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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... |
I've obtained some analytical results that I'd like to verify numerically by doing a double path integral. I haven't done this before with Mathematica and am unsure if it's possible, I'd like to do the following path integral;
$\int^{x_{a}}_{{x_{b}}} \int^{y_{a}}_{{y_{b}}}\exp \left[ \frac{i}{\hbar} \left( S[x(t)] - S[... |
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Now showing items 1-10 of 24
Production of Σ(1385)± and Ξ(1530)0 in proton–proton collisions at √s = 7 TeV
(Springer, 2015-01-10)
The production of the strange and double-strange baryon resonances ((1385)±, Ξ(1530)0) has been measured at mid-rapidity (|y|< 0.5) in proton–proton collisions at √s = 7 TeV with the ... |
We consider a wireless communication system in which $N$ transmitter-receiverpairs want to communicate with each other. Each transmitter transmits data at acertain rate using a power that depends on the channel gain to its receiver. Ifa receiver can successfully receive the message, it sends an acknowledgment(ACK), els... |
The main purpose of linear regression is to estimate a mean difference of outcomes comparing adjacent levels of a regressor. There are many types of means. We are most familiar with the arithmetic mean.
$$AM(X) = \frac{\left( X_1 + X_2 + \ldots + X_n \right)}{n}$$
The AM is what is estimated using OLS and untransformed... |
Details
Use the graphics module, to write a program that can plot an arbitrary polynomial. To accomplish this, you should define a function called
polynomial(x), which takes a floating point value x, and returns the result of calculating the value of the polynomial with the value of x. You should define some polynomial... |
The affine evaluation map is a surjective homomorphism from the quantumtoroidal ${\mathfrak {gl}}_n$ algebra ${\mathcal E}'_n(q_1,q_2,q_3)$ to thequantum affine algebra $U'_q\widehat{\mathfrak {gl}}_n$ at level $\kappa$completed with respect to the homogeneous grading, where $q_2=q^2$ and$q_3^n=\kappa^2$. We discuss ${... |
Both the set of rational numbers $\mathbb{Q}$ and its complement are dense in $\mathbb{R}$, but the relationship between them is very asymmetric. For instance, the rationals are countable and have Lebesgue measure 0, whereas the irrationals are uncountable and have infinite Lebesgue measure. Is it possibly to decompose... |
Given the sequence $a_1 = 0$ and $a_{n+1} = \dfrac{1}{2 \cdot\lfloor{a_n}\rfloor-a_n+1}$ and $p,q\in \mathbb N$ and coprime find $x$ so that $a_x = \dfrac{p}{q}$. I do not even know where would you start with a problem like this.
Observation: $a_k<1$ iff $k$ is odd.
Lemma: If $a_{2n}$ = $a_n$+1.
Proof: By induction. $a... |
I'm calculating molar changes in thermodynamic properties due to reactions between gasses (assumed to be ideal gases). I can calculate $\Delta H$ easily enough, because it's just $\sum_i \nu_i\Delta_f H^\circ_i$, with $\nu_i$ the stoichiometric coefficients. $\Delta G$ (at standard pressure) can be calculated from $\su... |
I am working on the problem
Consider the steady-state of the heat equation in a ball of radius a centred at the origin. In spherical coordinates, the ball occupied the region $0 \le r \le a$, $0 \le \theta \le \pi$ and $0 \le \phi < 2\pi$. It has a given temperature $g(\theta)$ imposed along its boundary, which is the ... |
Spring 2018, Math 171 Week 8 Exponential Distribution
Let \(X \sim \mathrm{exp}(\lambda)\).
Find the distribution of \(Y = \lceil X \rceil\)
(Answer) \(\mathrm{geometric}(1-e^{-\lambda})\)
Show that \(X\) and \(Y\) are both memoryless
Find the distribution of \(\beta X\)
(Answer) \(\mathrm{exponential}(\lambda/\beta)\)... |
For the experiment of drawing two cards from the specified deck, define the random variable, $A$ as the count of aces drawn, and the event $A_1, A_2$ as "an ace is drawn first" and "... second" respectively.
