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Research Open Access Published: On global behavior of weak solutions to the Navier-Stokes equations of compressible fluid for \(\gamma=5/3\) Boundary Value Problems volume 2015, Article number: 176 (2015) Article metrics
919 Accesses
1 Citations
Abstract
In this article, we consider the global behavior of weak solution... |
By stars-and-bars, there are $\binom{2007}{2}$ ways to select 2005 balls
without the even and odd conditions.
Write each choice as $(2R+r, 2Y+y, G)$ where $r,y\in\{0,1\}$. Most of the possible combinations come in matched quadruples with the same $R$ and $Y$, and in each such quadruple 3 of the four possibilities meet ... |
My reading of Joy's paper —just as it is, without having carefully read the arXiv paper I cited, nor all of Joy's responses to critics that I also mentioned— is, so far: the left and right hand sides of eq(1) and eq(2), without the central interpolations, state that $A(\mathbf{a},\lambda)=\lambda$ and $B(\mathbf{b},\la... |
Here is a closely related pair of examples from operator theory, von Neumann's inequality and the theory of unitary dilations of contractions on Hilbert space, where things work for 1 or 2 variables but not for 3 or more.
In one variable, von Neumann's inequality says that if $T$ is an operator on a (complex) Hilbert s... |
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f(x)=(a2−3a+2)(cos2x4−sin2x4)+(a−1)x+sin1f\left( x \right) =\left( { a }^{ 2 }-3a+2 \right) \left( \cos ^{ 2 }{ \frac { x }{ 4 } } -\sin ^{ 2 }{ \frac { x }{ 4 } } \right) +\left( a-1 \right) x+\sin { 1 } f(x)=(a2−3a+2)(cos24x−sin24x)+(a−1)x+sin1
The set of all v... |
2019-09-04 12:06
Soft QCD and Central Exclusive Production at LHCb / Kucharczyk, Marcin (Polish Academy of Sciences (PL)) The LHCb detector, owing to its unique acceptance coverage $(2 < \eta < 5)$ and a precise track and vertex reconstruction, is a universal tool allowing the study of various aspects of electroweak an... |
If I understood correctly, you have a signal $x[n]$ and an unknown discrete-time LTI filter, so that you can look at the output of the filter $y[n]$. Now you are looking for the impulse response of the filter $h[n]$.
The output follows a convolution rule$$y[n]=x[n]*h[n]=\sum_{m=-\infty}^{\infty}x[m]h[n-m]$$The process ... |
I recently plotted Gamma and Vega against Delta for a European call option and found that the graphs look very similar. This makes sense to me mathematically since the two formulas are pretty much the same from Black Scholes, just with a few different constants
$$ \Gamma = Ke^{-rT}\phi(d_2)\frac{1}{S^2\sigma\sqrt{T}} $... |
Research Open Access Published: Topological sensitivity analysis of a time-dependent nonlinear problem Boundary Value Problems volume 2019, Article number: 23 (2019) Article metrics
351 Accesses
Abstract
We are interested in the optimization of the pipe shape allowing minimization of the dissipated energy in time-depen... |
Existence Property Pattern
Untimed existence
Pattern Name and Classification Existence : Occurrence Specification Pattern Structured English Specification Scope, P eventually [holds]. (see the English grammar). Pattern Intent To describe a portion of a system's execution that contains an instance of certain events or s... |
For a PDF version of this article, please click this link
Introduction
You may well have come across impedance expressed in the the terms real and imaginary (or resistance and reactance) when using equipment such an Antenna Analyser or impedance in the form R + jX. This may mean something to some readers whilst it prob... |
I'm trying to align equations with already aligned case by case answers in them
What I am currently getting is:
and what I need is to align all the equals signs throughout the function
The required excerpt from my LaTex is
\documentclass[10pt,a4paper]{article}\usepackage[latin1]{inputenc} \usepackage{amsmath}\usepackag... |
I am getting a little confused about the huge number of slight variations on the Sobolev Embedding Theorem.
