text stringlengths 256 16.4k |
|---|
EDIT: See denesp's answer.
Here is some work I have so far. Someone can hopefully suggest help or provide a separate full answer.
So we have
$$u_A(x_A, y_A) = x_A + f(y_A)$$$$u_B(x_B, y_B) = x_B + f(y_B)$$
and we'll say that $x_A + x_B = X$ and $y_A + y_B = Y$
A's MRS:
$$-\frac{dx_A}{dy_A} = \frac{\frac{\partial U_A}{\... |
Let us consider $N$ independent scalar fields which satisfy the Euler-Lagrange equations of motion and are denoted by $\phi^{(i)}(x) \ ( i = 1,...,N)$, and are extended in a region $\Omega$ in a $D$-dimensional model spacetime $\mathcal{M}_D$. Now consider the classical Lagrangian density, $\mathcal{L}(\phi^{(i)}, \par... |
There are commands for the top two symbols
\ltimes and
\rtimes, however I have not been able to find commands for the other 4 symbols. Is there a simple way that I could create commands for these symbols?
There are commands for the top two symbols
Just combine existing symbols:
\documentclass{article}\usepackage{amssym... |
In the Numberlink puzzle [1] we need to connect end-points by paths over a board with cells such that:
Each cell is part of a path Paths do not cross
E.g. the puzzle on the left has a solution as depicted on the right [1]:
The picture on the left provides the end-points. The solution in the picture on the right can be ... |
The aims of this option are to introduce limit theorems and convergence of series, and to use calculus results to solve differential equations. Before beginning any work in this option, it is recommended that you revise Topic 1 and Topic 7 of the core syllabus, as a lot of background knowledge of those topics are helpf... |
Let $F$ be a cumulative density function on $\mathbb{R}$. From an argument in a textbook, it is shown that $F$ must be right-continuous:
Let $x$ be a real number and let $y_1$, $y_2$, $\ldots$ be a sequence of real numbers such that $y_1 > y_2 > \ldots$ and $\lim_i y_i = x$. Let $A_i = (-\infty, y_i]$ and let $A = (- \... |
The exponential distribution is the $\mathbf{\underline{only}}$ distribution that has the memoryless property. See this MathSE post.
Now that doesn't necessarily imply a Markov process must have only exponential jump times, but any examples without exponential jump times will likely be fairly trivial. The requirement i... |
Search
Now showing items 1-10 of 312
Series de Fourier aplicadas a problemas de cálculo de variaciones con retardo Series de Fourier aplicadas a problemas de cálculo de variaciones con retardo
(2012-03-22)
In this article we present an approximation of the minimizing function of the functional J[x]=\int_0^T F(t,X(t),X(... |
It's hard to say just from the sheet music; not having an actual keyboard here. The first line seems difficult, I would guess that second and third are playable. But you would have to ask somebody more experienced.
Having a few experienced users here, do you think that limsup could be an useful tag? I think there are a... |
In Conquering the Physics GRE 2nd edition, Exam 3 problem 20, the statement is as follows:
A metal bar is pulled at constant velocity $v\mathbf{\hat{x}}$ along two metal rails a distance $d$ apart connected by a resistor or resistance R, as shown in the diagram. There is a magnetic field, pointing into the page, of mag... |
Journal of Symbolic Logic J. Symbolic Logic Volume 56, Issue 3 (1991), 853-861. XVIIeme Probleme de Hilbert sur les Corps Chaine-Clos Abstract
A chain-closed field is defined as a chainable field (i.e. a real field such that, for all $n \in \mathbf{N}, \mathbf{\Sigma K^{2n+1}} \neq \mathbf{\Sigma K^{2n}}$) which does n... |
1. Direct Relationship Analysis
Direct relationship analysis includes partial dependence plot, individual conditional expectation, feature interaction, feature importance, and etc.
1.1 Partial Dependence Plot (PDP)
PDP shows marginal effect which one or two features have on the predicted outcome of a machine learning m... |
The set \(\mathbb{P}^1(\QQ)\) of cusps¶
EXAMPLES:
sage: CuspsSet P^1(QQ) of all cusps
sage: Cusp(oo)Infinity
class
sage.modular.cusps.
