Ruth Durrer, Elisa Fenu, Daniel G. Figueroa, Martin Kunz Abstract: We present a new and especially powerful signature of cosmic strings and other topological or non-topological defects in the polariza... |
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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 ... |
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 ... |
Ground state solutions for asymptotically periodic modified Schr$ \ddot{\mbox{o}} $dinger-Poisson system involving critical exponent
1.
School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China
2.
College of Mathematics and Information Sciences, Xin-Yang Normal University, Xinyang, 464000, Ch... |
Descartes' rule of signs Statement
The rule states that if the terms of a single-variable polynomial with real coefficients are ordered by descending variable exponent, then the number of positive roots of the polynomial is either equal to the number of sign differences between consecutive nonzero coefficients, or is l... |
how can a prove that at least one of those is less than or equal to 1/4. $$\forall a,b,c\in \mathbb R^+, \ a(1-b)\leq 1/4 \lor b(1-c) \leq 1/4 \lor c(1-a) \leq 1/4.$$ help please!
We can assume $1-a, 1-b, 1-c \geq 0$, since otherwise we are done.
By the AM-GM inequality (see http://en.wikipedia.org/wiki/AM-GM_inequalit... |
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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 ... |
Difference between revisions of "Huge"
(→Definitions)
Line 12: Line 12:
=== Elementary embedding definitions ===
=== Elementary embedding definitions ===
−
The elementary embedding definitions are somewhat standard. Let $j:V\rightarrow M$ be
+
The elementary embedding definitions are somewhat standard. Let $j:V\rightar... |
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Now showing items 1-10 of 26
Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
Megaupload.com was the 72nd most visited site on the Internet. It was headed by Kim Dotcom; at least that's how most people called Kim Schmitz (originally from Germany), probably because he resembles a dotcom bubble.
American authorities decided to arrest Mr Dotcom a few weeks ago and the dream came true in New Zealand... |
Reflecting cardinals
Reflection is a fundamental motivating concern in set theory. The theory of ZFC can be equivalently axiomatized over the very weak Kripke-Platek set theory by the addition of the reflection theorem scheme, below, since instances of the replacement axiom will follow from an instance of $\Delta_0$-se... |
Sample Quantiles
The generic function
quantile produces sample quantiles corresponding to the given probabilities. The smallest observation corresponds to a probability of 0 and the largest to a probability of 1.
Keywords univar Usage
quantile(x, …)
# S3 method for defaultquantile(x, probs = seq(0, 1, 0.25), na.rm = FA... |
$a+b\sin{x}$ and $b+a\sin{x}$ are two algebraic trigonometric expressions, where $a$ and $b$ are constants, and $x$ represents an angle of a right triangle and also a variable. In this derivative problem, the differentiation of quotient of $a+b\sin{x}$ by $b+a\sin{x}$ has to calculate with respect to $x$.
$= \,\,\,$ $\... |
$a, b, c$ are positives such that $a + b + c = 1$. Determine the maximal value of $$\large \sum_{cyc}\frac{1}{a(b + c)} - \frac{a^2 + b^2 + c^2}{2abc}$$
This is a problem in a recent exam, I got $3/20$ points (and also almost everybody did worse). I didn't know how to solve this problem, then our teacher went on our gr... |
Tool to make calculations with time dilation. Time dilation is an effect of the special relativity which states that time is going slower if an object is moving.
Time Dilation - dCode
Tag(s) : Physics-Chemistry, Date and Time
dCode is free and its tools are a valuable help in games, maths, geocaching, puzzles and probl... |
I'm going to try to design an algorithm to find all the rational roots of a polynomial equation in range [a, b]. Can someone please tell me which algorithm currently solves the problem with lowest worst-case complexity? This algorithm will be for a general purpose computer(Turing Machine).
The paper Computing Real Root... |
In every Hilbert space $H \neq \{0 \}$, there exists a total orthonormal set.
I think I've understood the proof given by Erwin Kreyszig in
Introductory Functional Analysis With Applications.
The following questions arise in my mind:
Is there a total orthonormal set in \emph{every} inner product space?
Is there a total ... |
Wikipedia says that if we can prove $\forall x_1...\forall x_n \exists! y . \phi(y,x_1,...,x_n)$, then introducing a function symbol $f$ and the axiom $\forall x_1...\forall x_n.\phi(f(x_1,...,x_n),x_1,...,x_n)$ gives a conservative extension of the original theory. I'd like to understand the importance of the uniquene... |
The question I have been given is
Given that $z=2e^{i\frac{\pi}{7}}$, find the smallest positive integer of $k$ such that $z\times{z^2}\times{z^3}\times{...}\times{z^k}$ is real, and state the value of $|z\times{z^2}\times{z^3}\times{...}\times{z^k}|$ in this case.
