text stringlengths 256 16.4k |
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03-14-2015, 09:44 AM
Pages: 12
03-14-2015, 09:48 AM
Thanks for the reminder, forgot it (being a DMY-er). Happy pi-day!
03-14-2015, 09:57 AM
(03-14-2015 09:48 AM)Thomas Radtke Wrote: [ -> ]Thanks for the reminder, forgot it (being a DMY-er). Happy pi-day!
As it's 20150314 I have a long time to wait.
03-14-2015, 10:16 AM... |
Automorphisms of the Upper Half Plane
Welcome back to our little series on automorphisms of four (though, for all practical purposes, it's really
three) different Riemann surfaces: the unit disc, the upper half plane, the complex plane, and the Riemann sphere. Last time, we proved that the automorphisms of the unit dis... |
I will take pretty much the same approach that 9-BBN does except I will do it a little bit differently. I have never heard of setting the reactants to zero and I'm not very good at making matrices, so I'll just jump right into the systems of equations.
First of all, define your coefficients $a,b,c,d,e$ for each of the ... |
Sorry, but my first answer was completely and utterly wrong. Since this question is one of the top search results for the query "braid group fundamental group configuration space" I think it's high time I've updated with a correct explanation! :-)
I am not sure why there is a non-trivial loop. My understanding of homot... |
When you fit a generalized linear model (GLM) in R and call
confint on the model object, you get confidence intervals for the model coefficients. But you also get an interesting message:
Waiting for profiling to be done...
What's that all about? What exactly is being profiled? Put simply, it's telling you that it's cal... |
Ranklist, scores and difficulties Your score
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 ... |
Both roughness length $z_0$ and zero plane displacement $d$ seemed to be defined as the height above the ground at which wind speed theoretically becomes zero. But wind speed is also supposed to go to zero at $d+z_0$. What is the difference between the two, and how should they actually be defined?
First some definition... |
We model the expansion history of the Universe as a Gaussian process and find constraints on the dark energy density and its low-redshift evolution using distances inferred from the Luminous Red Galaxy (LRG) and Lyman-alpha (Ly$\alpha$) datasets of the Baryon Oscillation Spectroscopic Survey, supernova data from the Jo... |
I am trying to understand some results and would appreciate some general comments on tackling nonlinear problems.
Fisher's equation (a nonlinear reaction-diffusion PDE),
$$ u_t = du_{xx} + \beta u (1 - u) = F(u) $$
in discretised form,
$$ u_j^{\prime} = \boldsymbol{L}\boldsymbol{u} + \beta u_j (1 - u_j) = F(\boldsymbol... |
The impulse response of the LTI system is
$$h(t)=e^{-4t} u(t)$$
The expression for the step response is
$$\frac14 \left(1-e^{-4t}\right)u(t)$$
My question is how $u(t)$ appears in the answer.
Signal Processing Stack Exchange is a question and answer site for practitioners of the art and science of signal, image and vid... |
I'm writing a basic gear train simulation, where it is possible for every gear to be attached to a source of torque/angular friction. All the online resources I've found only deal with systems where a
single gear is powered and all others simply accept torque from that gear, so I've kind of had to build the equations f... |
Consider the Hamiltonian: $$H=\sum_{\vec k} \varepsilon (\vec k)a_{\vec k}^\dagger a_{\vec k}$$ with $\varepsilon(\vec k) \rightarrow 0$ as $|\vec k|\rightarrow 0$. I know that this has gapless excitations and therefore Goldstone modes but I am confused about the actual definition of what counts as a Goldstone mode. Do... |
Inhalt des Dokuments Kolloquium
In unserem Kolloquium algorithmische Mathematik und Komplexitätstheorie tragen Mitarbeiter und Gäste über aktuelle Themen ihrer Forschung vor. Organisiert mit Hilfe von Alperen Ali Ergür.