Cusp(
a, b=None, parent=None, check=True)¶
A cusp.
A cusp is either a rational number or infinity, i.e., an element of the projective line over Q. A Cusp is stored as a pair (a,b), wher... |
Fraction of payment to interest during the ith payment
\(\phi = \frac{rB_i}{P} \)
\( \phi \)
Fraction of payment to interest
\(\phi = \frac{rB}{P} \)
\( r \)
Interest rate
\( t_\text{term} \)
Loan term
\( n \)
Number of loan payments
\( \Delta t \)
Time between loan payments
\( \Delta t = \frac{t_\text{term}}{n} \)
\( ... |
In complex analysis, the winding number (around the origin) of a continuous loop $\gamma: [0,1] \to \mathbb{C} \setminus \{0\}$ is the number of times the loops "winds" around zero, which is given by the integral
$$\frac{1}{2 \pi i}\int_\gamma \frac{dz}{z}$$
One of the basic results of algebraic topology is that loops ... |
I'm having issue understanding the process of defining a domain while attempting to divide rational expressions:
$$ \frac {x^2+x-6}{x^2+3x-10} : \frac {x+3}{x-5} $$
We can factor to the form
$$ \frac {(x+3)(x-2)}{(x+5)(x-2)} : \frac {(x+3)}{(x-5)} $$ In the textbook I follow, I was told that the expression is undefined... |
According to Schwarzschild metric:
$$ c^2~\mathrm d\tau^2 = \left(1-\frac{r_s}{r}\right)c^2 ~\mathrm dt^2 - \left(1-\frac{r_s}{r}\right)^{-1}~\mathrm dr^2 - r^2\left(\mathrm d\theta^2 + \sin^2\theta~\mathrm d\varphi^2 \right) $$
,where $r_s$ is Schwarzschild radius: $ r_s = \frac{2GM}{c^2} $
the density element $$ \rho... |
We have the following generalized eigenvalue (set of) problem(s)
$$[K_R(\kappa)]\{u_R\} = \omega^2[M_R(\kappa)]\{u_R\}\quad \forall \kappa \in [\kappa_0, \kappa_1]$$
with
\begin{align} &K_R(\kappa) = T^H(\kappa) K T(\kappa)\, ,\\ &M_R(\kappa) = T^H(\kappa) M T(\kappa)\, ,\\ &u = T(\kappa) u_R\, . \end{align}
Where $K$ ... |
I am trying to interpret the variable weights given by fitting a linear SVM.
A good way to understand how the weights are calculated and how to interpret them in the case of linear SVM is to perform the calculations by hand on a very simple example.
Example
Consider the following dataset which is linearly separable
imp... |
Health Statistics (24). Note: In real-world analyses, the standard^ James R.Statisticalan average score of 1000 with a standard deviation of 100.
As the sample size increases, the sampling distribution be expected, larger sample sizes give smaller standard errors. Because the sample sizes are large enough, we standard ... |
In Union-Find with link-by-rank but no path compression find a sequence of operations Make-Set, Find, Union of length $m$, containing $n$ Make-Set operations, and with time complexity in $\Omega(m\log n)$.
My idea was to spawn $n$ nodes with $n$ Make-Set operations and then create a "tree" with $\log n$ height out of t... |
Search
Now showing items 1-2 of 2
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
I was looking for a formulation of 'free sets' and 'independent sets' from linear algebra that would extend to groups. This question was considered here but I couldn't find a satisfactory definition in the literature so I'd like to suggest the following simple approach. Let $G$ be a finite group, and for eac... |
This answer is a hard-science expansion of this answer. Please read that other answer to get a description of the system I am proposing, as well as justification of its technical feasibility. That post also has lots of reference links for various design decisions. I will summarize the system here and numerically addres... |
Almost everyone has heard of this sequence: 1,\ 1,\ 2,\ 3,\ 5,\ 8,\ etc. It is named after Leonardo of Pisa who introduced it to the western world in one of the most influential books ever published in mathematics – Liber Abaci. This book introduced Europe to the Hindu numerals 0 through 9, the word zero, the notion of... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
3.2. Linear Regression Implementation from Scratch¶
Now that you understand the key ideas behind linear regression, we canbegin to work through a hands-on implementation in code. In thissection, we will implement the entire method from scratch, including thedata pipeline, the model, the loss function, and the gradient ... |
I'd like to estimate the
drift of a continuous-paths, non-stationary, stochastic process $X_t$ from a time series of values $\{X_{i\Delta t}\}_{i=1,\dots,N}$ sampled from a single realisation of that process over $t \in [0,T]$.
