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how shall i study for IMO . what else shall is i study out of the CBSE course of class 10?
Note by Avn Bha 4 years, 11 months ago
Easy Math Editor
This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenge... |
It's not too hard to show that this isn't possible in general. For a counterexample, consider the 1-dimensional case with $K=2$ and $Gauss_a(0,1)$ the standard normal, and suppose we had the decomposition$$Gauss_a(0,1) = w_1 Gauss_1(\mu_1,\sigma_1) + w_2 Gauss_2(\mu_2,\sigma_2)$$for some parameters $w_i$, $\mu_i$, and ... |
Let $X_1, X_2, X_3, X_4$ be independent Bernoulli random variables. Then \begin{align} Pr[X_i=1]=Pr[X_i=0]=1/2. \end{align} I want to compute the following probability \begin{align} Pr( X_1+X_2+X_3=2, X_2+X_4=1 ). \end{align} My solution: Suppose that $X_1+X_2+X_3=2$ and $X_2+X_4=1$. Then $(X_2, X_4)=(0,1)$ or $(1,0)$.... |
I'm working on some exercise regarding the spin coupling of two electrons. There we have the wavefunctions corresponding to the S values as
$$\begin{align} S = 1: &\begin{array}{c}\uparrow\uparrow \\ \dfrac{1}{\sqrt 2}(\uparrow\downarrow+\downarrow \uparrow) \\ \downarrow\downarrow\end{array} \\[5mm] S = 0: &\ \frac{1}... |
Answer
900 degrees
Work Step by Step
We know that there are 180 degrees per pi radians. Thus, we find: $$=\frac{5\pi}{1} \ radians \times \frac{180^{\circ}}{\pi\ radians}=900^{\circ}$$
You can help us out by revising, improving and updating this answer.Update this answer
After you claim an answer you’ll have
24 hours t... |
Extraordinary claims require extraordinary proofs which really is the reason why this sorts of discussion is important. Similarly, sometimes, you are so blinded to some sorts of a truth and are faced with something so different that you can misread entirely what is being said. If you read this morning's entry, you migh... |
In addition to Lubos Motl's correct answer, I would like to make a few comments related to Norton's dome:
First a brief derivation of Norton's equation of motion (7). I prefer to call the (non-negative) arc length $r$ for $s$, and the vertical height $h$ for $z$. Like Lubos Motl, I will introduce a proportionality fact... |
In classical mechanics, the Newton–Euler equations describe the combined translational and rotational dynamics of a rigid body. [1] [2] [3] [4] [5]
Traditionally the Newton–Euler equations is the grouping together of Euler's two laws of motion for a rigid body into a single equation with 6 components, using column vect... |
Let $u_t$ be the random walk$$ u_t = u_{t-i} + \varepsilon_t $$ where $\mathrm{E}[\varepsilon_t]=0$ and $\mathrm{var}[\varepsilon_t]=\sigma^2$ , i.e. $\varepsilon_t$ is stationary.
Now let $$X_t = \alpha u_t +\nu_t$$ and$$Y_t = \beta u_t + \eta_t$$where $\nu_t$ and $\eta_t$ are stationary processes similar to $\varepsi... |
I would like to use brackets in math mode which stretch automatically like
\left( and
\right), but have a given minimum size, for example:
Using something like
\delimitershortfall and
\delimiterfactor does not work well because it stretches
all brackets (including the ones which are already big enough). I would just li... |
Research Open Access Published: Existence of positive stationary solutions for a reaction-diffusion system Boundary Value Problems volume 2016, Article number: 11 (2016) Article metrics
818 Accesses
Abstract
In this paper, we will establish some existence results of positive stationary solutions for a reaction-diffusio... |
The Maxwell stress tensor is introduced as analogue to the stress tensor in continuum mechanics, and its form is derived from the equation$$\frac{d}{dt} \int_V \boldsymbol{\mathscr{p}} + \boldsymbol{\mathscr{g}} \,dV = \oint_{S} d\mathbf S \cdot \mathbf T$$where $\boldsymbol{\mathscr{p}}$ is density of momentum of matt... |
The orthogonal group, consisting of all proper and improper rotations, is generated by reflections. Every proper rotation is the composition of two reflections, a special case of the Cartan–Dieudonné theorem.