In our Kolloquium on algorithmic mathematics and complexity theory, guests and members of the group ... |
I'll state the question from my book below:
If $A$, $B$ and $C$ are the angles of a triangle, then find the determinant value of $$\Delta = \begin{vmatrix}\sin^2A & \cot A & 1 \\ \sin^2B & \cot B & 1 \\ \sin^2C & \cot C & 1\end{vmatrix}.$$
Here's how I tried solving the problem:
$\Delta = \begin{vmatrix}\sin^2A & \cot ... |
Let $U \subseteq \mathbb{R}^n$ be open and denote by $\mathcal{D}(U)$ the space of all compactly supported smooth functions $U \to \mathbb{R}$. Let $\mathcal{D}^\prime(U)$ be the space of all distributions $\mathcal{D}(U) \to \mathbb{R}$ with the standard topology.
Given a distribution $T$, I would like to prove that t... |
In spaceflight, an
orbital maneuver is the use of propulsion systems to change the orbit of a spacecraft. For spacecraft far from Earth (for example those in orbits around the Sun) an orbital maneuver is called a deep-space maneuver (DSM).
The rest of the flight, especially in a transfer orbit, is called
coasting.
Cont... |
As I mentioned in comments, professor Jack Simons offers a relatively simple physical interpretation of the idea of mixing in excited detrminant for treating dynamical correlation in his book "Quantum Mechanics in Chemistry" (Chapter 8) freely available here, as well as in this video which is also authored by him.
An i... |
De Bruijn-Newman constant
For each real number [math]t[/math], define the entire function [math]H_t: {\mathbf C} \to {\mathbf C}[/math] by the formula
[math]\displaystyle H_t(z) := \int_0^\infty e^{tu^2} \Phi(u) \cos(zu)\ du[/math]
where [math]\Phi[/math] is the super-exponentially decaying function
[math]\displaystyle... |
One way to obtain the -2/3 is by singularity analysis.
The first step is to construct the generating function of your sequence.From the Taylor expansion of the Lambert $W$ function at 0, one gets that $-W(-x)$ is the generating function of the sequence $N^{N-1}/N!$ and therefore by differentiation$$\frac{-W(-x)}{1+W(-x... |
Difference between revisions of "Rank into rank"
(→$C^{(n)}$ variants: headers)
m (→$C^{(n)}$ variants: -m)
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$\mathrm{I3}$ and other $C^{(n)}$ variants:
$\mathrm{I3}$ and other $C^{(n)}$ variants:
−
*
+
* $\mathrm{I3}(κ, δ)$, if $δ$ is a limit cardinal (instead of a successor of a limit cardinal – Kune... |
Welcome back to our mini-series on quantum probability! Last time, we motivated the series by pondering over a thought from classical probability theory, namely that marginal probability doesn't have memory. That is, the process of summing over of a variable in a joint probability distribution causes information about ... |
Existence of solutions for a fractional hybrid boundary value problem via measures of noncompactness in Banach algebras Abstract
We study the existence of solutions for the following fractional hybrid boundary value problem
$$ \cases \displaystyle D_{0^+}^{\alpha}\bigg[\frac{x(t)}{f(t,x(t))}\bigg]+g(t,x(t))=0, &0< t< 1... |
While studying, I came upon this problem: "Find the maximum area of a rectangle circumscribed about a fixed rectangle of length 8 and width 4." I looked at the answer key, which showed that the maximum area possible was 72 inches squared. Also, it stated to use cosine and sine functions to solve the problem. However, I... |
A linear transformation is one where
$T(\alpha x) = \alpha T(x)$
and
$T(x + y ) = T(x) + T(y)$
That's all the is to it.