Although the objective is to calibrate a pricing model (specified under $\Bbb{Q}$) based on ... |
Motivation: I am studying the graph isomorphism problem. I am trying to construct a partitioning method to reduce search cases . Partition method:$G$ is an $r$ regular graph, $k$ connected (not a complete, cycle graph). A vertex of $G$ is $x_1$. All vertices which are not adjacent to $x_1$ create a sub-graph $C_1$. All... |
I can turn-the-crank and show that $\frac{1}{2}\otimes \frac{1}{2} = 1\oplus 0$ etc, but what would be a strategy to proving the general statement for spin representations that $j\otimes s =\bigoplus_{l=|s-j|}^{|s+j|} l$.
It's easy to prove the formula if you just look at the individual basis vectors of the tensor prod... |
It's hard to say just from the sheet music; not having an actual keyboard here. The first line seems difficult, I would guess that second and third are playable. But you would have to ask somebody more experienced.
Having a few experienced users here, do you think that limsup could be an useful tag? I think there are a... |
As many other have just said you cannot think to study just some particular subjects ignoring some other areas, expecially if you want to do research. Most of math was born from the observation of some similar phenomena in many different areas: for instance the concept of category itself was born from the observation t... |
Even though you say that the geometry of this is fairly clear to you, I think it is a good idea to review it. I made this back of an envelope sketch:
Left subplot is the same figure as in the book: consider two predictors $x_1$ and $x_2$; as vectors, $\mathbf x_1$ and $\mathbf x_2$ span a plane in the $n$-dimensional s... |
Definitions
Definition 1: Let $S$ be a set of words. We say that $S$ is nicely infinite prefix-free (made up name for the purpose of this answer) if there are words $u_0,\dots,u_n,\dots $ and $v_1,\dots,v_n,\dots $ such that:
For each $n\ge 1$, $u_n$ and $v_n$ are non-empty and start with distinct letters;
$S=\{u_0v_1,... |
Here is my take on it. It is somewhat similar to what many others have said but I will try to explain in greater detail, so bear with me in terms of length.
Power from engineFirst let us understand power-torque relationship for an engine. The working fluid of the engine (expanding combustion gases) apply a torque on th... |
I am self-studying electrodynamics and am wanting to know what is meant by a potential. I understand the concept of
potential energy but what is meant by a potential? Is it the same thing as a field, like gravitation or electromagnetic?
I am self-studying electrodynamics and am wanting to know what is meant by a potent... |
Let $X_1,\dots,X_n$ be compact Hausdorff spaces. Let's define the Varopoulos algebra as the projective tensor product: $$V(X_1,\dots,X_n) := C(X_1) \hat{\otimes} \dots \hat{\otimes} C(X_n),$$ i.e. the space of functions on $X_1 \times \dots \times X_n$ that can be represented as $$f = \sum_k f_{1k} \otimes \dots \otime... |
If one needs to write a limit as an exponent, one might have this dilemma: if you use
\displaymath, "x to infinity" will be nicely printed under the lim symbol, but your exponent will be using the normal font and will appear very big on the page. If you take out the
\displaymath instruction, the exponent will use the s... |
We will be offering mothur and R workshops throughout 2019. Learn more. Sharedace Example Calculations *.sharedAce Example calculations below will be performed using data from the Eckburg 70.stool_compare files with an OTU definition of 0.03. Estimating the richness of shared OTUs between two communities. A Non-paramet... |
Practical values for pullup resistors could be anywhere in the 4.7k to 20k, even 50k. The value is not always very critical. Try one of those, that may do the job.