Yeah it does seem unreasonable to expect a finite presentation
Let (V, b) be an n-dimensional, non-degenerate s... |
I wont post all the functions.I am practicing on continuity.So i wanna use definitions but i am not really sure how? Suppose i have the function
$$f(x)= \frac{x^4-y^4}{(x^2+y^2)^2}$$ When $(x,y)\neq (0,0)$ and
$f(x)=b $ when $(x,y)=(0,0)$
Proof:To be defined continouesly at $0$ the limit at zero must exist.So there mus... |
This post directly proves that
$$ P\left( \sum_{n=1}^{\infty} \frac{a_n}{n} = \infty \right) = 1$$
rather than study about different quantities so as to make a heuristic argument that helps convince that the result is plausible.
The method is
Decompose the sum into a sequence of independent, disjoint partial sums with ... |
In General Relativity (GR), it is standard to endow the spacetime manifold with a metric compatible connection, i.e. $\nabla_{\alpha}g_{\mu\nu}=0$. My question is: is metric compatibility of the connection an on-shell statement, i.e. does it only apply to metrics that satisfy the Einstein field equations (EFEs)?
The re... |
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i am going to class 11th next year and want some suggesstions.What were the mistakes which you committed during your machines.Please share your golden experience! Thanks in advance!
Note by Aman Ahmad 5 years, 7 months ago
Easy Math Editor
This discussion board i... |
2018-08-25 06:58
Recent developments of the CERN RD50 collaboration / Menichelli, David (U. Florence (main) ; INFN, Florence)/CERN RD50 The objective of the RD50 collaboration is to develop radiation hard semiconductor detectors for very high luminosity colliders, particularly to face the requirements of the possible u... |
A few days ago, whilst gazing upon the midnight sky, a totally justified question crawled into my mind.
How many SpaceX rockets does it take to deorbit the Moon? It went straight into one of those places where you can’t really ignore it or shake it off, you just have to know. I could have probably just calculated the r... |
The problem is that
your boundary conditions are incompatible with your equation.
Your choice of boundary data implies that, were $u$ to be in $C^1([0,1]\times[0,1])$ (meaning that the derivative extends continuously to the boundary), you must have $\nabla u(0,0) = 0$, since the two partials both vanish. This is clearl... |
I am very confused on how to derive the attached equation (15).
closed as off-topic by LocalVolatility, Quantuple, Helin, Gordon, chollida Oct 10 '17 at 17:33
This question appears to be off-topic. The users who voted to close gave this specific reason:
" Basic financial questionsare off-topic as they are assumed to be... |
1) Consider the semidirect product $G=\mathbf{Z}^2\rtimes\mathbf{Z}$ with action by the matrix $A=\begin{pmatrix}2 & 1 \\ 1 & 1\end{pmatrix}$. It has the presentation$$\langle t,x,y\mid txt^{-1}=x^2y,\; tyt^{-1}=xy,\; [x,y]=1\rangle.$$(It is actually generated by $(t,x)$).
Claim: some limit of markings on $G$ fails to ... |
I have been looking the number of methods to measure inductance of a coil if you don't have an LCR meter available, and I have had some difficulty. I designed and built a coil and I would like to confirm its inductance, which theoretically is ~\$2\mu\mathrm{H}\$.
One method is putting a resistor in series with the indu... |
Fill in the (usually small) details in the following:
It is probably easier to show the double negation: $\;\Bbb F\;$ is
inseparable iff $\;\Bbb F^p\setminus\Bbb F\neq\emptyset\;$
== So take $\;a\in\Bbb F^p\setminus\Bbb F\;$ . If $\;\beta\;$ in some non-trivial extension of $\;\Bbb F\;$ is s.t. $\;\beta^p=a\;$ , then
$... |
Ok so the way I see it, let's strip away the physics first. Then we're left with the math. So the question you're posing is, given only $\frac{d^nx(t)}{dt^n}|_{t=c} \forall n$, can we reconstruct the function $x(t)$ uniquely in some domain $(a,b)$ s.t. $c \in (a,b)$?
