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We know the schur basis, and many more, for the ring of symmetric functions over a field \( F \). The next step of generalization is consider the field \( F(t) \), and twist a little bit the inner product. In contrast with Macdonald polynomials, we can give a closed expression for Hall-Littlewood polynomials
Definition... |
NOT A DUPLICATE: Homeomorphism in the definition of a manifold for example is slightly different.
A manifold according to Wikipedia, a book by Spivak, and serveral other books has the following in common:
$\forall x\in M\exists n\in\mathbb{N}_{\ge 0}\exists U$ neighbourhood of $x$ such that $U$ is homeomorphic to (an o... |
While teaching a largely student-discovery style elementary number theory course to high schoolers at the Summer@Brown program, we were looking for instructive but interesting problems to challenge our students. By we, I mean Alex Walker, my academic little brother, and me. After a bit of experimentation with generator... |
In this series so far, we have looked at how we use decibels to put numbers on the loudness of sounds (Part 1), how we can compensate for humans hearing some sound frequencies better than others (Part 2), and how we can determine decibel numbers for sounds that vary significantly in time (Part 3). We can consider what ... |
If $a_a,a_2,\dots, a_n$ are positive reals in Arithmetic Progression, prove that $a_1a_2\dots a_n>(a_1a_n)^{n/2}$.
$a_2-a_1=a_3-a_2=\dots=a_n-a_{n-1}=d$ say, then $a_n-a_1=(n-1)d$
Is this approache correct? Some hint??
Mathematics Stack Exchange is a question and answer site for people studying math at any level and pr... |
Let's say I have a contour integral on a non-closed contour with starting point $z_0$ and ending point $z_1$. Am I allowed to do a substitution like this? And under what assumptions?
$$\displaystyle \int_{z_0}^{z_1} f (z) \, \mathrm d z = \int_{u^{-1}(z_0)}^{u^{-1}(z_1)} f (u (z))u'(z) \, \mathrm d u $$
For example,
$$... |
Given a union of open intervals $\bigcup_i (A_i,B_i)$ such that $\bigcup_i (A_i,B_i) \supset [A,B]$ we can take finite number of them $\bigcup_{i\le N} (A_i,B_i)$ such that $\bigcup_{i\le N} (A_i,B_i) \supset [A,B]$
Proof:
Step 1: Cover $A$ with an open interval $(A_i,B_i)$
Step 2: Choose an open interval $(A_{i_1},B_{... |
How many positive integer $n$ are there such that $2n+1$ , $3n+1$ are both perfect squares ?
$n=40$ is a solution . Is this the only solution ? Is it possible to tell whether finitely many or infinitely many solutions exist ?
Mathematics Stack Exchange is a question and answer site for people studying math at any level... |
I am trying to find the generator(s) of the Symmetric Group $S_3$ and I have attempted this via brute force by listing the permutations of $S_3$ and composing and repeating them but I have not found any generators. - thanks
$S_3$ can be generated by a 2 cycle and a 3 cycle. For example $(12)$ and $(1 2 3)$.
As James no... |
I have some problems to determine the eigenvectors of a given matrix:
The matrix is:
$$ A = \left( \begin{array}{ccc} 1 & 0 &0 \\ 0 & 1 & 1 \\ 0 & 0 & 2 \end{array} \right) $$
I calculated the eigenvalues first and got $$ \lambda_1 = 1, \lambda_2 = 2, \lambda_3 = 1$$ There was no problem for me so far. But I do not kno... |
I think there is some vagueness inherent in the "similarly define ...". How is one to assign the consistency statement $Con(ZF_\lambda)$ for computable $\lambda$? This looks trivial but it is not.
I think also ZF is something of a red herring here. The question arises in PA (since we are looking at $\Pi_1$ sentences qu... |
There is a question I would like to ask at MO, but it seems somewhat unorthodox compared most others, so I want to get some support (or discouragement) here first. What I want to do is to give a new definition, justify why it is a natural extension of a well known concept, and ask if someone has seen it or has somethin... |
This is a secondary supplemental note on the Gaussian integers, written for my Spring 2016 Elementary Number Theory Class at Brown University. This note is also available as a pdf document.