You are correct, the datasheet is talking about whatever will be driving that OE pin. Now, the driving pin has some maximum current sourcing/sinking capabil... |
56 6 Homework Statement Car A drives a curve of radius 60m with a constant velocity of 48 km/h. When A is at the given position, car B is at 30m away from the intersection and accelerating at 1.2 m/s^2 to the south. Calculate the lenght and direction of the acceleration that car B would measure of car A from its perspe... |
Search
Now showing items 1-10 of 15
A free-floating planet candidate from the OGLE and KMTNet surveys
(2017)
Current microlensing surveys are sensitive to free-floating planets down to Earth-mass objects. All published microlensing events attributed to unbound planets were identified based on their short timescale (bel... |
Building a plugin¶
Writing your own PennyLane plugin, to allow an external quantum library to take advantage of the automatic differentiation ability of PennyLane, is a simple and easy process. In this section, we will walk through the steps for creating your own PennyLane plugin. In addition, we also provide two defau... |
I want to find the roots for $\kappa$ for the equation
$$\sqrt{\alpha - 1} \cos{\left (\frac{\sqrt{2} \sqrt{\alpha - 1}}{2 \sqrt{\epsilon}} \right )} \cosh{\left (\frac{\sqrt{2} \sqrt{\alpha + 1}}{2 \sqrt{\epsilon}} \right )} - \sqrt{\alpha - 1} \\ -\frac{1}{\sqrt{\alpha + 1}} \sin{\left (\frac{\sqrt{2} \sqrt{\alpha - ... |
The net cell reaction of an electrochemical cell and its standard potential is given below: $$\ce{ Mg + 2Ag+ ->Mg^{2+} + 2Ag} \ \ \ \ \ \ \ \ E^\circ=3.17\:\mathrm{V}$$ The question is to find the maximum work obtainable from this electrochemical cell if the initial concentrations of $\ce{Mg^{2+}}=0.1\ \mathrm{M}$ and ... |
I am looking for an example where $f:Y\to X$ and $f':Y'\to X$, are both smooth maps of smooth manifolds, but the pullback does not exist.
Remarks:
1) A pullback in a certain category is defined as a space satisfying a universal property, not as a fiber product. (Which is just the usual form of many pullbacks...). See a... |
Suppose a particle that is under a quantum oscillator potential and is, initially, in the state $\Psi(x,0)=\frac{1}{\sqrt3}\phi_1(x)+\sqrt{\frac23}\phi_2(x)$, where $\phi_1(x)$ and $\phi_2(x)$ are eigenstates of the operator $\hat{H}$. Three consecutive measurements are performed: first, the energy $E$ is measured; the... |
One shouldn't imagine the T-duality between the two heterotic strings to be a $Z_2$ group, like in the case of type II string theories' T-duality. In type II string theory, there is only one relevant scalar field, the radius of the circle producing T-duality, and it gets reverted $R\to 1/R$ under T-duality.
In the hete... |
In [1] a simple optimization model is presented for the scheduling of patients receiving cancer treatments. [2] tried to use this model. This was not so easy: small bugs in [1] can make life difficult when replicating things.
We use the data set in [2]:
There are \(T=40\) time slots of 15 minutes We have 23 chairs wher... |
The factor $\frac12$ comes in because we're integrating the equation$$\frac{\mathrm dE}{\mathrm dv}=mv$$once.
