text
stringlengths
256
16.4k
ISSN: 1531-3492 eISSN: 1553-524X All Issues Discrete & Continuous Dynamical Systems - B July 2010 , Volume 14 , Issue 1 Select all articles Export/Reference: Abstract: The purpose of this paper is to study the relations between different concepts of dispersive solution for the Vlasov-Poisson system in the gravitational...
Difference between revisions of "Middle attic" Line 7: Line 7: * [[correct]] cardinals, [[reflecting | $V_\delta\prec V$]] and the [[reflecting#Feferman theory | Feferman theory]] * [[correct]] cardinals, [[reflecting | $V_\delta\prec V$]] and the [[reflecting#Feferman theory | Feferman theory]] * [[reflecting#$\Sigma_...
Search Now showing items 1-10 of 33 The ALICE Transition Radiation Detector: Construction, operation, and performance (Elsevier, 2018-02) The Transition Radiation Detector (TRD) was designed and built to enhance the capabilities of the ALICE detector at the Large Hadron Collider (LHC). While aimed at providing electron...
SCM Repository View of /branches/vis12/test/unicode-cheatsheet.diderot Revision File size: 782 byte(s) 1927- ( download) ( annotate) Sat Jun 23 18:09:16 2012 UTC(7 years, 3 months ago) by jhr File size: 782 byte(s) converting to use "image" instead of "load" for image nrrd loading /* useful unicode characters for Dider...
Advanced Monitoring Strategy The algorithm incorporated in OptiLayer takes various criteria into account: The strategy is available at: Results --> Monitor --> Strategy button --> Strategy 4 \[ A=V_\max-V_\min \] \[ S_{in}= \frac{V_\max-V_{in}}{A}\cdot 100\%, \]if the first extremum is maximum;\[ S_{in}= \frac{V_{in}-V...
NonEquilibriumHeatExchange¶ class NonEquilibriumHeatExchange( configuration, heating_power, heat_source, heat_sink, exchange_interval=1, update_profile_interval=0, profile_resolution=None)¶ A class that implements a heat flow by constant heating power exchange technique via a hook function. Parameters: configuration( B...
Question: A {eq}5.00 g {/eq} bullet moving with an initial speed of {eq}410 \frac{m}{s} {/eq} is fired into and passes through a {eq}1.00 kg {/eq} block. The block, initially at rest on a frictionless, horizontal surface, is connected to a spring of force constant {eq}910 \frac{N}{m} {/eq}. (a) If the block moves {eq}5...
OptiLayer Targets: Conventional Targets OptiLayer allows you to specify all possible target characteristics. Target Window can be used to enter and to edit target data. In the information fields you should specify the number of spectral points at which target data will be entered, the incidence angle(s) at which data w...
Woodin Cardinal Woodin cardinals are a generalization of the notion of strong cardinals and have been used to calibrate the exact proof-theoretic strength of the Axiom of Determinacy. Woodin cardinals are weaker than superstrong cardinals in consistency strength and fail to be weakly compact in general, since they are ...
I know that bond angle decreases in the order $\ce{H2O}$, $\ce{H2S}$ and $\ce{H2Se}$. I wish to know the reason for this. I think this is because of the lone pair repulsion but how? Here are the $\ce{H-X-H}$ bond angles and the $\ce{H-X}$ bond lengths: \begin{array}{lcc} \text{molecule} & \text{bond angle}/^\circ & \te...
Show, that every continious function $f:\mathbb{R}P^2\to S^1$ is a homotopy to a constant function. (Hint: Has $f$ a lift $\tilde{f}:\mathbb{R}P^2\to\mathbb{R}$) Hello, I want to solve this problem, but I am kinda stuck and the given hint just confuses me even more... I would appreciate, if someone could clarify this a...
I am working on a project to approximate numerically the solution $X_t$ of a stochastic differential equation (SDE) using the Euler method. I have do to this for the Brownian motion with drift. I am asked to stimulate $N$ paths under both the P and Q measure on the interval $[0,T]$. The pseudo code is as follows: for i ...
Let $X$ be the collection of all sequences of positive integers. If $x=(n_j)_{j=1}^\infty$ and $y=(m_j)_{j=1}^\infty$ are two elements of $X$, set $$k(x,y)=\inf\{j:n_j\neq m_j\}$$ and $$d(x,y)= \begin{cases} 0 & \text{if $x=y$} \\ \frac{1}{k(x,y)} & \text{if $x \neq y$} \end{cases}$$ We know that $d$ is a metric on $X$...