Let $\Omega\subseteq\mathbb{R}^n$ be a bounded Lipschitz domain and suppose that $f\in L_\infty(\Omega)\cap W^{\tau,2}(\Omega)$ for some $\tau\in\mathbb{R}$ with $\tau>n/2$. Do we have the inequality
$$ \left\Ver... |
Proposition: We assume the following.
1) The force exerted by the air on a surface is pure pressure thus normal to the surface without friction. The pressure increases with respect to the magnitude of the surface normal component of the incident air flow velocity and is zero when the surface normal component becomes ne... |
In this chapter you will do more work with fractions written in the decimal notation. When fractions are written in the decimal notation, calculations can be done in the same way as for whole numbers. It is important to always keep in mind that the common fraction form, the decimal form and the percentage form are just... |
I have recently acquired a couple of mysterious ultra/super capacitors from my brother. Apparently he doesn't remember any of the specifications or even brand... To further complicate matters, they have no meaningful identification information stamped or printed on them. (There is a bar code label with alphanumeric cod... |
In this chapter you will do more work with fractions written in the decimal notation. When fractions are written in the decimal notation, calculations can be done in the same way as for whole numbers. It is important to always keep in mind that the common fraction form, the decimal form and the percentage form are just... |
I believe you are confusing the wing angle of attack with the pitch of the aircraft. Aircraft moving at a slow, near-stall speed, despite pointing the nose up, will still be traveling more or less horizontally. Their VSI instrument will read near zero. Whereas, if you take an aircraft moving quickly and pull the nose u... |
good night... I was looking into the Pedersen Book, $C^{*}$-Algebras and their automorphism groups, and found the definition of analytic elements $x\in A$, where $(A,\alpha)$ is a $C^{*}-$dynamical system.
We say that an element $x\in A$ is analytic for $\alpha$ if the function $t\mapsto \alpha_{t}(x)$ has an extension... |
Siméon Denis Poisson (French: ; 21 June 1781 – 25 April 1840), was a French mathematician, geometer, and physicist. He obtained many important results, but within the elite Académie des Sciences he also was the final leading opponent of the wave theory of light and was proven wrong on that matter by Augustin-Jean Fresn... |
In mathematical logic and model theory, one considers
interpretations of syntactic expressions: terms without free variables are interpreted as elements of some structure, formulas without free variables have truth values, formulas with free variables can be interpreted as relations.
Multiple expressions may have ident... |
I am trying to calculate the work done on an ideal gas in a piston set up where temperature is kept constant. I am given the volume, pressure and temperature.
I know from Boyle's law that volume is inversely proportional to pressure that is,
$$V \propto \frac{1}{p}$$
using this I can calculate the two volumes I need fo... |
Research Open Access Published: Blow-up solutions, global existence, and exponential decay estimates for second order parabolic problems Boundary Value Problems volume 2015, Article number: 160 (2015) Article metrics
852 Accesses
3 Citations
Abstract
In this paper, we study the blow-up solutions, global existence, and ... |
The prototype of L-functions is the Riemann zeta-function defined by \[ \zeta(s)=\sum_{n=1}^\infty \frac {1}{n^s} \] for $\Re s>1$. Euler was interested in this function and discovered the beautiful fact that $\zeta(2)=\frac{\pi^2}{6}.$ He also found the fundamental identity \[ \zeta(s)=\prod_p \left(1-\frac{1}{p^s}\ri... |
The probability density function (PDF) of the normal distribution or Bell Curve Gaussian Distribution by Guy Lakeman The probability density function (PDF) of the normal distribution or Bell Curve of Normal or Gaussian Distribution is the mean or expectation of the distribution (and also its median and mode).
The param... |
My Lyttle Lytton entry for 2020:
"Actually, you do like this," maverick CEO Eric Davies, Ph.D., insisted as he pulled my foreskin back and cunnilingussed my pee hole.
I’m not exactly proud of it, but I’m glad it’s no longer in my head.