In the event of $A=1$, the order is
not important. It does not matter whether the single ace is the first or sec... |
Yes, list $E\cap C = \{x_n:n=1,2..\}$. For each $x$ let $N_x=\{n:x_n<x\}$. Define $f(x)=\sum_{n\in N_x}2^{-n}$.
I do not quite see what is the role of $E$ in this question, we could define $f$ as above, initially disregarding $E$ (and using $C = \{x_n:n=1,2..\}$) and then later restricting this function to $E$.
Edit. T... |
Analysis --> Errors --> Error analysis
The Errors Analysis initiates a computational procedure that provides a statistical evaluation of the effect that errors in the layer thicknesses and refractive indices in a design will have on the spectral response of a designated spectral characteristic.
As the computations proc... |
In (quasi) stable atoms the positive and negative charges form "charged" clouds, which can be represented as fractionally charged sub-clouds. In order to observe them as such, we have to have the same atomic state in the in- and out-states, i.e., we have to deal with elastic scattering in the first Born approximation. ... |
Ultrapower
The intuitive idea behind ultrapower constructions (and ultraproduct constructions in general) is to take a sequence of already existing models and construct new ones from some combination of the already existing models. Ultrapower constructions are used in many major results involving elementary embeddings.... |
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... |
K C Mittal
Articles written in Pramana – Journal of Physics
Volume 71 Issue 6 December 2008 pp 1279-1289 Research Articles
BARC is developing a technology for the accelerator-driven subcritical system (ADSS) that will be mainly utilized for the transmutation of nuclear waste and enrichment of U
233. Design and developm... |
@egreg It does this "I just need to make use of the standard hyphenation function of LaTeX, except "behind the scenes", without actually typesetting anything." (if not typesetting includes typesetting in a hidden box) it doesn't address the use case that he said he wanted that for
@JosephWright ah yes, unlike the hyphe... |
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... |
We denote with $\mathcal{U}_0$ the family of all subsets $U \in \mathcal{D}(\Omega)$ convex and balanced such that $U \cap \mathcal{D}_K(\Omega) \in \mathcal{T}_K$, where $\mathcal{T}_K$ is the topology on $\mathcal{D}_K(\Omega):=\lbrace \varphi \in C^{\infty}(\Omega) : \mathrm{supp}(\varphi) \subset K \rbrace$, define... |
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... |
Misiurewicz points in the Mandelbrot set are strictly preperiodic. Defining the quadratic polynomial \(F_c(z) = z^2 + c\), then a Misiurewicz point with preperiod \(q > 0\) and period \(p > 0\) satisfies:
\[\begin{aligned} {F_c}^{q + p}(c) &= {F_c}^{q}(c) \\ {F_c}^{q' + p}(c) &\ne {F_c}^{q'}(c)\text{ for all } 0 \le q'... |
Generally, if the frequency of a signal or a particular band of signals is high, the bandwidth utilization is high as the signal provides more space for other signals to get accumulated. However, high frequency signals can't travel longer distances without getting attenuated. We have studied that transmission lines hel... |
Epimorphism Preserves Commutativity Theorem
Let $\left({S, \circ}\right)$ and $\left({T, *}\right)$ be algebraic structures.
Let $\phi: \left({S, \circ}\right) \to \left({T, *}\right)$ be an epimorphism.
Let $\circ$ be a commutative operation.
Then $*$ is also a commutative operation. Proof
Let $\phi: \left({S, \circ}\... |
Yes, they're representations of $SO(8)$, more precisely $Spin(8)$ which is an "improvement" of $SO(8)$ that allows the rotation by 360 degrees to be represented by a matrix different from the unit matrix, namely minus unit matrix.