Well the answer is no. Even if you impose a $C^\inft... |
Differential and Integral Equations Differential Integral Equations Volume 13, Number 1-3 (2000), 227-254. Asymptotic behavior for minimizers of an anisotropic Ginzburg-Landau functional Abstract
Minimizers $u_{\varepsilon}$ of some anisotropic Ginzburg-Landau functional $E_{\varepsilon}$ defined in (1.4) below on a sm... |
Well, by Cayley--Hamilton, each matrix $A\in {\rm GL}(n,p)$ generates an at most $n$-dimensional subalgebra ${\mathbb F}_p[A]\subseteq M(n,p)$ thus containing at most $p^n-1$ nonzero elements. Hence the order of $A$ cannot exceed $p^n-1$.
On the other hand, consider a degree $n$ monic polynomial $P_n$ whose root is a g... |
In this answer we will only consider the leading semi-classical approximation of a $1$-dimensional problem with Hamiltonian
$$ H(x,p) ~=~ \frac{p^2}{2m}+ \Phi(x), $$
where $\Phi$ is a potential. Semi-classically, the number of states $N(E)$ below energy-level $E$ is given by the area of phase space that is classically ... |
Building a Magnetohydrodynamic Multiphysics Model in COMSOL®
The COMSOL Multiphysics® software is built from the ground up to be multiphysics capable so that the user can easily combine models representing different physics phenomena in whichever way they wish. Sometimes this can be achieved simply by using built-in fe... |
How can I prove that the following limit exist? $$ \mathop {\lim }\limits_{x,y \to 0} \frac{{x^2 + y^4 }} {{\left| x \right| + 3\left| y \right|}} $$ I tried a lot of tricks. At least assuming that this limit exist, I can prove using some special path (for example y=x) that the limit is zero. But how can I prove the ex... |
As noted in 1806.05647, given a
symmetric matrix $A$, the leading eigenvector value problem (LEVP)
$$Av = \lambda v,$$
where $A = A^T \in \mathbb{R}^{n \times n}$, $\lambda$ is the largest eigenvalue of $A$ and $v$ is the corresponding eigenvector, can be written as an unconstrained optimisation problem
$$\min_{x \in \... |
I have a CO
2 sensor that output signal values 30-50 mV. I need to translate these voltages to 0-5 V for my microcontroller with the highest resolution. I understand that I can amplify the voltage using a non-inverting op-amp circuit, as shown, to a range of 3-5 V, but is it possible to expand that range to 0-5 V in or... |
This question is related to one I asked previously. Sorry if some of the notation or discussion below is unwieldy or nonstandard. I am still trying to learn the relevant terminology, so it's likely that what follows could be expressed more clearly.
Consider the Veronese embedding of degree 2: $\nu_2:\mathbb{RP}^n\right... |
Consider an $n$-dimensional complex vector space $V$ with a chosen basis $e_1,\ldots,e_n$. This basis defines a Cartan decompostion of $GL(V)\cong GL_n$ and for an (integral dominant) highest weight $\lambda$ we may consider the irreducible representation $L_\lambda$. In $L_\lambda$ we have the Gelfand-Tsetlin basis fo... |
The general idea
For equity securities, a simple backtest will typically consist of two steps:
Computation of the portfolio return resulting from your portfolio formation rule (or trading strategy) Risk-adjustment of portfolio returns using an asset pricing model
Step 2 is simply a regression and computationally very s... |
How do I plot this on Mathematica version 5.2?
$\frac{4}{\pi} \sin{x} + \frac{4}{3 \pi} \sin{3 x} + \cdots + \frac{4}{(2 N+1) \pi} \sin{(2 N+1) x}$
over $x \in [-\pi,\pi]$ for $N= 3, 6, 12, 24$.
I tried and got this error:
Mathematica Stack Exchange is a question and answer site for users of Wolfram Mathematica. It onl... |
I have a question regarding the Levi-Civita symbol and contravariance vs covariance. Some of this was asked in a previous post, but I think I need more clarification.