My Lyttle Lytton entry for 2020:
"Actually, you do like this," maverick CEO Eric Dav... |
WordPress.com supports the use of standard LaTeX in posts and comments, which is displayed using embedded PNG images with the LaTeX source code appearing in the alt text. So, including inline maths in your comments is easy! All you have to do is to surround your code by the tags $latex … $. For example, typing
$latex \... |
Determining the η− η′ mixing by the newly measured \(\mathit{BR}(D(D_{s})\to\eta(\eta')+\bar{l}+\nu_{l}\) 43 Downloads Citations Abstract
The mixing of
η− η′ or η− η′− G is of a great theoretical interest, because it concerns many aspects of the underlying dynamics and hadronic structure of pseudoscalar mesons and glue... |
Answer
98.4
Work Step by Step
We assume the length of the first diagonal to be about: $2(8.2)=16.4$ The apothem is 12, and this is the other diagonal. Thus, we approximate area: $A = \frac{d_1d_2}{2} = \frac{16.4 \times 12}{2} \approx 98.4$
You can help us out by revising, improving and updating this answer.Update this... |
Research Open Access Published: Existence criterion for the solutions of fractional order p-Laplacian boundary value problems Boundary Value Problems volume 2015, Article number: 164 (2015) Article metrics
1039 Accesses
19 Citations
Abstract
The existence criterion has been extensively studied for different classes in ... |
Research Open Access Published: Approximate controllability of a class of coupled degenerate systems Boundary Value Problems volume 2016, Article number: 127 (2016) Article metrics
998 Accesses
Abstract
This paper concerns the approximate controllability of a class systems governed by coupled degenerate equations. The ... |
What was the velocity of the Command Module after it had penetrated through the Earth's atmosphere at the point where the parachutes were deployed?
If you're asking about the deployment of the three main parachutes of C/M-ELS (Apollo Command Module Earth Landing System), then this is simple enough to answer, the pilot ... |
April 21st, 2017, 07:38 PM
# 1
Member
Joined: Feb 2017
From: East U.S.
Posts: 40
Thanks: 0
Riemann Sums and Definite Integrals
Use Example 1 as a model to evaluate the limit
$\displaystyle \lim _{n\to \infty }\left(\sum _{i=1}^n\left(f\left(ci\right)Δxi\right)\right)$
over the region bounded by the graphs of the equati... |
Sorry, but my first answer was completely and utterly wrong. Since this question is one of the top search results for the query "braid group fundamental group configuration space" I think it's high time I've updated with a correct explanation! :-)
I am not sure why there is a non-trivial loop. My understanding of homot... |
Question:
Suppose $a,b \in \Bbb N$, $\gcd (a,n) = \gcd(b,n) = 1$. The question is to prove or give a counterexample: $\gcd(ab,n) = 1$.
My Work:
This is what I have so far (for $\alpha, \beta, \gamma, \delta \in \Bbb Z$): \begin{align*} \gcd(a,n) = 1 \ &\Rightarrow 1 = \alpha a + \beta n\\ \gcd(b,n) = 1 \ &\Rightarrow 1... |
Let $p$ be a prime number, and $a \in \mathbb{Q}$, a number such that there is no integer $k$ satisfying $p^k=a$. Write $f= X^p -a \in \mathbb{Q}[X]$. I have to prove the following statements:
The degree of the splitting field $\Omega/\mathbb{Q}$ equals $p(p-1)$ Prove that the Galois group is isomorphic to the followin... |
Animation of an evolving network according to the initial Barabasi–Albert model
Evolving Networks are networks that change as a function of time. They are a natural extension of network science since almost all real world networks evolve over time, either by adding or removing nodes or links over time. Often all of the... |
Your equation: $$(R^2 + (\omega L - \frac{1}{\omega C})^2)^{\frac{1}{2}} = 100R $$has the form of:$$\sqrt{R^2 + X^2} = |Z| = Z $$which defines the MAGNITUDE of Z, where X is reactance and R is resistance. So we can say 100R is the magnitude of the impedance. Notice the equation above looks alot like the pythagorean the... |
Here’s something I thought of when I couldn’t sleep last night.
