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While reading chapter 7.1.2 of di Francesco I encountered following definition of character of Verma module:$$\chi_{(c,h)}(\tau)=\text{Tr }q^{L_0 -c/24}$$where $q = e^{2 \pi i \tau}$ and $\tau$ and c are two parameters (c-central charge, $\tau$ - some parameter connected to so called modular invariance). I am trying to... |
Question:
How thick (minimum) should the air layer be between two flat glass surfaces if the glass is to appear bright when 540 mm light is incident normally?
{eq}T_{min} {/eq} = _____ m
What if the glass is to appear dark?
{eq}T_{min-} {/eq} = _____ m
Interference:
Interference is a phenomenon in which two waves inter... |
In fluid dynamics,
wave shoaling is the effect by which surface waves entering shallower water change in wave height. It is caused by the fact that the group velocity, which is also the wave-energy transport velocity, changes with water depth. Under stationary conditions, a decrease in transport speed must be compensat... |
TL;DR
I'd propose that weak force life has a tiny change of existing in environments where particles travel at high speeds. A possible example is the jets produced by an active galactic nucleus. At the high energies (and high speeds) particles reach in these jets, the range of the weak force could be sizably extended t... |
Question:
Two-in-phase loudspeakers that emit sound with the same frequency are placed along a wall and are separated by a distance of {eq}5.00\ m {/eq}. A person is standing {eq}12.0\ m {/eq} away from the wall, equidistant from the loudspeakers. When the person moves {eq}1.00\ m {/eq} parallel to the wall, she experi... |
Fast Logistic Regression
When we are programming Logistic Regression or Neural Networks we should avoid explicit \(for \) loops. It’s not always possible, but when we can, we should use built-in functions or find some other ways to compute it. Vectorizing the implementation of Logistic Regression makes the code highly ... |
Inverse boundary value problems for diffusion-wave equation with generalized functions in right-hand sides Abstract
We prove the unique solvability of the problem on determination of the solution $u(x,t)$ of the first boundary value problem for equation
$$u^{(\beta)}_t-a(t)\Delta u=F_0(x)\cdot g(t), \;\;\; (x,t) \in (0... |
Dimensionality reduction is used to remove irrelevant and redundant features.
When the number of features in a dataset is bigger than the number of examples, then the probability density function of the dataset becomes difficult to calculate.
For example, if we model a dataset \(S = \{x^{(i)}\}_{i=1}^m,\ x \in R^{n}\) ... |
As you have seen, calculating multiple integrals is tricky even for simple functions and regions. For complicated functions, it may not be possible to evaluate one of the iterated integrals in a simple closed form. Luckily there are numerical methods for approximating the value of a multiple integral. The method we wil... |
I have seen two definitions of Beta one is $$\beta = \rho\dfrac{\sigma_{asset}}{\sigma_{market}}$$ Here $\rho$ is the correlated coeffient
another one is$$\beta = \dfrac{r_{expect} - r_{risk\ free}}{r_{market} - r_{risk\ free}}$$I don't know which one is correct or they are equivalent? By the way, here $\sigma_{asset}$... |
And I think people said that reading first chapter of Do Carmo mostly fixed the problems in that regard. The only person I asked about the second pset said that his main difficulty was in solving the ODEs
Yeah here there's the double whammy in grad school that every grad student has to take the full year of algebra/ana... |
Natural waters contain a wide variety of solutes that act together to determine the pH, which typically ranges from 6 to 9. Some of the major processes that affect the acid-base balance of natural systems are:
Contact with atmospheric carbon dioxide Input of acidic gases from volcanic and industrial emissions Contact w... |
№ 8
All Issues Volume 68, № 4, 2016
Ukr. Mat. Zh. - 2016. - 68, № 4. - pp. 435-448
The purpose of this work is to obtain Jackson and converse inequalities of the polynomial approximation in Bergman spaces. Some known results presented for the moduli of continuity are extended to the moduli of smoothness. We proved some... |
@user193319 I believe the natural extension to multigraphs is just ensuring that $\#(u,v) = \#(\sigma(u),\sigma(v))$ where $\# : V \times V \rightarrow \mathbb{N}$ counts the number of edges between $u$ and $v$ (which would be zero).