$T((x, y)) = (2x + y, y, 0)$
Is linear because $T(c(x,y)) = T((cx,cy)) = (2cx + cy, cy, 0) = c(2x + y, cy, 0) = cT((x,y))$
and $T((x,y) + (w,z)) = T((x+w, y + z)) = (2x + 2w + y + z, y + z, 0) = (2x +... |
We can start by analyzing equation #15 from the Derivation of Ideal Gas Law below:
\(P=\frac{N}{V}\frac{m\overline{v^2}}{3}=\frac{N}{V}\frac{2E_{kinetic}}{3}=\frac{N}{V}kT=\frac{NkT}{V}\)
Because we want to derive the equation to the speed of gaseous molecules, the most important factor come to mind is the speed v
x. T... |
Limits and Colimits, Part 2 (Definitions)
Welcome back to our mini-series on categorical limits and colimits! In Part 1 we gave an intuitive answer to the question, "What
are limits and colimits?" As we saw then, there are two main ways that mathematicians construct new objects from a collection of given objects: 1) ta... |
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Production of light nuclei and anti-nuclei in $pp$ and Pb-Pb collisions at energies available at the CERN Large Hadron Collider
(American Physical Society, 2016-02)
The production of (anti-)deuteron and (anti-)$^{3}$He nuclei in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV has ... |
I want to trace electrostatic field lines emerging from 2D surfaces in 3D space. Eventually I want to find their intersection with an (uncharged) mesh.
The charge distribution $\sigma(x), x \in \Gamma \subset \mathbb{R}^3$ is defined by requiring a constant potential $\phi(x) = \phi_\Gamma\ \forall x\in\Gamma$.
For the... |
Here, I give a quick review of the concept of a Martingale. A Martingale is a sequence of random variables satisfying a specific expectation conservation law. If one can identify a Martingale relating to some other sequence of random variables, its use can sometimes make quick work of certain expectation value evaluati... |
Let the random variable $X$ has Rician distribution (unit power in direct and scattered paths), whose PDF is given by
$$f_X(x)=\frac{2x}{\alpha}\text{exp}\left(\frac{-(x^2+v^2)}{\alpha}\right)I_0\left(\frac{2xv}{\alpha}\right)$$ with $\frac{v^2}{\alpha}=1$ and $I_0(z)$ is the modified Bessel function of the first kind ... |
In this answer we will only consider the leading semi-classical approximation of a $1$-dimensional problem with Hamiltonian
$$ H(x,p) ~=~ \frac{p^2}{2m}+ \Phi(x), $$
where $\Phi$ is a potential. Semi-classically, the number of states $N(E)$ below energy-level $E$ is given by the area of phase space that is classically ... |
This tutorial illustrates how impurity and information gain can be calculated in Python using the
NumPy and
pandas modules for information-based machine learning. The impurity calculation methods described in here are as follows:
Entropy Gini index
We start off with a simple example, which is followed by the Vegetation... |
Difference between revisions of "Vopenka"
m (→Formalizations: inaccessible so MK!)
(weakly!)
Line 123: Line 123:
* If $gVP(Σ_{n+1})$ holds, then either there is a proper class of $n$-remarkable cardinals or there is a proper class of [[rank-into-rank|virtually rank-into-rank]] cardinals.<cite>GitmanHamkins2018:GenericV... |
The orthogonal group, consisting of all proper and improper rotations, is generated by reflections. Every proper rotation is the composition of two reflections, a special case of the Cartan–Dieudonné theorem.
Yeah it does seem unreasonable to expect a finite presentation
Let (V, b) be an n-dimensional, non-degenerate s... |
(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... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Has Fulltext no (9) (remove)
320
Power-ordered sets are not always lattices. In the case of distributive lattices we give a description by disjoint of chains. Finite power-ordered sets have a polarity. We introduct the leveled lattices and show examples with triv... |
I'm very new to elementary number theory proofs and have been trying to figure out how to prove these seemingly straightforward identities with divisibility with no success.
For some integers $a,b,c \in \mathbb{Z}$
1) If ${a\mid bc}$ and ${a \not\mid b}$ then ${a\mid c}$
2) If ${a\mid c}$, ${b\mid c}$ and ${\gcd(a,b) =... |
Let $G$ be a connected, finite graph. (For me a graph is undirected, and it possibly has multiple edges, although the latter is not really crucial for this question). The
complexity $c(G)$ (also known as the tree-number of $G$) is defined to be the number of spanning trees of $G$.
There is another number $k(G)$ that on... |
A common resistor circuit goes by the nickname
voltage divider.