Less abstract and only using basic arithmetics, the story goes like this:
When accelerating a body by applying a (constant) force $F$ along a distance $\Delta s$, the body gains energy according to$$\Delta E=F\... |
Negative Factorials and their Quotients
Dante
A factorial of a number is, for most cases, an equation that multiplies an integer by every other integer less than itself. Or, mathematically speaking,
$$1!=1$$
$$2!=2\cdot 1=2$$
$$3!=3\cdot2\cdot1=6$$
$$4!=4\cdot3\cdot2\cdot1=24$$
$$5!=5\cdot4\cdot3\cdot2\cdot1=120$$
Noti... |
The arc length of a graph of a function $f(x)$ is
$$\mathcal{l} = \int_a^b \sqrt {1 + f'(x)^2} dx$$
If you choose $f$ to be a parametrization of the ellipse with $a=1, b=\frac{1}{2}$, i.e. $f(x) = \frac{1}{2} \sqrt{1-x^2}$, the arc length of the graph of this function is
$$\mathcal{l} = \int_0^1 \sqrt\frac{1-\frac{3x^2... |
I was trying to solve $ \displaystyle \sum_{n = 1}^{\infty} \frac{n^3}{8^n}$ and I found a way to solve it and I want if there are generalizations for, say, $\displaystyle \sum_{n=1}^{\infty} \frac{n^k}{a^n}$ in terms of $k$ and $a$. I would also like to know if there is a better way to solve it. Here's how I did it:
F... |
Easier Eigenvectors For Hermitian Matrices
Dante
If you're wondering what an eigenvalue, or eigenvector is, thank whatever god you pray to and move on. However, if you're morbidly curious,
eigenvalues
and their respective
eigenvectors
are nontrivial solutions the
this equation
.
$$A\vec{v}=\lambda\vec{v}$$
And by nontr... |
Deformation: Continuously modify the structure constants! Contraction: Generators are multiplied with contraction parameters that are then sent to zero or infinity.
Both concepts are mutually the opposite. However while one can always deform to a group where we contracted from, the opposite procedure is not always poss... |
Posted: January 15, 2013
In a previous post, I discussed how an equation-oriented language like Madonna/STELLA could be translated into Modelica. The point of that post was to demonstrate how constructs in those languages could be mapped to Modelica. But an important caveat in that discussion was that a straight transl... |
I just started to learn how to quantise Dirac field. Meanwhile, as we can write the Dirac equation in terms of gamma matrices :
$$ (i\hbar\gamma^\mu\partial_\mu - m)\psi = 0 $$ where $\gamma_\mu$ matrices obey Clifford algebra $$ \{\gamma^\mu,\gamma^\nu\} = \eta^{\mu\nu} $$
Now I just came across that the adjoint of th... |
Determine whether the following series : $$\sum_{n=2}^\infty \frac {1+xn}{\sqrt{n^2+n^6x}}, x \in \mathbb R^+_0$$ converges absolutely, conditionally or diverges.
I tried to estimate the series for $n > x$ using the following: $$\sum_{n=2}^\infty \frac {1+xn}{\sqrt{n^2+n^6x}} \leq \sum_{n=2}^\infty \frac {2xn}{\sqrt{n^... |
Hello, I have a question which is related to a partial order in a set of self-adjoint operators.
Let $\mathcal{M}$ be a semifinite von Neumann algebra with a faithful semi-finite normal trace $\tau$. Let $T$ and $S$ be two self-adjoint operators (possibly unbounded) $\tau$-measurable (here probably the assumption that ... |
An atom with two energy levels has 2 states (excited and ground), represented by kets $|e\rangle$ and $|g\rangle$ respectively. The atom has energy $\frac{1}{2}E_\theta$ when excited and $-\frac{1}{2}E_\theta$ when in ground state.
Suppose it is prepared in the state $$|\Psi\rangle = \frac{1}{5}((2-i)|e\rangle + (4+2i)... |
This may not be a consequence of biased estimators or sampling error. I don't think it is a coincidence that$$\frac{6}{\pi} \arcsin\left(\frac{0.9}{2} \right) = 0.891457\ldots \approx 0.891$$Copula construction involves applying nonlinear transformations to random variables which need not preserve correlation.If random... |
Suppose I have an operation on a set X which I want to denote with something like
$X^\prime$,
$X^\bullet$, or
$X^\circ$, except with a different symbol. I found out that some of the diacritics available in math mode (see here) make a decent candidate when used “standalone”, for instance as
$X \: \tilde{}$ or
$X \: \hat... |
Documenting MagAO-X¶ Where the documentation lives¶
This source code for this documentation lives in the magao-x/handbook repository. Parts of the documentation pertaining to the core C++ code are generated from the code in magao-x/MagAOX, which is documented in Doxygen. (TODO: explain how to make cross-references.)