The curvature tensor of a Kähler metric can be viewed as a Hermitian form on \(\bigwedge^{1,1} T_X^*\) by mapping \(\operatorname{End} T_X \to \bigwedge^{1,1} T_X^*\) via the metric.
If we’re on a compact Kähler manifold with zero first Chern class, then f... |
Let $H$ be a complex, separable Hilbert space, and $T:H \rightarrow H$ a linear, bounded operator. Assume that $$\sigma(T) = \sigma(T^*) = \{ \lambda \in \mathbb{C}: a \leq |\lambda| \leq b \}$$ for $0< a < b$. Now assume that for $a < |\lambda| < b$ we have that $\lambda$ is an eigenvalue for $T^*$ but $T - \lambda I$... |
For the maximum: Suppose we have fixed values $x_1 \leq \frac{1}{n}$ and $x_n \geq \frac{1}{n}$. Then there is a unique point $x^*=(x_1, x_2, \dots, x_n)$ satisfying $\sum x_i=1$ with at most one index $j$ satisfying $x_1 < x_j < x_n$ (imagine starting with all the variables equal to $x_1$, then increasing them one by ... |
November 30th, 2018, 03:38 AM
# 1
Senior Member
Joined: Dec 2015
From: somewhere
Posts: 711
Thanks: 96
Need explanation
Let $\displaystyle A$ denote the largest of the numbers $\displaystyle a_1 , a_2 , ... , a_p$ for $\displaystyle p,n \in N $
Need explanation for $\displaystyle \frac{A}{\sqrt[n]{p}}\leq \sqrt[\displa... |
Research Open Access Published: Multiplicity of positive radial solutions of p-Laplacian problems with nonlinear gradient term Boundary Value Problems volume 2017, Article number: 36 (2017) Article metrics
798 Accesses
1 Citations
Abstract
In the present paper, we prove the existence of at least three radial solutions ... |
AuNem
Limiting case \(q\!\rightarrow\!0\) also can be considered.
Value of \(q\) can be indicated as subscript after the name of the function.
\(\mathrm{SuNem}_q(\mathrm{AuNem}_q(z))=z\)
\(G=\mathrm{Nem}_q\) is solution of the Abel equation for the transfer function \(T=\mathrm{Nem}_q\) :
\(G(T(z))=G(z)+1\)
For real va... |
First of all, in lower dimensions (2+1 and 1+1) the gravity is much simpler. This is because in 3d curvature tensor is completely defined by Ricci tensor (and metric at a given point) while in 2d curvature tensor is completely defined by scalar curvature. This means that there are no purely gravitational dynamical degr... |
I want to include some
TeX output (mainly math) in an
SVG image. The
SVG is meant to be used in a presentation and I would like to use a
sans serif font for this (currently, I use
Biolinum but another font would be acceptable as well).
The font used in the
TeX output should match the one used in the
SVG. Therefore, I a... |
The following identity seems to follow from a simple analysis of the sieve of Eratosthenes and inclusion-exclusion, where $p_i, p_j, p_k, \ldots$ denote primes and $N$ is an integer $\geq 2$:
$\Sigma_{p_i\leq N} \lfloor{N/p_i}\rfloor - \Sigma_{p_i, p_j\leq N} \lfloor{N/(p_i.p_j)}\rfloor + \Sigma_{p_i, p_j, p_k\leq N} \... |
What is meant by a theory to be (1) perturbatively renormalizable, (2) perturbatively non-renormalizable, (3) non-perturbatively renormalizable, and non-perturbatively non-renormalizable? In each case, what are at least one example of such theories?
Perturbatively renormalizable (or simply renormalizable) theories are ... |
I've been studying statistical mechanics for a while, the topic is very far from what I've learned till now so my questions may be superficial. When trying to see what my entropy is in an isobaric-isothermal ensemble, which turns out to be applicable in reactive systems, if I write my partition function $\Delta$ withou... |
Name of function
Name is important to deal with any object or subject, in order to distinguish it/him/her from other element of the same set. For functions, the name is especially important because it allows to denote the complicated expression or article in TORI with few digits.