Consider $\sum_{n=1}^{\infty}nx^n\sin(nx)$. Find $R > 0$ such that the series is convergent for all $x\in(-R,R)$. Calculate the sum of the series. I could find the radius of convergence is $R=1$, hence for any $x\in (-1,1)$ the series is continuous and convergent, However, I have some problem in finding the exact sum o...
Short version: Is it possible to arrange the fluxes for the Kagomé lattice with triangle flux $\phi_\triangle=\frac{\pi}2$ and hexagon flux $\phi_{hex}=0$ using a single unit cell? Longer version: I am looking at fermionic mean field theories on the Kagomé lattice that describe a chiral spin liquid state for spin-1/2. ...
VINAYAK B KAMBLE Articles written in Bulletin of Materials Science Volume 40 Issue 7 December 2017 pp 1291-1299 Monovalent ion doped lanthanum cobaltate La$_{1−x}$Na$_x$CoO$_3$ ($0 \leq x \leq 0.25$) compositions were synthesized by the nitrate–citrate gel combustion method. All the heat treatments were limited to belo...
Definition- An ellipse is a curve on a plane such that the sum of the distances to its two focal points is always a constant quantity from any chosen point on that curve. The ellipse belongs to the family of circles with both the focal points at the same location. In an ellipse if you make the minor and major axis of t...
I am studying a book about relativistic equations and special relativity, and I keep seeing $\sqrt{1-{v^2/c^2}}$ everywhere. It is not, as with most of the concepts in special relativity, simply a mathematical construct; it is a logical consequence of accepting the experimental fact that the speed of light is the same ...
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response) Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ...
Search Now showing items 1-10 of 108 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 ...
Difference between revisions of "Wholeness axioms" Line 8: Line 8: language $\{\in,j\}$, augmenting the usual language of set language $\{\in,j\}$, augmenting the usual language of set theory $\{\in\}$ with an additional unary function symbol $j$ theory $\{\in\}$ with an additional unary function symbol $j$ − to repres...
ISSN: 1930-8337 eISSN: 1930-8345 All Issues Inverse Problems & Imaging February 2010 , Volume 4 , Issue 1 Select all articles Export/Reference: Abstract: We extend the classical spectral estimation problem to the infinite-dimensional case and propose a new approach to this problem using the Boundary Control (BC) method...
I would approach this by building a general equilibrium model of the economy. Here is the high-level idea: There is a single perishable consumption good and all prices are measured in terms of it. There is a fully equity financed firm with one unit of share outstanding. The firm pays a continuous dividend at a stochast...
Basic Examples on Parabolas Set 3 Example – 12 A circle on any focal chord of a parabola as diameter cuts the curve again in P and Q. Show that PQ passes through a fixed point. Solution: In example -8, we wrote the equation of a circle described on any focal chord as diameter in terms of one of its end points \({t_0}\)...
Difference between revisions of "Con ZFC" Line 1: Line 1: − {{DISPLAYTITLE: Con(ZFC)}} + {{DISPLAYTITLE: Con(ZFC)}} + − The + The Gödel theorem that $\ZFC$ is consistent, then it does not prove Con(ZFC), and so the addition of this axiom is strictly stronger than ZFCalone. − + − + == Consistency hierarchy == == Consist...
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...
Definition:Set Theory Contents Definition There are several "versions" of set theory, all of which share the same basic ideas but whose foundations are completely different. A popular alternative (and inaccurate) definition describes this as a non-formalized definition of set theory which describes sets and the relatio...
Naidu, Thirupathi D and Kumar, AV and Chakradhar, RPS and Ratnakaram, YC (2006) Spectral studies of $Sm^{3+}$ and $Dy^{3+}$ doped lithium cesium mixed alkali borate glasses. In: International Symposium on Non Oxide and new Optical Glasses (ISNOG), 10 - 14 April, 2006, Indian Institue of Science, Bangalore. PDF Chakradh...
Calculate the longest wavelength of the electromagnetic radiation emitted by the hydrogen atom in undergoing a transition from the n = 7 level. Solution: Show me the final answer↓ The electron will go from n = 7 to the n = 6 level. We will use the following equation to figure out the frequency. (Where E is energy, h is...