Consider the magnetic field: \begin{equation} B^k = \tilde{\varepsilon}^{ijk}\partial_i A_j \end{equation}
Qn 1: In the formula I wrote it as the Levi-Ci... |
I stumbled upon this old question and I would like to share my solution. As mentioned in other answers, there is no analytical solution, but the function to be minimized behaves nicely and the optimal value of $\alpha$ can be found easily with a few Newton iterations. There is also a formula to check the optimality of ... |
I started to set up a template document with
Alegreya as font which is supposed to be compilable on all three engines, PDFLaTeX, XeLaTeX, and LuaLaTeX. To also set
Alegreya as the math font, I have chosen
mathastext package because this works for all three engines. But I don't get numbers and greek symbols in math mode... |
On the existence of weak solutions of an unsteady
p-Laplace thermistor system with strictly monotone electrical conductivities
Department of Mathematics, Humboldt University Berlin, Unter den Linden 6,10099 Berlin, Germany
$\Omega\subset\mathbb{R}^n$
$n=2$
$n=3$
$\text{(1)}\quad \nabla\cdot \boldsymbol{J}=0,\qquad \tex... |
2019-10-01 16:19 [PUBDB-2019-03551] Book/Report/Dissertation / PhD Thesis Development of a compact hard X-ray split-and-delay line for studying ultrafast dynamics at free electron laser sources [DESY-THESIS-2019-023] Hamburg : Verlag Deutsches Elektronen-Synchrotron, DESY-THESIS 140 pp. (2019) [10.3204/PUBDB-2019-03551... |
Considering an LTI system, its impulse response $h[n]$ and the step response $s[n]$ are related by $$h[n] = s[n]-s[n-1]$$ and $$s[n] = u[n] \star h[n] = \sum_{k=-\infty}^{n} h[k] = \sum_{k=0}^{\infty} h[n-k] $$
Given your definition of $s[n]$ therefore its $h[n]$ is$$h[n] = \left[5 - 4 \left( \frac{4}{5} \right)^n \rig... |
CryptoDB Paper: Explicit Rate-1 Non-malleable Codes for Local Tampering
Authors: Divya Gupta Hemanta K. Maji Mingyuan Wang Download: DOI: 10.1007/978-3-030-26948-7_16 Search ePrint Search Google Abstract: This paper constructs high-rate non-malleable codes in the information-theoretic plain model against tampering func... |
LaTeX uses internal counters that provide numbering of pages, sections, tables, figures, etc. This article explains how to access and modify those counters and how to create new ones.
Contents
A counter can be easily set to any arbitrary value with
\setcounter. See the example below:
\section{Introduction} This documen... |
This question already has an answer here:
What is $\mathop {\lim }\limits_{n \to \infty } \frac{{\tan (n)}}{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
This quest... |
The listing of our experiments has changed. When you click the experiments link above, you will find a database of experiments, which you can filter by information and media available for each experiment.
As additional news, we now also feature worksheets for school. Unfortunately, so far these are only in German. If y... |
When 50.00 mL of an unknown 0.2461 M weak acid are titrated with 0.1968 M NaOH, it was found after the addition of exactly 16.00 mL of base that the pH of the solution was 3.79. From this information, calculate the Ka of the acid.
I have an idea of how to do this question, but looking in my book, I seem to be arriving ... |
Does λ here mean anything?
Yes, it means, in this context, precisely what it usually means: $\lambda$ is distance over which the wave completes one (spatial) cycle, i.e., the distance over which the argument changes by $2 \pi $
Look at the 2nd drawing from the top. It is clear that exactly one
cycle completes in precis... |
To send content items to your account,please confirm that you agree to abide by our usage policies.If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.Find out more about sending content to .
To send content items to your Kindle, first ensure no-rep... |
Pretty self explanatory. I’m wondering if the strong nuclear force could be overcome by a strong enough magnet?
Protons and neutrons are in orbitals within the nucleus which have angular momentum , so the statement of "stationary charges" is true only to first order.
The magnetic fields in laboratory experiments are no... |
The VaR of level $\alpha$ a loss random variable (the bigger the worse) is the quantity $q$ such that the loss is bigger with probability $1-\alpha$.
