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Answer
Please see the work below.
Work Step by Step
We know that $\Delta T_F=(\frac{9}{5})\Delta T_C$ We plug in the known values to obtain: $\Delta T_F=(\frac{9}{5})(10)$ $\Delta T_F=18F^{\circ}$
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After you claim an answer you’ll hav... |
Speaker: Affiliation:
Indian Institute of Technology
Department of Computer Science and Engineering Hauz Khas New Delhi 110016 Time: Venue: A-201 (STCS Seminar Room) Organisers:
We develop new techniques for rounding packing integer programs using iterative randomized rounding. It is based on a novel application of mul... |
I have been recently working with generating functions in my discrete mathematics course, and I was interested in one particular generating function. I want to find the generating function for the number of ways one can split $n$ into odd parts. I can see that the first coefficients of the sequence are $$0,1,1,2,2,3,4,... |
Basic Properties Regarding Ring Homomorphisms
Basic Properties Regarding Ring Homomorphisms
Recall from the Ring Homomorphisms page that if $(R, +_1, *_1)$ and $(S, +_2, *_2)$ are rings with multiplicative identities $1_R$ and $1_S$ respectively, then a ring homomorphism between them is a function $\phi : R \to S$ such... |
The easiest explanation for why the maximum distance one can see is not simply the product of the speed of light with the age of the universe is because the universe is non-static.
Different things (i.e. matter vs. dark energy) have different effects on the coordinates of the universe, and their influence can change wi... |
There is a wide litterature for the classical Gauss sums. For $\chi$ a primitive Dirichlet character modulo $N$, it is given by $$\tau(\chi) = \sum_{n \text{ mod } N} \chi(n) \exp(2i\pi n/N).$$
An interesting fact is that primitive Dirichlet characters are essentially their own Fourier transform, up to this associated ... |
When reading some literatures on topological insulators, I've seen authors taking Brillouin zone(BZ) to be a sphere sometimes, especially when it comes to strong topological insulators. Also I've seen the usage of spherical BZ in these answers(1,2) by SE user Heidar. I can think of two possibilities:
(1)Some physical s... |
I am working my way through LDA and I think I got they main idea of it. Please correct me if I am wrong. Given the Plate notation:
The variables $\alpha$ and $\beta$ are Dirichlet distribution parameters. The variable $Z_{d,n}$ assigns observed word $W_{d,n}$ to topic $\phi_k$, which is a distribution over words. Varia... |
$S$ cannot be a 3-dimensional real hyperboloid unless $\psi$ is of the same form as $\phi$, though it can be a 2-dimensional real hyperboloid*.Excluding the possibilities achievable when $\psi$is a real quadratic form, and working up to similarity of $\psi$ over $\mathcal{R}$,$S$ is one of the following:
$\quad\bullet\... |
The Annals of Statistics Ann. Statist. Volume 18, Number 2 (1990), 717-741. Large-Sample Inference for Log-Spline Models Abstract
Let $f$ be a continuous and positive unknown density on a known compact interval $\mathscr{Y}$. Let $F$ denote the distribution function of $f$ and let $Q = F^{-1}$ denote its quantile funct... |
The Internal Direct Product of Two Groups
Recall from The External Direct Product of Two Groups page that if $(G, *)$ and $(H, +)$ are two groups then the external direct product of these groups is the new group $(G \times H, \cdot)$ where $\cdot$ is the binary operation defined for all $(g_1, h_1), (g_2, h_2) \in G \t... |
With the given \$X(e^{jw})\$ you won't get that answer.
Graphical proof:
If we try to plot \$X(e^{jw})\$, it will be a train of pulses with pulse width = \$\pi/2\$ and amplitude = \$\sqrt2\$ . And pulse will be centered at integer multiple of \$2\pi\$ as shown in the figure.