This question already has an answer here: I was given the following problem: Let $f:[0,1] \to \Bbb R $ be a differentiable function on $[0,1]$ such that $f(0)=0$, and $\forall x \in[0,1]$ : $\lvert f'(x)\rvert \le \lvert f(x)\rvert$. Prove that $f(x)=0$ $\forall x \in [0,1]$. I tried to solve it using mean value theore...
Kodai Mathematical Journal Kodai Math. J. Volume 27, Number 3 (2004), 354-359. Mean growth of the derivative of a Blaschke product Abstract If $B$ is a Blaschke product with zeros $\{a_n\}$ and if $\sum_n(1-|a_n|)^{\alpha}$ is finite for some $\alpha \in (1/2,1]$, then limits are found on the rate of growth of $\int_0^...
As whuber has commented: the Kolmogorov-Smirnov test is only valid as a comparison against a fully specified distribution. You cannot use it to compare an observed distribution against a distribution whose parameters have been estimated based on your observed sample. If you do so, your p-values will not be uniformly di...
Resolution Of Vectors RESOLUTION OF A VECTOR IN A GIVEN BASIS Consider two non-collinear vectors \(\vec a\,\,{\text{and}}\,\,\vec b\); as discussed earlier, these will form a basis of the plane in which they lie. Any vector \(\vec r\) in the plane of \(\vec a\,\,{\text{and}}\,\,\vec b\) can be expressed as a linear com...
It is already known, that for $latex { Y\in {\mathbb R} }&fg=000000$ and $latex { X \in {\mathbb R}^{p} }&fg=000000$, the regression problem $latex \displaystyle Y = f(\mathbf{X}) + \varepsilon, &fg=000000$ when $latex { p }&fg=000000$ is larger than the data available, it is well-known that the curse of dimensionality...
December 14th, 2018, 08:02 AM # 1 Newbie Joined: Dec 2018 From: Germany Posts: 2 Thanks: 0 Ackermann function modulo calculations There's a programming puzzle at Programming Praxis in which one is to calculate values of the Ackermann function A(m, n). One comment was particularly helpful, you can see it . here The func...
Several online sources (e.g. Wikipedia, the nLab) assert that the Gelfand representation defines a contravariant equivalence from the category of (non-unital) commutative $C^{\ast}$-algebras to the category of locally compact Hausdorff (LCH) spaces. This seems wrong to me. The naive choice is to take all continuous map...
Finite groups with some weakly $s$-permutably embedded and weakly $s$-supplemented subgroups Integer solutions to x^2 + y^2 = z^2 - k for a fixed integer value k A two-step conditionally bounded numerical integrator to approximate some traveling-wave solutions of a diffusion-reaction equation A two-step conditionally b...
September 13th, 2018, 06:33 PM # 1 Newbie Joined: Aug 2018 From: United States Posts: 2 Thanks: 0 geometric transformations Matt wants to reflect a shape over the x-axis and then reflect it over the y-axis. Cathy says that this would be the same as rotating the shape 180 degrees. Do you agree or disagree with Cathy? Ju...
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...
Category:Zermelo-Fraenkel Class Theory In $\textrm{ZF}$, classes are written using class builder notation: $\left\{{x : P \left({x}\right)}\right\}$ \(\displaystyle y \in \left\{ {x: P \left({x}\right)}\right\}\) \(\quad \text{for} \quad\) \(\displaystyle P \left({y}\right)\) \(\displaystyle \left\{ {x: P \left({x}\rig...
Using the Flow Coefficient to Characterize the Performance of a Piping System Fluid flow through a piping system that consists of components such as valves, fittings, heat exchangers, nozzles, filters, and pipelines will result in a loss of energy due to the friction between the fluid and internal surfaces, changes in ...
I recently came across this in a textbook (NCERT class 12 , chapter: wave optics , pg:367 , example 10.4(d)) of mine while studying the Young's double slit experiment. It says a condition for the formation of interference pattern is$$\frac{s}{S} < \frac{\lambda}{d}$$Where $s$ is the size of ... The accepted answer is c...
Can someone give me suggestions how can I construct a 2-tape Turing machine which simulates PDA ? closed as unclear what you're asking by Evil, David Richerby, Rick Decker, Juho, hengxin Jul 9 '17 at 13:00 Please clarify your specific problem or add additional details to highlight exactly what you need. As it's current...
