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Question: Can we have a model of $ZF-\text {Regularity}$ where there exist an ordinal $\kappa$ such that $H_{\kappa}$ exists and $H_{\kappa}$ is not equinumerous to any well founded set?
The motivation for this question comes in connection with defining Cardinality under some situations beyond Regularity and Choice. Es... |
This problem can arise not just in vehicle routing but in many sorts of sequencing problems (such as scheduling jobs for production). Of course, preserving the original ordering to the extent possible is not always a concern, but it might be if, for instance, the existing stops are customers who have been promised some... |
493 0 an integral expression for Pi(x)....
hello i have discovered a new method to calculate [tex]\pi(e^x) [/tex] it runs in O(x^d) operations d>0 it is very simple:
Forst of all we have the integral for Pi(x) as knows:
[tex]Ln\zeta(s)=s\int_0^{\infty}\frac{\pi(x)}{x^{s}-1}dx [/tex]
we make the change of variable x=exp... |
In Locatello et al's Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations he claims to prove unsupervised disentanglement is impossible.
His entire claim is founded on a theorem (proven in the appendix) that states in my own words:
Theorem: for any distribution $p(z)$ where each v... |
How does one get the frequency response of a filter, given an input signal and the signal output by the filter?
The plant output data is usually generated using Gaussian white-noise excitation, although more informative input signals can be generated by experiment design, if prior information about the plant is known [... |
closed as no longer relevant by Robin Chapman, Akhil Mathew, Yemon Choi, Qiaochu Yuan, Pete L. Clark Aug 22 '10 at 9:00
This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicabl... |
Advances in Differential Equations Adv. Differential Equations Volume 16, Number 11/12 (2011), 1087-1137. Local well-posedness and a priori bounds for the modified Benjamin-Ono equation Abstract
We prove that the complex-valued modified Benjamin-Ono (mBO) equation is analytically locally well posed if the initial data ... |
Get your free trial content now! Video Transcript Transcript Zero and Negative Exponents
In a land of two kingdoms, rival
Kings Wallace the 4th and Frederick the negative 3rd enjoy playing pranks on each other. King Wallace receives a package from his rival, but is it a package or a prank ? It’s a painting…
Oh my! How ... |
The convolution of two signals in the time domain is equivalent to the multiplication of their representation in frequency domain. Mathematically, we can write the convolution of two signals as$$y(t) = x_{1}(t)*x_{2}(t)$$ $$= \int_{-\infty}^{\infty}x_{1}(p).x_{2}(t-p)dp$$
Let us do the convolution of a step signal u(t)... |
Babb, Jeff; Currie, James(Montana Council of Teachers of Mathematics & Information Age Publishing, 2008)
Large context problems (LCP) are useful in teaching the history of science. In this article we consider the brachistochrone problem in a context stretching from Euclid through the Bernoullis. We highlight a variety ... |
I would like to particularly address this nice question relating the Hamiltonian formulation of this superconducting state (via Bogoliubov-de Gennes (BdG) equation) to the low energy quantum field theory, especially the Topological Quantum Field Theory (TQFT).
What is a $p_x+i p_y$ superconductor:
It is a chiral $p$-wa... |
Since several other people have posted solutions using the same packages you were using, here is an alternative. I would personally recommend a modern toolchain with Unicode and OpenType math fonts whenever you aren't forced to use the legacy packages. Every single OpenType math font, including the default, comes with ... |
The trick here is to notice that the Witten index for a finite temperature $\beta$ is given by
$$\text{Tr}\left\{(-1)^Fe^{-\beta H}\right\}=\int_{\text{PBC}}\mathcal{D}\phi\mathcal{D}\overline\psi\mathcal{D}\psi\,e^{-S},$$
where the boundary conditions are on a circle of circumference $\beta$. Next, we know that the Wi... |
Can anyone throw some light on using accelerometers to measure angular acceleration and hence angular velocity. This approach is to avoid gyroscopes due to drifting errors. Any links for this also would be very helpful.
Thank you.
Robotics Stack Exchange is a question and answer site for professional robotic engineers,... |
Edit: I'm a dumbass. The thing below is supposed to be just the motivation of asking. I want to ask for below and in general, hehe.
Assume that we have a general one-period market model consisting of d+1 assets and N states.