In this note, we cover the following topics.
Assumed prerequisites from other lectures. Which regular integer primes are sums of s... |
Consider $n$ processes sharing the CPU in a round-robin fashion. Assuming that each process switch takes $s$ seconds, what must be the quantum size $q$ such that the overhead resulting from process switching is minimized but at the same time each process is guaranteed to get its turn at the CPU at least every $t$ secon... |
On existence, uniform decay rates and blow up for solutions of systems of nonlinear wave equations with damping and source terms
1.
Department of Mathematics and Statistics, Federal University of Campina Grande, 58109-970, Campina Grande, PB, Brazil
2.
Department of Mathematics - State University of Maringá, 87020-900 ... |
Hi guys I have an equation like this: $$2n-n^8<0$$
How can I simplify this equation and get the value of $n$?
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 community
Hi guys I hav... |
For $p \in \mathbb{R}$, consider the following problem: \begin{equation} \label{1} \begin{cases} \operatorname{div}(a \nabla u ) = p\delta_{x_0} \quad \text{in } \Omega \\ u=0 \quad \text{on } \partial \Omega ; \end{cases} \end{equation} under the assumption that $a \in L^\infty$ is constant in some neighbourhood of $x... |
Consider the equation
\[ f(x,y) = C. \]
Taking the gradient we get
\[ f_x(x,y)\hat{\textbf{i}} + f_y(x,y)\hat{\textbf{j}} = 0.\]
We can write this equation in differential form as
\[ f_x(x,y)\, dx+ f_y(x,y)\, dy = 0.\]
Now divide by \( dx \) (we are not pretending to be rigorous here) to get
\[ f_x(x,y)+ f_y(x,y) \dfra... |
A simple, but important and useful, type of separable equation is the
first order homogeneous linear equation:
Definition: first order homogeneous linear differential equation
A first order homogeneous linear differential equation is one of the form
\[\dot y + p(t)y=0\]
or equivalently
\[\dot y = -p(t)y.\]
"Linear'' in... |
14 0 Homework Statement A yo-yo is placed on a conveyor belt accelerating ##a_C = 1 m/s^2## to the left. The end of the rope of the yo-yo is fixed to a wall on the right. The moment of inertia is ##I = 200 kg \cdot m^2##. Its mass is ##m = 100kg##. The radius of the outer circle is ##R = 2m## and the radius of the inne... |
I was given this innocent looking homework question.
Given two nonempty sets $A,B \subseteq X$ where $(X,d)$ is a metric space.
Show that $\mathrm{dist}(A,B) = \inf \{d(x,y) \mid x \in A, y \in B \}$ is well-defined. Suppose $A \cap B = \emptyset$. Suppose $A$ is closed and $B$ is compact. Show that $\mathrm{dist}(A, B... |
Global existence of weak solution in a chemotaxis-fluid system with nonlinear diffusion and rotational flux
1.
School of Mathematics, Southeast University, Nanjing 210096, China
2.
Institute for Applied Mathematics, School of Mathematics, Southeast University, Nanjing 211189, China
$\begin{eqnarray*} \left\{\begin{arra... |
I’m back! Croatia, Greece, Turkey… all behind me. In the meantime, I’ve fallen even more in love with math.stackexchange and have ended up as a temporary moderator for philsophy.stackexchange (check them out). To announce my return, a little fun:
from Loers Hey everyone thanx for the amazing effort that u provide us wi... |
Emergence of large densities and simultaneous blow-up in a two-species chemotaxis system with competitive kinetics
School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210023, China
$ \begin{eqnarray*} \left\{\begin{array}{lll} u_t = \Delta u-\chi_1\nabla\cdot(u\nabla w)+\mu_1u(1-u-a_1v),\ \ \... |
This is joint work with Thomas Hulse, Chan Ieong Kuan, and Alex Walker.