Notes from 9 Sep REPL tip The repl.it environment requires there to be a main function, evenif you only want to experiment with other functions. This isn’t toomuch of a problem, you can just define main = putStrLn "Okay" but the minimal main function is actually main = return () so use that as a placeholder if you don’...
Trapping of Magnetic Flux in Bi-2223 Ceramic Superconductors Doped with α-Al 2 O 3 Nanoparticles 38 Downloads Abstract By combining experimental results and a simple model, we offer here an explanation for the role played by the low-angle grain boundaries and the doping with α-Al 2 O 3 nanoparticles in the trapping of ...
Seed If $j:V \to M$ is an elementary embedding and $a \in j(D)$ for some set $D$, then $a$ is a seed for the measure $\mu$ on $D$ defined by $X \in \mu \iff X \subseteq D$ and $a \in j(X)$. In this case, we say that $a$ generates $\mu$ via $j$. If $b=j(f)(a)$ for some function $f \in V$, then we say that $a$ generates ...
Does anyone here understand why he set the Velocity of Center Mass = 0 here? He keeps setting the Velocity of center mass , and acceleration of center mass(on other questions) to zero which i dont comprehend why? @amanuel2 Yes, this is a conservation of momentum question. The initial momentum is zero, and since there a...
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ...
Difference between revisions of "Linear representation theory of symmetric group:S5" (→Character table) (→Family contexts) (9 intermediate revisions by the same user not shown) Line 8: Line 8: ==Summary== ==Summary== + {| class="sortable" border="1" {| class="sortable" border="1" ! Item !! Value ! Item !! Value |- |- −...
I am a Postdoc at the Faculty of Mathematics of the Bielefeld University. I am a member of the research group Groups and Geometry, and my mentor is Prof. Kai-Uwe Bux. I am supported by my own grant within the Schwerpunktprogram "Geometry at Infinity" of the DFG. Next year I will start to work on my project "Fibring" fu...
A new version of Unicode Technical Note #28, UnicodeMath, a Nearly Plain-Text Encoding of Mathematics is now available. It updates several topics and references and uses the name UnicodeMath instead of Unicode linear format. Since there are several math linear formats, such as Nemeth braille, [La]TeX, and AsciiMath, ha...
The OP first stated the problem as: Knowing $K_\mathrm{s} = 6\cdot10^{-38}$ for $\ce{Fe(OH)3}$ in neutral solutions, calculate the minimum pH of an acidic solution in order to completely dissolve $\pu{10 mg}$ of $\ce{Fe(OH)3}$. Data: $V = \pu{0.1 L}$. I took that to mean that acid was added to a solution containing 10 ...
Among many fascinating sides of mathematics, there is one that I praise, especially in teaching at the boundary between undergraduate/graduate level : the parallels that can be drawn between a "Continuous world" and a "Discrete world". A concept, an explanation, etc. in one these worlds that can be "paralleled" into th...
I can't seem to get anywhere with this problem. Any hints would be much appreciated: Suppose that $p$ and $q$ are distinct primes satisfying $p, q \equiv 1 \bmod{4}$. Show that the congruence $x^2 \equiv -1 \bmod {pq}$ has a solution. Mathematics Stack Exchange is a question and answer site for people studying math at ...
Examples On Vector Dot Product Set-3 Example – 21 If a, b, c are the lengths of the sides of \(\Delta ABC\) opposite to the angles A, B and C respectively, prove using vector methods that \[a(1 + \cos A) + b(1 + \cos B) + c(1 + \cos C) = (a + b + c)(\cos A + \cos B + \cos C)\] Solutions: We have, by the triangle law, \...
Learning Objectives Explain the concepts of stress and strain in describing elastic deformations of materials Describe the types of elastic deformation of objects and materials A model of a rigid body is an idealized example of an object that does not deform under the actions of external forces. It is very useful when ...
Please assume that this graph is a highly magnified section of the derivative of some function, say $F(x)$. Let's denote the derivative by $f(x)$.Let's denote the width of a sample by $h$ where $$h\rightarrow0$$Now, for finding the area under the curve between the bounds $a ~\& ~b $ we can a... @Ultradark You can try d...
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...
Examples on Point and Angle of Intersection of Two Straight Lines Example – 5 Find the equation to the straight line which passes through (3, –2) and is inclined at \({{60}^{\circ }}\) to the line \(\sqrt 3 \,x + y = 1.\) Solution: Observe carefully that there will be two such lines. Denote the two lines by \({L_1}\,\,...