Thus we need a $q$ such that $$P[L>q] = 1-\alpha,$$ where we can imagine $\alpha=99\%$ and thus we need the starting point of the $1\%$ tail. Because we have a probabilit... |
The fourth black hole law
Using this new theory, we can thus formulate a new
fourth law of black hole dynamics: it is never possible to change the angular velocity of a black hole,
and its resulting corollary:
every black hole grows towards its ultimate maximum size, set by the maximal limit when the circumference reac... |
Question: $\ce{H2S}$ ($\pu{0.1M}$; $K_\mathrm{a} = 1.2×10^{-20} $) and $\ce{HCl}$ ($\pu{0.3M}$) with same volume are mixed together. What is the resultant $\mathrm{pH}$?
My approach: Let the volume of each be $x \; \pu{L}$ $$ \begin{array}{lcc} &\ce{H2S & -> & 2H+ & + & S^2-} \\ \text{initially} & 0.1 && 0 && 0 \\ \tex... |
Bulletin of the Belgian Mathematical Society - Simon Stevin Bull. Belg. Math. Soc. Simon Stevin Volume 17, Number 5 (2010), 781-806. Spherical associated homogeneous distributions on $R^{n}$ Abstract
A structure theorem for spherically symmetric associated homogeneous distributions (SAHDs) based on $R^{n}$ is given. It... |
I'm trying to use the
cases environment inside an
equation environment.The sample code is quite simple:
\begin{equation*} X(\omega) = \begin{cases} 1 \text{se $\omega \in A$} \\ 0 \text{se $\omega \in A^c$} \end{cases}\end{equation*}
Compiling it with Kile results in this error:
Missing $ inserted
and some other messag... |
In this tutorial, you will learn how to Purpose:
optimizea general crystal structure. An explicit example is given for hexagonalstructures. Here, you will set up and execute a series of calculations for different volumes (at constant $c/a$ ratio) and for different $c/a$ ratios (at constant volume) for Be in the hexagon... |
There is no shortage of idiots and assholes in this world. I see them everyday in my mail inbox. The rich Nigerian widow, Idi Amin’s grandson, Gaddafi’s daughter-in-law, Saddam Husain’s son-in-law, are all looking for a “reliable” partner in their business adventures and seek my help in this matter. Of course, they pro... |
Notation notes:
The cycle $(i,i+1,\dots,j)\in S_n$ is the permutation $(1)(2)...(i,i+1,\dots,j)\dots(n)$ in cycle notation. Motivation
Given a factorization of a permutation into certain cycles with non negative exponents, is it possible to find a factorization of the permutation to the same cycle factors (in the same ... |
Scientific and technical writing, native to the web
Use the
New R Markdown dialog within RStudio to create a new Distill article:
You can also create a new Distill article from the command line with:
library(rmarkdown)draft("article.Rmd", "distill_article", package = "distill")
Distill articles use
distill::distill_art... |
Adding, Subtracting, Multiplying, and Dividing Rational Expressions 05:30 minutes Get your free trial content now! Video Transcript Transcript Adding, Subtracting, Multiplying, and Dividing Rational Expressions
Chris and two of his best friends formed a group to build a drone for their school’s science fair project.The... |
Let $a_k=\pi(10^k)-\pi(10^{k-1})$ be the number of $k$ digit primes. All of them (for $k \gt 1$) are from the $4\cdot 10^{k-1}$ integers in that range which are co-prime to $10.$ The heuristic is that, for $k$ not too small, there should be about $\frac{2^k}{4\cdot10^{k-1}}a_k$ primes in that range using only the digit... |
2019-09-04 12:06
Soft QCD and Central Exclusive Production at LHCb / Kucharczyk, Marcin (Polish Academy of Sciences (PL)) The LHCb detector, owing to its unique acceptance coverage $(2 < \eta < 5)$ and a precise track and vertex reconstruction, is a universal tool allowing the study of various aspects of electroweak an... |
I'm currently studying superstring theory from the book 'String Theory and M-Theory' by Becker, Schwarz etc.
In particular, I'm working my way through the spacetime supersymmetric string action in the GS-formalism.
