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In Carr and Madan (2005), the authors give sufficient conditions for a set of call prices to arise as integrals of a risk-neutral probability distribution (See Breeden and Litzenberger (1978)), and therefore be free of static arbitrage (via the Fundamental Theorem of Asset Pricing)
These conditions are:
Call spreads ar... |
Exponentially Weighted Average for Deep Neural Networks A fast and efficient way to compute moving averages - implemented in the different optimization algorithms.
Example: Temperature over days, calculate the moving averages
: Moving average value at day ‘t’
= 0
..
if $\beta$ = 0.9
The above equation would give the mo... |
I would like to price Asian and Digital options under Merton's jump-diffusion model. To that end, I will have to simulate from a jump diffusion process.
In general, the stock price process is given by $$S(t) = S(0)e^{(r-q-\omega)t+X(t)},$$ where $\omega$ is the drift term that makes the discounted stock price process a... |
Wikipedia informs us that quartz is the second most abundant mineral on earth. It’s composed of silicon and oxygen (not exactly exotic elements) in a “continuous framework of SiO
4 silicon–oxygen tetrahedra” (not sure what that means...). Based on this information, would you ever have thought that quartz crystals would... |
Definition of Singular Solution
A function \(\varphi \left( x \right)\) is called the singular solution of the differential equation \(F\left( {x,y,y’} \right) = 0,\) if uniqueness of solution is violated at each point of the domain of the equation. Geometrically this means that more than one integral curve with the co... |
Quote:
The length of one of the sides of a triangle is 25 units. If the area of the triangle is 120 units squared and the length of another side of the triangle is 10 units, which of the following could be the length of the third side?
A) \(\sqrt{255}\) B) \(\sqrt{585}\) C) \(\sqrt{572}\) D) \(\sqrt{558}\) E) 24
\(? = ... |
Here is an alternative to Count Dracula's (correct) argument that emphasizes instead the constancy of the Hilbert polynomial for a flat family of projective schemes.
As above, assume that $Y$ is a DVR. For one fixed irreducible component $Z_{\eta}$ of $X_\eta$ of minimal dimension $d$, denote by $Z$ the Zariski closure... |
Can n! be a perfect square when n is an integer greater than 1? (But is it possible, to prove without Bertrand's postulate. Because bertrands postulate is quite a strong result.)
Assume, $n\geq 4$. By Bertrand's postulate there is a prime, let's call it $p$ such that $\frac{n}{2}<p<n$ . Suppose, $p^2$ divides $n$. Then... |
First consider a scheme $X$ with an open cover $\mathcal{U}=\{U_i\}$. An object with descent data on $\mathcal{U}$ is a collection $(\mathcal{E}_i,\phi_{ij})$ where $\mathcal{E}_i$ is a quasi-coherent sheaf on each $U_i$ and $\phi_{ij}$ is an isomorphism $pr_2^*\mathcal{E}_j\to pr_1^*\mathcal{E}_i$ in $Qcoh(U_{ij})$ wh... |
I think the easiest way to to what you want is to use
confidence intervals (statistical inference).
In other words, assuming the population has a true variance $\sigma$, the sampling distribution of the variance $s^2$ of an $n$-sample verifies:$$ \frac{s^2(n-1)}{\sigma^2}\sim \chi^2_{n-1}$$
You can exploit this result ... |
I am trying to find the action associated with the Lagrangian density $$ \mathcal{L} = \frac{1}{2}\left( \frac{\partial\phi}{\partial x} \right)^2 + \frac{1}{2}m^2\phi^2. \tag{1} $$ I am supposed to use the discrete expansions $$\phi_j = \frac{1}{\sqrt{Na}}\sum_p \tilde{\phi}_pe^{ipja} = \frac{1}{\sqrt{Na}}\sum_{-p} \t... |
Math.NET Symbolics is a basic open source computer algebra library for .Net and Mono written in F#.
This project does not aim to become a full computer algebra system. If you need such a system, have a look at Axiom or Maxima instead, or for commercial solutions Maple, Mathematica or Wolfram Alpha.