Search Now showing items 1-1 of 1 Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV (Elsevier, 2014-09) Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ...
Search Now showing items 1-1 of 1 Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV (Elsevier, 2014-09) Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ...
I've wondered why the tape/tapes are not part of the formal definition of a Turing Machine. Consider, for example, the formal definition of a Turing machine on Wikipedia page. The definition, following Hopcroft and Ullman, includes: the finite set of states $Q$, the tape alphabet $\Gamma$, the blank symbol $b \in \Gamm...
Vector Equations Of Lines VECTOR EQUATIONS OF A LINE Consider a straight line passing through the point \(A(\vec{a})\) and parallel to the vector \(\vec{b}.\) Any point \(\vec{r}\) on this line can be written in terms of real parameter \(\lambda \). \[\begin{align}& \vec{r}=\overrightarrow{OA}+\overrightarrow{AR} \\\\ ...
The standard Newtonian centripetal acceleration is: $$g = \frac{V^2}{R}$$ where \(V\) is the rectilinear velocity being bent into a circular motion and \(R\) is the radius of the circular trajectory that it is being bent into. When the velocity is closer to lightspeed, the Lorentzian gamma-factor gets involved: $$\gamm...
Does anyone here understand why he set the Velocity of Center Mass = 0 here? He keeps setting the Velocity of center mass , and acceleration of center mass(on other questions) to zero which i dont comprehend why? @amanuel2 Yes, this is a conservation of momentum question. The initial momentum is zero, and since there a...
Back in January this year I was commuting to work and routinely opened the daily coding problem email: “Good morning! Here’s your coding interview problem for today. […] Assume you have access to a function toss_biased() which returns 0 or 1 with a probability that’s not 50-50 (but also not 0-100 or 100-0). You do not ...
Potential energy From Academic Kids Potential energy ( U, or E p), a kind of scalar potential, is energy by virtue of matter being able to move to a lower-energy state, releasing energy in some form. For example a mass released above the Earth has energy resulting from the gravitational attraction of the Earth which is...
I'm attempting to prove that for a closed, path-connected, volume $V$ of $\mathbb{R}^3$, $$\iiint_{V} (\operatorname{div} F) \, \text{d}V = \iint_{\partial V} F \cdot \mathbf{\hat n} \, \text{d}S$$ Where $F : \mathbb{R}^3 \to \mathbb{R}^3$ is any differentiable function. Is there anything wrong with my proof? Can I mak...
Sum of Reciprocals in Base 10 with Zeroes Removed Jump to navigation Jump to search Theorem The infinite series $\displaystyle \sum_{P \left({n}\right)} \dfrac 1 n$ where $P \left({n}\right)$ is the propositional function: $\forall n \in \Z_{>0}: P \left({n}\right) \iff$ the decimal representation of $n$ contains no in...
ECE 641 Fall 2008 Professor Bouman Hi everybody! Here is an example of a page_ECE641Fall2008bouman. Getting started Rhea works very much like Kiwi. So if you want to learn how to edit this Rhea wiki, you can watch the Kiwi instructional video. Configuration settings list MediaWiki FAQ MediaWiki release mailing list Err...
ISSN: 1937-5093 eISSN: 1937-5077 Kinetic & Related Models September 2015 , Volume 8 , Issue 3 Issue on the workshop “Electromagnetics-Modelling, Simulation, Control and Industrial Applications" Select all articles Export/Reference: Abstract: This paper is devoted to the study of the inviscid Boussinesq equations. We es...
ISSN: 1937-5093 eISSN: 1937-5077 Kinetic & Related Models December 2015 , Volume 8 , Issue 4 Issue on rate-independent evolutions and hysteresis modelling Select all articles Export/Reference: Abstract: This paper is devoted to some a priori estimates for the homogeneous Landau equation with soft potentials. Using coer...
Search Now showing items 1-1 of 1 Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV (Elsevier, 2014-09) Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ...
Spring 2018, Math 171 Week 2 Markov/Non-Markov Chains (Discussed) Example 1.2 from the book (Ehrenfest Chain) (Discussed) At \(t=0\) an urn contains \(N\) balls, \(M\) of which are red, \(N-M\) of which are green. Each day (\(t = 1, 2, \dots\)) a ball is drawn without replacement. Let \(X_n\) be the color of the ball d...