To construct such a spacetime supersymmetric action, one adds a second part, $S_2$ to the action, so that... |
As you might have seen the London brothers were the first to construct a successful theoretical model of superconductivity, translated in the two famous London equations, of which the second one, $$\textbf{B}=-\mu_0\lambda_L^2 \nabla\times\textbf{j}_s$$describes the Meissner effect. Now this was more of a phenomenologi... |
Research Open Access Published: Levin’s type boundary behaviors for functions harmonic and admitting certain lower bounds Boundary Value Problems volume 2015, Article number: 159 (2015) Article metrics
648 Accesses
3 Citations
Abstract
In this paper, we prove Levin’s type boundary behaviors for functions harmonic and a... |
Research Open Access Published: Existence and uniqueness of positive solutions for fractional differential equations Boundary Value Problems volume 2019, Article number: 22 (2019) Article metrics
1052 Accesses
Abstract
By some new integral inequalities of Henry–Gronwall type, we investigate the existence and uniqueness... |
I kind of get the idea of singlet and triplet states. But why are they called singlet and triplet (what is the single and what is the triple in these cases)?
I feel that I am missing something obvious!
Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field ... |
As @PaulDuBois commented, the above answer (@hjhjhj57) is incorrect for obtuse angles.
In fact, we can classify the outside of the triangle in
three regions:
1) $\alpha\geq 0$ and $\beta<0$, in which case $P$ is closest to either $AB$ or $AC$,
2) $\beta\geq 0$ and $\gamma<0$, in which case $P$ is closest to either $AB$... |
How can I show a Lebesgue measure on $\mathbb{R}$ is $\sigma$-finite? I know that a measure $\mu$ on $(\mathbb{R},\mathfrak{B}(\mathbb{R}))$is a Lebesgue measure on $R$ if $\mu (A)$ is the length of A for every interval of A. But how do I show such a measure is $\sigma$ finite?
Remember that a space is $\sigma$-finite ... |
In the book Randomized Algorithms from Motwani and Raghavan, it is stated in page 44 that
$$\mathbb{P}[X_1(k^\ast)] \leq \left( \frac{e}{k^\ast} \right)^{k^\ast} \frac{1}{1-e/k^\ast} \leq n^{-2}.$$
This inequality is used to prove the theorem "With probability at least $1 - \frac{1}{n}$, no bin has more than $k^\ast = ... |
Gibbs free energy and spontaneity (article) | Khan Academy
The rate of a chemical reaction is the change in concentration over the change in time. rate of disappearance of A \[\text{rate}=-\dfrac{\Delta[A]}{\Delta{t}}\] products increase, there is a sign difference between the two rates. Investigate factors which affec... |
Scalar means$$U(\Lambda)\phi(x) U(\Lambda)^\dagger=\phi(\Lambda x)$$or, in other words, it transforms trivially under the Lorentz Group, as opposed to, say, vectors or spinors, which transform as$$U(\Lambda)\psi(x) U(\Lambda)^\dagger=\color{red}{D(\Lambda)}\psi(\Lambda x)$$for a non trivial matrix $D(\Lambda)$.