We have just uploaded a paper to the arXiv on the second moment of sums of Fourier coefficients of cusp forms. This is the first in a trio of papers that we will be uploading and submitting in the near future.
Suppose $latex {f(z)}$ and $latex {g(z... |
Here is a general continuity type result on perturbations of the spectral radius:
Theorem. Let $A,B \in \mathbb{C}^{n \times n}$ be matrices and let $r(A)$ denote the spectral radius of $A$. For each $r > r(A)$ we set\begin{align*} \alpha(r) := \sup_{\lvert\lambda\rvert \ge r} \lVert (\lambda - A)^{-1} \rVert\end{align... |
Uniqueness of Meromorphic Functions Concerning Sharing Two Small Functions with Their Derivatives
Ma Linke,Liu Dan,Fang Mingliang
Keywords:Meromorphic functions, Shared small functions, Derivatives.
Abstract:
In this paper, we study the uniqueness of meromorphic functions that share two small functions with their deriv... |
Many authors pull the definitions of the raising and lowering (or ladder) operators out of their butt with no attempt at motivation. This is pointed out nicely in [1] by Eli along with one justification based on factoring the Hamiltonian.
In [2] is a small exception to the usual presentation. In that text, these operat... |
Question:
Watson is filling a pool with water. The flow rate {eq}r(t) {/eq} gives the gallons per second at which the water is flowing into the pool at time {eq}t {/eq} seconds after he turns on the faucet. We are going to make a new function, {eq}\displaystyle f (\hat t) = \int_{t = 5}^{\hat t} r(t)dt {/eq}. First, le... |
FtYou writes
Hello everyone ! There is a concept I have a hard time getting my head wrap around. If you have a Vector Space V and a subspace W, I understand that you can find the least square vector approximation from any vector in V to a vector in W. And this correspond to the projection of V to the subspace W. Now , ... |
Simple question. When are we allowed to exchange limits and integrals? I'm talking about situations like$$\lim_{\varepsilon\to0^+} \int_{-\infty}^\infty dk f(k,\varepsilon) \overset{?}{=} \int_{-\infty}^\infty dk\lim_{\varepsilon\to0^+} f(k,\varepsilon).$$Everyone refers to either
dominated convergence theorem or monot... |
Could 2 moons that orbit same terrestrial planet never see each other if they orbit the planet at same time?
Moons have different mass and gravity.
Worldbuilding Stack Exchange is a question and answer site for writers/artists using science, geography and culture to construct imaginary worlds and settings. It only take... |
Modeling of Materials in Wave Electromagnetics Problems
Whenever we are solving a wave electromagnetics problem in COMSOL Multiphysics, we build a model that is composed of domains and boundary conditions. Within the domains, we use various material models to represent a wide range of substances. However, from a mathem... |
Now we know that some functions can be expressed as power series, which look like infinite polynomials. Since calculus, that is, computation of derivatives and antiderivatives, is easy for polynomials, the obvious question is whether the same is true for infinite series. The answer is yes:
Theorem 13.9.1 Suppose the po... |
The previous section showed that, in some ways, derivatives behave nicely. The Constant Multiple and Sum/Difference Rules established that the derivative of \(f(x) = 5x^2+\sin x \) was not complicated. We neglected computing the derivative of things like \(g(x) = 5x^2\sin x\) and \(h(x) = \frac{5x^2}{\sin x}\) on purpo... |
Since log is such basic element in secondary education, such questions are accessible to most students. In fact, they appear frequently in one of Taiwan's university qualifying exam AST. You are given the value of log 2 and log 3, then you are required to approximate some
logged numbers, without calculator of course.
I... |
Let $S=\prod_{i=1}^{n}{R_i}$ where each $R_i$ is a commutative ring with identity. The prime ideals of $S$ are of the form $\prod_{i=1}^{n}{P_i}$ where for some $j$, $P_j$ is a prime ideal of $R_j$ and for $i\neq j$, $P_i=R_i$.