I'm considering a Cox-Ingersoll-Ross (CIR) process $$ dx_{t} = \alpha\left(\theta - x_{t}\right)dt + \sigma \sqrt{x_{t}}\,dW_{t}\,,\qquad \alpha,\beta,\sigma > 0 $$ which by assumption has $2\alpha \theta < \sigma^{2}$ (violates the Feller condition) and can therefore reach $x_{t}=0$ for some $t$ . The conditional dist...
I want to solve the following ODE using NDSolveProcessEquations but in an iterative way. $\ddot{x}(t)+5\dot{x}(t)+3x(t)=2\cos(2\pi t)$ $\dot{x}(0)=0,\,x(0)=1$ I wrote the below code ClearAll["Global`*"] (*----------------------------------------------------------*) dxdt0 = 0; x0 = 1; ti = 0; tf = 10; \[Delta]t = 0.01; ...
I'm using MCMC to simulation the distribution of some parameters in a Bayesian hierarchical model, which has the following form: $$\gamma_{ik} \sim Ber(\omega_{ik}).$$ Then I make a logit-transiformation, more specifically, $\theta_{ik}$ = $log(\frac{\omega_{ik}}{1-\omega_{ik}}).$ In order to incorporate covariates $x_...
The Exponential Family: Getting Weird Expectations! I spent quite some time delving into the beauty of variational inference in the recent month. I did not realize how simple and convenient it is to derive the expectations of various forms (e.g. logarithm) of random variables under variational distributions until I fin...
ISSN: 1078-0947 eISSN: 1553-5231 All Issues Discrete & Continuous Dynamical Systems - A January 1996 , Volume 2 , Issue 1 Select all articles Export/Reference: Abstract: Here we established the partial regularity of suitable weak solutions to the dynamical systems modelling the flow of liquid crystals. It is a natural ...
At room temperature, the electrical conductivity of PbS is 25 (Ω.m) -1 , whereas the electron and hole mobilities are 0.06 and 0.02 m 2/V.s, respectively. Calculate the intrinsic carrier concentration for PbS at room temperature. (AMIE, Material Science, Summer 2019) Solution \[\begin{array}{l}\sigma = 25{(\Omega m)^{ ...
Merit function \[MF=\left[\frac 1L \sum\limits_{j=1}^{L}\left(\frac{R(X,\lambda_j)-\hat{R}(\lambda_j)}{\Delta R_j}\right)^2\right]^{1/2} \] where \(\Delta R_j\) are tolerances, \(X\) is a vector of layer thicknesses. Optimization methods Sequential QP method is based on a sequential approximations of the optimization p...
Generally speaking, atomic and molecular orbitals are not physical quantities, and generally they cannot be connected directly to any physical observable. (Indirect connections, however, do exist, and they do permit a window that helps validate much of the geometry we use.) There are several reasons for this. Some of t...
Let $ \Delta =\frac{\partial^2}{\partial x_1^2}+\frac{\partial^2}{\partial x_2^2}+\frac{\partial^2}{\partial x_3^2}$ be the Laplacian on $ \mathbb{R}^3$ . Consider an operator $ H$ on complex valued functions on $ \mathbb{R}^3$ $ $ H\psi=\Delta\psi(x) +i\sum_{p=1}^3A_p(x)\frac{\partial \psi(x)}{\partial x_p} +B(x)\psi(...
Briefly, we shall see the definition of a kernel density estimator in the multivariate case. Suppose that the data is d-dimensional so that $latex {X_{i}=(X_{i1},\ldots,X_{id})}&fg=000000$. We will use the product kernel $latex \displaystyle \hat{f}_{h}(x)=\frac{1}{nh_{1}\cdots h_{d}}\left\{ \prod_{j=1}^{d}K\left(\frac...
The golden ratio is well known and is associated with the Fibonacci sequence of numbers. \(\varphi\) is the positive root of the quadratic equation \(x^2-x-1 = 0\). The exact value is given by \(\displaystyle \frac{1 + \sqrt5}{2} \approx 1.61803\) Its continued fraction is \([1; 1, 1, 1, …]\). I have written on the sil...
Search Now showing items 1-5 of 5 Forward-backward multiplicity correlations in pp collisions at √s = 0.9, 2.76 and 7 TeV (Springer, 2015-05-20) The strength of forward-backward (FB) multiplicity correlations is measured by the ALICE detector in proton-proton (pp) collisions at s√ = 0.9, 2.76 and 7 TeV. The measurement...