In this... |
Let's suppose the asset price process follows a Geometric Brownian motion $S_t \sim GBM(\mu, \sigma),\,t\ge 0$, and define the two process: $$ \begin{align} \text{MSF}_t &:= \max_{\tau\in[0,t]} S_\tau\\ \text{MDD_Ratio}_t &: = \max_{\tau\in[0,t]} ((\text{MSF}_\tau- S_\tau) / \text{MSF}_\tau) \end{align} $$ where MSF me... |
Consider an exponential polynomial $$f(t)=\sum_{k=1}^na_k\exp(i\lambda_kt),$$ where $a_k$ are complex and $\lambda_k, t$ real. The usual form of the Mean Motion Theorem says that the limit $$\lim_{t\to+\infty}\frac{\arg f(t)}{t}$$ exists. (If $f$ has real zeros one defines $\arg f$ by bypassing them along small half-ci... |
Get your free trial content now! Video Transcript Transcript Percent: Word Problems
Shannon is searching the Internet for some crime
statistics for an article she's writing for her school newspaper. The statistics she found are a lot like word problems with percentages. Let's see what Shannon found out. Percent Word Pr... |
It depends, roughly speaking, on what is the operator that you interpret as the number operator of the theory. It is customary to choose $N$ as the operator such that: a vector $\phi$ of the Fock space is in the $n$-particle sector if $N\phi=n\phi$, i.e. if it is an eigenvector of the number operator $N$ with eigenvalu... |
One knows that the price of a bermudan claim exercisable at times $T_1, T_2,\ldots, T_N$ is $$V_0 = \sup_{\tau\in\Gamma} \mathbf{E} \left[ e^{\int_0^{\tau} r_s ds} \varphi_{\tau}\left( x_{\tau} \right) \right]$$ where
$x$ is the $d$-dimensional underlying $\varphi_t(x_t)$ is the payoff value if exercised at $t$ $\Gamma... |
Answer
This is a graph of $~~r = a~\theta~~$ for $a=2$ and values of $\theta$ such that $-4\pi \leq \theta \leq 4\pi$
Work Step by Step
This is a graph of $~~r = a~\theta~~$ for $a=2$ and values of $\theta$ such that $-4\pi \leq \theta \leq 4\pi$ Note that $r = 0$ when $\theta = 0$, and the magnitude of $r$ continues t... |
it's a theoretical question. is there any voltage drop when measuring a 12v battery with a multimeter(voltmeter mode)? so if we get 12 Volts reading near the battery, does this changes if we extends the cables of multimeter to 1 km ??
A typical DMM has a very high (but not infinite) input impedance, typically ~10Mohm o... |
The answer does not violate the "conjugate roots theorem" (!) because the "theorem" is only valid for polynomial with real coefficients.
For your problem, to find the two values of $\sqrt{3 - 4 i}$, or of a general $\sqrt{x + i y}$, you have to solve the equation $(X+iY)^2 = x+iy$. This is equivalent to $X^2 - Y^2 = x$... |
Refined asymptotics around solitons for gKdV equations
1.
Université de Versailles Saint-Quentin-en-Yvelines, Mathématiques, 45, av. des Etats-Unis, 78035 Versailles cedex, France
2.
Université de Cergy-Pontoise and IHES, Laboratoire de mathématiques, UMR CNRS 8088, 2, av. Adolphe Chauvin, 95302 Cergy-Pontoise cedex, F... |
Research Open Access Published: Existence and iterative solutions of a new kind of Sturm-Liouville-type boundary value problem with one-dimensional p-Laplacian Boundary Value Problems volume 2016, Article number: 86 (2016) Article metrics
810 Accesses
Abstract
We study a kind of Sturm-Liouville-type four-point boundary... |
I'm a high school student with basic knowledge about chemical thermodynamics. I have three questions regarding the thermodynamic state functions $H, S, G$. I have searched a lot in textbooks but they don't give the complete information as to whether the properties taken are that of the system or surroundings.
Q1):-Enth... |
I'm facing this new concept: the quasi likelihood. I'm looking for some clear explanation of what it is. I have a very basic knowledge about this, so I need to go step by step very slowly. I discovered this concept in dealing with overdispersed count data.
Quasipoisson models will estimate relative rates with no distri... |
I am trying to understand a result involving the power of a series that occurs in Gradstein and Ryzhik's
Table of Integrals, Series, and Products. Result 0.314 (p.17, 7th ed.) is:
$$\left(\sum_{k=0}^\infty a_k x^k\right)^n=\sum_{k=0}^\infty c_k x^k$$
where $$c_0 = a_0^n, c_m=\frac 1 {ma_0} \sum_{k=1}^m (kn-m+k) a_k c_{... |
I understand the difference between Excess, Residual and Active Returns.
I also understand what
Active Risk; defined as: $\sigma_{r_P-r_B}$ (i.e. standard deviation of the difference in returns between our portfolio and benchmark).