It is clear that any ideal of $S$ of the form stated above is prime. Let $P$ be a prime idea... |
Convolution & Cross-correlation
The primary implement of convolution and cross-correlation.
Notes
You can refer to the complete notes from 04 Notes
Linear Systems(Filter)
Denotes the input function:
$$f[m,n]$$
Filter is used to convert input function to an output(or response) function:
$$g[m,n]$$
$\mathcal{S}$ is refer... |
Edit: I am seeking a solution that uses only calculus and real analysis methods -- not complex analysis. This is an old advanced calculus exam question, and I think we are not allowed to use any complex analysis that could make the problem statement a triviality.
Show that the series
$$\sum_{n=2}^{\infty} \frac{\sin(n)... |
I'm learning to integrate and I'd like to hear what are you favorite integration tricks?
I can't contribute much to this thread, but I like the fact that:
$$\int_{-a}^{a}{f(x)}dx=0 \space\text{if}\space f(x) \space\text{is odd}$$
Mathematics Stack Exchange is a question and answer site for people studying math at any l... |
The motivation comes from the following question on MathOverflow:
Question 1.Is there a natural number $n$ satisfying the equation $n(n+1)=2^{[\log^{n}_{2}]+2}$ where $[.]$ indicates the floor function. I am also interested in the minimum $n$ satisfying this equation if there is any.
As the answer to the above question... |
Division Theorem for Polynomial Forms over Field/Proof 1 Theorem
Let $X$ be transcendental over $F$.
Let $F \sqbrk X$ be the ring of polynomials in $X$ over $F$.
Then $\forall f \in F \sqbrk X: \exists q, r \in F \sqbrk X: f = q \circ d + r$ such that either: $(1): \quad r = 0_F$
or:
$(2): \quad r \ne 0_F$ and $r$ has ... |
Let $\{X_1, X_2, \ldots, X_n\}$ be independent and identically distributed (i.i.d.) random variables sampled from a common distribution with density $f_{\theta}(x)$, where $\theta$ is an unknown parameter. We want to estimate $\theta$ given these $n$ samples. Suppose $\hat{\theta}$ is an estimator based on these sample... |
The fraction \frac{num}{den} are usually rendered by centering the numerator and the denominator.
Unfortunately, I find the result in the following MWE quite ugly:
\documentclass{article}\begin{document}If $r\neq 1$, then \[\sum_{k=0}^nr^k = \frac{1-r^{n+1}}{1-r}\]\end{document}
Indeed, the $r^{n+1}$ part is too big. I... |
The first thing to observe is that by rotating the triangle about the hypotenuse I obtain two cones having the same base and opposite vertices.
To find the volume of a cone you need its height and the radius of its base. So you need to calculate the radius and the height of each cone.
$$V = \frac{1}{3}\pi r^2 h$$
The r... |
\( \renewcommand{\vec}[1]{ \mathbf{#1} } \)
Introduction
When people hear "implicit surface" most of them think about metaballs, blobby objects and the marching cube. I want to define here implicit surface as a much more general concept and basic jargon related to this field. Let's be clear from the start, implicit sur... |
Say for the following problem, suppose boundary of $\Omega$ is $C^{1,1}$: $$ \left\{ \begin{aligned} -\Delta \phi &= \mathrm{div} \,\vec{u}\quad \text{ in } \Omega \\ \phi&=0 \quad \text{ on }\partial \Omega \end{aligned} \right. $$ Could we deduce $\nabla \phi\cdot \vec{n}$ on $\partial \Omega$ by the following reason... |
I am a beginner student of Algebraic Number Theory and I am starting to learn ramification theory (of global fields). My question asks for motivation for a definition I was given.
Let $K$ be an algebraic number field, $\mathcal{O}_{K}$ its ring of integers, $L/K$ a Galois extension and $\mathcal{O}_{L}$ the integral cl... |
This answer is a hard-science expansion of this answer. Please read that other answer to get a description of the system I am proposing, as well as justification of its technical feasibility. That post also has lots of reference links for various design decisions. I will summarize the system here and numerically addres... |
Research kicks up, writing kicks back. So in this brief note, we examine a pair of methods to examine an integral. They’re both very clever, I think. We seek to understand $$ I := \int_0^{\pi/2}\frac{\sin(x)}{\sin(x) + \cos(x)} dx $$
We base our first idea on an innocuous-seeming integral identity.