The recommended way ... |
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Production of charged pions, kaons and protons at large transverse momenta in pp and Pb-Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV
(Elsevier, 2014-09)
Transverse momentum spectra of $\pi^{\pm}, K^{\pm}$ and $p(\bar{p})$ up to $p_T$ = 20 GeV/c at mid-rapidity, |y| $\le$ 0.8, in pp and ... |
[In view of the discussion let me mention that the context is that of Poincare-covariant quantum field field theories . It is clear that giving up covariance makes many things possible that are not possible otherwise, and allow to make rogorous sense of renormalization in simpler situations such as for free covariant f... |
I would say that when the capacitor is connected to the battery there will be a transient flow of charge during which the plate which is connected to the positive terminal will acquire charge $Q$ and rise to voltage $V$.
Consider the other plate which is connected to the dangling wire. This piece of metal has net charg... |
In this question, I am testing what was previously discussed. I can't seem to get my results to match D'Inverno's electromagnetic tensor for a charged point (page 239 of his book -
Introducing Einstein's Relativity). Here are D'Inverno's steps:
The line element in spherical coordinates is ($\eta$ and $\lambda$ are func... |
Here is a bubble chamber picture of an event
It is interpreted as particles:
$${\newcommand{Subreaction}[2]{{\rlap{\hspace{0.38em} \lower{25px}{{\rlap{\rule{1px}{20px}}} {\lower{0.5ex}{\hspace{-1px} \longrightarrow {#2}}}}}} {#1} }}{K}^{-} ~~ p ~~ {\longrightarrow} ~~ {\Subreaction{{\Omega}^{-}}{ {\Subreaction{{\Lambda... |
Chapters
Chapter 2: Polynomials
Chapter 3: Pair of Linear Equations in Two Variables
Chapter 4: Quadratic Equations
Chapter 5: Arithmetic Progressions
Chapter 6: Triangles
Chapter 7: Coordinate Geometry
Chapter 8: Introduction to Trigonometry
Chapter 9: Some Applications of Trigonometry
Chapter 10: Circles
Chapter 11: ... |
Application of Derivatives Increasing and Decreasing Functions A function ƒ is said to be (a) increasing on an interval (a, b) if x 1< x 2in (a, b) ⇒ f(x 1) ≤ f(x 2) for all x 1, x 2∈ (a, b). Alternatively, if f'(x) ≥ 0 for each xin (a, b) (b) decreasing on (a, b) if x 1< x 2in (a, b) ⇒ f(x 1) ≥ f(x 2) for all x 1, x 2... |
Electrostatic Potential and Capacitance Electrostatics of Conductors, Dielectrics and polarization
Inside a conductor, electric field is zero. At the surface of a charged conductor, electric field must be normal to the surface at every point. The interior of a conductor can have no excess charge in the static situation... |
Wave Optics Polarisation Polarisation is the property of obstructing the vibration of particle. Polarisation Establishes the transverse nature of Light waves If the Electric vector vibrates in all directions in a plane perpendicular to the direction of propagation is called unpolarised light. If the Electric field vect... |
I am learning Probabilistic Graphical Models with the help of the videos on Coursera. I am in week 4 and I see cliques being mentioned often. But the graphs being discussed are cluster graphs. So are the cliques and clusters the same?
A
clique is a rigorously defined, exact part of a graph $G=(V,E)$;
$\qquad\displaysty... |
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If fn(x)=cosnx+cosn(x+2π3)+cosn(x+4π3)\displaystyle{{ f }_{ n }(x)={ \cos ^{ n }{ x } +\cos ^{ n }{ (x+\cfrac { 2\pi }{ 3 } ) } +\cos ^{ n }{ (x+\cfrac { 4\pi }{ 3 } ) } }}fn(x)=cosnx+cosn(x+32π)+cosn(x+34π). Then Solve for x if f7(x)=0\displaystyle{{ f }_{ 7 }(x... |
Be a set of numbers $v=(a_1, a_2, \ldots, a_n)$
I want to form the following average vector $\mu = (\frac{\sum a_i}{n}, \frac{\sum a_i}{n}, \ldots, \frac{\sum a_i}{n})$.