The name can be used to find descriptio... |
Detectors (in my case I'm interested in homodyne detectors) with imperfect efficiency and losses are said to be able to be modeled using a beamsplitter and are to be in a statistical mixture with vacuum.
I am struggling to reproduce this "statistical mixture" result by modeling the system as a beamsplitter.
Just to ove... |
The goal is to have a shortcut for all letters of the latin and greek alphabets in bold font and upper/lower case.
For the latin alphabet the current solution works fine, but for the greek one it won't work.
So I actually have two questions here:
1: Is it possible to automatically loop over greek letters with pgffor, j... |
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... |
Can anybody tell me what is known about the classification of abelian transitive groups of the symmetric groups?
Let $G$ be a an abelian transitive subgroup of the symmetric group $S_n$. Show that $G$ has order $n$.
Thanks for your help!
Mathematics Stack Exchange is a question and answer site for people studying math ... |
This question already has an answer here:
I want to draw the roots of
z^5=1-i.
I am totally novice to latex and really have no idea about drawing. Thanks for helping!
TeX - LaTeX Stack Exchange is a question and answer site for users of TeX, LaTeX, ConTeXt, and related typesetting systems. It only takes a minute to sig... |
Defending the Schwarzschild singularity
Since the paper by Oppenheimer and Snyder1 was published, the myth that the Schwarzschild singularity is merely a coordinate singularity and so is of little consequence has become ubiquitous2, 3, 4, 5. Pejorative language is a part of this, by describing the Schwarzschild metric ... |
Basically, define
\closure and
\interior (or shorter names if you want) and use those symbolic definitions, this way, you can
program things into the macros.
\documentclass{scrartcl}
\usepackage{mathtools,amssymb}
\usepackage{xparse}
\NewDocumentCommand\closure{sm}
{\IfBooleanTF{#1}{\overline{#2}}{\bar{#2}}}
\NewDocume... |
Aliases:
tf.linalg.lstsq
tf.matrix_solve_ls
tf.matrix_solve_ls(
matrix,
rhs,
l2_regularizer=0.0,
fast=True,
name=None
)
Defined in
tensorflow/python/ops/linalg_ops.py.
See the guide: Math > Matrix Math Functions
Solves one or more linear least-squares problems.
matrix is a tensor of shape
[..., M, N] whose inner-most 2... |
2019-10-09 06:01
HiRadMat: A facility beyond the realms of materials testing / Harden, Fiona (CERN) ; Bouvard, Aymeric (CERN) ; Charitonidis, Nikolaos (CERN) ; Kadi, Yacine (CERN)/HiRadMat experiments and facility support teams The ever-expanding requirements of high-power targets and accelerator equipment has highligh... |
User:Jan A. Sanders/An introduction to Lie algebra cohomology/Lecture 3
Contents abstract
In this lecture we define the cohomology modules \(H^n(\mathfrak{g},\mathfrak{a})\)
Lifting the representation to the forms definition
\(\mathfrak{g}\) is called an
ideal in \(\mathfrak{l}\) if\[[\mathfrak{l},\mathfrak{g}]\subset ... |
Until Property Pattern
Untimed version
Pattern Name and Classification Until: Order Specification Pattern Structured English Specification Scope, P [holds] without interruption until S [holds]. Pattern Intent Until has been proposed by Grunske (2008) in [1] . This pattern describes a scenario in which an event/state wi... |
Research Open Access Published: On stability with respect to boundary conditions for anisotropic parabolic equations with variable exponents Boundary Value Problems volume 2018, Article number: 27 (2018) Article metrics
577 Accesses
Abstract
The anisotropic parabolic equations with variable exponents are considered. If... |
I would like to draw a frame around one equation to point it out. I used
\fbox{...}
but it didn't work out. Here is a minimal example where I tried it. Any package suggestions?