For $latex {f(x)}$ i... |
Difference between revisions of "User:Nikita2"
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(15 intermediate revisions by the same user not shown) Line 3: Line 3: −
I am Nikita Evseev
+
I am Nikita Evseev Novosibirsk, Russia.
My research interests are in [[Mathematical_analysis | Analysis]] and [[Sobolev space|Sobolev spaces]].
My research interests are in [[... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Year of publication 1996 (22) (remove)
293
Tangent measure distributions were introduced by Bandt and Graf as a means to describe the local geometry of self-similar sets generated by iteration of contractive similitudes. In this paper we study the tangent measure... |
Trying to understand how rearrangements work. A very common example of rearrangements seems to be the alternating harmonic series,
$$\sum _{n=1}^{\infty} \frac {(-1)^{n+1}}{n}$$
Plugging in values of $n$ gives,
$$1-\frac{1}{2}+\frac {1}{3}-....$$ and so on. How can I rearrange this sum so that the first $10$ sum to $0$... |
Definition : Let $S$ be a subset of a metric space $(X,d)$. A point $x \in S$ is called an isolated point if $\exists \varepsilon >0 $ s.t $B(x,\varepsilon) \cap S \setminus \{x\}= \emptyset. $
Baire's Theorem : Let $ (X,d)$ be a complete metric space. Then, the interior of any countable union of closed subsets is none... |
Main question. Does there exist a smooth projective morphism $X\to$ Spec $\mathbf Z$ of relative dimension two such that the canonical sheaf $\omega_{X_{\mathbf Q}}$ of the generic fibre $X_{\mathbf Q}$ is ample?
Replacing "relative dimension two" by "relative dimension one", the answer is negative by a theorem of Abra... |
2019-10-11 06:14
Implementation of CERN secondary beam lines T9 and T10 in BDSIM / D'Alessandro, Gian Luigi (CERN ; JAI, UK) ; Bernhard, Johannes (CERN) ; Boogert, Stewart (JAI, UK) ; Gerbershagen, Alexander (CERN) ; Gibson, Stephen (JAI, UK) ; Nevay, Laurence (JAI, UK) ; Rosenthal, Marcel (CERN) ; Shields, William (JA... |
Although the study of gemology requires no formal prior training, a high school diploma would make it easier to understand basic math. Knowledge of trigonometry especially might serve you well.
Below are some basic calculations that you may want to understand.
Cross-multiplication
Some people have trouble with cross mu... |
Summary 29886 - Plenary Session: QM talk rehearsal , 10:00 $\Lambda$($K_{S}^{0}$)-$h^{\pm}$ Azimuthal Correlations with Respect to Reaction Plane and Searches for CME and CVE Presenter : Feng Zhao 30321 - Light Flavor Spectra Parallel Session - III , 09:30 A Fixed-Target Program for STAR: Extending the Low Energy Reach... |
Let $X$ and $Y$ be two independent random variables, exponentially distributed with parameter $\lambda=1$ and let $U=X$ and $V=X+Y$.
Determine the joint CDF of the random pair $(U,V)$ and determine the CDF of the random variable V.
I know that $f_{(U,V)}(U=u,V=v)=f_{(X,Y)}(X=u,Y=v-u)*1$, $1$ being the Jacobian. So give... |
I have the following nasty expression that I would like to expand in powers of $\frac{1}{N}$:
\begin{align} \frac{2^{\frac{3}{2}} 3^{\frac{1}{2}} \Biggl[ \sqrt{u} \cdot \Gamma\left(\frac{2+N}{4}\right) \cdot {}_1F_1 \left( \frac{2+N}{4},\frac{1}{2},\frac{3r^2}{2u} \right) -\sqrt{6} r \cdot \Gamma \left( \frac{4+N}{4} \... |
You have several preformed misconceptions about relativity in your question. I will try to address them all here.