${\bf 8}_v$ transforms normally as $$ v\mapsto M v$$where $MM^T=1$ is the $8\times 8$ rea... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
Definition:Fermat Number Contents Definition
A
Fermat number is a natural number of the form $2^{\paren {2^n} } + 1$, where $n = 0, 1, 2, \ldots$.
The number $2^{\paren {2^n} } + 1$ is, in this context, often denoted $F_n$.
\(\displaystyle 2^{\paren {2^0} } + 1\) \(=\) \(\displaystyle 3\) \(\displaystyle 2^{\paren {2^1... |
Definition:Permutation on Polynomial Definition
Let $\map f {x_1, x_2, \ldots, x_n}$ denote a polynomial in $n$ variables $x_1, x_2, \ldots, x_n$.
Let $S_n$ denote the symmetric group on $n$ letters.
Let $\pi, \rho \in S_n$.
Then $\pi * f$ is the polynomial obtained by applying the permutation $\pi$ to the subscripts o... |
How to Model Moisture Flow in COMSOL Multiphysics®
Computing laminar and turbulent moisture flows in air is both flexible and user friendly with the
Moisture Flow multiphysics interfaces and coupling in the COMSOL Multiphysics® software. Available as of version 5.3a, this comprehensive set of functionality can be used ... |
Solving linear Inequalities means that comparison of two values or expressions. A linear inequality means that a relationship between two quantities that are not equal. In equations, one side is equal to the other side. To solving the linear inequalities, multiply, divide, or subtract the both side of the inequality eq... |
In general, you won't be able to replicate the option by a portfolio of the form $\Delta_t S_t + B_t$, though it is possible to do so with a portfolio of the form $\Delta_t^1 S_t + \Delta_t^2B_t$; see Chapter 3 of this book. Here, $B_t=e^{rt}$ is the value of the money-market account, and $r$ is the risk-free interest ... |
Idempotent idempotent element
An element $e$ of a ring, semi-group or groupoid equal to its own square: $e^2=e$. An idempotent $e$ is said to contain an idempotent $f$ (denoted by $e\geq f$) if $ef=e=fe$. For associative rings and semi-groups, the relation $\geq$ is a partial order on the set $E$ of idempotent elements... |
Integral Targets
OptiLayer enables you to specify
In OptiLayer, integral targets are represented as finite sums and can be considered as approximations of an integral expression with the help of rectangle rule.
As in conventional targets it is possible to specify
In the example (Fig. 1), transmittance (TA, no polarizat... |
We prove that square-tiled surfaces having fixed combinatorics of horizontalcylinder decomposition and tiled with smaller and smaller squares becomeasymptotically equidistributed in any ambient linear $GL(\mathbb R)$-invariantsuborbifold defined over $\mathbb Q$ in the moduli space of Abeliandifferentials. Moreover, we... |
Global boundedness in a quasilinear fully parabolic chemotaxis system with indirect signal production
1.
School of Mathematical Sciences, Peking University, Beijing, 100871, China
2.
School of Mathematical Sciences, Dalian University of Technology, Dalian, 116024, China
In this paper we develop a new and convenient tec... |
Existence of ground state solutions for the planar axially symmetric Schrödinger-Poisson system
School of Mathematics and Statistics, Central South University, Changsha 410083, Hunan, China
$ \left\{ \begin{array}{ll} -\triangle u+V(x)u+\phi u = f(x,u), \ \ \ \ x\in { \mathbb{R} }^{2},\\ \triangle \phi = u^2, \ \ \ \ x... |
Spring 2018, Math 171 Week 6 Exit Distributions
A person is terminally ill. On a day when the person is awake, there is an 0.2 chance they will die overnight, and they are equally likely to be awake or unconscious the next day. On a day when the person is unconscious, there is an 0.2 chance they will be awake the next ... |
To be precise, that code generates draws from a
shifted lognormal distribution.
