text stringlengths 256 16.4k |
|---|
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... |
The equation to approximate an input signal with a unit impulse in Continuous Time, is shown below, before we take the limit $\hat{x}(t)=\frac{lim}{\Delta\rightarrow0}\sum^{\infty}_{-\infty}x(k\Delta)\delta_\Delta(t-k\Delta)\Delta$ <-- why is there a final $\Delta$ multiplying the $\delta_\Delta(t-k\Delta)$?
Here the s... |
Let {$f_n$} be defined recursively as $f_1 = f_2 = f_3 = 1$ and $f_n = f_{n-1} + f_{n-3}$ for all $n \gt 3$.
Also, define {$a_n$} as the ratio of the terms of {$f_n$}. That is, $a_n = \frac{f_{n+1}}{f_n}$ for some $n \geq 1$.
So, the terms of {$f_n$} are $$f_1 = 1,f_2 = 1,f_3 = 1,f_4 = 2,f_5 = 3,f_6 = 4,f_7 = 6,\ldots,... |
Abbreviation:
MultLat
A
(or multiplicative lattice ) is a structure $\mathbf{A}=\langle A,\vee,\wedge,\cdot\rangle$ of type $\langle 2,2,2\rangle$ such that $m$-lattice
$\langle A,\vee,\wedge\rangle$ is a lattice
$\cdot$ distributes over $\vee$: $x(y\vee z)=xy\vee xz$, $(x\vee y)z=xz\vee yz$
Remark: This is a template.... |
Generally in RSA we encrypt as $m^e \pmod n$. Will RSA work if we replace the power by normal multiplication? $E = (m \times e) \mod n$ and decryption as $c \times d \mod n$. What will be $d$ disadvantage if it works ?
Suppose an RSA public key is still $(e, N)$ and the private key is still $d$. We have $Enc = (m*e) \t... |
In order to set up a system of equations using matrices, you need to understand how matrices multiply one another. Not all matrices can be multiplied together – they need to be compatible with one another. Not only that, unlike scalar (single number) arithmetic, multiplication does not commute, that is, the order of th... |
This question already has an answer here:
I would like the limits to be vertically above and below the summation sign. I also need a larger summation sign... This is currently what I have:
$x^2sin(x) = \sum_{n=-\infty\atop n\ne \pm 1}^\infty \dfrac {4i(-1)^{n}n}{(n^2 - 1)^2} $
Any help appreciated! |
The hypergeometric distribution arises when one samples from a finite population, thus making the trials dependent on each other. There are five characteristics of a hypergeometric experiment.
Characteristics of a hypergeometric experiment
You take samples from twogroups. You are concerned with a group of interest, cal... |
Classical entropy quantities are a way to quantify how much information is revealed in a random event. Shannon first introduced a way to quantify information by associating to an event occuring with probability p, an amount of information -\log p (as is standard in information theory, logarithms are taken in base 2 and... |
Site Index Site is defined by the Society of American Foresters (1971) as “an area considered in terms of its own environment, particularly as this determines the type and quality of the vegetation the area can carry.” Forest and natural resource managers use site measurement to identify the potential productivity of a... |
If $I=(a_1,\dots, a_m)$ and $J=(b_1, \dots, b_n)$ are ideals in a commutative ring, then we have\[IJ=(a_ib_j),\]where $1\leq i \leq m$ and $1\leq j \leq n$.
Proof.
(a) Prove that $IJ=(x, 6)$.
Note that the product ideal $IJ$ is generated by the products of generators of $I$ and $J$, that is, $x^2, 2x, 3x, 6$. That is, ... |
This picture is a copy of the pattern on my curtains. The points of a hexagonal lattice are each coloured with one of four possible colours. It has translational symmetry in two directions: a vertical shift by four lines and a horizontal shift by six lines. One generating patch is shown with a solid line.
However if yo... |
This is for a thought experiment I'm programming.
Let's say I have 2 cars; 1 in front, 1 in back. I'm adjusting the rear car's acceleration so that it will never be closer than 1 second's worth of distance from a half car's length behind the front car.
I have created the below formulae to calculate the acceleration, ve... |
In BDF schemes for $\dot y = f$, one uses $$f(t_n)=\dot y(t_n)$$and tries to approximate $\dot y(t_n)\approx \sum_{j=0}^k\alpha_k y_{n-j}$ by the current value $y_n$ (that is to be computed) and the $k$ previously computed approximations.
In the presented approach, in $(5)$, $y$ is approximated as a polynomial $p$ in $... |
Wave energy converters in coastal structures Introduction
Fig 1: Construction of a coastal structure.