Using a replicating portfolio $\phi$, determine $\Pi(0;X)$, the price of a European call option... |
Local principles
Part of the Universitext book series (UTX)
Chapter
Abstract
Before we start our walk through the world of local principles, it is useful to give a general idea of what a local principle should be. A local principle will allow us to study invertibility properties of an element of an algebra by studying ... |
December 1st, 2018, 04:33 AM
# 1
Newbie
Joined: Dec 2018
From: Canada
Posts: 1
Thanks: 0
The inverse of one angle and the side opposite to the angle, which is equal to one, in all triangles gives a diameter of the circumscribed circle.
In a right triangle, the inverse of the angle is always 1, which is the circle's dia... |
Research Open Access Published: Multiple periodic solutions for second order Josephson-type differential systems Boundary Value Problems volume 2017, Article number: 99 (2017) Article metrics
831 Accesses
Abstract
In this paper, some new existence theorems are obtained for multiple periodic solutions of second order Jo... |
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In the figure above, area of circle is 50 and area of triangle is 15.
If the value of sinθ+sinα+sinβ \sin\theta + \sin\alpha + \sin\beta sinθ+sinα+sinβ equal to mnπ\dfrac mn \pi nmπ for coprime positive integers mmm and nnn, find the value of m+nm+nm+n.
Problem L... |
This is a problem from Billingsley's text
Probability and measure.
Suppose that $f$ is nonnegative on a $\sigma$-finite measure space $(\Omega, \mathscr{F}, \mu)$. Show that $$\int_\Omega f d \mu = (\mu \times \lambda)[(\omega, y) \in \Omega \times \mathbb{R}^1: 0 \leq y \leq f(\omega)]. \tag{1}$$ Prove that the set on... |
How to find the Horizontal asymptote for this function:
$f(x)= \sqrt {9x^2+2x}-3x$
I have tried to find the lim where x goes to infinity and negative infinity then what ?
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 m... |
For simplicity, let us talk about a scalar field $\phi : \mathbb{R}^4 \rightarrow \mathbb{R}$.
The action for a
free scalar field is
$$S[\phi] = \frac{1}{2}\int_{\mathbb{R}^4} \partial_\mu\phi\partial^\mu\phi - m^2\phi^2$$
and its classical equations of motion is the
Klein-Gordon equation
$$ (\partial_\mu\partial^\mu +... |
The inverse tangent function atan(z)(denoted by Atan(z) in the Fungrim formula language) is a function of a single variable. The following table lists conditions such that Atan(z) is defined in Fungrim.
The inverse tangent function atan2(y,x)(denoted by Atan2(y, x) in the Fungrim formula language) is a function of two ... |
A Lack of Confidence Interval
Thu 15 February 2018by Steven E. Pav
For some years now I have been playing around with a certain problemin portfolio statistics: suppose you observe \(n\) independent observationsof a \(p\) vector of returns, then form the Markowitz portfolio based onthose returns. What then is the distri... |
Line 35: Line 35:
This algorithm is mainly used to construct long exposure star-trails images.
This algorithm is mainly used to construct long exposure star-trails images.
Pixels of the image are replaced by pixels at the same coordinates if intensity is greater.
Pixels of the image are replaced by pixels at the same c... |
Notice:
If you happen to see a question you know the answer to, please do chime in and help your fellow community members. We encourage our fourm members to be more involved, jump in and help out your fellow researchers with their questions. GATK forum is a community forum and helping each other with using GATK tools a... |
Background Information:
This question is from Lectures on Financial Mathematics: Discrete Asset Pricing.
Theorem 3.2 First Fundamental Theorem of Asset Pricing - Suppose $\nu$ is any measure such that $S/S^{0}$ is a $\nu$-martingale. For an attainable claim $X$ with replicating strategy $\phi$ and $0\leq t\leq T$, we h... |
In this paper we consider dynamic networks that can change over time. Often, such networks have a repetitive pattern despite constant and otherwise unpredictable changes. Based on this observation, we introduce the notion of a
ρ-recurring family
of a dynamic network, which has the property that the dynamic network freq... |
Inside a Schwarzschild black hole
Hello and welcome
Ever wondered what lies beyond the of a ? Current thinking asserts any one of numerous outcomes; time travel, wormholes, being crushed to a point, or instead, perhaps a fiery end in a wall of flame, making it very hard to know what to believe. We offer a somewhat more... |
Geometry is a branch of mathematics that concerned with shapes, points, lines and much more. Geometry Formulas are used to calculate the length, perimeter, area and volume of different geometric figures and shapes. They are also used to calculate the arc length, radius etc.