If I do it iteratively step by step, in each step we pick three components, $a_i,a_j$ and $a_k$ that are not all equal, and we replace them by their m... |
The link is not freely available. And your question is not entirely clear. I will guess you are trying to estimate an unknownparameter.
Suppose $\theta$ is the unknown parameter, and you have anestimator $T$ of $\theta$ based on $n$ observations.We say that $T$ is an unbiased estimator of $\theta$ if $E(T) = \theta.$
I... |
Chapters
Chapter 2: Relations
Chapter 3: Functions
Chapter 4: Measurement of Angles
Chapter 5: Trigonometric Functions
Chapter 6: Graphs of Trigonometric Functions
Chapter 7: Values of Trigonometric function at sum or difference of angles
Chapter 8: Transformation formulae
Chapter 9: Values of Trigonometric function at... |
primarily of use when the sampling distribution is normally distributed, or approximately normally distributed. Are leet variation is reduced—this idea underlies the sample size calculation for a controlled trial, for example. deviation a sample from all the actual voters.
In this scenario, the 400 patients are a sampl... |
Random Graph Models¶ This tutorial will introduce the following random graph models:¶ Erdos-Reyni (ER) Degree-corrected Erdos-Reyni (DCER) Stochastic block model (SBM) Degree-corrected stochastic block model (DCSBM) Random dot product graph (RDPG) Load some data from GraSPy¶
For this example we will use the
Drosophila ... |
2.1 The terminal velocity is the maximum (constant) velocity a dropping object reaches. In this problem, we use Equation (2.2.6) for the drag force.
Use dimensional analysis to relate the terminal velocity of a falling object to the various relevant parameters. Estimate the terminal velocity of a paraglider (Figure 2.3... |
This is a very smart question! Yes, reversibility does not have any
intrinsic reference to time, but no, reversible processes are slow in practice. Let's talk about why.
We'll just start with the pebbles on a piston. What realistically happens if you pull the pebbles away too fast? Well, it's like making the pebble sud... |
For a school project, I'm working on a software-defined radio transmitter intended for the HF amateur radio bands. I'm planning to support SSB transmission with the formula
$$f(t) = m(t) \cos(2\pi f_\text{carrier}t) \pm \hat m(t)\sin(2\pi f_\text {carrier}t)$$
where $f_\text{carrier}$ is the IF carrier and $\hat m$ is ... |
Theorem. $\int_0^\infty \sin x \phantom. dx/x = \pi/2$.
Poof. For $x>0$ write $1/x = \int_0^\infty e^{-xt} \phantom. dt$,and deduce that $\int_0^\infty \sin x \phantom. dx/x$ is$$\int_0^\infty \sin x \int_0^\infty e^{-xt} \phantom. dt \phantom. dx= \int_0^\infty \left( \int_0^\infty e^{-tx} \sin x \phantom. dx \right)\... |
In the late of \(17\)th century British scientist Isaac Newton studied cooling of bodies. Experiments showed that the cooling rate approximately proportional to the difference of temperatures between the heated body and the environment. This fact can be written as the differential relationship:
\[\frac{{dQ}}{{dt}} = \a... |
Let $x_1 < x_2 < \ldots < x_n$ and $y_1 < y_2 < \ldots < y_n$ be two sequences of $n$ real numbers. It is well known that there are polynomials that "interpolate" in that $f(x_i)=y_i$ for all $i$, and the Lagrange interpolating polynomial even warrants a solution of degree $ < n$. Now, what happens if we want the polyn... |
Take $\alpha$ to be any ordinal greater than or equal to $\omega$. The set of ordinals $S(\alpha)$ obtained generated from $\alpha$ using ordinal exponentiation are the ordinals of the form $\alpha^{\alpha^{E(\alpha)}}$ where $E(\alpha)$ is an exponential polynomial over the base $\alpha$. By "exponential polynomial ov... |
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... |
One-Step Subgroup Test Contents Theorem
Let $\struct {G, \circ}$ be a group.