Now, what exactly is
Residual Risk? I often see it defined (e.g. here) as:
$\omega_p = \... |
When designing a boost converter to take a low input voltage to a high output voltage, there are many knowns that you control, such as the choice of inductor and the duty cycle of the switching that is at the heart of the boosting voltage. The below circuit is a demonstration of what I'm talking about - no values since... |
So I want to check if I have the right idea here. I am told and abelian group $G$ is generated by elements $a,b,c$ such that $3a + 6b + 3c = 9b + 9c = -3a + 3b + 6c = $ From my understanding, I proceed by constructing a matrix with the coefficients of these relations as so:
$$ X = \left( \begin{matrix} 3 & 0 & -3 \\ 6 ... |
Answer
$$x=-1.23,2.23$$
Work Step by Step
Using the quadratic formula, we obtain: $$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$$ $$x=\frac{1\pm \sqrt{(-1)^2-4(2.75)(-1)}}{2(1)}$$ $$x=-1.23,2.23$$
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Class "Logis"
The Logistic distribution with
location \(= \mu\), by default
= 0, and
scale \(= \sigma\), by default
= 1, has distribution function $$ p(x) = \frac{1}{1 + e^{-(x-\mu)/\sigma}}% $$ and density $$ d(x)= \frac{1}{\sigma}\frac{e^{(x-\mu)/\sigma}}{(1 + e^{(x-\mu)/\sigma})^2}% $$
It is a long-tailed distributi... |
Right now I am learning about analysis of stochastic processes and the Malliavin calculus. It seems though, that most of the theory works for Brownian motion in $\mathbb{R}^n$, and it seems non-obvious to generalize these things to Brownian motion on Riemannian manifolds.
Let $M$ be a Riemannian manifold and let $W \su... |
I know that all groups of order $\leq$ 5 are Abelian and all groups of prime order are Abelian. Are there any other examples? If so is there something special about the orders of these groups?
Yes, such numbers are called
abelian numbers.
A number $n$ is abelian, if and only if it is cube-free and there is no prime pow... |
This is a basic question (I think). I am trying to grasp the idea behind this example, where we define a "logistic function" and use that to work towards the maximum likelihood estimate (MLE).
We have a sample of $n$ people, with recorded data $(x_1,y_1),\ldots,(x_n,y_n)$, where $x_i$ is the BMI and $y_i\in\{0,1\}$ ind... |
Here's some intuition:
The Heine-Cantor theorem tells us that any function between two metric spaces that is continuous on a compact set is also uniformly continuous on that set (see
here for discussion). Next, if $f:X \rightarrow Y$ is a uniformly continuous function, it is easy to show that the restriction of $f$ to ... |
In order to perform an
calculation an exciting
input file called
XML
must be provided.
input.xml
This web page lists all
and elements
that can be used in the input file of an
attributes
calculation:
exciting
are defined according to the
elements
.
general XML conventions
The element is used to set up a self-consistent ... |
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... |
The question is Let $f_n \ge 0$ Be integrable and $f_n \rightarrow f$ a.e. Then $\lim_{n\rightarrow \infty} \mu(f_n)$ exists
My Proof: Firsly, we know that $f_n\rightarrow f$ And $f_n$ Is measurable , so is $f$. Then, $\inf_{m\ge n}f_m \le f_k$ for some $k\ge n$. Similarly, $\sup_{m\ge n}f_m \ge f_k$. Then, we know tha... |
When defining tensor products $M\otimes_R N$ over a commutative ring $R$ one can use a universal property with respect to bilinear maps $M\times N\rightarrow P$, for any $R$-module $P$.
On the other hand, in the general case, for noncommutative rings one has to use balanced maps $M \times N \rightarrow Z$ instead of bi... |
Consider testing hypotheses about the regression coefficients \( \boldsymbol{\beta} \). Sometimes we will be interested in testing the significance of a single coefficient, say \( \beta_j \), but on other occasions we will want to test the joint significance of several components of \( \boldsymbol{\beta} \). In the nex... |
I am currently to create my own volatility smile for cryptocurrency options. I am basically reading the bids and offers and calculating the implied volatilities.
I now want to shape and parametrise my own volatility smile. What is a good way to do it? I tried the Corrado-Su Model, but I was not too happy about the resu... |
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