In class 9 students will learn about coordina... |
Why does the phase shift between the input and the output of a transfer function vary with the frequency of the input sinusoid?
Assuming you're asking about Linear and Time-Invariant systems (LTI), the phase is shifted only for such systems that have
"reactive" elements in the system.
LTI systems are made up of signal-... |
(The society is limited to people with PhDs after 1990, occasioning the title of this post, a reference to a song about a bar limited to people under 21, a reference you will not get unless your PhD was granted well before 1990.)
I can't blog all the great papers and discussions, so I'll pick one of particular interest... |
Research Open Access Published: Some new results on the boundary behaviors of harmonic functions with integral boundary conditions Boundary Value Problems volume 2016, Article number: 136 (2016) Article metrics
616 Accesses
1 Citations
Abstract
In this paper, using a generalized Carleman formula, we prove two new resul... |
In Coleman's paper
Fate of the false vacuum: Semiclassical theory while working out the exponential coefficient for tunneling probability through a potential barrier, he studies the problem with Wick's rotation $\tau=it$, getting to the Euclidean Lagrangian
$$L_E = \frac{1}{2}\left(\frac{dq}{d\tau}\right)^2+V(q),\tag{2... |
Journal of Symbolic Logic J. Symbolic Logic Volume 56, Issue 3 (1991), 949-963. Model-Theoretic Properties Characterizing Peano Arithmetic Abstract
Let $\mathscr{L} = \{0, 1, +, \cdot, <\}$ be the usual first-order language of arithmetic. We show that Peano arithmetic is the least first-order $\mathscr{L}$-theory conta... |
In-sample fits are not a reliable guide to out-of-sample forecasting accuracy. The gold standard in forecasting accuracy measurement is to use a holdout sample. Remove the last 30 days from the training sample, fit your models to the rest of the data, use the fitted models to forecast the holdout sample and simply comp... |
First i began with the definition of $\theta$ as below: $c_1n \leq k \log(k) \leq c_2n \implies c_1\frac{n}{logk} \leq k \leq c_2\frac{n}{logk}$ and we also know if $k\log(k) = \theta (n)$ then $k = O(n)$ then $k \leq cn$ thus $c\frac{n}{logn} \leq c_1\frac{n}{logk}\leq k $ and thus $k = \omega(\frac{n}{\log(n)})$. In ... |
If I run a
randomForest model, I can then make predictions based on the model. Is there a way to get a prediction interval of each of the predictions such that I know how "sure" the model is of its answer. If this is possible is it simply based on the variability of the dependent variable for the whole model or will it... |
$f:[0,1]\times [0,1]\to\mathbb R,$ defined by $$f(x,y)= \begin{cases}1,\quad \ \ y\in\mathbb R\text{\\}\mathbb Q\\2x,\quad\text{otherwise}\end{cases}$$.
$1.1$: $\int_0^1f(x,y)dx$ exists for every $y\in[0,1]$ and is equal to $1$.
$1.2$: The iterated integral $\int_0^1(\int_0^1f(x,y)dx)dy$ exists and is $1$.
$1.3$: The d... |
The following question is taken from Royden Real Analysis $4$th edition, Chapter $4,$ question $20.$
Let $\{f_n\}$ be a sequence of nonnegative measurable functions that converges to $f$ pointwise on $E.$ Let $M\geq 0$ be such that $\int_E f_n\leq M$ for all $n.$ Show that $\int_E f\leq M.$ Verify that this property is... |
Let us consider Example 16.1 in Wooldridge (2010), concerning school and employment decisions for young men. The data contain information on employment and schooling for young men over several years. We will work with the data for 1987.
The outcome is status, coded 1=in school, 2=at home (meaning not in school and not ... |
This web page lists all elements and attributes that can be used in the input file of an
calculation: exciting
elements are defined according to the general XML conventions. Example:The element
is used to set up a self-consistent calculation of the ground-state energy.
groundstate attributes are defined according to th... |
Here is a string of comments which might be helpful.
UPDATE at the end I conjecture an upper bound $a(n) \leq \lfloor (\frac{n-1}{2})^2 \rfloor$ which satisfies a stronger property.