Let $H$ be a subset of $G$.
$(1): \quad H \ne \O$, that is, $H$ is non-empty $(2): \quad \forall a, b \in H: a \circ b^{-1} \in H$. Proof Necessary Condition
Let $H$ be a subset of $G$ that fulfils the conditions given.
It is noted that the fa... |
Abbreviation:
Pos
A
(also called partially ordered set or ordered set for short) is a structure $\mathbf{P}=\langle P,\leq \rangle $ such that $P$ is a set and $\leq $ is a binary relation on $P$ that is poset
reflexive: $x\leq x$
transitive: $x\leq y$, $y\leq z\Longrightarrow x\leq y$
antisymmetric: $x\leq y$, $y\leq ... |
Consider the following problem. Given a set of $n$ items having weight $w_i$ and value $v_i$ and a maximum capacity $W$, maximize $\sum\limits_{i=1}^n a _i v_i$ under $\sum\limits_{i=1}^n a_i w_i \leq W$ where $a_i \in \{0,1\}$. That is, choose a subset of items giving the maximum total value while still fitting into t... |
On the DNA Computer Binary Code
In any finite set we can define a
, a partial order in different ways. But here, a partial order is defined in the set of four DNA bases in such a manner that a Boolean lattice structure is obtained. A Boolean lattice is an algebraic structure that captures essential properties of both s... |
Let $R$ be a commutative ring and $I_1, \dots, I_n$ pairwise comaximal ideals in $R$, i.e., $I_i + I_j = R$ for $i \neq j$. Why are the ideals $I_1^{n_1}, ... , I_r^{n_r}$ (for any $n_1,...,n_r \in\mathbb N$) also comaximal?
It is sufficient to prove this for the case two comaximal ideals, say $I,J$. Need to show, $I^m... |
I have encountered quite recently the "Compton edge", which made me review the Compton effect again. A photon with wave length $\lambda$ "bumps" into a charged particle (usually an electron) and passes some of its energy to the electron, while the remaining energy goes to another photon with wavelength $\lambda ' $. On... |
Definition:Differential/Real Function Definition
Let $U \subset \R$ be an open set.
Let $f: U \to \R$ be a real function.
Let $f$ be differentiable at a point $x \in U$.
The differential of $f$ at $x$ is the linear transformation $\rd f \left({x}\right) : \R \to \R$ defined as: $\rd f \left({x}\right) \left({h}\right) ... |
I want to find the following limit using L Hospital's rule: $$ \lim_{x \to \infty} \sqrt{x} \sin( \frac{1}{x}) $$ I know that this can be solved using squeezed theorem from Cal 1: $$ 0 < \sqrt{x}\sin( \frac{1}{x} ) < \frac{1}{x} $$ since $0 < \sin( \frac{1}{x}) < \frac{1}{x} $. What I have done so far is trying to conv... |
Votes cast (618)
all time by type month 608 up 284 question 1 10 down 334 answer
40
How to find the sum of this series : $1+\frac{1}{2}+ \frac{1}{3}+\frac{1}{4}+\dots+\frac{1}{n}$
18
Prove that $ n < 2^{n}$ for all natural numbers $n$.
17
What functions satisfy such equation?
17
How to compute $\prod_{n=1}^\infty\left(... |
Let $\mathcal{V}$ be the space $C^r$ vector fields on a non-compact (smooth) manifold $M$. Being a subspace of $C^r(M, T M)$, it inherits the natural $C^r$ topology (i.e. the strong topology) of that space. Furthermore, since $C^r(M, T M)$ is Baire and $\mathcal{V}$ is closed in $C^r(M, T M)$, $\mathcal{V}$ is Baire to... |
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Journal of Industrial & Management Optimization
October 2013 , Volume 9 , Issue 4
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Abstract:
In this paper, we propose a primal-dual approach for solving the generalized fractional programming problem. The outer iteration of the algorithm ... |
First:
Yes, when you are dealing with a function $f$ of one real variable $x$, the partial derivative $\frac{\partial f}{\partial x}$ coincides with the total derivative of $f$ with respect to $x$. Be ware that those are generally two different things. They only coincide for functions that have purely explicit relation... |
I am trying to prove that the dihedral group $D_n$ has $2n$ elements by using the theory of group actions. Specifically I want to use the orbit stabilizer theorem. So I need $D_n$ to act on a specific set $X$ and then compute the order of the stabilizer and the orbit for some $x\in X$.