Define $R_t = \frac{P_t + D_t}{P_{t-1}} - 1$ as the
return from $t-1$ to $t$.
Define $r_t = \log \left( 1 + R_t \right)$ as the
log return from $t-1$ to $t$. (Note if $D_t=0$ then $r_t = \log P_t - \log P_{t-1}$.)
Your code above generates
... |
Orthogonal group An orthogonal group is a group of all linear transformations of an $n$-dimensional vector space $V$ over a field $k$ which preserve a fixed non-singular quadratic form $Q$ on $V$ (i.e. linear transformations $\def\phi{\varphi}\phi$ such that $Q(\phi(v))=Q(v)$ for all $v\in V$). An orthogonal group is a... |
Difference between revisions of "Inaccessible"
(Organized a bit)
(→Hyper-inaccessible: Meta-ordinal)
Line 65: Line 65:
Therefore $2$-inaccessibility is weaker than $3$-inaccessibility, which is weaker than $4$-inaccessibility... all of which are weaker than $\omega$-inaccessibility, which is weaker than $\omega+1$-inac... |
@egreg It does this "I just need to make use of the standard hyphenation function of LaTeX, except "behind the scenes", without actually typesetting anything." (if not typesetting includes typesetting in a hidden box) it doesn't address the use case that he said he wanted that for
@JosephWright ah yes, unlike the hyphe... |
-
Physics
(
http://mymathforum.com/physics/
)
SenatorArmstrong October 5th, 2017 11:44 AM
Finding frequency of oscillation
I am a little stuck and would love a hint or two if anyone has got any for me.
There's a particle with mass m that is trapped in a potential.
$$U(x) = \frac{-U_o}{(\frac{a}{a})^2 + 1}$$
where $$U_o... |
1 2006-Spring 1.2 Problem 1
Define an indicator variable \(I_i\) as:
\[ I_i = \begin{cases} 1 & \text{if $i^{th}$ and $(i+1)^{th}$ cards are different (H,T) or (T,H)},\\ 0 & \text{otherwise} \end{cases} \]
Now the number of runs in a sequence of \(n\) coin tosses is given by: \[ R_n = 1+ \sum_{i=2}^{n-1} I_i \forall n\... |
OptiChar Module of OptiLayer Thin Film Software
In OptiChar, a thin film is represented by a model including spectral dependencies of refractive index and extinction coefficient, film thickness, dependence of optical parameters on the thickness of a thin film (bulk inhomogeneity), thickness of surface overlayer, and po... |
Epsilon naught, $\epsilon_0$ The ordinal $\epsilon_0$, commonly given the British pronunciation "epsilon naught," is the smallest ordinal $\alpha$ for which $\alpha=\omega^\alpha$ and can be equivalently characterized as the supremum
$$\epsilon_0=\sup\{\omega,\omega^\omega,\omega^{\omega^\omega},\ldots\}$$
The ordinals... |
Neurons (Activation Functions)¶
Neurons can be attached to any layer. 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. Layers have an identity neuron by default [1].
class
Neurons.
Identity¶
An activation function th... |
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... |
fixed in 10.0.2 Update
I have tried like these. I think there is a bug.
Plot[1/Sqrt[-1 + 2^2 Sech[x]^2], {x, 0, ArcCosh[2]}, Ticks -> {{ArcCosh[2]}, Automatic}]
This is the antiderivative.
primitive = Integrate[1/Sqrt[-1 + 2^2*Sech[x]^2], x]; Plot[primitive, {x, 0, ArcCosh[2]}, Ticks -> {{ArcCosh[2]}, {π/4, π/2}}]
Limi... |
Symbols:Greek/Sigma Contents Sigma
The $18$th letter of the Greek alphabet.
Minuscules: $\sigma$ and $\varsigma$ Majuscule: $\Sigma$
The $\LaTeX$ code for \(\sigma\) is
\sigma .
The $\LaTeX$ code for \(\varsigma\) is
\varsigma .