Consider instead cases of $$\prod_1^k(x_i+a)= \prod_1^k(y_i+a) \tag{*}$$ where the multisets $\{x_1,\cdots ,x_k\}$ and $\{y_1,\cdots ,y_k\... |
Question 1 I think the short answer is no. Try testing functions of the form $|x|^{-n + 1}$ around $0$. Its gradient would be like $|x|^{-n}$ and thus in $L^{1,\infty}$ but the function is not in the required $L_p$ space. The Sobolev inequalities for $p=1$ are connected with the isoperimetric inequality, see [S] and ar... |
Superfunctions Contents Covers
The back cover suggests short abstract of the Book and few notes about the Author.
About the topic
Assume some given holomorphic function \(T\). The superfunction is holomorphic solution F of equation \(T(F(z))=F(z+1)\)
The Abel function (or abelfunction) is the inverse of superfunction, ... |
With a stationary loop of wire and field $\vec B$ varying in time it doesn't seem that you'd be able to exploit the Lorentz force, because it's difficult to introduce the velocity $v$. But another configuration may be more helpful, see picture.
A metallic rod (orange) crosses the magnetic lines (light-blue) with a cons... |
I haven't actually done the derivation but the approach you would take would be to write a ray tracing matrix for the whole system, including the object distance $s_1$ and the image distance $s_2$:
$$\begin{bmatrix}x_f \\ \theta_f\end{bmatrix} =\begin{bmatrix}1 & s_2 \\ 0 & 1\end{bmatrix}\begin{bmatrix}1 & 0 \\ -1/f_2 ... |
In signal processing, cross-correlation is a measure of similarity of two waveforms as a function of a time-lag applied to one of them. This is also known as a sliding dot product or sliding inner-product. It is commonly used for searching a long signal for a shorter, known feature. It has applications in pattern recog... |
In this tutorial, you will learn how to perform a series of phonon calculations in order to obtain the mode Grüneisen parameters and the thermal-expansion coefficient of diamond. Purpose:
0. Prerequisites
This tutorial assumes that you have already set the relevant environment variables. Otherwise, please have a look a... |
Help:Editing Contents General
To edit a MediaWiki page, click on the "
Edit this page" (or just " edit") link at one of its edges. This will bring you to a page with a text box containing the wikitext: the editable source code from which the server produces the webpage. For the special codes, see below.
After adding to... |
If you have a series of a group of operators defined at the same space time point (as you might find in e.g interaction terms in a lagrangian consisting of local operator terms for maintenance of locality) then one can derive that $$T((AB \dots)_{x_1} \dots (PQ \dots)_{x_n})_{\text{No E.T.C}} = T(N(AB \dots)_{x_1} \dot... |
We present a two dimensional model describing the elastic behaviour of the wall of a curved pipe to model blood vessels in particular. The wall has a laminate structure consisting of several anisotropic layers of varying thickness and is assumed to be much smaller in thickness than the radius of the vessel which itself... |
Can anybody explain in simple terms how the critical value of the ADF test can be derived using Monte Carlo simulation?
The ADF test assumes the DGP $$ \Delta y_t = \alpha +\beta t +\gamma y_t +\delta_1 \Delta y_{t-1}+\cdots +\delta_k \Delta y_{t-k}+\epsilon_t $$ The parameters are estimated using OLS on a sample of le... |
77 11
The institute where I'm studying consists of books, problems and exams which seems to me completely senseless. I have been a self-study guy ( actually this was a compulsion, not a desire) so I read some well renowned books like
The institutes in which I'm right now have something which I hate and I try to depict ... |
Markdown help Code and Preformatted Text
Indent four spaces to create an escaped
<pre> <code> block:
printf("%d\n", 42); /* what was the question again? */
You can also select text and press
CTRL+
K to toggle indenting as code.
The text will be wrapped in tags, and displayed in a monospaced font. The first four spaces ... |
Proof of Proposition 1
If party \(B\) accepts the offer of party \(A\), its utility will be \(W_{B}(p_{A})+t+c_{B}\). If \(B\) rejects \(A\)’s offer, its utility will be \(W_{B}(q)+c_{B}^{\prime }\).
If SIG wants \(B\)
to accept \(A\)
’s proposal, it should choose \(c_{B}\)
and \( c_{B}^{\prime }\)
such that
$$\begin{a... |
Given two uncorrelated strategies, each with a Sharpe ratio of 1, what is the of Sharpe ratio of the ensemble?