My question is presuming $X=\{1,2... |
Let $$z(x,y)=\int_{1}^{x^{2}-y^{2}}[\int_{0}^{u}\sin(t^{2})dt]du.$$ Calculate $$\frac{\partial^{2}z}{\partial x\partial y}$$
I tried to solve this using the Fundamental Theorem of Calculus.
I also found an solution like this: using Fundamental Theorem of Calculus, we get: $$\frac{\partial z}{\partial y}=\left[\int_{0}^... |
Forgive me for what is probably a simple question, I am new to this field. I am studying the Hirzebruch surfaces and their higher dimensional analogues $M_{n,k}$, defined to be the projective line bundles
\begin{equation} M_{n,k}=\mathbb{P}(\mathcal{O}(-k)\oplus\mathcal{O}(0)) \end{equation} over $\mathbb{CP}^{n-1}$. H... |
Let $X$ be a (connected) topological space with a $C^\infty$ atlas. It is a known theorem that if $X$ is second-countable and Hausdorff, then it admits partitions of unity. I'm trying to prove the "reverse" theorem:
Let $X$ be a (connected) topological space with a $C^\infty$ atlas. If $X$ admits partitions of unity, t... |
Suppose that $A$ and $B$ are DFAs. We know that there is some DFA $M$ such that $L(M) = L(A) \bigtriangleup L(B)$, the symmetric difference. Also, we can construct this $M$ by some Turing machine $N$. But can we ensure that $N$ has the following form?
$N$ consists of (i) a read-only input tape, (ii) a work tape that is... |
On the DNA Computer Binary Code
In any finite set we can define a
, a partial order in different ways. But here, a partial order is defined in the set of four DNA bases in such a manner that a Boolean lattice structure is obtained. A Boolean lattice is an algebraic structure that captures essential properties of both s... |
Answer
The diesel engine is more efficient.
Work Step by Step
We know that the value of $\gamma$ in air is 1.4. We use the efficiency of the gas engine found in problem 55: $e=1-r^{1-\gamma}$ $e=1-8.3^{1-1.4}=.57$ In problem 57, we found that the efficiency of the diesel engine is given by: $e_{diesel}=1-\frac{r^{1-\ga... |
The $\mathbb{Z_5}$-vector space $\mathfrak{B}$ 3 over the field $(\mathbb{Z_5}, +, .)$ $\mathfrak{B}$ 3over the field $(\mathbb{Z_5}, +, .)$ 1. BackgroundThis is a formal introduction to the genetic code $\mathbb{Z_5}$-vector space $\mathfrak{B}^3$ over the field $(\mathbb{Z_5}, +, .)$. This mathematical model is defin... |
Let $f:\mathbb{R}^n \to \mathbb{R}^n$ be continuous and let there exist $\alpha > 0$ such that $||f(\mathbf{x}) - f(\mathbf{y})|| \geq \alpha || \mathbf{x} - \mathbf{y}||$ for all $\mathbf{x}, \mathbf{y} \in \mathbb{R}^n$. Prove that $f$ is one-one, onto and that $f^{-1}$ is continuous.