1- Time Dilation Due To Relativity/Speed
It happens that time dilation due to relativity becomes really evident at extremely high speeds. The time dilation experienced due to velocity is expressed as $$\Del... |
The R package
mlergm, appropriately named“Multilevel Exponential-Family Random Graph Models,” aims to provide a convenient platform for estimating exponential-family random graph models (ERGMs) with multilevel structure. Presently, the beta release of the package supports estimation of ERGMswith non-overlapping block s... |
Journal of Differential Geometry J. Differential Geom. Volume 67, Number 2 (2004), 289-333. Momentum Maps and Morita Equivalence Abstract
We introduce quasi-symplectic groupoids and explain their relation with momentum map theories. This approach enables us to unify into a single framework various momentum map theories... |
Lines and planes are perhaps the simplest of curves and surfaces in three dimensional space. They also will prove important as we seek to understand more complicated curves and surfaces.
The equation of a line in two dimensions is $ax+by=c$; it is reasonable to expect that a line in three dimensions is given by $ax + b... |
The short answer is that the $2 \pi$ comes from the inversion formula.
Here is an informal perspective which gives as hint as to how this can be mademore rigorous:
A distribution is defined by itsaction on a space of nicely behaved test functions.
For a function $f$ from a restricted class of ordinary functions, we can... |
I'm trying to prove the following statement:
Let $F$ be a finite field of prime characteristic $p$ and let $E$ be the field generated by $F$ and the elements $\{t^{1/p},n \geq 1\}$, where $t$ is an indeterminate. Then, any algebraic extension of $E$ is separable.
I've already proved that the Frobenius Endomorphism on $... |
Beside the wonderful examples above, there should also be counterexamples, where visually intuitive demonstrations are actually wrong. (e.g. missing square puzzle)
Do you know the other examples?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related ... |
作者：Bo Li , Meilin Lu ... 来源：[J].Nanoscale Research Letters(IF 2.524), 2017, Vol.12 (1)Springer 摘要：Semiconductor quantum dots (QDs) are widely used in light-emitting diodes and solar cells. Electrochemical modulation is a good way to understand the electrical and optical properties of QDs. In this work, the effects of e... |
What are the solutions of the functional equation $f(x) + f(x^2) = 2$? Will they be one to one or many to one? Will they be periodic or not?
closed as off-topic by LutzL, Crostul, Thomas Andrews, Servaes, user223391 Nov 9 '15 at 0:12
This question appears to be off-topic. The users who voted to close gave this specific... |
Modelling and inverse Problems in Nanometrology
Nanometrology is the science of measurement of distances and displacements of objects at the nanoscale. Mathematical modelling and the numerical simulation in nanometrology supports evaluations of measurements and estimations of uncertainties at the nanoscale level.
Scatt... |
Hydrogen peroxide is said to be unstable, for it undergoes auto-oxidation on standing/heating:
$$\ce{2H_2O_2 -> 2H_2O + O_2}$$
where $\Delta S=\pu{70.5 J {mol}^{-1}K^{-1}}$ and $\Delta H^{\Theta} = \pu{-98.2 kJ {mol}^{-1}}$.