I have this exercise: Consider the ring $R$ of polynomials in $n$ variables with integ... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
The classical version of this question is for Hamiltonian cycles, but there is probably little difference. I will only consider the version with cycles.
In order for a graph to contain a Hamiltonian cycle, the minimal degree should be at least 2. This is essentially the only obstruction for Hamiltonicity. To state this... |
Portfolio optimization techniques, such as those defined under Modern Portfolio Theory (MPT), are mildly predicated on the assumption of joint normality. Even though there will be a set of portfolio weights which minimizes variance regardless of the underlying distributions, correlation is only a complete measure of as... |
I have read in Bayesian Data Analysis by Andrew Gelman that log predictive density can be used to compare Bayesian models due to its connection to the Kullback-Leibler information.
The log predictive density has an important role in statistical model comparison because of its connection to the Kullback-Leibler informat... |
Third, since $\sf{L} \subseteq \sf{NC}^2$, is there an algorithm to convert any logspace algorithm into a parallel version?
It can be shown (Arora and Barak textbook) given a $t(n)$-time TM $M$, that an oblivious TM $M'$ (i.e. a TM whose head movement is independent of its input $x$) can construct a circuit $C_n$ to co... |
Keeping Track of Element Order in Multiphysics Models
Whenever you are building a finite element model in COMSOL Multiphysics, you should be aware of the element order that is being used. This is particularly important for multiphysics models as there are some distinct benefits to using different element orders for dif... |
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1. Measurement of the ratio of the production cross sections times branching fractions of B c ± → J/ψπ ± and B± → J/ψK ± and ℬ B c ± → J / ψ π ± π ± π ∓ / ℬ B c ± → J / ψ... |
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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 w... |
Chaperone-aided Protein Folding
Surprisingly, unfolded proteins are toxic to the cell because of their potential to form large, difficult-to-degrade aggregates consisting of many proteins. Machinery for safely "catalyzing" protein folding is therefore an essential part of cell functioning.
Chaperones are a class of pro... |
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Displaying entries 21-30 out of 44.
Surface plasmon polariton excitation in Kretschmann configuration
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Excitation of surface plasmon polaritions at the gold-air interface in Kretschmann configuration.
Tutorial models for COMSOL Webinar "Simulating ... |
I asked a question earlier about Saving to the Database, which was very general and about the requirements for a proof when you go through many layers of non-verified systems such as the network and databases.
In this question I am wondering about a more middle-level proof, this time about transforming an object $f : A... |
I'm not sure if this will precisely answer your question concerning "metrics".... but this might have the spirit ofwhat you may be seeking.
Here's an overview of a coordinate-free derivation of the Schwarzschild solution by Robert Geroch.
[
short answer: using symmetries specified by Killing vector fields, construct va... |
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Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
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D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
Since this is my first time writing a blog post here, let me start with a word of introduction. I am a computer scientist at the Tata Institute of Fundamental Research, broadly interested in connections between Biology and Computer Science, with a particular interest in reaction networks. I first started thinking about... |
I'm having a bit of trouble formulating a bijection between the sets $\{0,1\} \times \mathbb N$ and $\mathbb Z$. I understand how to find a bijection between $\mathbb N$ and $\mathbb Z$ using a piecewise function that sends even values of $\mathbb N$ to positive integers and odd values of $\mathbb N$ to negative intege... |
As Lubos Motl and twistor59 explain, a necessary condition for unitarity is that the Yang Mills (YM) gauge group $G$ with corresponding Lie algebra $g$ should be real and have a positive (semi)definite associative/invariant bilinear form $\kappa: g\times g \to \mathbb{R}$, cf. the kinetic part of the Yang Mills action.... |
$L = \dfrac{1}{\pi}\displaystyle \int_{-\infty}^\infty \dfrac{b}{(z-a)^2+b^2} dz = 1$
we take a closed contour on the upper-half complex plane. This means we only consider the $z=a+ib$ pole when finding residues. I know this has to do with the winding number, but can you give a more physical explanation of why we do th... |
Suppose we have a matrix of $n$ by $n$ dimension $M$ is that is
full rank, symmetric, and positive semi-definite, in that $z^TMz \geq 0$ for all $z \in \mathbb{R}^p$. This can be thought of as a covariance matrix in statistics. If I were to take a square partition, would that square partition still be full rank? In exa... |
I was learning ϴ(n) notation in my course "Asymptotic Analysis for Algorithms" when I encountered the following example:
For any non-negative constants $c_1\geq 0,c_2\geq 0,n\geq n_0$ we have the following inequality:
$$c_1\leq\frac{1}{2}-\frac{3}{n}\leq c_2$$
For these constants to satisfy this inequality, will be $c_... |
Show that the two straight lines $x^2(\tan^2 (\theta)+\cos^2 (\theta))-2xy\tan (\theta)+y^2.\sin^2 (\theta)=0$ make with x axis such that the difference of their tangents is $2$.