A previous part of the question had me show that for a... |
A trigonometric identity to expand a trigonometric function having difference of two angles is called the angle difference identity. In trigonometry, there are four angle difference trigonometric identities and they’re used as formulas in mathematics. Let’s start to study all the angle difference identities with proofs... |
Mathematically, the exact value of cot of $45$ degrees can be derived in three different methods. One of three methods is trigonometric approach but the remaining two methods are slightly different geometric methods. Study all of them here to know how to find the $\cot{(50^g)}$ value in trigonometry.
On the basis of di... |
Let $Z^t = (Y_1,\ldots,Y_t)$ be a sequence of random variables each taking values in $Y$. The random variables are not necessarily i.i.d but we know the joint distributions. i.e for every $z = (z_1,...,z_t)$ we know $P^{Z^t}(z)$
The min-entropy of a random variable $X$ is defined as $-\log_2(\max P(x) )$ for x in the v... |
Let $V$ be a finite-dimensional vector space, $\:A\:$ a matrix (or linear transformation) from $V$ to $W$ (which sends a vector $v \in V$ to $Av \in W$) , $x,y \in Rowspace(A),\: x \neq y$. $$If Ax = Ay \:\text{then}\: Ax-Ay=A(x-y)=0, \text{then}\: x-y \in Nullspace(A)$$ Since $Rowspace(A)$ is a linear subspace of $V$,... |
Equivalence of Definitions of Equivalent Division Ring Norms Contents 1 Theorem 2 Proof 2.1 Topologically Equivalent implies Convergently Equivalent 2.2 Convergently Equivalent implies Null Sequence Equivalent 2.3 Null Sequence Equivalent implies Open Unit Ball Equivalent 2.4 Open Unit Ball Equivalent implies Norm is P... |
$\log_{3}{(5x-2)}$ $-$ $2\log_{3}{\sqrt{3x+1}}$ $\,=\,$ $1-\log_{3}{4}$ is a logarithmic equation. It is developed in mathematics by taking number $3$ as base of the logarithms.
The square root of $3x+1$ can be eliminated from second term by the multiply factor $2$ as exponent of the $3x+1$. It can be done by using pow... |
@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... |
If $c$ is odd=$2k+1$(say),
(i)$c^2=(2k+1)^2=8\frac{k(k+1)}{2}+1=8y+1$ for some integer $y$.
$c^4=(c^2)^2=(8y+1)^2=64y^2+16y+1=1+16(y+4y^2)=1+16z$ for some integer $z$.
(ii) $c^4=(2k+1)^4=(2k)^4+ ^4C_1(2k)^3+ ^4C_2(2k)^2+ ^4C_3(2k)+ 1$
$=16k^4+32k^3+24k^2+8k+1≡8k^2+8k+1\pmod {16}=16\frac{k(k+1)}{2}+1≡1\pmod {16}$
(iii)w... |
I am reading an article entitled "Diffuse Interface Models on Graphs for Classification of High Dimensional Data." Seems like the idea is to use the Ginzburg-Landau functional, in association with graph partitioning methods to apply classification on high-dimensional data.
The Ginzburg-Landau functional looks like: $$ ... |
I am trying to recreate the Bayesian Hierarchical Clustering algorithm using Python. The example in section two requires evaluating the following double integral (univariate case):
\begin{align} p(D_k|H_k) &= \int_\theta p(D_k | \theta) p(\theta | \theta_0) d\theta \\ &= \int_\mu \int_\phi \prod_{i = 1}^n \mathcal{N}(x... |
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In this tutorial, we write an Alphabets (or Alpha, for now the two are synonymous) program, starting from a mathematical equation for LU decomposition. Then we will generate code to execute the alpha program, and test the generated code for correctness.
The equation for LU Decom... |
Heat loss within a control volume
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Hello,
I have the following problem:
I got an electrical component within a chamber and the chamber has an opening, where air can be supplied from and an outlet. Attached you can see an illustration of the problem.
What I want to know is:
The first thing I attempted by ... |
turicreate.recommender.item_similarity_recommender.ItemSimilarityRecommender¶ class
turicreate.recommender.item_similarity_recommender.
ItemSimilarityRecommender(
model_proxy)¶
A model that ranks an item according to its similarity to other items observed for the user in question.
Creating an ItemSimilarityRecommender
... |
The point is not to know if it’s easier or smarter to look at the dual of G = Gal(L/K) instead of G itself. To understand the motivation, I think one should take the « experimental » point of view : given any Galois extension L/K, how does one describe its Galois group ? In exercises in Galois theory, generators of the... |
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(1997)Dynamical properties of the baker's transformation B with integer base $b\ge 2$ and several related maps on discrete subsets of the domain are studied. The baker's transformation with base $b,\ ... |
I am reading Kolenkow and Kleppner's
Classical Mechanics and they have tried to calculate the gravitational force between a uniform thin spherical shell of mass $M$ and a particle of mass $m$ located at a distance $r$ from the center.
The shell has been divided into narrow rings.$R$ has been assumed to be the radius of... |
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