I speculate if the decomposition can be reversed in some way under suitable conditions, particu... |
Suppose that $X$ is a compact metric space, $\mathcal{H}$ is a Hilbert space, and that $A: \mathcal{B}(X) \rightarrow \mathcal{B}(\mathcal{H})$ is a Positive Operator Valued Measure (POVM), where $\mathcal{B}(X)$ denotes the Borel $\sigma$-algebra of subsets of $X$. That is,
$A(\Delta)$ is a positive operator in $\math... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
10:00 --- Meson Distribution Amplitudes --- 10:00 On exclusive hard processes with light-mesons - Dr Kornelija Passek-Kumericki (IRB Zagreb) () 10:30 Twist-3 effects in electroproduction of pions - Peter Kroll (University of Wuppertal) () 11:00 --- Coffee Break --- 11:30 --- Meson DA's and GPD's --- 11:30 Phenomenologi... |
Practice Paper 4 Question 12
Consider the square \(ABCD\) of side \(x,\) and the equilateral triangle \(BCE\) as in the figure shown. The square rotates clockwise around \(B\) until \(A\) overlaps \(E,\) then rotates around \(E\) until \(D\) overlaps \(C,\) and so on, until \(A\) retakes its initial position. Sketch th... |
Answer
When we sketch the graph of these two functions, we can see that the graphs are the same. This is an identity: $tan(\frac{\pi}{2}-\theta) = cot~\theta$
Work Step by Step
$y = tan(\frac{\pi}{2}-\theta)$ $y = cot~\theta$ When we sketch the graph of these two functions, we can see that the graphs are the same. We c... |
Practice Paper 4 Question 13
Sketch \((1+x)^y=e\) for all real values. Take care to point out all key points and key behaviour.
Related topics Warm-up Questions Sketch the graph of \(y=\frac{x-1}{x+1}\). Find the second derivative of \(f(x)=2^{x}.\) Evaluate \(\lim_{x\to\frac{\pi}{2}} \frac{1}{\tan x}.\) Hints Hint 1Ha... |
In order to apply mathematical methods to a physical or “real life” problem, we must formulate the problem in mathematical terms; that is, we must construct a mathematical model for the problem. Many physical problems concern relationships between changing quantities. Since rates of change are represented mathematicall... |
This is the problem :
Given two arrays of $n$ elements A and B, let's define their sum as $$ A + B = \{ a + b \mid a \in A \text{ and } b \in B \}. $$ Calculate $A + A$ in optimal time given that $A[i] \in [1,10n^{1.5}]$ for all $i$.
In order to solve this problem I used FFT by representing a polynomial in the followin... |
A blast of such despair that it can send destruction even into other dimensions. Dissidia 012 Final Fantasy Supernova (スーパーノヴァ, Sūpānova?), also known as Super Nova and Sunburst, is a recurring enemy ability. It generally deals a large amount of non-elemental magic damage to all opponents. The same spell is also used b... |
While I was working on my stuff, another question suddenly came to mind, the one you see below
$$\int_0^\infty \frac{ \left(\sum_{n=1}^\infty\sin\left(\frac{x}{2^n}\right)\right)-\sin(x)}{x^2} \ dx$$
Which way should I look at this integral?
Mathematics Stack Exchange is a question and answer site for people studying m... |
I have found answers on how to calculate the self-inductance of toroid of rectangular cross section, however my question says that "The winding are seen as a thin homogeneous currentlayer around the core" (excuse the translation). What does that mean for N? Does it mean N=1?
I am an undergrad physics major in my final ... |
Practice Paper 4 Question 17
The figure shows a non-overlapping trace on a \(4\times4\) grid which visits all points exactly once. Imagine the same type of trace on an \(n\times n\) grid, where \(n\) can be arbitrarily large. Using the fact that \(\sum_{k=1}^\infty {1\over k}\) diverges to infinity, show that the sum o... |
The terms can mean almost anything, but I will try to present here
one way in which the terms "parallel algorithms" and "distributed algorithms" are understood. Here we interpret "distributed algorithms" from the perspective of "network computing" (think: algorithms that keep the Internet running).