If we assume that by ensemble you mean an equally weighted portfolio of the two. We can express that portfolio as $$P = \frac{1}{2}x + \frac{1}{2}y$$ and the sharpe ratio of $P$, $S(P)$, will be $$\frac{\frac{... |
Research Open Access Published: Existence and boundary behavior of weak solutions for Schrödingerean TOPSIS equations Boundary Value Problems volume 2018, Article number: 12 (2018) Article metrics
613 Accesses
Abstract
In this paper, we prove that there exists a weak solution for Schrödingerean technique for order perf... |
Answer
$a = 306~m$ $b = 1248~m$ $B = 76^{\circ}12'$
Work Step by Step
We can convert angle A to degrees: $A = 13^{\circ}47' = (13+\frac{47}{60})^{\circ} = 13.8^{\circ}$ We can use angle A and angle C to find angle B: $B = 180^{\circ}-90^{\circ}-13.8^{\circ} = 76.2^{\circ}$ $B = 76.2^{\circ}$ which is $76^{\circ}12'$ We... |
Disclaimer: This answer derives the prices of two different binary options within the Black/Scholes framework. Note that this is not an appropriate valuation model to use for non-European contracts in most real-world markets.
Up-and-In Binary Call
After reading your question for a second time, I agree with Quantuple's ... |
In this example we use the package to infer the modes of a bimodal, 2d Gaussian using stochastic gradient Hamiltonian Monte Carlo. So we assume we have independent and identically distributed data \(x_1, \dots, x_N\) with \(X_i | \theta \sim 0.5 N( \theta_1, I_2 ) + 0.5 N( \theta_2, I_2 )\), and we want to infer \(\the... |
In this example we use the package to infer the mean of a 2d Gaussian using stochastic gradient Langevin dynamics. So we assume we have independent and identically distributed data \(x_1, \dots, x_N\) with \(X_i | \theta \sim N( \theta, I_2 )\), and we want to infer \(\theta\).
First, let’s simulate the data with the f... |
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... |
Moment area method
Method for finding deflections in a framed structure by the use of moment area curve.
First Theorem
Theorem 1: The change in slope between any two points on the elastic curve equals the area of the M/EI diagram between these two points.
\[\theta_{AB} = {\int_A}^B \frac{M}{EI}\;dx\]
where
M moment EI ... |
I don't know what people mean by 'vanilla policy gradient', but what comes to mind is REINFORCE, which is the simplest policy gradient algorithm I can think of. Is this an accurate statement?
By REINFORCE I mean this surrogate objective
$$ \frac{1}{m} \sum_i \sum_t log(\pi(a_t|s_t)) R_i $$
Where I indices over the $m$ ... |
I'am a little confused. In my text book it is written that all odd function can be described by a sine series.
I have this following equation from an exercise:
$$A_{0}+\sum\limits_{n=1}^\infty \Big(A_{n} \cos(n \phi) + B_{n} \sin(n \phi)\Big)c^{n} = \sin\left(\frac{\phi}{2}\right)$$
It's a standard fourier series, wher... |
Let $f(x,y)$ be a binary quadratic form with co-prime integer coefficients. We say that $f$ is a
proper subform of $g(x,y)$ if there exists an integer matrix $A = \left(\begin{smallmatrix} a_1 & a_2 \\ a_3 & a_4 \end{smallmatrix}\right)$ with $|\det A| > 1$ such that
$$\displaystyle f(x,y) = g(a_1 x + a_2 y, a_3 x + a_... |
Linear fraction
Linear fraction is meromorphic function that can be expressed with
\((1) ~ ~ ~ \displaystyle T(z)=\frac{u+v z}{w+z}\)
where \(u\), \(v\), \(w\) are parameters from the some set of numbers that allows operations of summation, multiplication and division. Usually, it is assumed, that they are complex numb... |
I was reading the book "Genetics and Analysis of Quantitative Traits", by Lynch and Walsh. I how the covariance between two individuals with IBD $\Theta$ gets divided into just the additive variance and dominance variance component, even in the simple $1$ locus case.
Here my understanding of the modelling (for the simp... |
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... |
Is the photon pair generated from the electron-positron annihilation entangled?
And would they work as a source of entangled photons suitable for experiments in quantum optics?