Coastal works along European coasts are composed of very diverse structures. Many coastal structures are ageing and facing problems of stability, sustainability and erosion. Moreover climate change and especially sea l... |
I define a
$n$-labeling of a directed acyclic graph $G = (V, E)$ as a function $f$ from $V$ to the power set of {1, ..., $n$} such that for any $x, y \in V$, $x \neq y$, we have $f(y) \subset f(x)$ iff $x \rightarrow^+ y$ (i.e. there is a path of length >0 from $x$ to $y$ in $G$). Clearly, any DAG $G$ admits a $|V|$-la... |
I have two scenarios where I use arrows with a super-scripted asterisk: math mode and
tikz-cd diagrams. I would like to be able to show such an arrow in both scenarios such that the arrows look the same, i.e., with respect to positioning of the asterisk.
Consider the below MWE. This is how I would like the arrow to loo... |
Definition: Angular acceleration of an object undergoing circular motion is defined as the rate with which its angular velocity changes with time. Angular acceleration is also referred to as rotational acceleration. It is a vector quantity, that is, it has both magnitude and direction.
Angular acceleration is denoted b... |
In the article
Pricing via utility maximization and entropy from Richard Rouge and Nicole El Karoui, they define the value function of the optimization problem as
\begin{align} V(x,C) = \dfrac{1}{\gamma} \ln E\left[ -\hat{U}(x,-C) \right] = \inf_{\pi \in \mathcal{A}} \dfrac{1}{\gamma} \ln E[\exp -\gamma ( X_{T}^{x, \pi... |
Defining parameters
Level: \( N \) = \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) Weight: \( k \) = \( 2 \) Nonzero newspaces: \( 12 \) Newforms: \( 32 \) Sturm bound: \(4608\) Trace bound: \(4\) Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(210))\).
Total New Old Modular forms 1... |
I never thought these posts would get to 5.
Now I said I would do a population problem but I have decided to go with a radioactive decay problem instead. I will use the example of carbon dating as this is based on radioactive decay. But first, let’s look at the general equation for exponential decay:
\[
{A}\hspace{0.33... |
There are proofs that treat the cases of real and non-real $\chi$ on an equal footing. One proof is in Serre's Course in Arithmetic, which the answers by Pete and David are basically about. That method is using the (hidden) fact that the zeta-function of the $m$-th cyclotomic field has a simple pole at $s = 1$, just li... |
Bonus: An ATLAS \(\mu\mu j\) event with \(m=2.9\TeV\) will be discussed at the end of this blog post. A model with exactly this prediction was published in June
Two days ago, I discussed four LHC collisions suggesting a particle of mass \(5.2\TeV\). Today, just two days later, Tommaso Dorigo described a spectacular die... |
2019-05-20 15:18 Detailed record - Similar records 2019-01-23 09:13
nuSTORM at CERN: Feasibility Study / Long, Kenneth Richard (Imperial College (GB)) The Neutrinos from Stored Muons, nuSTORM, facility has been designed to deliver a definitive neutrino-nucleus scattering programme using beams of $\bar{\nu}_e$ and $\bar... |
Now the fractions we have been working with are called
proper fractions: these are fractions where the numerator is smaller than the denominator. These types of fractions are smaller than one, which is why they are called proper as they are a fractional part of one. This implies there are things called improper fractio... |
Instead of writting very long lines to create complex equations it would be great to use variables to substitute smaller chunks...
A simple example:
\[\frac{ \sqrt{ \mu(i)^{ \frac{3}{2}} (i^{2} -1) } }{ \sqrt[3]{\rho(i) - 2} + \sqrt[3]{\rho(i) - 1} }\]
It would be done something like this:
A = \sqrt{ \mu(i)^{ \frac{3}{... |
So now I’m up to “4” on Newton’s clock:
So the expression\[
{\left({2\sin\frac{\mathit{\pi}}{2}}\right)}^{2}
\]
uses the sine function which has been talked about many posts before. Only this time, it is using radian measure of angles instead of degrees. If your calculator is in degree mode, you can substitute 90° in p... |
Consider the function $f$ on $S_n$ which equals $1/n$ on all adjacent transpositions $(i,i+1)$, where we let $n+1 = 1$, and $0$ otherwise, and its Fourier transform $\hat{f}(\rho)$ evaluated at the irreducible representations.
Recall the irreducible representations of $S_n$ are indexed by the set of partitions of $n$. ... |
Hi, I’m Chris and I teach people to teach machines. But I am a reluctant computer scientist. Sometimes I get concerned that the thing I know the most about is not directly linked to my survival. My father knew how to keep machines running. My wife grows vegetables. In a post-apocalyptic world, they would be […]
Check o... |
Extension.
This post is about set theory, which is a framework to reason about collections, elements and membership.
We start with a informal and naïve outline, which is (very loosely) based on a Godel-Bernays version of set theory. This theory is about sets (collections) which contain elements, which can in turn be se... |
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... |
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... |
Firstly, I will define what
Pythagorean Triples are for those who do not know.