In the previous article we developed an equation for voltage dividing,
$v_{out} = v_{in}\,\dfrac{\text R2}{\text R1 + \text R2}$
The derivation assumed the current flowing away from the center node is very small.
In this article we challenge that assumptio... |
I've been deriving Bass diffusion model and keep consistently finding a different result than Bass' original answer. To make things worse, every single link in the Google results page just copies the Bass original solution, while I am finding the different one. You don't have to know the model, just let me show you the... |
I'm trying to clarify the notion of being contractible in homotopy theory vs. homotopy
type theory. Is the following right?
"
In homotopy theory the real interval $[0,1]$, considered as a subset of $\mathbb R$, is contractible. In contrast, for a set in homotopy type theory, isContr is only inhabited if that the set (e... |
Now, let’s get some practice on calculating centre of mass of objects.
An object of mass $M$ is in the shape of a right-angle triangle whose dimensions are shown in the figure. Locate the coordinates of the centre of mass, assuming that the object has a uniform mass per unit area.
Recall that the equations for centre o... |
Difference between revisions of "Extendible"
(→Variants: === $C^{(n)}$-extendible cardinals ===)
(→$C^{(n)}$-extendible cardinals: I3)
Line 59: Line 59:
** There exists a $C(n)$-extendible cardinal.
** There exists a $C(n)$-extendible cardinal.
* “For every $n$ there exists a $C(n)$-extendible cardinal.” is equivalent ... |
(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... |
Answer
$2cis240^\circ$ or $2(cos 240^\circ + isin240^\circ)$
Work Step by Step
$arctan(\frac{-\sqrt{3}}{-1}) = 60^\circ$, but since, $- 1 - i\sqrt{3}$ is in the 3rd quadrant, its angle is $240^\circ$. The absolute value of $- 1 - i\sqrt{3}$ is $\sqrt{(-1)^2 + (-\sqrt{3})^2} = 2$, the equivalent trigonometric form is $2... |
I'm trying to apply a Fourier transform of a one dimensional list of a time history of some quantity using the
Fourier function. I'm interested in the frequency spectrum, but the problem is that the
Fourier function uses the fast Fourier transform algorithm which places the zero frequency at the beginning, complicating... |
$$U(g_1)U(g_2)=e^{i \phi(g_1,g_2)}U(g_1g_2)\tag{1}$$
Using local coordinates $\{x^a \}$ near identity element, $g1.g2=g(x_1).g(x_2)=g(x_3(x_1,x_2))$ $$x^a_3(x_1,x_2)=x^a_1+x^a_2+\gamma^{abc}{x^b_1}x_2^c+\cdots\tag{2}$$ $$\phi(g_1,g_2)\equiv\phi(x_1,x_2)=\gamma^{bc}x_1^bx_2^c+\cdots\tag{3}$$ $$U(g(x))=1+ix^aT^a+\frac{1}... |
Microwave rotational spectroscopy uses microwave radiation to measure the energies of rotational transitions for molecules in the gas phase. It accomplishes this through the interaction of the electric dipole moment of the molecules with the electromagnetic field of the exciting microwave photon.
Introduction
To probe ... |
Here is another perspective, which perhaps shifts where the intrigue should be directed. An important question to consider: How do you define $\pi$? If you take the definition of $\pi$ to be the usual one we first encounter involving circles, then it is fairly remarkable that this geometric constant should have anythin... |
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1. Observation of a peaking structure in the J/psi phi mass spectrum from B-+/- -> J/psi phi K-+/- decays
PHYSICS LETTERS B, ISSN 0370-2693, 06/2014, Volume 734, Issue 37... |
Continuous random variables have many applications. Baseball batting averages, IQ scores, the length of time a long distance telephone call lasts, the amount of money a person carries, the length of time a computer chip lasts, and SAT scores are just a few. The field of reliability depends on a variety of continuous ra... |
In school, I have learnt to plot simple graphs such as $y=x^2$ followed by $y=x^3$.