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It only takes a minute to sign ... |
Consider the finite multisets $\mathbf{Bag}\:X$. Its elements are given by $\{x_1,\ldots,x_n\}$ quotiented by permutations, so that $\{x_1,\ldots,x_n\}=\{x_{\pi 1},\ldots,x_{\pi n}\}$ for any $\pi\in\mathbf{S}_n$. What is a one-hole context for an element in such a thing? Well, we must have had $n>0$ to select a positi... |
For a random integer $x$ chosen uniformly between 2 and $n$, what is the expected value of the smallest prime factor of $x$ as a function of $n$?
What is the behavior of the function as $n$ tends to infinity?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professional... |
I'm currently working on a project were I need to cascade several transformers (the core we use does not nearly work as good as it ought to..). I'm using the equivalent circuit shown in (A), transformed it into an ideal transformer and equivalent circuit (B) by dragging over the circuit on the secondary side, where $$\... |
For a PDF version of this article, please click this link
Introduction
You may well have come across impedance expressed in the the terms real and imaginary (or resistance and reactance) when using equipment such an Antenna Analyser or impedance in the form R + jX. This may mean something to some readers whilst it prob... |
Edit: A colleague informed me that my method below is an instance of the general method in the following paper, when specialized to the entropy function,
Overton, Michael L., and Robert S. Womersley. "Second derivatives for optimizing eigenvalues of symmetric matrices." SIAM Journal on Matrix Analysis and Applications ... |
How do derivatives of operators work? Do they act on the terms in the derivative or do they just get "added to the tail"? Is there a conceptual way to understand this?
For example: say you had the operator $\hat{X} = x$. Would $\frac{\mathrm{d}}{\mathrm{d}x}\hat{X}$ be $1$ or $\frac{\mathrm{d}}{\mathrm{d}x}x$? The diff... |
Someone’s inspirational iterative approach index card wasn’t 100% accurate.
Better.
Someone’s inspirational iterative approach index card wasn’t 100% accurate.
Better.
Eating at a picnic spot or wilderness campsite is great, but prep can be tricky.
You still want decent kitchen utensils, but for knives there’s a downsi... |
<< ToK
ToK Warszawa meeting - Rough Notes Thu 15 Feb 2007 These are just rough notes - feel free to correct them, add links, etc. Hector Rubinstein - stockholm - magnetic fields
Magnetic fields on kpc scales exist. They may exist on intergalacticscales - it's unclear whether or not their origin is primordial.
CMB - Pla... |
Now I want you to consider a single particle, P,
inside this event horizon, at a distance \(r'\) from the origin, on its way to the centre. In a thought experiment or Gedanken, compare the motion of this particle P with that of an identical particle, P', on the surface of an identical distribution of matter but with al... |
90 6 Homework Statement A body of mass ##10 kg## is connected to a spring of constant ##490 \frac{N}{m}## and it lies on an frictionless inclined plane. The angle formed by the plane and the floor is ##30°##. This block is inside a room which accelerates upwards with ##a=5 \frac{m}{s^2}##. Prove that if the mass is mov... |
Here is a beautiful result from numerical analysis. Given any nonsingular $n\times n$ system of linear equations $Ax=b$, an optimal Krylov subspace method like GMRES must necessarily terminate with the exact solution $x=A^{-1}b$ in no more than $n$ iterations (assuming exact arithmetic).
The Cayley-Hamilton theorem pro... |
Research Open Access Published: Uniqueness and stability of solutions without the boundary condition Boundary Value Problems volume 2019, Article number: 21 (2019) Article metrics
336 Accesses
Abstract
A parabolic equation related to the
p-Laplacian is considered. If the equation is degenerate on the boundary, then dem... |
The recent question Complete the following sequence: point, triangle, octahedron, . . . in a dg-category reminded me of something I wanted to clarify long time ago; most likely this is now well known but unfortunately I did not follow literature in the field attentively enough.
Shortly, any composable $n$-tuple of morp... |
I believe that the process you postulate has a Beta conditional distribution. If my memory serves me well, I have encountered it in the book by Liptser and Shiryayev "Statistics of Random Processes" as the evolution of the conditional probability in a HMM. This was 10+ years ago, therefore I might be well off.