Calculating the value of \$Y\$ at \$w=0\$,
$... |
Asteroidal triples¶
This module contains the following function:
is_asteroidal_triple_free()
Test if the input graph is asteroidal triple-free Definition¶
Three independent vertices of a graph form an
asteroidal triple if every twoof them are connected by a path avoiding the neighborhood of the third one. Agraph is ast... |
Main Page The Problem
Let [math][3]^n[/math] be the set of all length [math]n[/math] strings over the alphabet [math]1, 2, 3[/math]. A
combinatorial line is a set of three points in [math][3]^n[/math], formed by taking a string with one or more wildcards [math]x[/math] in it, e.g., [math]112x1xx3\ldots[/math], and repl... |
Classical Mechanics Kinematics (Equations of Motion) Newton's Laws Vector physics Work Energy Power Momentum Conservation Statics (Friction) Circular Motion (Angular stuff) Kepler's Laws (Satellite Motion) Harmonic Motion (Springs) Problem 1
You may need to modify the Newtonian theory of gravitation at short ranges. Su... |
However there is already a cloud on the horizon: constraints. Here are two situations I've already encountered:
In SSP without recourse, the graph structure for a particular realization might not be fully connected. I want to ensure the underlying CSMC doesn't select an infeasible edge. In the Ad Selection Problem, the... |
Subgroups of Finite Groups with Unique Order are Normal Subgroups
Table of Contents
Subgroups of Finite Groups with Unique Order are Normal Subgroups
Proposition 1: Let $G$ be a finite group. If $G$ has only one subgroup $H$ of order $n \mid |G|$ then $H$ is a normal subgroup of $G$. Proof:For each $g \in G$ let $\phi_... |
This shows you the differences between two versions of the page.
Both sides previous revision Previous revision cs-401r:axioms-of-probability-theory [2014/09/05 17:02]
cs401rpml [Second Axiom]
cs-401r:axioms-of-probability-theory [2014/09/05 17:02] (current)
cs401rpml [Third Axiom]
Line 12: Line 12: == Third Axiom == =... |
I know I came across a 2 op-amp, 2 capacitor circuit that can be used for a single section of an Inverse Chebyshev (a.k.a. "Chebyshev Type II) or an Elliptic (Cauer) filter. It has a pair of zeros on the \$j\omega\$-axis at \$\pm j\omega_z\$, and with resonant frequency \$\omega_0<\omega_z\$ and the transfer function i... |
In this answer, AccidentalFourierTransform explains that
Renormalisation has nothing to do with Classical vs Quantum. Any theory, classical or quantum mechanical, needs renomalisation if and only if it is non-linear.
Can anyone help me understand the idea of renormalization in classical field theory (CFT) and how is it... |
Range of a Linear Map
Definition: If $T \in \mathcal L (V, W)$ then the Range of the linear transformation $T$ is the subset of $W$ defined as $\mathrm{range} (T) = \{ T(v) : v \in V \}$, that is, the set of all vectors $T(v) \in W$ to which are mapped to from vectors $v \in V$.
Before we look at some examples of range... |
My question is really as to whether I can consider the following results as proof of one another, since $(2a)$&$(2b)$ cannot be true unless $(0)$ is true, and vice versa.
So if for below I prove $(0)$ using the elementary means in Real Analysis, can I also then consider this to be proof for $(2a)$&$(2b)$?
I am looking ... |
Let $\operatorname{Klein}$ denote the category of principal homogeneous bundles. An object in this category is a tuple $\mathbf Q = (Q, P; G, H; q, a, \tilde a)$, where:
$G$ is a Lie group, and $H$ is a closed subgroup;
$P$ is a $G$-torsor and the manifold $Q$ is diffeomorphic to the quotient $G/H$;
The (left) actions ... |
Hey guys! I built the voltage multiplier with alternating square wave from a 555 timer as a source (which is measured 4.5V by my multimeter) but the voltage multiplier doesn't seem to work. I tried first making a voltage doubler and it showed 9V (which is correct I suppose) but when I try a quadrupler for example and t... |
I consider a spin manifold $M$, with the Dirac operator $D$ and spinors $\psi$. I consider the differential equation:
$$ D \psi = \frac {1} {2} (\frac {d < \psi, \psi >}{<\psi, \psi>})^* .\psi $$
with the Clifford multiplication of the vectors.