A grade or two later, I learnt to plot other interesting graphs such as $y=1/x$, $y=\ln x$, $y=e^x$. I have also recently learnt about trigonometric graphs and circle equations. In the internet, I have seen users posting graphs of diffe... |
K-function of a Three-Dimensional Point Pattern
Estimates the \(K\)-function from a three-dimensional point pattern.
Usage
K3est(X, …, rmax = NULL, nrval = 128, correction = c("translation", "isotropic"), ratio=FALSE)
Arguments X
Three-dimensional point pattern (object of class
"pp3").
…
Ignored.
rmax
Optional. Maximum... |
Suppose that $X$ and $Y$ are smooth varieties over a field $k$ (not necessarily algebraically closed), of dimension $m$ and $n$. Suppose we are given a morphism $\pi:X\rightarrow Y$.
We know that if $\pi$ is smooth, it is flat (by definition) and all the fibers are smooth of dimension $m-n$.
Under these assumptions:
if... |
In the article Finding Intermediate Values in Arithmetic Mean a linear formula was obtained to solve intermediate values in an Arithmetic Mean sequence. The same problem of finding the intermediate values on the Geometric Mean sequence was placed, refer to paper. During the simplification process the following sequence... |
You are right that the Yoneda lemma plays the key role in the proof.
By the definition of convolution:$$(F \otimes G) \otimes H \approx \int^{C, D} \left(\int^{A, B} F(A) \times G(B) \times \hom(C, A \otimes B)\right) \times H(D) \times \hom(-, C \otimes D)$$Because products in $\mathbf{Set}$ preserve coends, the above... |
The Weierstrass approximation theorem says any continuous function $f(x): [0,1] \to \mathbb{R}$ can be approximated uniformly by polynomials. Given any $\epsilon$, we can find $p(x) = x^n + \dots $ such that:
$$ |f(x) - p(x)| < \epsilon $$
is always true. In practice how to do we find $p$? Let's say $f(x)$ was the step... |
Alladi Ramakrishnan Hall
Tensor product decomposition for the general linear supergroup GL(m|n)
Thorsten Heidersdorf
Max Planck Institute, Bonn.
Let $\mathfrak{gl}(n)$ denote the Lie algebra of the general linear group $GL(n). Given two finite dimensional irreducible representations $L(\lambda), L(\mu)$ of $\mathfrak{g... |
Suppose you use a neural network for a classification problem and the neurons in the output layer should return a valid discrete probability distribution. If you set the number of output neurons \(n\) equal to the number of classes of your classification problem, you have the nice interpretation that the result for eac... |
Mesuration
Category : 7th Class
Mensuration
Standard Units of Area
The inter relationship among various units of measurement of area are listed below.
\[1\,{{m}^{2}}\] = \[(100\times 100)\,c{{m}^{2}}={{10}^{4}}\,c{{m}^{2}}\]
\[1\,{{m}^{2}}\] = \[(10\times 10)\,d{{m}^{2}}=100\,d{{m}^{2}}\]
\[1\,d{{m}^{2}}\] = \[(10\time... |
De Bruijn-Newman constant
For each real number [math]t[/math], define the entire function [math]H_t: {\mathbf C} \to {\mathbf C}[/math] by the formula
[math]\displaystyle H_t(z) := \int_0^\infty e^{tu^2} \Phi(u) \cos(zu)\ du[/math]
where [math]\Phi[/math] is the super-exponentially decaying function
[math]\displaystyle... |
If I understood correctly, you have a signal $x[n]$ and an unknown discrete-time LTI filter, so that you can look at the output of the filter $y[n]$. Now you are looking for the impulse response of the filter $h[n]$.
The output follows a convolution rule$$y[n]=x[n]*h[n]=\sum_{m=-\infty}^{\infty}x[m]h[n-m]$$The process ... |
I'm new to Mathematica, and for most purposes the program has served me well and been straightforward. However, I'm hitting a snag while trying to create a contour plot for the distribution function
$\qquad f(x,y) = (x\,y)^{p-1}/(\alpha + \beta\,x + \gamma\,y + \delta\,x\,y)^{p + q}$
Notice $x,y$ are variables, and $\a... |
Let $\lambda_1,\ldots,\lambda_n$ be complex numbers such that for each positive integer $k\geq 0$, $$\sum_{i=1}^n \lambda_i^k=0.$$ Here I am supposed to show that $\lambda_i=0$ for each $i\in 1,\ldots,n$. One of my friends said it sounds that I should use Vandermonde determinant. I tried to find an appropriate version ... |
I will outline how the problem can be approached and statewhat I think the end result will be for the special casewhen the shape parameters are integers, but not fill in thedetails.