Th... |
How to find the dimension of the group $O_{p,q}(\mathbb R)= \{g \in GL_n(\mathbb R): g^TI_{p,q} \ g = I_{p,q}\}$, where $I_{p,q}= diag(1,..., 1,-1,...,-1)$ and $p+q=n$?
closed as off-topic by Derek Holt, Watson, Bobson Dugnutt, vrugtehagel, colormegone Mar 10 '16 at 23:16
This question appears to be off-topic. The user... |
As others have mentioned, performing a 2D FFT on the kernel will give you the frequency response of the filter. However, it's worth mentioning that 2D filters can be analyzed using the Z-transform, which may or may not provide deeper insight, depending on the filter (and what you want to know).
For example, given the k... |
fskilnik wrote:
GMATH practice exercise (Quant Class 20)
A triangle of area 30 is formed by the line x/c + y/(c+7) - 1 = 0 (where c is a positive constant) and the coordinate axes. What is the perimeter of this triangle? (A) 12 (B) 24 (C) 30 (D) 36 (E) 52
Yes... 5-12-13 is an important GMAT Pythagorean Triple...
\(?\,\... |
Initial investment Final value of investment Rate of return
Here we will answer the question, where does the rule of 72 come from? And how can we derive similar rules for other tripling or other multiplicative factors?
The rule of 72 is an estimate for the doubling time of an investment at a given rate of return.
As an... |
Initial Note
The highest priority input is RESET. If low, the FF is actively
. But you have that tied high. So RESET isn't active. reset 1st Schematic Results
The next highest priority input is TRIG. But only if it is low (below it's \$\frac13\$\$^\text{rd}\$ threshold.) If low, it actively
the FF. If it is above that ... |
A copper rod with length L is moving on two frictionless conducting rails, in a distance a from an very long straight conductor. The rods resistance: R. Ignore any self inductance. The magnetic permeability is $\mu_0$
a) Find the direction and magnitude of the induced current.
I know I could probably just use faradays ... |
What you have to do is to show that the dollar gamma satisfies the Black-Scholes PDE. Using Feynman-Kac it then follows that the dollar gamma is an expectation of a "payoff", just like the Black-Scholes claim price is an expectation of a payoff. And if something is the expectation of a payoff then it's a martingale.I'l... |
Problem:Consider a graph $G = (V, E)$ on $n$ vertices and $m > n$ edges, $u$ and $v$ are two vertices of $G$.
What is the asymptotic complexity to calculate the shortest path from $u$ to $v$ with Dijkstra's algorithm using Binary Heap ?
To clarify, Dijkstra's algorithm is run from the source and allowed to terminate wh... |
I'm implementing a Finite Difference WENO5 with Lax-Friedrich flux splitting on a uniform, structured grid to solve the 2D Euler equations of fluid dynamics on a rectangular domain in cartesian coordinates.
$$\frac{\partial U}{\partial t}+\frac{\partial F}{\partial x}+\frac{\partial G}{\partial y}=0$$
where:
$$U = (\rh... |
The feature that makes LaTeX the right editing tool for scientific documents is the ability to render complex mathematical expressions. This article explains the basic commands to display equations.
Contents
Basic equations in LaTeX can be easily "programmed", for example:
The well known Pythagorean theorem \(x^2 + y^2... |
Prove that$$I=\int_0^\infty \frac{\ln(1+x+x^2)}{1+x^2}dx=\frac{\pi}{3}\ln(2+\sqrt 3)+\frac43G$$
I've found this integral in my notebook and perhaps I encountered it before since it looks quite familiar. Anyway I thought it's quite a trivial integral so I'm gonna solve it quickly, but I am having some hard time to finis... |
Is there somewhere on the internet I can find cosmological redshift data. In particular, I would like to know the redshift around the time when the acceleration of the Universe began to accelerate.
One of the main places where data about galaxies gets aggregated is the NASA Extragalactic Database (NED). For example, he... |
How can I make all the text in math mode as bold and italics? I need some code which will make all the math text bold and italics at once.