Then it can be showed that the real gauge group ${\cal C }^{\infty} (M,R^*)... |
The prime number theorem says that the density of prime numbers is inverse as the number of digits of $n$:
$$\displaystyle \frac{\{1 \leq k \leq n : \text{ prime } \}}{n} \approx \frac{1}{\log n}$$
Strategies to prove this result usually resort to estimating generating functions of various types. And it seems to be pro... |
NTS ABSTRACTSpring2019
Return to [1]
Contents Jan 23
Yunqing Tang Reductions of abelian surfaces over global function fields For a non-isotrivial ordinary abelian surface $A$ over a global function field, under mild assumptions, we prove that there are infinitely many places modulo which $A$ is geometrically isogenous ... |
The price of the stock XYZ follows a brownian motion pattern with starting price = 10, μ = 0 and σ = 20 (on annual basis). What's the probability that in 6 months the price is less or equal to 8? Also i must solve this with paper and pen (I can consult the Normal distribution tabel)
Let $(S_t)$ be the price process of ... |
Can I be a pedant and say that if the question states that $\langle \alpha \vert A \vert \alpha \rangle = 0$ for every vector $\lvert \alpha \rangle$, that means that $A$ is everywhere defined, so there are no domain issues?
Gravitational optics is very different from quantum optics, if by the latter you mean the quant... |
Table of Contents
The Riesz Representation Theorem for Hilbert Spaces
Let $H$ be a Hilbert space. For each $g \in H$ let $f_g : H \to \mathbb{R}$ be defined for all $h \in H$ by:(1)
Note that each $f_g$ is linear since if $h_1, h_2 \in H$ we have that:(2)
And for all $h \in H$ and all $a \in \mathbb{R}$ we have that:(3... |
Thesis BELLE2-MTHESIS-2019-006 Untagged Exclusive Analysis of the Semileptonic Decay $B\rightarrow\pi\ell\nu$ from Belle II Data in Preparation for |$V_{ub}$| Extraction
Svenja Granderath ; Prof. Dr. Jochen Dingfelder ; Dr. Peter Lewis
2019 Physikalisches InstitutBonn, Germany
Abstract: In this thesis an untagged exclu... |
$\DeclareMathOperator{Hom}{Hom}$Let $R$ be a ring with $1$, $D$ a divisible $\mathbb{Z}$-module. Denote $X=\Hom_{\mathbb{Z}}(R,D)$ as the set of homomorphisms from $R$ to $D$ when viewing $R$ and $D$ as $\mathbb{Z}$-modules. We can associate an $R$-module structure on $X$ by defining $(rf)(x) = f(xr)$ for $r\in R, f\in... |
I am trying to learn about Green's functions as part of my graduate studies and have a rather basic question about them:
In my maths textbooks and a lot of places online, the basic Greens function G for a linear differential operator L is stated as
$$ L G = \delta (x-x') $$
which is all well and good. I am now reading ... |
Table of Contents
Adherent, Accumulation, and Isolated Points in Metric Spaces
Recall from the Adherent Points of Subsets in Euclidean Space page that if $S \subseteq \mathbb{R}^n$ then a point $\mathbf{x} \in \mathbb{R}^n$ is an adherent point of $S$ if there exists an $\mathbf{s} \in S$ such that $\mathbf{s} \in B(\m... |
I am trying to solve a set of DAEs.
\begin{equation} -4 \nu (\lambda(s))^{(-1 - 4 \nu)} \theta'(s) \lambda'(s) + (\lambda(s))^{(-4 \nu)} \theta''(s) = -\alpha_y \cos\theta(s) + \alpha_x \sin\theta(s) \end{equation}
\begin{equation} (\lambda(s))^{(-2 \nu)} \log(\lambda(s)) = f_s (\alpha_x \cos\theta(s) + \alpha_y \sin\t... |
The Nested Intervals Theorem
The Nested Intervals Theorem
We have just looked at what exactly a Nested Interval is, and we are about to look at a critically important theorem in Real Analysis. Before we look at the Nested Intervals Theorem let's first look at the following important lemma that will be used to prove the... |
Abstract:
Let $\Omega$ be an open and connected subset of the complex plane. A real valued function $u: \omega \rightarrow \mathbb{r}$ is said to be harmonic if it has continuous first and second partial derivatives and satisfies Laplace's equation $\Delta u = \frac{\partial^2 u}{\partial x^2}+\frac{\partial^2 u}{\part... |
Powers of a Matrix
Definition: Given a square matrix $A$, for $n$ being a nonnegative integer, $A^n$ is defined as the product matrix taking $A$ and multiplying it by itself $n$-times. If $A$ is invertible, then $A^{-n} = (A^{-1})^{n}$, or the product matrix taking $A^{-1}$ and multiplying it by itself $n$-times.