One-one is trivial. It is onto-n... |
A typical chips and crepe packaging cone, for example, has V = 355 cm3.) What dimensions (height and radius) will minimize the cost of recycled paper to construct the cone?
closed as off-topic by max_zorn, GNUSupporter 8964民主女神 地下教會, Ak19, Thomas Shelby, Lord Shark the Unknown Jun 16 at 5:50
This question appears to be... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
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October 2015 , Volume 35 , Issue 10
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Abstract:
We study the set of periods of degree 1 continuous maps from $\sigma$ into itself, where $\sigma$ denotes the space shaped like the letter $\sigma$ ... |
@egreg It does this "I just need to make use of the standard hyphenation function of LaTeX, except "behind the scenes", without actually typesetting anything." (if not typesetting includes typesetting in a hidden box) it doesn't address the use case that he said he wanted that for
@JosephWright ah yes, unlike the hyphe... |
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I'm going to start my answer by going back to what I was taught at Uni - basically how each of the parameters of the transistor scale - an approach called "Constant Electric Field Scaling".
Lets say we have a transistor, and want to scale it's length \$L\$ and width \$W\$ by, \$\alpha\$ (both are scaled to keep the asp... |
The i.i.d. assumption about the pairs $(\mathbf{X}_i, y_i)$, $i = 1, \ldots, N$, is often made in statistics and in machine learning. Sometimes for a good reason, sometimes out of convenience and sometimes just because we usually make this assumption. To satisfactorily answer if the assumption is really necessary, and ... |
I have been having trouble with how to go forward with a proof for about three days now. I know the basic structure of the proof, but can't seem to construct it.
Basically, I am trying to do a proof by contradiction for the following:
Say $u: x \rightarrow \mathbb{R}$ has no local maxima. Let $p \in \mathbb{R^l}_{++}$ ... |
Just have been trying to approach this problem from Resnick's book on probability but have got no clue so far.
The problem is like this:
We are giving two random variables X, Y on the same space $(\Omega, \mathcal{B})$, and we are asked to show: $\sup_{A \in \mathcal{B} } | P[X\in A] - P[Y\in A] | \leq P[X \neq Y] $.
W... |
This problem is simpler than it might look: although it might get confusing when one tries to apply routine Calculus methods, it is easy when worked from general principles.
By definition, the likelihood $\mathcal L$ is the probability of the data. Since the data are (implicitly) assumed independent, this is the produc... |
An example of methylation analysis with simulated datasets
Part 2: Potential DMPs from the methylation signal
Methylation analysis with Methyl-IT is illustrated on simulated datasets of methylated and unmethylated read counts with relatively high average of methylation levels: 0.15 and 0.286 for control and treatment g... |
Preamble:
If one considers an ideal gas of non interacting charged particles of charge $q$ in a uniform magnetic field $\mathbf{B} = \mathbf{\nabla} \wedge \mathbf{A}$, then the classical partition function in the canonical ensemble reads (in SI units):
$Q(\beta,V,N,\mathbf{B}) = \frac{1}{N!}q(\beta,V,\mathbf{B})^N$
wh... |
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Now let's look at a mathematical approach to resource theories. As I've mentioned, resource theories let us tackle questions like these:
Our first approach will only tackle question 1. Given \(y\), we will only ask
is it possible to... |
At small values close to $x=1$, you can use taylor expansion for $\ln x$:
$$ \ln x = (x-1) - \frac{1}{2}(x-1)^2 + ....$$
Is there any valid expansion or approximation for large values (or at infinity)?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in re... |
Let for integers $n\geq 1$ the radical of an integer, see the definition of this arithmetical function, for example, from this Wikipedia.
I wondered next question when I did a comparison with a well-known identity from the literature.
Question.Does converge $$\sum_{n=2}^\infty\frac{(-1)^n\zeta(n)}{\operatorname{rad}(n)... |
Please read this introduction first before looking through the solutions. Here’s a quick index to all the problems in this section.