Hope this may help you:
\documentclass{book}\usepackage{amsmath}\mathversion{bold}%this does the trick\begin{document}This is for test $a+b=c\alpha\beta\gamma$\end{document}
Merry X... |
Problem 1: Food
This is the major contributing factor to the
size of the biosphere. Humans need to consume around 2,250 calories per day (averaged between men and women) to sustain themselves, and more if they are doing physical work. 2,250 cal = 10,460 joules (or 10.46kJ), but that's not very useful. More useful: 100g... |
I am reading a paper called "Rational Proof". It mentioned the following one-to-one reduction. I cannot google an introduction of it.
An excerpt from the paper. "Recall that a one-to-one reduction from a function $f$ to another function $g$ is a triple of polynomial time computable functions ($\alpha$, $\beta$, $\gamma... |
(HP65) Factorial and Gamma Function
10-21-2017, 08:32 AM (This post was last modified: 10-26-2017 05:10 AM by Gamo.)
Post: #1
(HP65) Factorial and Gamma Function
Just noticed that HP 65 cannot calculate decimal Factorial and HP67 app for Android also cannot do it.
Here is a handy program using Stirling's approximation ... |
A famous result by Motzkin and Straus expresses the $k$-clique problem as the maximization of a quadratic function subject to a system of linear constraints. In particular, they prove:
Let $G$ be a graph with vertices $1,\ldots,n$ and edge set $E$.
Then $G$ contains a $k$-clique,
if and only if there exist real numbers... |
Without magnetic monopoles, the Maxwell equations are these (I'm dropping vector notations and all constants, for simplicity): \begin{align} \nabla \cdot E &= \rho_{elec}, \tag{1} \\[12pt] \nabla \times E &= -\, \frac{\partial B}{\partial t}, \tag{2} \\[12pt] \nabla \cdot B &= 0, \tag{3} \\[12pt] \nabla \times B &= J_{... |
Support vector machines are the canonical example of the close ties between convex optimization and machine learning. Trained on a set of labeled data (i.e. this is a
supervised learning algorithm) they are algorithmically simple and can scale well to large numbers of features or data samples, and have been shown to be... |
Goals
I need to design resonant parallel circuit and simulate it with LTSpice so that it match with the design requirements correctly.
Requirements Source Impedance \$R_s = 100\ \Omega\$ Load Impedance \$R_l = 1\ k\Omega\$ Resonant Frequency \$f_o = 100\ MHz\$ Bandwidth \$BW_{3dB} = 150\ kHz\$ Schematic Approach
Find t... |
I am working on a project which requires that I calculate homotopy limits of homotopy theories (i.e. $(\infty,1)$-categories). It may be relevant that the homotopy limits which interest me are in the shape of towers; that is, the indexing category looks like $\cdots\rightarrow\cdot\rightarrow\cdot$. Because I am intere... |
I would like to use the following model in QuantLib:
$\frac{dF(t,T)}{F(t,T)} = \sigma_se^{-\beta(T-t)}dW_{t}^{1} + \sigma_L\left(1-e^{-\beta(T-t)}\right)dW_{t}^{2}$
This is a reformulation of the Schwartz Smith model (Schwartz-Smith). $F(t,T)$ is the commodity future price and the model is to be calibrated to American ... |
I am interested in the topology on schemes where surjective morphisms of finite presentation are coverings. In particular, I am interested in the topology on Noetherian schemes where surjective morphisms of finite type are coverings. So, the morphism $U\sqcup Z\to X$, where $Z\subset X$ is a closed subscheme of a Noeth... |
I have the followwing Lagrangian for the free electromagnetic field,
$$\mathcal{L} = -\frac{1}{4} F^{\mu \nu}F_{\mu \nu},$$
and the canonical stress tensor is,
$$T^{\alpha \beta}=\frac{\partial \mathcal{L}}{\partial \left(\partial_{\alpha} A^{\lambda}\right)}\partial^{\beta} A^{\lambda}-g^{\alpha \beta}\mathcal{L}.$$
M... |
If I have an optical transparent slab with refractive index $n$ depending on the distance $x$ from the surface of the slab, the refractive index can be described by: $$n(x)=f(x)$$ where $f(x)$ is a generic function of $x$. so, we can write: $$\dfrac{dn(x)}{dx}=f'(x)$$ The snell law of refraction states: $$n_1\sin(\thet... |
I was reviewing time series textbooks recently and have been left confused since.