\documentclass[ german, paper=a4, ]{scrbook} %KOMA-\usepackage[latin1]{inputenc}\usepackage[ngerman]{babel} \usepackage[babel,german=guillemets... |
78 0
Hi everyone--I'm a bit stuck trying to follow a calculation in an article (Nucl. Phys. B360 (1991) p. 145-179) regarding the lab-frame relative velocity of two colliding particles as a function of the kinetic energy per unit mass. (I'll include references to equations in the article, but the article is not require... |
In this chapter you will do more work with fractions written in the decimal notation. When fractions are written in the decimal notation, calculations can be done in the same way as for whole numbers. It is important to always keep in mind that the common fraction form, the decimal form and the percentage form are just... |
Let $I \subseteq \mathbb{R}$ be an interval and $g: I \to \mathbb{C}$ continuous. Define $f: \mathbb{C} \backslash \overline{Im(f)} \to \mathbb{C}$ by
$f(z) := \int_I \frac{1}{g(x) - z} dx$
(with $\overline{Im(f)}$ being the closure of $Im(f)$.)
I now want to show that $f$ is analytic, and rewrite it into a power serie... |
Performing Topology Optimization with the Density Method
Engineers are given significant freedom in their pursuit of lightweight structural components in airplanes and space applications, so it makes sense to use methods that can exploit this freedom, making topology optimization a popular choice in the early design ph... |
In this chapter you will do more work with fractions written in the decimal notation. When fractions are written in the decimal notation, calculations can be done in the same way as for whole numbers. It is important to always keep in mind that the common fraction form, the decimal form and the percentage form are just... |
If $\text{Ker}(A) \ne \{0\}$, $A$ certainly doesn't have the property, as you cantake $B$ whose columns are all copies of a nonzero member of $\text{Ker}(A)$ and have$AB$ all $0$. So assume $\text{Ker}(A) = \{0\}$.
Now the columns of $AB$ are $p$ arbitrary members of $\text{Ran}(A)$ other than $0$. The question is whet... |
When we perform a Legendre transform on the connected generate functional $W[J]$ we get the quantum action (or 1PI action)
$$ \Gamma[\phi] = W[J(\phi)] - \int\mathrm{d}^4x\,\phi J,\quad\phi(J)=\frac{\delta W}{\delta J}. $$
Then it can be shown that
$$ \Gamma[\phi] = S[\phi] \mp\frac{1}{2}\log\det\left(\frac{\delta^2S}{... |
tl;d: At only a handful of milliGauss, the Earth's field out there is so weak that it probably wouldn't be very useful. It's doubtful that the critical GPS satellites would depend on it.
What's the Earth's field like out where the GPS satellites are?
First of all, where are they? The approximate period of a satellite w... |
As far as I can see, this question has a simple solution.
Let's limit ourselves to Hamiltonian cycles, and forget about the constraint that the coloring is legal.
Theorem:Let $c$ be an edge-coloring of $K_n$ such that no two Hamiltonian cycles have the same set of colors. Then $c\geq (1+o(1))\left(\frac{n}{e}\right)^2$... |
How to Couple Radiating and Receiving Antennas in Your Simulations
In Part 3 of our series on multiscale modeling in high-frequency electromagnetics, let’s turn our attention to the receiving antenna. We’ve already covered theory and definitions in Part 1 and radiating antennas in Part 2. Today, we will couple a radiat... |
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The value of the integral ∫0π/2dx2+cosx\int_0^{\pi/2}\dfrac{\text dx}{2+\cos x}∫0π/22+cosxdx can be expressed in the form πABC\dfrac{\pi^A\sqrt{B}}{C}CπAB where AAA, BBB, CCC are positive integers and BBB is not divisible by the square of any prime. Find the valu... |
I am driving an OLED display via two AAA batteries plus a charge pump to step up the voltage to 9V. I was wondering if there is likely to be any significant difference in efficiency between (a) using the two batteries in parallel and using a charge pump to step up from 1.5V to 9V, or (b) connecting the batteries in ser... |