My Attempt: $$x^2(\tan^2 (\theta) +\cos^2 (\theta))-2xy\tan (\theta) + y^2 \sin^2 (\theta)=0$$
Let $y-m_1x=0$ and $y-m_2x=0$ be the two lines... |
Imagine the speed of light to be $1$ meter per second and the speed of light in the medium with a high refractive index to be $\frac{1}{2}$ meters per second.
If you have a single peak of a wave in the slower medium, that peak must move forwards at speed $\frac{1}{2}$, no matter what angle it's facing. In the faster me... |
Solutions to Try Its
1. 5.5556
2. About 1.548 billion people; by the year 2031, India’s population will exceed China’s by about 0.001 billion, or 1 million people.
3. [latex]\left(0,129\right)[/latex] and [latex]\left(2,236\right);N\left(t\right)=129{\left(\text{1}\text{.3526}\right)}^{t}[/latex]
4. [latex]f\left(x\rig... |
Electronic Journal of Probability Electron. J. Probab. Volume 15 (2010), paper no. 22, 684-709. Poisson-Type Processes Governed by Fractional and Higher-Order Recursive Differential Equations Abstract
We consider some fractional extensions of the recursive differential equation governing the Poisson process, i.e. $\par... |
Define the Nucleus?
An atom consists of the nucleus which is positively charged. The atomic radius is larger than the nucleus’s radius. The mass of an atom is focused on the nucleus. The atom consists of neutrons which have the same mass as protons. The protons and neutrons are bound with each other with a nuclear forc... |
Given a specific function, a parabola in this instance, I can calculate the length of a segment using integrals to sum infinite right angled triangles hypotenuse lengths. My question is, can I reverse the process? If this question has an obvious answer please forgive me as I have just started studying integrals. I am s... |
Summer came and went, and Fall begins at full throttle with a (metric) ton of papers. Eight that we counted — if any was missed, please mention it in the comments!
Efficient Removal without Efficient Regularity, by Lior Gishboliner, Asaf Shapira (arXiv). Obtaining efficient removal lemmata for graphs pattern (such as t... |
Suppose you have three positive integers $a, b, c$ that form a Pythagorean triple:\begin{equation} a^2 + b^2 = c^2. \tag{1}\label{1}\end{equation}Additionally, suppose that when you apply Euler's totient function to each term, the equation still holds:$$ \phi(a^2) + \phi(b^2) = \phi(c^2). \tag{2}\label{2}$$One way this... |
I am trying to read my probability book on the "Strong Law of Large Numbers", and came across this example that is really confusing me.
Let $X_i$ be a sequence of independent uniformly distributed random variables in $[0, 1]$ and $Y_n = \min(X_1, ..., X_n)$. Show that $Y_n$ converges to zero with probability 1.
The boo... |
I'm stuck on how to evaluate the following using L'Hôpital's rule:
$$\lim_{x \to \infty}\left(1 + \frac{2}{x}\right)^{3x}$$
This is a problem that I encountered on Khan Academy and I attempted to understand it using the resources there. Here are the tips given for the problem; the portion that I'm having trouble unders... |
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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 in... |
Motivation: It is a well-known fact that $ay''+by'+cy=0$ has solutions which are found from substituting the ansatz $y=e^{\lambda t}$ into the DEqn. It turns out that we replace the calculus problem $ay''+by'+cy=0$ with the algebra problem of solving the characteristic equation $a\lambda^2+b\lambda+c=0$. When the solut... |
Although this questions is very much math related, I posted it in Physics since it is related to variational (Lagrangian/Hamiltonian) principles for dynamical systems. If I should migrate this elsewhere, please tell me.