For e... |
Riemann-Stieltjes Integrals with the Greatest Integer Function as an Integrator
Recall from the Riemann-Stieltjes Integrals with Multiple-Discontinuity Step Functions as Integrators page that if $f$ is a function on the interval $[a, b]$ and $\alpha$ is a step function on $[a, b]$ with jump discontinuities at $x_1, x_2... |
Table of Contents
The Uniform Continuity of Composite Functions on Metric Spaces
Recall from the Uniform Continuity of Functions on Metric Spaces page that if $(S, d_S)$ and $(T, d_T)$ are two metric spaces, $A \subseteq S$, and $f : A \to T$ then $f$ is said to be uniformly continuous on $A$ if for all $\epsilon > 0$ ... |
I am trying to reduce the following ODE to Bessel's ODE form and hence solve it: $$x^{2}y''(x)+x(4x^{3}-3)y'(x)+(4x^{8}-5x^{2}+3)y(x)=0\tag{1} \, .$$
I tried to solve it via the standard method, i.e., by comparing it with a generalised ODE form and finding the solution from then on. The general form (as given in Mary L... |
Do you think, when you train a
Convolutional Neural Network (CNN) to classify between images it is exactly understanding the image as we humans perceive? It’s difficult to answer, as for most of the times Deep learning models are often considered to be a black box. We feed in the data and then we get the output. Whatev... |
Astronomy Kepler's Laws of Planetary Motion The orbit of every planet is an ellipse with the sun at a focus A line joining a planet and the sun sweeps out equal areas during equal intervals of time The square of the orbital period of a planet is proportional to the cube of the semi-major axis of its orbit. Hubble's Law... |
Alright, I have this group $\langle x_i, i\in\mathbb{Z}\mid x_i^2=x_{i-1}x_{i+1}\rangle$ and I'm trying to determine whether $x_ix_j=x_jx_i$ or not. I'm unsure there is enough information to decide this, to be honest.
Nah, I have a pretty garbage question. Let me spell it out.
I have a fiber bundle $p : E \to M$ where ... |
UOV
The first thing you need to know about UOV is that the input variables are partitioned into vinegar variables $x_1, \ldots, x_v$ and oil variables $x_{v+1}, \ldots, x_{v+o}$. The number of vinegar variables is roughly twice the number of oil variables: $v = 2o$. The name oil and vinegar comes from the fact that oil... |
Obviously (;-) @egreg’s answer is great and goes right to the point, but it does have an infinitesimal drawback: a pervert who tried
$\overline{\sin x}$ would get a surprise. Moreover, one could argue that the placement of the radical sign in
$\sqrt{\sin x}$ is suboptimal.
The positioning of superscripts in math formul... |
Chokshi, Paresh and Kumaran, V (2007)
Stability of the viscous flow of a polymeric fluid past a flexible surface. In: Physics of Fluids, 19 . 034102-1-034102-15.
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Abstract
The instability in plane Couette flow of... |
The Measure of Countable Subsets of Real Numbers
Recall from the Subsets of Real Numbers with Measure Zero that a subset $S \subset \mathbb{R}$ is said to have measure $0$ denoted $m(S) = 0$ if there exists a countable open interval covering $\{ I_k = (a_k, b_k) \}_{k \in K}$ (where $K$ is some countable indexing set) ... |
Preface: International Conference On Matrix Analysis And Its Applications -- Mattriad 2017, 2018 University of Tampere
Preface: International Conference On Matrix Analysis And Its Applications -- Mattriad 2017, Oskar Maria Baksalary, Natalia Bebiano, Heike Fassbender, Simo Puntanen Electronic Journal of Linear Algebra
... |
Cauchy Product of Power Series
The following theorem will give us a way to in a sense, "multiply" two power series together.