The $\LaTeX$ code for \(\Sigma\) is
\Sigma .
$\Sigma$ Let $\mathcal E$ be an experiment. Th... |
Linear ordering isotonic regression can be understood as approximating given series of 1-dimensional observations with non-decreasing function. It is similar to inexact smoothing splines, with the difference that we use monotonicity, rather than smoothness, to remove noise from the data. General isotonic regression is ... |
I'd like to plot the function $f$ in this answer https://math.stackexchange.com/a/788818/66096
Let $h(x) = \begin{cases} e^{ -\frac{1}{1 - (1-2x)^2}} & \mbox{ for } 0<x < 1\\ 0 & \mbox{ otherwise} \end{cases}$ Then let $$g(x)=\sum_{n=1}^\infty h(n^2(x-n))=\begin{cases}h(n^2(x-n))&\text{if }n\le x<n+1, n\in\mathbb N\\0&... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
Compounds of boron with hydrogen are called boranes. One of these boranes has the empirical formula BH_3 and a molecular mass of 28 amu. What is its molecular formula?
Solution: We will first find the formula mass of the empirical formula, BH_3.
mass = 10.81\,\text{amu} + (3\times 1.008\,\text{amu})=13.83 amu We now kn... |
Spring 2018, Math 171 Week 9 Miscillaneous Poisson Process Problems
Let \(X_1, X_2, \dots\overset{\mathrm{i.i.d}}{\sim} \mathrm{exp}(\lambda)\), and let \(N(t)\) be a poisson process with rate \(\lambda\)
Show the equality \(P(\sum_{i=1}^n X_i \le t) = P(N(t) \ge n)\)
Find an analogous equality for \(P(s \le \sum_{i=1}... |
Every vector space over a field of positive characteristic $p$ is in particular a vector space over $\mathbb{F}_p$. Any subgroup of such a vector space is a subspace (exercise), and conversely. Assuming the axiom of choice, any such subspace is a direct sum of copies of $\mathbb{F}_p$.
Every vector space over a field o... |
The question shows you already found the correct numeric result.I would just suggest working on the presentation so that people readingyour calculations do not misunderstand them. (Eventually you may alsobe solving problems that are complicated enough that even
you willnot be able to remember what you're doing unless y... |
This question already has an answer here:
how to prove :
an odd perfect number cannot be a prime number or a product of two prime numbers or power of prime number.
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 t... |
(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... |
Loss Layers¶ class
HingeLossLayer¶
Compute the hinge loss for binary classification problems:\[\frac{1}{N}\sum_{i=1}^N \max(1 - \mathbf{y}_i \cdot \hat{\mathbf{y}}_i, 0)\]
Here \(N\) is the batch-size, \(\mathbf{y}_i \in \{-1,1\}\) is the ground-truth label of the \(i\)-th sample, and \(\hat{\mathbf{y}}_i\) is the corr... |
Today i ran onto this simple problem, which seemed to be interesting to me. Given the illustration bellow, the problem is states as:
Two identical cylinders roll in between two identical planks. If the velocity of each cylinder is $\vec{v}$ and the velocity of the bottom plank is $\vec{u}$ ($|\vec{v}| > |\vec{u}|$), fi... |
The title is a little ambiguous, but I didn't know how else to put it. What I'm trying to do is solve a system of equations
system1 = {-I*ω*a1 == -I*ω1*a1 - I*J12*a2 - I*J13*a3 - κ1[ω]/2*a1 - γ1[ω]/2*a1 + Sqrt[κ1[ω]]*ain, -I*ω*a2 == -I*ω2*a2 - I*J12*a1 - I*J23*a3 - γ2/2*a2, -I*ω*a3 == -I*ω3*a3 - I*J13*a1 - I*J23*a2 - γ... |
Inaccessible
Inaccessible cardinals are the traditional entry-point to the large cardinal hierarchy (although there are some weaker large cardinal notions, such as universe cardinals).