Often times, in graduate and undergraduate courses, we are told that we can only formulate the Lagra... |
Definition:Symmetric Difference/Notation
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Notation for Symmetric Difference
There is no standard symbol for symmetric difference. The one used here, and in general on $\mathsf{Pr} \infty \mathsf{fWiki}$:
$S * T$ The following are often found for $S * T$: $S \oplus T$ $S + T$ $S \mathop ... |
How disheartening it is to know that many of the advanced knowledge in science and mathematics and astronomy and medicine that we know today are said to be the discoveries of Europeans while the truth is that long before the west even came out of Stone Age, ancient Indian sages and scholars had not only discovered them... |
A spacetime diagram might help elaborate on the comment and answer you have already received.
I am going to use a spacetime diagram on rotated graph paperso that we can visualize the time and space intervals.
Let each light-clock diamond represent "0.1 sec".
Using Minkowski-right triangle $OPQ$, Alice has velocity $v_{... |
Your score is simply the sum of difficulties of your solved problems. Solving the same problem twice does not give any extra points. Note that Kattis' difficulty estimates vary over time, and that this can cause your score to go up or down without you doing anything.
Scores are only updated every few minutes – your sco... |
I have a set of discrete points (at most a single $y$ value for a given $x$) and I need to find two parallel lines which contain all of these points and minimize the distance between them. Note that the lines do not have to be parallel with the $x$ axis as in the picture, they can have arbitrary angle. Is there a well ... |
Let \((a,b),(c,d)\) be ordered pairs of natural numbers. We consider them equivalent, if there exist a natural number \(h\) such that one ordered pair can be obtained from the other ordered pair by adding \(h\) to both natural numbers of that pair, formally
\[(a,b)\sim (c,d)\quad\Longleftrightarrow\quad\begin{cases}(a+... |
Tverberg plus minus Connections for Women Workshop: Geometric and Topological Combinatorics August 31, 2017 - September 01, 2017 Speaker(s):Imre Barany (Alfréd Rényi Institute of Mathematics) Location:MSRI: Simons Auditorium Tags/Keywords
Tverberg's theorem
sign conditions
Primary Mathematics Subject Classification Sec... |
For anyone viewing this question who is not familiar with the notion of Induced EMF in the coil of wire let me briefly explain what i understood by it.
EMF is induced inside a coil of wire whenever you change the environment of coil-magnetic field system. That means that if you change the magnetic field that it sits in... |
Lets say we have following case:
Probability of bring a drunk driver = $0.10$
Probability of a drinking test coming positive = $0.30$
Probability of a drinking test coming negative, given the subject was not drunk = $0.90$
Then by Bayes theorem,
$$P(Not Drunk|Negative Test) = \frac{P(Negative Test|Not Drunk) \times P(N... |
I am trying to find the frequency of the artifact on the MRI image of the knee below both manually and with ImageJ:
As you can see the artifact results in a bar pattern extending horizontally along the image - i.e. a spike artifact.
After transforming to Fourier space, there are a couple of dots along the x-axis that s... |
Northern Illinois Center for Accelerator and Detector Development Research Projects Detector Development Group Detector Development Group
Our detector group works toward the development of the next linear collider. The group focuses on the design and prototyping of two collider components: a hadron calorimeter and a ta... |
Starting from special relativity, here I see
the de Broglie approximation is valid only if $m_0=0$. Derivation:
$E^2=P^2C^2+m_0^2C^4$. Here we put Plank-Einstein relation $E=h\nu=h\frac{C}{\lambda}$. Finally,
$\lambda=\frac{h}{\sqrt{P^2+m_0^2C^2}} \hspace{2cm} (1)$.