In particular I have looked into the book of Brockwell and Davis (Introduction to Time Series and Forecasting, Second Edition).
In section 2.3 it is said (just after eq 2.3.4) that there is a unique stationary solution to the ARMA(1,1) eq... |
Codeforces Round #498 (Div. 3) Finished
Mishka got an integer array $$$a$$$ of length $$$n$$$ as a birthday present (what a surprise!).
Mishka doesn't like this present and wants to change it somehow. He has invented an algorithm and called it "Mishka's Adjacent Replacements Algorithm". This algorithm can be represente... |
Perhaps the right way for you to think about it is this: there is only one generator, and it is a big $N\times N$ matrix where $N$ is the number of all of the independent fermion degrees of freedom. To be exact, all of the generators of a symmetry are like this, but we are often able to ignore the full size of each mat... |
Property \((UW_\Pi )\) holds for a bounded linear operator \(T \in B(X),\) defined on a complex infinite dimensional Banach space X, if the poles of the resolvent of T are exactly the spectral points \(\lambda \) for which \(\lambda I-T\) is upper semi-Weyl. In this paper, we discuss the relationship between property \... |
Take the 1st order Taylor series the function $log(x)$. around one:$$ log(x) \approx log(1) + \frac{x-1}{1} = x-1$$
Therefore, for a random variable r that is close to zero:$$ log(1+r) \approx r$$
Log returns are typically something like $log(P_{new}/P_{old})$:$$\Delta log(P_t) = log(P_{new}/P_{old}) = log((P_{old} + \... |
The expression in question is in footnote $11$ of the referenced article. Reading the paper, we see that the decision variable here is "the payout rate", which is the reciprocal of $P$. So equivalently, we can solve the maximization problem with respect to $P$ (and not w.r.t. $Q$). More over, "price elasticity of deman... |
This question already has an answer here:
It’s not clear what exactly is happening.
Chemistry Stack Exchange is a question and answer site for scientists, academics, teachers, and students in the field of chemistry. It only takes a minute to sign up.Sign up to join this community
This question already has an answer her... |
Every time I think I get what Rice's theorem means, I find a counterexample to confuse myself. Maybe someone can tell me where I'm thinking wrong.
Lets take some non-trivial property of the set of computable functions, for example let $L = \{ f : \mathbb{N} \to \mathbb{N} \;|\; \text{f is a computable and total functio... |
T. Nagell in [
Norsk Mat. Forenings Skrifter. 1:4 (1921)]shows that, for an odd prime $q$, the equation$$x^2-y^q=1 \qquad (*)$$has a solution in integers $x>1$, $y>1$, then $y$ is even and $q\mid x$.In his proof of the latter divisibility he uses a similar trick as follows.
Assuming $q\nmid x$ write ($*$) as$$x^2=(y+1)... |
The Dirac Equation is given by $$\left(i\gamma^\mu\partial_\mu- \frac{mc}{\hbar}\right)\Psi_D = 0,$$
where $\gamma^\mu$ are the Dirac $\gamma$-matrices and $\Psi_D$ is a Dirac spinor. I would like to find the transformation $U$ such that the two-component Weyl spinors $\Psi, \hat{\Psi}$ solve the equation $$i\left( \be... |
I was reading about differentiable manifolds on wikipedia, and in the definition it never specifies that the differentiable manifold has a metric on it. I understand that you can set up limits of functions in topological spaces without a metric being defined, but my understanding of derivatives...
HiI am currently tryi... |
Consider a charged black hole in four-dimensional Minkowski spacetime, with charge $Q$, mass $M>Q$:
$ds^2=-f(r)dt^2+\frac{1}{f(r)}dr^2+r^2d\Omega_2^2$, with
$f(r)=1-\frac{2M}{r}+\frac{Q^2}{r^2}$.
When an observer at radial coordinate $r_1$ emits a photon, an observer at radial coordinate $r_2>r_1$ will perceive the pho... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.