If $\kappa$ is inaccessible, then $V_\kappa$ is a model of ZFC, but this is not an equivalence, since the weaker notion of universe car... |
Remember that we have supposed two hypothesis $latex {\left\{ f_{0},f_{1}\right\} }&fg=000000$ elements of $latex {\mathcal{F}}&fg=000000$. Denote $latex {P_{0}}&fg=000000$ and $latex {P_{1}}&fg=000000$ two probability measures under $latex {(\mathcal{X},\mathcal{A})}&fg=000000$ under $latex {f_{0}}&fg=000000$ and $lat... |
I would like to start this blog with some basic ideas about density estimation and nonparametric regression.
The study of the probability density function (pdf) is called nonparametric estimation. This kind of estimation can serve as a block building in nonparametric regression.
The typical regression problem is settin... |
Difference between revisions of "Superstrong"
(The target of a superstrong embedding need not be inaccessible.)
Line 1: Line 1:
[[Category:Large cardinal axioms]]
[[Category:Large cardinal axioms]]
[[Category:Critical points]]
[[Category:Critical points]]
−
Superstrong cardinals were first utilized by Hugh Woodin in 19... |
Transform to $y_i=\sin^2 x_i$. Then $\sum_iy_i=1$, and with $\sin x_i=\sqrt{y_i}$ and $\cos x_i=\sqrt{1-y_i}$ the inequality becomes
$$\sum_i\left(\sqrt{1-y_i}-3\sqrt{y_i}\right)\ge0\;.$$
The left-hand side is $10$ times the average value of $f(y)=\sqrt{1-y}-3\sqrt y$ at the $y_i$. The graph of $f$ has an inflection po... |
I've never actually solved a problem like this before, but it looks pretty trivial so I'll give it a shot. My apologies if this is wrong.
i. Let $\Phi$ denote the formulae of propositional logic that can be formed from the connectives in $C$ and the variables in $P$. More precisely, lets us defined that $\Phi$ is the s... |
As the title says:
Suppose $a,b,c > 0$ are constants. Consider $ay'' + by' + cy = 0$. Suppose that $y(x)$ is a solution. Prove that $\lim_{x\to\infty}y(x) = 0$. This is problem 34 from p.1160 in section 17.1 of Stewart Single Variable Calculus, 8th edition (2015).
The characteristic equation is of course $ar^2 + br + c... |
We are going to introduce the histogram as a simple nonparametric density estimator. I will divide this presentation in several posts for simplicity reasons.
Select and origin $latex {x_0}&fg=000000$ and divide the real line into bins of binwidth
$latex \displaystyle B_j = \left[x_0 – (j-1)h, x_0 + (j-1)h\right) \quad ... |
$\pu{3 g}$ of $\ce{Mg}$ are placed in $\pu{500 mL}$ of $\pu{0.625 M}$ $\ce{AgNO3}$. When the reaction is complete, what is the molarity of the $\ce{AgNO3}$ solution?
I'm thinking you need to use $M_1V_1=M_2V_2$, but I'm stuck on how to use it.
Chemistry Stack Exchange is a question and answer site for scientists, acade... |
I'm not sure where I could pose a challenge to find best $f(n)$ so people will join in. $n\ge 5$ will never probably be proven optimal, but some lucky computations or out of the box analysis might give nice results.
(Given $n$ fixed digits and operations $(+,-,\times,\div)$, whats the highest $N\in\mathbb N$, such that... |
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... |
Spring 2018, Math 171 Week 7 Martingales
Let \((X_n)_{n \ge 0}\) be i.i.d. uniform on \([-1, 0) \cup (0, 1]\)
Show that \((M_n)_{n \ge 0}\) with \(M_n = X_0 + \dots + X_n\) is a Martingale.
Show that \((M_n)_{n \ge 0}\) with \(M_n = \frac{1}{X_0} + \dots + \frac{1}{X_n}\) is not a Martingale.