I will use as a runn... |
I'm been working on a theory, though my math is weak. Let's say I've managed to determine that I can arrive at an answer A by always using the formula
BCD / D. Of course this evaluates to BC after canceling out D. However sometimes D can be zero 0 which results in an undefined answer. My question is theoretical in natu... |
Practice Paper 4 Question 18
A poll with 2 choices is run among \(n>2\) participants. Each participant chooses at random. The poll shows the results for the 2 options as percentages rounded to the nearest integer, i.e. \(x\) rounded is \(\lfloor x+0.5\rfloor\), where \(\lfloor x\rfloor\) is the greatest integer less th... |
534674 results
Contributors: Ganian, Robert, Kalany, Martin, Szeider, Stefan, Träff, Jesper Larsson
Date: 2015-06-30
... We show that the problem of constructing tree-structured descriptions of data layouts that are optimal with respect to space or other criteria from given sequences of displacements, can be solved in ... |
Newtonian gravity of a point-source can described by a potential $\Phi = -\mu/r$. If we suppress one spatial dimension and use it to graph the value of this potential instead, we get something that looks very close to this illustration, and is indeed infinitely deep at the center--at least, in the idealization of a poi... |
If you need to include simple diagrams or figures in your document, the
picture environment may be helpful. This article describes circles, lines, and other graphic elements created with LaTeX.
Contents
Images can be "programmed" directly in your LaTeX file
\setlength{\unitlength}{1cm} \thicklines \begin{picture}(10,6)... |
I'm really stumped on a homework problem asking me to evaluate $\int \frac{ln\ 6x\ sin^{-1}(ln6x)}{x}dx$, and after a few hours of trying different approaches I'd definitely be appreciative for a bump in the right direction. As a caveat, I should add that I've already received credit for the assignment, I'm simply look... |
1) According to the Royal Mint, a copper coin weighs 3.56g. The relative atomic mass (RAM) is 63.5. The coin therefore contains approximately $\frac{3.56}{63.5}\times6.02\times10^{23} = 3.28\times10^{22}$ copper atoms. Assuming each atom is neutral, each atom contains 29 electrons, so there are $9.52\times10^{23}$ elec... |
Dielectrophoretic Separation
How can you use an electric field to control the movement of electrically neutral particles? This may sound impossible, but in this blog entry, we will see that the phenomenon of dielectrophoresis (DEP) can do the trick. We will learn how DEP can be applied to particle separation and demons... |
this means that 9-a+b-c+2 is divisible by 11, so b-(a+c) is divisible by 11.
so this value is either -11 or 0.
if it is -11, we can use casework.
first take the case where b is 0.
the a can be 2, c can be 9, or a can be 3, and c can be 8, all the way up to the case where a is 9 and c is 2.
this has 8 possibilities.
now... |
Warning: Heavy use of LaTeX follows. Make sure you enabled Javascript to read those equations properly. It is highly recommended to enlarge the page so that the equations are not in congested form.
First of all, seasons greetings everyone. Let's see if I can get the customization article done before the end of 2016...
... |
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Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c wit... |
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Now showing items 1-2 of 2
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 ... |
By Dr Adam Falkowski (Résonaances; Orsay, France)
The title of this post is purposely over-optimistic in order to increase the traffic. A more accurate statement is that a recent analysis
of X-ray spectrum of galactic clusters claims the presence of a monochromatic \(3.5\keV\) photon line which can be interpreted as a ... |
Find the least positive four-digit solution to the following system of congruences.
\(7x \equiv 21 \pmod{14} \)
\(2x+13 \equiv 16 \pmod{9} \)
\(-2x+1 \equiv x \pmod{25} \)
from the first one, you can see that x is odd.
now you do the second one.
this means 2x leaves a remainder of 3 when divided by 9.
this means x is a... |
Bernoulli Bernoulli Volume 25, Number 1 (2019), 375-394. On the longest gap between power-rate arrivals Abstract
Let $L_{t}$ be the longest gap before time $t$ in an inhomogeneous Poisson process with rate function $\lambda_{t}$ proportional to $t^{\alpha-1}$ for some $\alpha\in(0,1)$. It is shown that $\lambda_{t}L_{t... |
As before, let \(V\) be a complex vector space.
Let \(T\in\mathcal{L}(V,V)\) and \((v_1,\ldots,v_n)\) be a basis for \(V\). Recall that we can associate a matrix \(M(T)\ \in \mathbb{C}^{n\times n}\) to the operator \(T\). By Theorem 7.4.1, we know that \(T\) has at least one eigenvalue, say \(\lambda\in \mathbb{C}\). L... |
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