If $m_0=0$ then $\lambda=\frac{h}{p}$ (de Broglie app... |
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1. Polybrominated diphenyl ethers, 2,2′,4,4′,5,5′- hexachlorobiphenyl (PCB-153), and p, p ′-dichlorodiphenyldichloroethylene (p, p ′-DDE) concentrations in sera collected... |
Acoustic Topology Optimization with Thermoviscous Losses Today, guest blogger René Christensen of GN Hearing discusses including thermoviscous losses in the topology optimization of microacoustic devices.
Topology optimization helps engineers design applications in an optimized manner with respect to certain
a priori o... |
I'm developing an application to calculate the optimal build order for a strategy game. While doing so, I stumbled over an interesting problem which might be applicable to other cases as well. I will give my specific problem below as example, but I wan't to ask for an general answer. Therefore, i will give formulate th... |
Gravitational Force Exerted by a Rod
In this lesson, we'll derive a formula which will allow us to calculate the gravitational force exerted by a rod of length \(L\) on a particle a horizontal distance \(x\) away from the rod as illustrated in Figure 1. We'll assume that the width and depth of the rod are negligible an... |
Green's Theorem allows us to convert the line integral into a double integral over the region enclosed by \(C\). The discussion is given in terms of velocity fields of fluid flows (a fluid is a liquid or a gas) because they are easy to visualize. However, Green's Theorem applies to any vector field, independent of any ... |
What helps to solve your problem is the rule ${\rm vec}\{A \cdot {\rm diag}(b) \cdot C^T\} = (C \diamond A)\cdot b$, where
${\rm vec}\{X\}$ is the vectorization operator that rearranges the elements of a matrix $X \in \mathbb{R}^{m \times n}$ into a vector $\in \mathbb{R}^{m \cdot n \times 1}$ The $\diamond$ operator i... |
https://doi.org/10.1351/goldbook.M03774
Defined by the equation: \[a_{\pm }=\mathrm{e}^{(\mu _{\text{B}}- \mu _{\text{B}}^{\unicode{x29B5}})\ \nu \ R\ T}\] where \(\mu _{\text{B}}\) is the @C01032@ of the solute B in a solution containing B and other species. The nature of B must be clearly stated: it is taken as a gro... |
Asteroid LauncherThe ship sneaks into the asteroid belt and starts manufacturing engines on the asteroids. When enough is made, it launches them at the Earth and/or other targets.Sure the Earth forces can try and blow them up but that's not really going to help as it just changes a single shot round into a shotgun roun... |
Maclaurin polynomials and series
In this lesson, we're going to focus on developing a technique for
approximating the value of any arbitrary function \(f(x)\) at each value of \(x\) such that \(f(x)\) is smooth and continuous for all \(x\) values. How can we approximate \(f(x)\)? We'll approximate the value of \(f(x)\)... |
The fundamental thermodynamic equations follow from five primary thermodynamic definitions and describe internal energy, enthalpy, Helmholtz energy, and Gibbs energy in terms of their natural variables. Here they will be presented in their differential forms.
Introduction
The fundamental thermodynamic equations describ... |
Article
Keywords: $M$-estimator; generalized linear models; pseudolinear models
Summary: Real valued $M$-estimators $\hat{\theta }_n:=\min \sum _1^n\rho (Y_i-\tau (\theta ))$ in a statistical model with observations $Y_i\sim F_{\theta _0}$ are replaced by $\mathbb{R}^p$-valued $M$-estimators $\hat{\beta }_n:=\min \sum ... |
Equilibrium and Detailed Balance Equilibrium and Detailed Balance Equlibrium has a very precise meaning in statistical physics, which also applies to biology. Equilibrium describes the average behavior (averaged over many systems under identical conditions) in which there is no net flow of material, probability or reac... |
An integral is useful for finding the area underneath a function. Let \(f(x)\) be any arbitrary function such that it is smooth and continuous at every point. To find the area underneath \(f(x)\), we must go through several steps. First, we'll start off by drawing an \(n\) (where \(n\) is any positive integer) number o... |
Cantor's diagonal method shows that the set $S=\{x\in \Bbb R|x \in [0,1)\}$ is uncountably infinite, because there is no bijection between the set $S$ and the set of natural number $\Bbb N$.
I came up with this method of mapping the set $S$ to $\Bbb N$. It should be wrong, but I don't know where.