Composing two general equiareal transformations, we get a transformation of the form below. $$\begin{pmatrix} a_{12}b_{21} + a_{11}b_{11} & a_{12}b_{22} + a_{11}b_{12} & a_{12}b_{23} + a_{... |
I am using
Analysis on Manifolds by Munkres to study for a course and the following question comes from an early section in topology. Definition of limit point: Let $A \subset R^n$ and let $x_o \in R^n$. $x_o$ is a limit point of $A$ if, for every $r>0,B(x_o,r)$ contains a point of $A \setminus \{x_o\}$ Exercise: Let $... |
The following question from Furdui's book (Exercise 1.32. page 6) is an "open problem" :
Let $f: [0,1] \to \mathbb{R}$ be a continuous (and not a continuously differentiable) function and let
$$x_n = f\left(\dfrac{1}{n}\right) + f\left(\dfrac{2}{n}\right) + \dots + f\left(\dfrac{n-1}{n}\right).$$
Calculate $\lim_{n \to... |
This doesn't seem to have been presented or published anywhere other than as a somewhat casual/informal document on the arXiv, which probably helps explain why it's been ignored.
Well, that and the fact that it's ignorant of all the relevant research and is very, very wrong.
Since I'm not really a GR person, I'll pass ... |
Abbreviation:
BilinA
A
is a structure $\mathbf{A}=\langle A,+,-,0,\cdot,s_r\ (r\in F)\rangle$ of type $\langle 2,1,0,2,1_r\ (r\in F)\rangle$ such that bilinear algebra
$\langle A,+,-,0,s_r\ (r\in F)\rangle$ is a vector space over a field $F$
$\cdot$ is
: $x(y+z)=xy+xz$, $(x+y)z=xz+yz$, and $s_r(xy)=s_r(x)y=xs_r(y)$ bil... |
SettingExactly as the title stated:
Give an example of an $\mathsf{NL}$-complete context free language. $\newcommand{\angle}[1]{\langle #1 \rangle}$
Current Solution
Recall in the past we proved that $E_{DFA}$ is regular, so it is also context free. $E_{DFA}$ is in $\mathsf{NL}$ since given DFA $\mathcal M$ over $n$ st... |
Yes. Denote the entrywise absolute value of a complex matrix $X$ by $|X|$. In general, if $|X|\le Y$ entrywise, then $\rho(X)\le\rho(|X|)\le\rho(Y)$.
Your $P$ is an orthogonal projection. Therefore the moduli of its entries are bounded above by $1$. Hence $|A|\le|B||D|$ and $\rho(A)\le\rho(|B||D|)$. So, it suffices to ... |
Suppose we have a feedforward neural network with L2 regularization and we train it using SGD initializing the weights with the standard Gaussian. The weight update scheme can be written as:
$$w \rightarrow \left( 1 - {\eta \lambda \over n} \right)w - {\eta \over m} \sum_x{\partial C_x \over \partial w}$$
where $w$ is ... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
Problem: Let $f\in L^2(0,\infty)$ and let $(Tf)(s)=\frac1s\int_0^sf(t)dt$. Find the adjoint, $T^*$. Attempt: I know that problems like these should be very simple, but oftentimes I find them very difficult, to my shame. I understand that the adjoint in this case is defined as being the $T^*:L^2(0,\infty)\to L^2(0,\inft... |
Finding Additive Biclusters with Random Background Abstract
The biclustering problem has been extensively studied in many areas including e-commerce, data mining, machine learning, pattern recognition, statistics, and more recently in computational biology. Given an
n × m matrix A ( n ≥ m), the main goal of biclusterin... |
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... |
Let's consider a rooted tree $T$ of $n$ nodes. For any node $u$ of the tree, define $L(u,d)$ to be the list of descendants of $u$ that are distance $d$ away from $u$. Let $|L(u,d)|$ denote the number of nodes that are present in the list $L(u,d)$.
Prove that the sum of $|L(u,d)|$ over all distinct lists $L(u,d)$ is bou... |
Why has the message $P$ to be relative prime to $n$ in RSA encryption?