(Answer) \(\mathbb{E}|M_n|... |
Type:Improvement Status:Closed Priority:Major Resolution:Fixed Affects Version/s:3.7 Fix Version/s:3.7 Component/s:Forum Testing Instructions: Log in as admin Create a site with 2 users (ensure both users have profile images set) Create a course with a forum and discussion Enrol the 2 users in the course Enable portfol... |
OptiRE module of OptiLayer Thin Film Software
OptiRE is intended for the post-production characterization (reverse engineering) of optical coatings based on spectral photometric or/and ellipsometric data. Reverse engineering provides a feedback for the design-production chain. Its main purpose is to discover errors in ... |
Consider the famous work equation due to a continuous charge distribution:
$W=\frac{\varepsilon_{0}}{2}\left ( \int_{volume \space space}\left \| \vec{E} \right \|^{2}.d \tau+\oint_{S}V.\vec{E}.d \vec{a} \right )$
Note:
$V\left(r \right)=\frac{1}{4 \pi \varepsilon _{0}}\frac{q}{r}$
$\vec{E}= \frac{1}{4\pi\varepsilon _{... |
In finance, many stochastic processes $X(t)$ are defined via \begin{equation} dX = \text{(some drift term)} dt + \sigma X^\gamma dW_t \end{equation} with $\gamma = 1/2$ (for instance the Heston model or the CIR process). Generally, this is called a square-root process. My question is: How does one justify the choice of... |
06/04/2011, 09:43 PM (This post was last modified: 06/04/2011, 10:26 PM by tommy1729.)
(06/04/2011, 01:13 PM)Gottfried Wrote: Sometimes we find easter-eggs even after easter...
For the alternating iteration-series
(definitions as copied and extended from previous post, see below)
we find a rational polynomial for p=4. ... |
When we measure position for example, how does the system "know" that we're measuring position in order to collapse to a position eigenvector? Does the wave function always evolve from the state that it collapsed to? For example, if we measure the position (whatever that means) does the wave evolve from a delta functio... |
Learning Objectives
Apply the work-energy theorem to find information about the motion of a particle, given the forces acting on it Use the work-energy theorem to find information about the forces acting on a particle, given information about its motion
We have discussed how to find the work done on a particle by the f... |
The last post I forget to say that we use Mikownski classes of densities because the MISE is a risk corresponding to the $latex {\mathbb L^2({\mathbb R})}&fg=000000$ norm. Thus, it is natural to assume that $latex {p}&fg=000000$ is smooth with respect to this norm. Another way to describe smoothness in $latex {\mathbb ... |
These exercises are not tied to a specific programming language. Example implementations are provided under the Code tab, but the Exercises can be implemented in whatever platform you wish to use (e.g., Excel, Python, MATLAB, etc.).
# Exercise 1: Derive the Equations of Motion
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The Lagrange points are the Solar Syst... |
Naive Bayes methods are a set of supervised learning algorithms based on applying Bayes’ theorem with the “naive” assumption of conditional independence between every pair of features given the value of the class variable. Bayes’ theorem states the following relationship, given class variable \(y\) and dependent featur... |
For physics research, there is a differential equation that I simulate again and again. It would be wonderful to speed it up. Each time I run it, part of the input function $I(t)$ changes. It takes a few minutes each time, and after running a few hundred iterations per day, it is eating up a bunch of time. Each time I ... |
Hello guys! I was wondering if you knew some books/articles that have a good introduction to convexity in the context of variational calculus (functional analysis). I was reading Young's "calculus of variations and optimal control theory" but I'm not that far into the book and I don't know if skipping chapters is a goo... |
Definition:Factorial/Definition 1 Definition
Let $n \in \Z_{\ge 0}$ be a positive integer.