First, note that $X-Y$ takes on values in $(-\infty,\infty)$and so $f_{X-Y}(z)$ has support $(-\infty,\infty)$.
Second, from the standard ... |
What is an Operad? Part 1
If you browse through the research of your local algebraist, homotopy theorist, algebraic topologist or―well, anyone whose research involves an
operation of some type, you might come across the word "operad." But what are operads? And what are they good for? Loosely speaking, operads―which com... |
A method of integration that simplifies the function by rewriting it in terms of a different variable. The goal is to transform the integral into another that is easier to solve. It is the inverse of the chain rule in differentiation.
The new variable used is usually \(u\) by convention, hence this method is also known... |
What is an Operad? Part 2
Last week we introduced the definition of an
operad: it's a sequence $\mathcal{O}(1),\mathcal{O}(2), \mathcal{O}(3),\ldots$ of sets or vector spaces or topological spaces or most anything you like (whose elements we think of as abstract operations), together with composition maps $\circ_i\colo... |
I have been given the following definition: $\rule{17cm}{0.4pt}$
Let $\{a_n\}$ be a sequence in $\mathbb{R}$. The series: $$\sum_{n=0}^\infty a_n$$ is $\textbf{convergent}$ if the sequence $\{s_m\}$ of the $\textbf{partial sums}$ $$s_m=\sum_{n=0}^m a_n$$ converges, that is for all $\varepsilon >0$ there exists $N=N(\va... |
I have the following question which has given rise to a doubt.
One end of a rod of uniform density is attached to the ceiling in such a way that the rod can swing about freely with no resistance. The other end of the rod is held still so that it touches the ceiling as well. Then the second end is released. If the lengt... |
When you fit a generalized linear model (GLM) in R and call
confint on the model object, you get confidence intervals for the model coefficients. But you also get an interesting message:
Waiting for profiling to be done...
What's that all about? What exactly is being profiled? Put simply, it's telling you that it's cal... |
In calculus, students are often asked to find the “derivative” of a function. You can think of this graphically: the derivative of a function is the slope of the tangent line to the function at the given point. Still seems confusing? Let's take an example: You should know that the slope of any horizontal line is 0. The... |
The condition is mostly referred to as the No-Ponzi (-scheme) [NP] condition. It is
one additional constraint, that prevents Ponzi-schemes: Paying debt with new higher debt, ad infinitum.
By the way: The NP condition is
one condition, hence the associated multiplier should be $\psi$ instead of $\psi_t$. While certainly... |
I need to program in an algorithm that recursively makes algebraic replacements which leads to an utterly complicated algebraic function of $x$, but whose final result is only needed at fixed order in the Laurent series in $x$. I wish to use this fact to make the algorithm go faster. Here is sample problem that mimics ... |
Consider the following graph $G=(V,E)$ where $V=\mathbb{R}^2$ and $E = \{\{x,y\}: x,y \in \mathbb{R}^2 \text{ and } |x-y|\in \mathbb{Q}\}$.
What is $\chi(G)$?
(This is a variant of the Hadwiger-Nelson problem.)
MathOverflow is a question and answer site for professional mathematicians. It only takes a minute to sign up... |
In quantum mechanics, if the wavefunction is normalizable, then it would represent a particle. Why does it not represent a particle when it is not normalizable?
By definition, the probability to detect a particle with normalized wavefunction $\psi(x)$ in an interval $[x_1,x_2]$ is$$ P(x_1,x_2) = \int_{x_1}^{x_2}\lvert\... |
Reinforcement Learning (DQN) Tutorial¶ Author: Adam Paszke
This tutorial shows how to use PyTorch to train a Deep Q Learning (DQN) agent on the CartPole-v0 task from the OpenAI Gym.