We start with any $x \... |
COMSOL 4.4 Brings Particle-Field and Fluid-Particle Interactions
The trajectories of particles through fields can often be modeled using a one-way coupling between physics interfaces. In other words, we can first compute the fields, such as an electric field, magnetic field, or fluid velocity field, and then use these ... |
Welcome to The Riddler. Every week, I offer up problems related to the things we hold dear around here: math, logic and probability. There are two types: Riddler Express for those of you who want something bite-sized and Riddler Classic for those of you in the slow-puzzle movement. Submit a correct answer for either,
1... |
I've been trying to understand what exactly is meant by parametrisation invariance of the Jeffreys prior.
Already I've read here that invariance is technically not the best term to use, and that it's more a case of covariance. My understanding of covariance is that it describes the property of transforming in a particu... |
Unfortunately, various definitions of Henry’s law and the corresponding proportionality constant $H$ or $K_\mathrm H$ exist. (For several definitions and corresponding parameter values, see Sander, R. Compilation of Henry’s law constants (version 4.0) for water as solvent.
Atmos. Chem. Phys. 2015, 15, 4399–4981.) There... |
Skills to Develop
In this section students will:
Simplify rational expressions. Multiply rational expressions. Divide rational expressions. Add and subtract rational expressions. Simplify complex rational expressions.
A pastry shop has fixed costs of \($280\) per week and variable costs of \($9\) per box of pastries. T... |
The growth of entire functions in the terms of generalized orders Abstract
Let $\Phi$ be a convex function on $[x_0,+\infty)$ such that$\frac{\Phi(x)}x\to+\infty$, $x\to+\infty$, $f(z)=\sum_{n=0}^\infty a_nz^n$ — a transcendental entire function, let $M(r,f)$ be the maximum modulus of $f$ and let
$$\rho_\Phi(f)=\limsup... |
Ok, well. One of the best way to understand a proof is to reproduce it via free recall after glancing over the basic components of the proof.
So the theorem is:
Let a and b be integers; let $a>b$. Applying Euclidean Algorithm to find the GCD will take n steps. The theorem says that if b has $d$ digits, then $n\leq 5d$.... |
Lesson Overview
In this lesson, we'll derive a formula known as Green's Theorem. This formula is useful because it gives
us a simpler way of calculating a specific subset of line integral problems—namely, problems in which the curve is closed (plus a few extra criteria described below). We won't concern ourselves with ... |
Let $V$ be a $\mathbb{R}$-vector space. Let $\Phi:V^n\to\mathbb{R}$ a multilinear symmetric operator.
Is it true and how do we show that for any $v_1,\ldots,v_n\in V$, we have:
$$\Phi[v_1,\ldots,v_n]=\frac{1}{n!} \sum_{k=1}^n \sum_{1\leq j_1<\cdots<j_k\leq n} (-1)^{n-k}\phi (v_{j_1}+\cdots+v_{j_k}),$$ where $\phi(v)=\P... |
Hello one and all! Is anyone here familiar with planar prolate spheroidal coordinates? I am reading a book on dynamics and the author states If we introduce planar prolate spheroidal coordinates $(R, \sigma)$ based on the distance parameter $b$, then, in terms of the Cartesian coordinates $(x, z)$ and also of the plane... |
I get the parameters (long-term mean, volatility, mean-reversion speed, correlation) of two correlated Ornstein-Uhlenbeck processes via a likelihood estimation from hourly data. If I want to transform these to use them to create a daily - instead of hourly - simulation (tree or Monte Carlo), what do I have to do? Thank... |
№ 8
All Issues Volume 60, № 10, 2008 Continuity with respect to initial data and absolute-continuity approach to the first-order regularity of nonlinear diffusions on noncompact manifolds
Ukr. Mat. Zh. - 2008. - 60, № 10. - pp. 1299–1316
We study the dependence on initial data for solutions of diffusion equations with ... |
Skills to Develop
Solve a system of nonlinear equations using substitution. Solve a system of nonlinear equations using elimination. Graph a nonlinear inequality. Graph a system of nonlinear inequalities.