The factorial of $n$ is defined inductively as: $n! = \begin{cases} 1 & : n = 0 \\ n \left({n - 1}\right)! & : n > 0 \end{cases}$
$\begin{array}{r|r} n & n! \\ \hline 0 & 1 \\ 1 & 1 \\ 2 & 2 \\ 3 & 6 \\ 4 & 24 \\ 5 & 120 \\ 6 & 7... |
ISSN:
1078-0947
eISSN:
1553-5231
All Issues
Discrete & Continuous Dynamical Systems - A
January 2013 , Volume 33 , Issue 1
Special Issue
Tribute to Jean Mawhin
Select all articles
Export/Reference:
Abstract:
Jean Mawhin will celebrate his seventieth birthday on December 11, 2012, most likely in Heusy (Verviers), a love... |
Definition:Quotient (Algebra) Definition
Let $a, b \in \Z$ be integers such that $b \ne 0$.
From the Division Theorem:
$\forall a, b \in \Z, b \ne 0: \exists_1 q, r \in \Z: a = q b + r, 0 \le r < \left|{b}\right|$ The value $q$ is defined as the quotient of $a$ on division by $b$, or the quotient of $\dfrac a b$.
When ... |
import "gonum.org/v1/gonum/mathext"
Package mathext implements special math functions not implemented by the Go standard library.
AiryAi returns the value of the Airy function at z. The Airy function here, Ai(z), is one of the two linearly independent solutions to
y'' - y*z = 0.
See http://mathworld.wolfram.com/AiryFun... |
We show that sheet closures appear as associated varieties of affine vertexalgebras. Further, we give new examples of non-admissible affine vertexalgebras whose associated variety is contained in the nilpotent cone. We alsoprove some conjectures from our previous paper and give new examples of lisseaffine W-algebras.
W... |
Learning Objectives
Calculate the acceleration vector given the velocity function in unit vector notation. Describe the motion of a particle with a constant acceleration in three dimensions. Use the one-dimensional motion equations along perpendicular axes to solve a problem in two or three dimensions with a constant a... |
Pythagoras's Theorem Contents Theorem
Then:
$a^2 + b^2 = c^2$
Consider the triangle shown below.
This new figure is shown below.
Now to calculate the area of this figure.
Thus we have the calculate of the large square to be:
$4 \left({\dfrac 1 2 a b}\right) + c^2 = 2 a b + c^2$
On the other hand, we can calculate the a... |
Upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations
School of Mathematics and Statistics, Zhengzhou University, No.100, Science Road, Zhengzhou, 450001, China
The paper investigates the upper semicontinuity of pullback attractors for non-autonomous Kirchhoff wave equations with struc... |
Hey guys! I built the voltage multiplier with alternating square wave from a 555 timer as a source (which is measured 4.5V by my multimeter) but the voltage multiplier doesn't seem to work. I tried first making a voltage doubler and it showed 9V (which is correct I suppose) but when I try a quadrupler for example and t... |
You have already got "practical" answers, so I intend to answer form another point of view.
There is a quite famous theorem due to Stone and von Neumann, later improved by Mackay, and finally by Dixmier and Nelson, roughly speaking establishing the following result within the most elementary version. (Another version o... |
@JosephWright Well, we still need table notes etc. But just being able to selectably switch off parts of the parsing one does not need... For example, if a user specifies format 2.4, does the parser even need to look for e syntax, or ()'s?
@daleif What I am doing to speed things up is to store the data in a dedicated f... |
The following problem is from CLRS (31.1-13, Page 933, 3rd edition):
Give an efficient algorithm to convert a given $\beta$-bit (binary) integer to a decimal representation. Argue that if multiplication or division of integers whose length is at most $\beta$ takes time $M(\beta)$, then we can convert binary to decimal ... |
The initial interest in the zeros is their connection with the distribution of primes, which is often done via asymptotic statements about the prime counting function. In analytic number theory, it is standard fare to have an arithmetic function defined by a summation formula, and then modify it into a form that is eas... |
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