In that ... |
Saddle-node bifurcation
Yuri A. Kuznetsov (2006), Scholarpedia, 1(10):1859. doi:10.4249/scholarpedia.1859 revision #151865 [link to/cite this article]
A
saddle-node bifurcation is a collision and disappearance of two equilibria in dynamical systems. In systems generated by autonomous ODEs, this occurs when the critical... |
Let $K$ be a field having two field extensions $L\supseteq K$ and $M\supseteq K$. Does there exist a field $N$ along with embeddings $L\to N$ and $M\to N$, such that the diagram$$ \require{AMScd}\begin{CD} K @>>> L\\ @V V V @VV V\\ M @>>> N \end{CD}$$is commutative? To put it less formally,
do $L$ and $M$ have a common... |
Get your free trial content now! Video Transcript Transcript Factoring by Grouping
Adventure Mike and his girlfriend plan to build a treehouse. Using a snake as a measuring stick, Mike figured out the polynomial expression to represent the total area.
Oh jeez, his girlfriend just remembered – she wants a balcony, so sh... |
I was reading BMO spaces (John-Nirenberg) on wikipidia http://en.wikipedia.org/wiki/Bounded_mean_oscillation. There they define BMO norm as $$sup_{Q}\frac{1}{Q}\int_Q |u(y) - u_Q|dy$$ where $u_Q$ is the average of $u(y)$ over $Q$ and the supremum is taken over all cubes of arbitrary diameter.
Questions: 1. I think what... |
A commutative algebra (with unity) over a field gives rise to the covariant functor F: Set_f->Vect from finite sets to vector spaces: F(E) := A^{otimes E}. Is it true that, over complex numbers, a finite dimensional algebra can be reconstructed from the corresponding functor?
(A Gamma-module is a functor from finite
po... |
Suppose I have a very simple asset whose price takes only three possible values: $X_t\in \{-1,0,1\}$. I also got some
discrete time series $X = (X_t)_{t\geq 0}$ and I would like to come up with a trading rule based on these observations. Let's focus on the following naive approach: given the current level of the asset,... |
The help pages in R assume I know what those numbers mean, but I don't. I'm trying to really intuitively understand every number here. I will just post the output and comment on what I found out. There might (will) be mistakes, as I'll just write what I assume. Mainly I'd like to know what the t-value in the coefficien... |
I'm trying to solve the exercise in the title and I think it makes no sense. Here's what it says:
An onto map $f: X \to Y$ is called an
elementary partial isomorphismbetween $\mathcal{A}$ and $\mathcal{B}$ if $X \subseteq A$, $Y \subseteq B$ and $$(\mathcal{A},\{x\}_{x\in X}) \equiv (\mathcal{B},\{f(x)\}_{x\in X})$$ $f... |
In probability studies we come across many situations and apply various concepts to find the probability of an event. The numerical value of possible outcomes in a random experiment varies from trial to trial. Suppose you roll a fair die, the number of possible outcomes is $6$. That is, the die can roll on $1, 2, 3, 4,... |
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∑cycabc+1\large \displaystyle \sum_{\text {cyc}} \dfrac{a}{bc+1}cyc∑bc+1aLet a,ba,ba,b and ccc be positive reals satisfying a+b+c=3a+b+c=3a+b+c=3.
Find the minimum value of the expression above.
Bonus: Find as many approaches as possible
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In a proof, I want to split the equations on the left and have a picture on the right using minipages. However for one of the equations on the left, the comment is too long and is too big for the minipage. How can I split the comment so that it goes across two lines? I understand it can be done equations, but not sure ... |
Pressing the envelope, presumably the best scenario would be a simple proof of the Prime Number Theorem. After all, Wilson’s Theorem gives a necessary and sufficient condition, in terms of the Gamma Function, for a number to be a prime, and Stirling’s Formula specifies the asymptotic behaviour of the Gamma Function.
Us... |
RD Sharma Solutions Class 8 Chapter 4 Exercise 4.5
Making use of the cube root table, find the table, find the cube roots of the following (correct to three decimal points):
7 70 700 7000 1100 780 7800 1346 940 5112 9800 732 7342 133100 37800 0.27 8.6 0.86 8.65 7532 833 34.2
Answer:
Q1. 7
Answer :
Because 7 lies betwee... |
Research Open Access Published: Boundary value problems for modified Dirac operators in Clifford analysis Boundary Value Problems volume 2015, Article number: 158 (2015) Article metrics
888 Accesses
Abstract
In this paper, we discuss two kinds of Riemann type boundary value problems for the operator \(\widetilde{D}_{\l... |
Like a option to post images while solving problems there should also be an option to post images in solutions . There is a problem while editing solutions , if any small minor changes are to be done in solutions then the whole solution has to be written again because when we click edit , the format of solution changes... |
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