Halley’s Comet (Figure \(\PageIndex{1}\)) orbits the sun about once every \(75\) years. Its path can be considered ... |
Seeing that in the Chomsky Hierarchy Type 3 languages can be recognised by a DFA (which has no stacks), Type 2 by a DFA with one stack (i.e. a push-down automaton) and Type 0 by a DFA with two stacks (i.e. with one queue, i.e. with a tape, i.e. by a Turing Machine), how do Type 1 languages fit in...
Considering this ps... |
And I think people said that reading first chapter of Do Carmo mostly fixed the problems in that regard. The only person I asked about the second pset said that his main difficulty was in solving the ODEs
Yeah here there's the double whammy in grad school that every grad student has to take the full year of algebra/ana... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
FELIPE Online Manual The following table provides links to webpages for various chapters of the
User Manual. The full manual can be accessed as a pdf file
here.
Introduction
FELIPE (Finite Element Learning Package) is a software package whose
primary objective is to help students understand the finite element method
in... |
Answer
C
Work Step by Step
Theoretical yield: $125\ g\ Al_4C_3\div 143.96\ g\ Al_4C_3/mol\ Al_4C_3\times \dfrac{3\ mol\ CH_4}{1\ mol\ Al_4C_3}\times16.04\ g\ CH_4/mol\ CH_4=41.78\ g\ CH_4$ Percent yield: $13.6\div41.78\times100\%=32.55\%$
You can help us out by revising, improving and updating this answer.Update this a... |
Seeing that in the Chomsky Hierarchy Type 3 languages can be recognised by a DFA (which has no stacks), Type 2 by a DFA with one stack (i.e. a push-down automaton) and Type 0 by a DFA with two stacks (i.e. with one queue, i.e. with a tape, i.e. by a Turing Machine), how do Type 1 languages fit in...
Considering this ps... |
Infinite Limits
Evaluating the limit of a function at a point or evaluating the limit of a function from the right and left at a point helps us to characterize the behavior of a function around a given value. As we shall see, we can also describe the behavior of functions that do not have finite limits.
We now turn our... |
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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... |
The Fundamental Theorem of Line Integrals
Consider the force field representing the wind shown below
You are a pilot attempting to minimize the work your engines need to do. Does it matter which path you take? Clearly the red path goes with the wind and the green path goes against the wind. With this vector field, work... |
Data
I have three $N \times N$ complex hermitian matrices $A=xx^{H}$,$R=rr^{H}$ and a positive-definite matrix $B$. Here $x$ and $r$ are two $N \times 1$ complex vectors. Let $\lambda_{i}, 1\leq i\leq N$ denotes the N eigenvalues of B which are also positive. Clearly $A$ and $R$ are two rank one positive semi-definite ... |
class
LinearMechanism¶ ↑
Syntax:
lm = new LinearMechanism(c, g, y, [y0], b)
section lm = new LinearMechanism(c, g, y, [y0], b, x)
lm = new LinearMechanism(c, g, y, [y0], b, sl, xvec, [layervec])
lm = new LinearMechanism(pycallable, c, g, y, ...)
Description:
Adds linear equations to the tree matrix current balance equa... |
The objective of this project is to evaluate the quality of human movements from visual information which has use in a broad range of applications, from diagnosis and rehabilitation to movement optimisation in sports science. Observed movements are compared with a model of normal movement and the amount of deviation fr... |
To start off, I was looking at the following ingeniously made form of the Gamma function:
$$\Gamma(z+1)=\lim_{n\to\infty}\frac{n!(n+1)^z}{(1+z)(2+z)\cdots(n+z)}$$
which lies on the back of
$$1=\lim_{n\to\infty}\frac{n!(n+1)^z}{(n+z)!}$$
for all integer $z$. One them multiplies through by $z!$ and use the recursive form... |
Consider a $C^k$, $k\ge 2$, Lorentzian manifold $(M,g)$ and let $\Box$ be the usual wave operator $\nabla^a\nabla_a$. Given $p\in M$, $s\in\Bbb R,$ and $v\in T_pM$, can we find a neighborhood $U$ of $p$ and $u\in C^k(U)$ such that $\Box u=0$, $u(p)=s$ and $\mathrm{grad}\, u(p)=v$?
The tog is a measure of thermal resist... |
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