This should be fault? \begin{align} C &\equiv P^e \pmod{n} \\ &\equiv 101112^{11111357} \pmod{9998000099} \\ &\equiv 3316546434 \pmod{9998000099} \end{align}
Mathematics Stack Exchange is a question and answer site for people studying math at any le... |
In the book APP. Math. Stat (https://books.google.com/books?id=enUouJ4EHzQC&pg=PA266&lpg=PA266&dq=serfling+variance+of+L+estimate&source=bl&ots=ehRxuMmiQ5&sig=lDK209BhPb5chwbBrbMG-RMDFFA&hl=en&sa=X&ved=0ahUKEwiHpbfotubJAhUBGh4KHZprB0oQ6AEITTAI#v=snippet&q=He%20establishes%20several%20results&f=false) by Robert Serfling... |
Okay consider a game $G$ if a strategy $s_i$ has the following property we call $s_i$ the strictly dominant strategy
$$u_i(s_i,s_{-i})>u_i(s_i',s_{-i}) \\ \forall s_{-i} \ \forall s_i' \epsilon S'_i$$
Where $s_{i}$ indicates the strategies of players other then $i$ in the game and $S'_i$ is the set for strategies of pl... |
For this particular question, I am wondering if Q1 must be in saturation mode or active? I am aware Q2 must be in saturation but upon trying to solve this circuit I feel as if I have more unknowns than equations. I would show my work but it does not make sense because I cannot straighten out my thought process. anythin... |
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Kaon femtoscopy in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV
(Elsevier, 2017-12-21)
We present the results of three-dimensional femtoscopic analyses for charged and neutral kaons recorded by ALICE in Pb-Pb collisions at $\sqrt{s_{\rm{NN}}}$ = 2.76 TeV. Femtoscopy is used to... |
Over the interval $[0,1]$, the function $f(x) = \cos(x)$ is a strictly decreasing continuous function mapping $[0,1]$ into itself. So $f\circ f$ is strictly increasing there. If one pick$a_1 = \frac{\pi}{4} \in [0,1]$ and generate a sequence by iteration $a_n = f(a_{n-1})$,it is not hard to check
$$a_2 < a_3 < a_1$$
Si... |
You have confused counting worlds with computing probabilities. They are different things.
If you measured $m$ systems identically prepared to give one of $n$ result $v_1,$ ...$v_n$ with respective frequencies $p_1,$ ... $p_n$, then there are $n^m$ aggregate outcomes.
But the MWI doesn't predict different probabilities... |
Calculates the Akaike's information criterion (AIC) of the given estimated ARMA model (with correction to small sample sizes).
Syntax ARMA_AIC( X, Order, mean, sigma, phi, theta) X is the univariate time series data (one dimensional array of cells (e.g. rows or columns)). Order is the time order in the data series (i.e... |
So is $\Theta$ undefined for insertion sort?
This question contains a category error. It's like saying, "I know that Donald Trump has a height of at least 5 and at most 7. So are numbers undefined for Donald Trump?
$\Theta$ is notation for expressing the growth rate of mathematical functions. "Insertion sort" is not a ... |
Context:
I have been trying to understand the genetic algorithm discussed in the paper Decomposition of unitary matrices for finding quantum circuits: Application to molecular Hamiltonians (Daskin & Kais, 2011) (PDF here) and Group Leaders Optimization Algorithm (Daskin & Kais, 2010). I'll try to summarize what I under... |
Suppose we are given a function
and we want to calculate the surface area of the function f {\displaystyle f} rotated around a given line. The calculation of surface area of revolution is related to the arc length calculation. f {\displaystyle f}
If the function
is a straight line, other methods such as surface area fo... |
Difference between revisions of "Unitriangular matrix group:UT(3,p)"
(→Subgroups)
m (→In coordinate form)
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<math>\left \{ \begin{pmatrix} 1 & a_{12} & a_{13} \\ 0 & 1 & a_{23} \\ 0 & 0 & 1 \\\end{pmatrix} \mid a_{12},a_{13},a_{23} \in \mathbb{F}_p \right ... |
For a general group of order $p$ and $q$, there are very few possibilities (though you need Sylow theorems to know this). The fact is, for $p>q$ and $G$ a group of order $pq$, we must have$$G\cong C_p\rtimes C_q$$where the semi-direct product is defined in terms of some homomorphism $$\Phi:C_q\to\mathrm{Aut}(C_p)\cong ... |
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