Theorem 1 (The Cauchy Product of Power Series): Consider the power series $\sum_{n=0}^{\infty} a_nx^n$ with a radius of convergence $R_1$, and the power series $\sum_{n=0}^{\infty} b_nx^n$ with a... |
De Bruijn-Newman constant
For each real number [math]t[/math], define the entire function [math]H_t: {\mathbf C} \to {\mathbf C}[/math] by the formula
[math]\displaystyle H_t(z) := \int_0^\infty e^{tu^2} \Phi(u) \cos(zu)\ du[/math]
where [math]\Phi[/math] is the super-exponentially decaying function
[math]\displaystyle... |
Absolute and Conditional Convergence of Double Series of Real Numbers
Recall from the Absolute and Conditional Convergence of Series of Real Numbers page that a series $\displaystyle{\sum_{n=1}^{\infty} a_n}$ is said to be absolutely convergent if $\displaystyle{\sum_{n=1}^{\infty} \mid a_n \mid}$ converges, and condit... |
A simulation of 50,000 iterations gives the average distance after a 2-step (unit step) random walk on a 2 dimensional plane, which is around 1.27. But how can one mathematically prove this?
Any insight is highly appreciated!
Mathematics Stack Exchange is a question and answer site for people studying math at any level... |
Let's say we have the following multiple regression model,
$$Y_i = \alpha + \beta_1 x_{i1} +\beta_2x_{i2} + ... + \beta_kx_{ik} + \varepsilon_i$$
with $ \varepsilon_i$ is $iid$ ~ $N(0,\sigma_{\varepsilon}^2) $ and least square estimators are $A, B_1,...,B_k $ for $\alpha, \beta_1,...,\beta_k $.
The sampling variance of... |
I'm working through Griffith's Intro to Quantum Mechanics, attempting to solve problem 2.27.
Consider the double delta-function potential $$ V(x)= -\alpha [\delta(x+a)+\delta(x-a)] $$ where $\alpha$ and $a$ are constants.
b) How many bound states does it possess? Find the allowed energies, for $\alpha=\hbar ^2 /ma$ and... |
Eigenvalues and Algebraic/Geometric Multiplicities of Matrix $A+cI$ Problem 378
Let $A$ be an $n \times n$ matrix and let $c$ be a complex number.
(a) For each eigenvalue $\lambda$ of $A$, prove that $\lambda+c$ is an eigenvalue of the matrix $A+cI$, where $I$ is the identity matrix. What can you say about the eigenvec... |
It would seem that far-away stars are at such a distance that I should be able to take a step to the side and not have the star's photons hit my eye. How do stars release so many photons to fill in such great angular distances?
The answer is simple: Yes, stars really do produce
that many photons. This calculation is a ... |
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D-meson nuclear modification factor and elliptic flow measurements in Pb–Pb collisions at $\sqrt {s_{NN}}$ = 5.02TeV with ALICE at the LHC
(Elsevier, 2017-11)
ALICE measured the nuclear modification factor ($R_{AA}$) and elliptic flow ($\nu_{2}$) of D mesons ($D^{0}$, $D^{+}$, $D^{⁎+}$... |
I am using a PIC micro with a 10bit ADC to take readings from an analog signal with a frequency less than 300 hz. However that analog signal is in the range of -2 V and +2 V. How can I condition the signal to get it into a usable range (assuming the input to the ADC has to be positive) Also I do not have a positive and... |
The most frequently used evaluation metric of survival models is the concordance index (c index, c statistic). It is a measure of rank correlation between predicted risk scores $\hat{f}$ and observed time points $y$ that is closely related to Kendall’s τ. It is defined as the ratio of correctly ordered (concordant) pai... |
Corollaries to the Open Mapping Theorem
Recall from The Open Mapping Theorem page that if $X$ and $Y$ are Banach spaces and if $T : X \to Y$ is a bounded linear operator then the range $T(X)$ is closed if and only if $T$ is an open map.
We will now present some corollaries to the open mapping theorem.