First My college book contains the following passage: the angle of incidence (relative to the fibre axis ) can't be too large else the ray would be refracting on the core\cladding boundary and transmitted outside the fiber and a very small percentage passes. Here's how I reasoned and I'd like to be corrected. The geome...
General case. In relativistic thermodynamics, inverse temperature $\beta^\mu$ is a vector field, namely the multipliers of the 4-momentum density in the exponent of the density operator specifying the system in terms of statistical mechanics, using the maximum entropy method, where $\beta^\mu p_\mu$ (in units where $c=...
I am looking for an explanation of the following fact, which seems to be rather simple yet I am missing something. Say that $S_t$ is a stock following GBM $$ dS_t = r S_td_t + \sigma S_t dW_t,$$ and I want to price a derivative with payoff $max(S_T^2-K,0)$. I know how to do this using the risk-neutral expectation, but ...
Hello, I've never ventured into char before but cfr suggested that I ask in here about a better name for the quiz package that I am getting ready to submit to ctan (tex.stackexchange.com/questions/393309/…). Is something like latex2quiz too audacious? Also, is anyone able to answer my questions about submitting to ctan...
Neurons (Activation Functions)¶ They could be attached to any layers. The neuron of each layer will affect the output in the forward pass and the gradient in the backward pass automatically unless it is an identity neuron. A layer have an identity neuron by default [1]. class Neurons. Identity¶ An activation function t...
amp-mathml Displays a MathML formula. Required Script <script async custom-element="amp-mathml" src="https://cdn.ampproject.org/v0/amp-mathml-0.1.js"></script> Supported Layouts container Examples amp-mathml.amp.html Behavior This extension creates an iframe and renders a MathML formula. Example: The Quadratic Formula ...
Photos of Sergey Nikolskii from The Russian Academy of Sciences The MSE gives an error of the estimator $latex {\hat{p}_{n}}&fg=000000$ at an arbitrary point $latex {x_{0}}&fg=000000$, but it is worth to study a global risk for $latex {\hat{p} _{n}}&fg=000000$. The mean integrated squared error (MISE) is an important g...
Bulletin of the American Physical Society APS March Meeting 2013 Volume 58, Number 1 Monday–Friday, March 18–22, 2013; Baltimore, Maryland Session G46: SPS Undergraduate V Hide Abstracts Sponsoring Units: SPS Chair: Kendra Redmond, American Institute of Physics Room: Hilton Baltimore Holiday Ballroom 5 Tuesday, March 1...
Systems containing thousand atoms and more (e.g. polymers, reactions in solution, molecules on surfaces) are hard to describe fully ab initio. In many applications, however, the main attention focusses on a small subset A of the large system (active sites, the dissolved/adsorbed molecules). While the interaction of par...
Harmonic Series is Divergent Contents Theorem The harmonic series: $\displaystyle \sum_{n \mathop = 1}^\infty \frac 1 n$ $\displaystyle \sum_{n \mathop = 1}^\infty \frac 1 n = \underbrace 1_{s_0} + \underbrace {\frac 1 2 + \frac 1 3}_{s_1} + \underbrace {\frac 1 4 + \frac 1 5 + \frac 1 6 + \frac 1 7}_{s_2} + \cdots$ wh...
Search Now showing items 1-1 of 1 Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV (Elsevier, 2014-09) Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ...
Background For a system consisting of two molecules (monomers or fragments are also used) X and Y, the binding energy is $$\Delta E_{\text{bind}} = E^{\ce{XY}}(\ce{XY}) - [E^{\ce{X}}(\ce{X}) + E^{\ce{Y}}(\ce{Y})]\label{eq:sherrill-1} \tag{Sherrill 1}$$ where the letters in the parentheses refer to the atoms present in ...
In Feynman's Statistical Mechanics - A Set of Lectures, upon the introduction of the path integral, a series of approximations are made in order to calculate integrals. I am unsure how exactly to get to the following important approximation. Section 3.1 Path Integral Formulation of the Density Matrix: For low $\epsilon...
This shows you the differences between two versions of the page. Both sides previous revision Previous revision gibson:teaching:spring-2018:math445:lab11 [2018/05/01 06:20] gibson gibson:teaching:spring-2018:math445:lab11 [2018/05/01 06:23] (current) gibson Line 38: Line 38: - **Problem 2:** Determine the minimum initi...