I am trying to reference a set of equations that are placed within a
alignat and
subequations environments. I would like to reference them as
Eq. 1 together, rather than
Eqs. 1a and 1b separately. The MWE below does exactly this, yet leaves a small indentation in the paragraph just below the equations. Is there a way t... |
57 0
I am having trouble with the following problem:
Find the value(s) of [tex] \omega [\tex] for which [tex] y = \cos(\omega * t) [\tex] satisfies
[tex]\frac{d^2*y}{d*t^2} + 9y = 0[\tex]
I am trying to use latex but it doesn't seem to be working when I do "preview post" so I will rewrite what I am saying to make it mo... |
Spherical aberration compensation plates specify the total amount of spherical aberration imparted on a collimated beam of light covering its entire clear aperture. However, it is often necessary to know the amount of spherical aberration generated by the corrector plate
Ultrafine Spherical Graphite Powder Air Classifi... |
Research Open Access Published: Stabilization of a laminated beam with interfacial slip by boundary controls Boundary Value Problems volume 2015, Article number: 169 (2015) Article metrics
925 Accesses
6 Citations
Abstract
We consider two identical beams on top of each other with an adhesive in between. A considerable ... |
Research Open Access Published: The Dirichlet problem for the time-fractional advection-diffusion equation in a line segment Boundary Value Problems volume 2016, Article number: 89 (2016) Article metrics
1244 Accesses
6 Citations
Abstract
The one-dimensional time-fractional advection-diffusion equation with the Caputo ... |
Linear $x$ and $y$ Motion Control: From the mathematical model one can see that the motion through the axes $x$ and $y$ depends on $U_{1}$. In fact $U_{1}$ is the total thrust vector oriented to obtain the desired linear motion. If we consider $U_{x}$ and $U_{y}$ the orientations of $U_{1}$ responsible for the motion t... |
I'm stuck at this exercise:
Let $G$ be a group, with $|G|=pqr$, $p,q,r$ different primes, $q<r$, $r \not\equiv 1$ (mod $q$), $qr<p$. Also suppose that $p \not\equiv 1$ (mod $r$), $p \not\equiv 1$ (mod $q$). Let $C$ (the commutator of $G$) and $K$ be subgroups of $G$, with $C \leq K$, $K \trianglelefteq G$ and $|K|=q$. ... |
The following is from page 31 of Stein and Shakarchi's
Real Analysis. My question is about an aspect of the proof of the following theorem.
Theorem 4.1Suppose $f$ is a non-negative measurable function on $\mathbb R^d$. Then there exists an increasing sequence of non-negative simple functions $\{\varphi_k\}_{k=1}^\infty... |
Let $X_1, X_2, \cdots$ be i.i.d. random variables with $E(X_1) = 0, E(X_1^2) = \sigma^2 >0, E(|X_1|^3) = \rho < \infty$.Let $Y_n = \frac{1}{n} \sum_{i=1}^n X_i$ and let us note $F_n$ (resp. $\Phi$) the
cumulative distribution function of $\frac{Y_n \sqrt{n}}{\sigma}$ (resp. of the standard normal distribution).Then, Be... |
There are many possible choices regarding the overall scaling coefficients as well as the scaling coefficient converting time and frequency. It is possible to summarize these conventions succinctly using two numbers $a$ and $b$. I use the same notation as used in the Mathematica Fourier Transform function.
We define th... |
Statistics: Data Distribution Learn easily with Video Lessons and Interactive Practice Problems Mean, Median, Mode, Range Mean, median, mode, and range are values that describe data. Mean and median are measures of central tendency and provide a number to represent the central position of data in a set. Mode is also a ... |
Defining parameters
Level: \( N \) = \( 7 \) Weight: \( k \) = \( 6 \) Nonzero newspaces: \( 2 \) Newforms: \( 3 \) Sturm bound: \(24\) Trace bound: \(1\) Dimensions
The following table gives the dimensions of various subspaces of \(M_{6}(\Gamma_1(7))\).
Total New Old Modular forms 13 11 2 Cusp forms 7 7 0 Eisenstein s... |
Overview
Euler angles is a way of describing the rotation in 3D space using three separate rotations around an axes.