Task
The agent has to decide between two actions - moving the cart left or right - so that the pole attached to it stays upright. You can ... |
Use Coulomb’s Law to find the force on a charge from two nearby charges.
Written by Willy McAllister.
Contents Coulomb’s Law Multiple charges Triangles Strategy Three point charges Summary Where we are headed
When you have more than two point charges pushing and pulling on each other, use Coulomb’s Law to find the forc... |
Consider the following convex continuous optimization problem:
min \(f(x)=\sqrt{(x'Qx)}-c'x\) s.t. \(e'x \leq 1\) \(x \geq 0,\)
where Q is positive definite, \(c\geq 0\) and \(e=(1,...,1)\).
I'm interested in any feasible point \(y\) satisfying \(f(y) < 0\). Assuming the \(f(z) < 0\) for the optimal solution \(z\). Is ... |
De Bruijn-Newman constant
For each real number [math]t[/math], define the entire function [math]H_t: {\mathbf C} \to {\mathbf C}[/math] by the formula
[math]\displaystyle H_t(z) := \int_0^\infty e^{tu^2} \Phi(u) \cos(zu)\ du[/math]
where [math]\Phi[/math] is the super-exponentially decaying function
[math]\displaystyle... |
F-singularities via alterations
Manuel Blickle, Karl Schwede, Kevin Tucker
Number 11 Author Prof. Dr. Manuel Blickle Year 2011
For a normal F-finite variety X and a boundary divisor \Delta we give a
uniform description of an ideal which in characteristic zero yields the
multiplier ideal, and in positive characteristic ... |
Noetherian Rings = Generalization of PIDs
When I was first introduced to Noetherian rings, I didn't understand why my professor made such a big
hoopla over these things. What makes Noetherian rings so special? Today's post is just a little intuition to stash in The Back Pocket, for anyone hearing the word "Noetherian" ... |
Today I learned about the Elliot Activation (or Sigmoid) Function. In fact, The MathWorks just included it in their most recent update to the Neural Network toolbox. The function was first introduced in 1993 by D.L. Elliot under the title A Better Activation Function for Artificial Neural Networks. The function closely... |
One can construct a finite measure on a compact metric space $(X,d)$ by the following procedure:
Fix a non-negative sequence $\{\epsilon_n\}$, $\epsilon_n \to 0$. Let $Y_{\epsilon_n}$ be the minimal covering net: $\bigcup_{y \in Y_{\epsilon_n}} \mathcal{B} (y, \epsilon_n ) = X$ and there is no lower-cardinality net wit... |
From previous lessons, you know that the derivative is the instantaneous rate of change of a function. We said that the derivative of a function at a certain point is just the slope of the function at that point. And to calculate that slope of the function at a given point, we make $\Delta x$ value smaller until it app... |
Difference between revisions of "Reflecting"
(typo)
(→$\Sigma_2$ correct cardinals: more information)
Line 31: Line 31:
If there is a pseudo [[uplifting]] cardinal, or indeed, merely a pseudo $0$-uplifting cardinal $\kappa$, then there is a transitive set model of ZFC with a reflecting cardinal and consequently also a ... |
Difference between revisions of "ORD is Mahlo"
(Vopěnka)
m (link)
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{{DISPLAYTITLE: $\text{Ord}$ is Mahlo}}
{{DISPLAYTITLE: $\text{Ord}$ is Mahlo}}
−
The assertion ''$\text{Ord}$ is Mahlo'' is the scheme expressing that the proper class
+
The assertion ''$\text{Ord}$ is Mahlo'' is the scheme expressing th... |
@Secret et al hows this for a video game? OE Cake! fluid dynamics simulator! have been looking for something like this for yrs! just discovered it wanna try it out! anyone heard of it? anyone else wanna do some serious research on it? think it could be used to experiment with solitons=D
OE-Cake, OE-CAKE! or OE Cake is ... |
The
Topic Model is a type of statistical model to find the topics that occur in a collection of documents.It is a frequently used text-mining tool for discovery of hidden semantic structures in a text body. For example, image to have some articles or a series of social media messages and we want to understand what is g... |
Difference between revisions of "Extendible"
(def etc.)
m (→Virtually extendible cardinals: ?)