Corollary 1 tells... |
Impacto
Junge, M. and Pérez García, David and Palazuelos Cabezón, Carlos and Villanueva, Ignacio and Wolf, Michael (2009)
Operator Space theory: a natural framework for Bell inequalities. Physical Review Letters, 104 . ISSN 0031-9007, ESSN: 1079-7114
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Abstract
In this letter we show that the field of Operator ... |
An integrator is a very important filter that proves useful in implementation of many blocks of a communication receiver. In continuous-time case, an integrator finds the area under the curve of a signal amplitude. A discrete-time system deals with just the signal samples and hence a discrete-time integrator serves the... |
You're asking a mathematical question. Given a function $f$, let $a_n = f(n)$, then does the limit $\epsilon \downarrow 0$ exist for
$$ \sum a_n e^{-n \epsilon} - \int f(t) e^{-t\epsilon}?$$The answer is no: the integral will generically only get ride of the 'hardest' divergence. The sum $\sum a_n e^{-n \epsilon}$ typi... |
On the fractal nature of the set of all binary sequences with almost perfect linear complexity profile Abstract
Stream ciphers usually employ some sort of pseudo-randomly generated bit strings to be added to the plaintext. The cryptographic properties of such binary sequences can be stated in terms of the so-called lin... |
(Sorry was asleep at that time but forgot to log out, hence the apparent lack of response)
Yes you can (since $k=\frac{2\pi}{\lambda}$). To convert from path difference to phase difference, divide by k, see this PSE for details http://physics.stackexchange.com/questions/75882/what-is-the-difference-between-phase-differ... |
Complex Numbers
We should already be familiar with the set of real numbers $\mathbb{R}$. We will now extend further and learn the basics about the set of complex numbers $\mathbb{C}$.
Definition: A number $z$ in the form $z = a + bi$ where $a, b \in \mathbb{R}$ and $i^2 = -1$ is said to be a Complex Number. The Real Pa... |
The Divergence and Curl of a Vector Field In Two Dimensions
From The Divergence of a Vector Field and The Curl of a Vector Field pages we gave formulas for the divergence and for the curl of a vector field $\mathbf{F}(x, y, z) = P(x, y, z) \vec{i} + Q(x, y, z) \vec{j} + R(x, y, z) \vec{k}$ on $\mathbb{R}^3$ given by th... |
Main Page The Problem
Let [math][3]^n[/math] be the set of all length [math]n[/math] strings over the alphabet [math]1, 2, 3[/math]. A
combinatorial line is a set of three points in [math][3]^n[/math], formed by taking a string with one or more wildcards [math]x[/math] in it, e.g., [math]112x1xx3\ldots[/math], and repl... |
This post was inspired by this answer of Dave Penneys.
In the category of (irreducible hyperfinite II$_1$) subfactors, the morphisms of $(N \subset M)$ to $(N' \subset M')$ are usually defined as the $W^*$-morphisms $\phi: M \to M'$ with $\phi (N) \subset N'$.
Unfortunately, through this definition, the category of fin... |
If we want to describe a static spherically symmetric star we can use a metric which matches the Schwarzschild solution with correct mass on the outside of the star but differs from Schwartzschild in the inside of the matter distribution.
Basically we solve the Einstein equations with a source $T_{\mu\nu}$, for instanc... |
Galois Fields
We have already looked at some examples of fields on the Field Axioms page. We will now look at another specific type of field known as a Galois Field. Before we do that though, we must first get a little bit acquainted to a special type of relation known as the
modulus of an integer $a$ to a divisor $m$.... |
A cylinder of radius $a$ is fixed in space. A hoop of mass $m$ and radius $b$ is in contact with the surface of the cylinder and it is able to rotate around of it without slipping. The force of gravity is acting on the system (figure below).
At $t=0$, the hoop is at rest and a tangential velocity $v_0$ is imposed in th... |
$X$ is multivariate normal distributed with $\mu = (2, 2)$ and $\Sigma = (1, 0 ; 0, 1)$ and I have 2 vectors $A = (1, 1)$ and $B = (1, -1)$. How can I than show that the linear combinations $AX$ and $BX$ are independent?
First of all independence follows from a lack of correlation when two random variables are jointly ... |
Let $G$ be a group. Let $a$ and $b$ be elements of $G$.If the order of $a, b$ are $m, n$ respectively, then is it true that the order of the product $ab$ divides $mn$? If so give a proof. If not, give a counterexample.