Syntax
Euler angles are usually defined one of the two symbol sets:
\( \alpha, \beta, \gamma \)(Alpha, Beta, Gamma). These are usually used with
proper Euler angles(see below).
\( \Phi, \Theta, \Psi \)(P... |
Get your free trial content now! Video Transcript Transcript Exponential Growth and Decay
The largest longhorn breeder’s competition is coming up and Old MacDonald is tired of coming in second place. His wife, Mrs. MacDonald, suggests that Old MacDonald create a
formula using exponential growth and decay to feed his fa... |
inclusion–exclusion principleis a counting technique which generalizes the familiar method of obtaining the number of elements in the union of two finite sets; symbolically expressed as Explain inclusion-exclusion principle with example.
posted by , on ,
In combinatorics (combinatorial mathematics), the
{\displaystyle ... |
I have the following question to solve:
Tungsten, $\ce{W}$, and chlorine, $\ce{Cl}$, form a series of compounds with the following compositions: \begin{array}{rr} \text{Mass % W} & \text{Mass % Cl}\\ \hline 72.17 & 27.83\\ 56.45 & 43.55\\ 50.91 & 49.09\\ 46.36 & 53.64\\ \end{array} If a molecule of each compound contai... |
Look at the following series: 1 + 2x + 3x^2 + 4x^3 + 5x^4 + ..... You can say by using any method that the series is divergent. It indeed diverges but we use this as a series expansion for 1/(1-x)^2. I think it is wrong to expand functions like that by using Maclaurin series expansion method. According to me calculatin... |
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Evaluate the integral:∫αβ(x−α)(x−β)dx\int_\alpha^\beta (x-\alpha)(x-\beta) dx∫αβ(x−α)(x−β)dx
SOLUTION∫αβ(x2−(α+β)x+αβ)dx\int_\alpha^\beta (x^2 - (\alpha + \beta)x + \alpha\beta ) dx∫αβ(x2−(α+β)x+αβ)dx
(x33−(α+β)x22+αβx)∣αβ\left(\frac{x^3}{3} - \frac{(\alpha + \be... |
The Central Board of Secondary education is responsible for conducting an examination of the schools affiliated to the Central Board. Students usually find maths as one of the most difficult paper. The major reason is due to lack of confidence and less of practice. It is suggested that practicing maths on daily basis w... |
Hi,
I’m looking for a symbolic manipulations library to do different sorts of analysis on a model. I’ve tried python SymPy but couldn’t get it to work; following a recent tweet by @cscherrer, I was wondering whether I can use Julia’s SymPy/SymEngine for this. In short, the expression I’m interested in is an exponential... |
In this chapter you will do more work with fractions written in the decimal notation. When fractions are written in the decimal notation, calculations can be done in the same way as for whole numbers. It is important to always keep in mind that the common fraction form, the decimal form and the percentage form are just... |
I'm solving problem in classical field theory and I have some difficulties. I'm trying to study small oscilations of heavy string with fixed points.
First of all I wrote down this Lagrangian:
$$S=\int dt ds \left[\frac{\rho}{2}(\dot{x}^2+\dot{y}^2)-\rho g y(s,t)+\frac{\lambda(s,t)}{2}\left(\left(\frac{\partial x}{\part... |
TL;DR: won't work with any spacecraft further away than one third of the larger semiaxis of the earth's path, even for fully-armed battlestation sized spacecraft.
Radar (more exactly, time-of-flight) is limited by two things:
speed of light: The nearest star is 4 light years away. So anything that we send into that dir... |
I know that if $W$ and $W′$ are two independent brownian motions, then $dWt \ dWt′$ = 0. How can I prove/demonstrate this theorem?
Additionaly, how can we prove that if $W$ and $W′$ are dependent, then $dWt \ dWt′ = \rho \ dt$?
Quantitative Finance Stack Exchange is a question and answer site for finance professionals ... |
Cumulative distribution function are the function talking about the probability of an an event over a given interval. The cumulative distribution function can be obtained by integrating the probability density function. The probability can be obtained by integrating the cumulative distribution function over a definite ... |
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