Line 138: Line 138:
* The generic Vopěnka scheme is equivalent over ZFC to the scheme asserting of every definable class $A$ that there is a proper class of weakly virtually $A$-extendible cardinals.<cite>GitmanHamkins2018:Ge... |
Ľuboš Elexa, Ľubica Lesáková, Vladimíra Klementová and Ladislav Klement
growth of the region. In developed EU countries, current trends in the planning of regional development policy are based on supporting the creation and cluster building. Trends represent a significant shift from the traditional approach, such as th... |
I am new to neural networks. I tried coding the
backpropogation alogrithm and tried running it on a test set which gave wrong results. I have used the following knowledge to code it,
For the forward pass, $$z^l = w^la^{l-1} + b^l$$ $$a^l = g^l (z^l)$$
For the backward pass, (Here $\circ\text{ - Element wise Product}$)
... |
Let $M=\left (\omega\mathbb{I}-A\right )\left(\omega^{*}\mathbb{I}-A^{\dagger}\right)$ be a Hermitian matrix of size $n\times n$ where $A$ is a real non symmetric matrix and $\omega=a+\mathrm{i}b$. $A^{\dagger}$ represents the conjugate transpose of $A$.
I want to compute $\det[M]^{-\frac{1}{2}}$.
I know that for a rea... |
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For any arbitrary matrix,
[an+1bn+1]=[3+11−33−11+3][anbn]\left[ \begin{matrix} { a }_{ n+1 } \\ { b }_{ n+1 } \end{matrix} \right] \quad =\quad \begin{bmatrix} \sqrt { 3 } +1 & \quad 1-\sqrt { 3 } \\ \sqrt { 3 } -1 & 1+\sqrt { 3 } \end{bmatrix}\quad \left[ \begin... |
Pseudoscore Diagnostic For Fitted Model against Saturation Alternative
Given a point process model fitted to a point pattern dataset, this function computes the pseudoscore diagnostic of goodness-of-fit for the model, against moderately clustered or moderately inhibited alternatives of saturation type.
Usage
psstG(obje... |
I am reading
Optics by Eugene Hecht, and I am confused about the author's derivation of the differential wave equation:
To relate the space and time dependencies of $\psi(x, t)$, take the partial derivative of $\psi(x, t) = f(x')$ with respect to $x$, holding $t$ constant. Using $x' = x \mp vt$, and inasmuch as
$$\dfra... |
Let $P$ be a
convex $n$-gon. Suppose that we have an infinite number of $P$s, and that each of them is colored either red or blue. Here, let us consider the following operations : Operation 1 : Place a red $P$ on a plane.
$\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ $
Operation 2 : Place $n$ blue $P$s around the ... |
Page Content There is no English translation for this web page. Berliner Kolloquium Wahrscheinlichkeitstheorie und Seminar RTG 1845 Sommerstemester 2015
Datum Sprecher GK-Seminar 17:15-18:00 Sprecher Kolloquium (18:00-19:00) Ort 22. 4. 2015 (keiner, Ausstellung) Herbert Spohn (München) 17:15-18:15 U Potsdam Haus 8, Rau... |
This is the third part of a series consisting of three articles with the goal to introduce some general concepts and concrete algorithms in the field of neural network optimizers. As a reminder, here is the table of contents:
We covered two important concepts of optimizers in the previous sections, namely the introduct... |
№ 9
All Issues Tedeev A. F. On the behavior of solutions of the Cauchy problem for a degenerate parabolic equation with source in the case where the initial function slowly vanishes
Ukr. Mat. Zh. - 2012. - 64, № 11. - pp. 1500-1515
We study the Cauchy problem for a degenerate parabolic equation with source and inhomoge... |
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