We claim that it is not true. As a counterexample, consider $G=S_3$, the symmetric group of three let... |
Problem 556
Let $\mathbf{v}$ be a nonzero vector in $\R^n$.
Then the dot product $\mathbf{v}\cdot \mathbf{v}=\mathbf{v}^{\trans}\mathbf{v}\neq 0$. Set $a:=\frac{2}{\mathbf{v}^{\trans}\mathbf{v}}$ and define the $n\times n$ matrix $A$ by \[A=I-a\mathbf{v}\mathbf{v}^{\trans},\] where $I$ is the $n\times n$ identity matri... |
Exponential Functions Form a Basis of a Vector SpaceLet $C[-1, 1]$ be the vector space over $\R$ of all continuous functions defined on the interval $[-1, 1]$. Let\[V:=\{f(x)\in C[-1,1] \mid f(x)=a e^x+b e^{2x}+c e^{3x}, a, b, c\in \R\}\]be a subset in $C[-1, 1]$.(a) Prove that $V$ is a subspace of $C[-1, 1]$.(b) […]
E... |
Original Question: What is the link between Gamma and the Volatility Risk?
It leads me to ask:
- What is the Volatility Risk definition and what are the good practices to measure it?
Thinking about that question, all I could figure out liking with it is this:
Consider a market $(S^0, S)$ composed of one non-risky asset... |
I recently came across this in a textbook (NCERT class 12 , chapter: wave optics , pg:367 , example 10.4(d)) of mine while studying the Young's double slit experiment. It says a condition for the formation of interference pattern is$$\frac{s}{S} < \frac{\lambda}{d}$$Where $s$ is the size of ...
The accepted answer is c... |
I'm currently researching 5G technology. Many videos/articles on this topic claim that 5G is designed for communicating on lower distances (than 4G), because of higher (than 4G) frequency. So to build a network we need more dense grid of access points. Is this some general rule, that the higher frequency means less ran... |
Blow-up for the 3-dimensional axially symmetric harmonic map flow into $ S^2 $
1.
Instituto de Matemáticas, Universidad de Antioquia, Calle 67, No. 53–108, Medellín, Colombia
2.
Departamento de Ingeniería Matemática-CMM, Universidad de Chile, Santiago 837-0456, Chile
3.
Department of Mathematical Sciences University of... |
Yes, it is possible to extend the state space with respect to which $Y$ is a Feller process. Then, $X$ will be a dense open subset of the extension $\hat X$. Furthermore, for any initial distribution of $Y_0\in\hat X$, then $Y$ will have a continuous modification which necessarily satisfies $Y_t\not\in\hat X\setminus X... |
This question already has an answer here:
I want to calculate
$ \lim_{n \to \infty }{\frac{{[n(n+1)(n+2)...(2n-1)]}^\frac1n}n} $
using
$$\int_0^1 f(x)\,dx=\lim_{n\to\infty}\frac1n \sum_{k=1}^n f\left(\frac{k}n\right)$$
I know I have to convert $\frac nk$ to $x$, but I am confused since all the factors are multiplied to... |
Flux, as I understand it, is the amount of substance passing through a particular surface over some time. So, from a simple perspective, considering photons that go through some virtual surface $A$ (or $S$, doesn't matter). They have a fixed speed in vacuum, $v=299,792,458$ $\text m/\text s$. To simplify even further, ... |
Electronic Journal of Probability Electron. J. Probab. Volume 24 (2019), paper no. 15, 51 pp. Asymptotic properties of expansive Galton-Watson trees Abstract
We consider a super-critical Galton-Watson tree $\tau $ whose non-degenerate offspring distribution has finite mean. We consider the random trees $\tau _n$ distri... |
Earth scientists recently celebrated the fifty-year anniversary of the theory of plate tectonics. The notion that the Earth’s surface is composed of a small number of slowly but continually-moving ‘rigid’ plates floating on a convecting, fluid interior is now firmly established as the foundational concept of the discip... |
Unit Normal and Unit Binormal Vectors to a Space Curve
We have already looked at an important class of vectors known as unit tangent vectors denoted $\hat{T}(t)$. If $\vec{r}(t) = (x(t), y(t), z(t))$ is a vector-valued function for $t \in [a, b]$ that is differentiable, then the unit tangent vector at $t$ denoted $\hat... |
i have the following question: let $\Omega$ an open in $\mathbb{R}^n$, and let $T \in \mathcal{D}'(\Omega)$.
We suppose that there exists an positive constant $C$ such that $$ \forall \varphi \in \mathcal{D}(\Omega): |\langle T,\varphi\rangle| \leq C \sqrt{ \displaystyle\int_{\Omega} |\varphi(x)|^2 dx } $$
The question... |
Electronic Journal of Probability Electron. J. Probab. Volume 24 (2019), paper no. 16, 71 pp. Exceedingly large deviations of the totally asymmetric exclusion process Abstract
Consider the Totally Asymmetric Simple Exclusion Process (TASEP) on the integer lattice $ \mathbb{Z} $. We study the functional Large Deviations... |
$\vec{s}=\vec{u}t+\frac{1}{2}\vec{a}t^2$
The above relation can be used for $x$-axis or y-axis separately, you just have to keep the vectors in your mind. This relation can be broken down into two components :
$s_x \hat{i} + s_y \hat{j}=(u\cos{\theta} \; \hat{i} + u\sin{\theta}\; \hat{j}) t + \frac{1}{2}(0\;\hat{i}+g\;... |
Summary: Possibilities for the Solution Set of a System of Linear Equations Problem 288
In this post, we summarize theorems about the possibilities for the solution set of a system of linear equations and solve the following problems.
Determine all possibilities for the solution set of the system of linear equations de... |
The most elementary reason is that the Dirac field Hamiltonian is bounded below only when you use anticommutation relations on the creation/annihilation operators instead of commutators. A free quantum field theory with energy unbounded below has no stable vacuum.
It is easiest to demonstrate this in two dimensions, wh... |
Global weak solution to the quantum Navier-Stokes-Landau-Lifshitz equations with density-dependent viscosity
1.
School of Mathematics and Information Science, Guangzhou University, Guangzhou, 510006, China
2.
Institute of Applied Physics and Computational Mathematics, China Academy of Engineering Physics, Beijing, 1000... |
I'm following Carroll's Spacetime and Geometry, chapter on Linearized Gravity, pag. 282. He splits up the metric perturbation in scalar, vector and tensor components, writes the Einstein tensor with respect to these components and plugs into the Einstein field equation. He claims that the vector part $w_i$ and the two ... |
In the diagram above, an incident light ray
PO strikes at point O the interface between two media of refractive indexes n 1 and n 2. Part of the ray is reflected as ray OQ and part refracted as ray OS. The angles that the incident, reflected and refracted rays make to the normal of the interface are given as θ i, θ r a... |
The minimum mass for the spontaneous collapse of a gas cloud is the Jeans mass. For low temperatures and high densities, this jeans mass is greater than the mass of a typical star. What are the implications of the fact that the Jeans masses of most clouds are larger than the masses of most stars?
The Jeans mass is give... |
I noted that there are two natural ways to aggregate $c_A$ and $c_B$ for someone who adheres to Probabilism, the principle that says that credences should be coherent. You might first fix up Adila's and Benoit's credences so that they are coherent, and then aggregate them using linear pooling -- let's call that
fix- th... |
The most elementary reason is that the Dirac field Hamiltonian is bounded below only when you use anticommutation relations on the creation/annihilation operators instead of commutators. A free quantum field theory with energy unbounded below has no stable vacuum.
It is easiest to demonstrate this in two dimensions, wh... |
Take the limit as x approaches 9 of $\frac{3}{\sqrt{x}-3} - \frac{18}{x-9}$ Multiplying by the conjugate $\sqrt{x}+3$ on the left side to get a common denominator of $x-9$, then using L'Hôpital's rule and solving gets the answer 1/2 Multiplying the denominators together to get a common denominator then using L'Hôpital'... |
I get so frustrated with modular arithmetic. It seems like every example I look at leaves steps out. I am trying to solve this problem:
Solve the linear congruence equations for x:
$x \equiv 2 \mod 7$
$x \equiv 1 \mod 3$
Ok, so I start
We know that 1st equation has a solution when $7 \mid (x-2)$. So there exists an int... |
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