Definition:
A Pythagorean Triple is a group of three integers $a$, $b$ and $c$ such that $a^2+b^2=c^2$, since the
Pythagorean Theoremasserts that for any $90^\circ$ (right-angle) triangle $ABC$ with sides $a$, $b$ and $c$, one will always ha... |
Artin's axioms do not apply in this case, because the stack is not limit-preserving. They only work with stacks that are locally finitely presented.
In any case, it is easy to give examples of quasi-coherent sheaves whose functor of automorphisms is not representable (for example, an infinite dimensional vector space),... |
Let $H$ be a mapping from some normed space $X$ into a normed space $Y$. When solving an equation of the form\begin{equation}H x = y\end{equation}with an ill-posed operator $H$,
Tikhonov Regularization replaces theunstable inverse $H^{-1}$ by a family of stable mappings $R_{\alpha}$ define dy\begin{equation}\label{Ralp... |
Let $C$ be the set of all (strictly) increasing functions $\Bbb Z^+\rightarrow\Bbb Z^+$.
First, consider this function $\sigma$ from $A$ to $C$. For each $f$ we define $\sigma(f)=\sigma_f$ defined so:$$\sigma_f(n)=\sum_{j=1}^n f(j)$$This funtion is bijective. Hence, $\#C=\#A$.
Let's show that indeed, this function is b... |
If you want an FPT algorithm for the problem (parameterized by treewidth $t$), you want an algorithm working in time $f(t) \cdot n^{O(1)}$, where $f$ is any computable function (depending solely on $t$). Of course, it would be nice to make $f$ as appealing as possible.In addition to the mentioned algorithm running in $... |
I was approaching the following problem:
"Let $f \colon X \to Y$ be continuous. Is it true that if $x$ is a limit point of $A \subset X$ then $f(x)$ is a limit point of $f(A)$?"
The answer is that it is false and here is a counterexample I found: $X = \mathbb{R}$ with the standard topology, $Y = \mathbb{N}$ with the di... |
Is there any polynomial $f(x,y)\in{\mathbb Q}[x,y]{}$ such that $f\colon\mathbb{Q}\times\mathbb{Q} \rightarrow\mathbb{Q}$ is a bijection?
Jonas Meyer's comment:
Quote from arxiv.org/abs/0902.3961, Bjorn Poonen, Feb. 2009: "Harvey Friedman asked whether there exists a polynomial $f(x,y)\in Q[x,y]$ such that the induced ... |
Up to this point, we have discussed inferences regarding a single population parameter (e.g., μ, p, \(\sigma^2\)). We have used sample data to construct confidence intervals to estimate the population mean or proportion and to test hypotheses about the population mean and proportion. In both of these chapters, all the ... |
Question 1
$$ H(e^{j\omega})=\sum_{n=0}^{N-1}h[n]e^{-jn\omega} =\mathbf{c}^H(\omega)\cdot \mathbf{h} \tag{1} $$ $$ =\mathbf{h}^H\cdot\mathbf{c}(\omega) \tag{2} $$
$$H(\mathbf{h})=\sum_{k=1}^Kh[k]e^{j\omega_k}\tag{3}$$
The design of filter in matlab ,if using:
$-$$(1)$ and $(3)$ the length of filter is $K$.
$-$$(2)$ the... |
The repeating decimal .36666... in base 8 can be written in a fraction in base 8. I understand simple patterns such as 1/9 in base 10 is .1111.... so 1/7 in base 8 is .1111. But I'm not too sure how to convert this decimal in this base to the fraction in the same base.
\begin{align} 0.3\bar{6}_8 &= \frac{3}{8} + 6\left... |
The question was the following:
There are $28$ students in a class, $15$ study chemistry, $18$ study physics and $2$ study neither chemistry nor physics.
Calculate the probability that a student chosen at random studies both chemistry and physics.
My approach was as follows:
We pick a random person, the chance that thi... |
Search
Now showing items 1-10 of 53
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... |
From Hartshorne:
If $Y$ is an irreducible subset of $X$, then its closure $\overline{Y}$ in $X$ is also irreducible.
By irreducible they mean that $Y$ cannot be written $Y_1 \cup Y_2$ for two proper subsets $Y_i$ of $Y$ that are closed in the subspace topology of $Y$.
My attempt
Suppose that $\overline{Y} = Y_1 \cup Y_... |
Consider an $n\times n$ chessboard whose top-left corner is colored white. But Alice likes darkness, so she wants you to cover those white cells for her. The only tool you have are black L-shaped tiles each of which covers $3$ unit cells.
Formally, each tile covers unit cells satisfying the following:
Two of the cells ... |
The form of the rendering equation that uses only the BRDF ($f$ in your example, often called $f_r$) and integrates over one hemisphere does not account for transmission.When adding in transmission, it's fairly common to add a second integral over the opposite hemisphere, using a different BTDF function (bidirectional ... |
Inferences about Two Population Proportions
We can apply the same methods we just learned with means to our two-sample proportion problems. We have two populations with two samples and we want to compare the population proportions.
Is the proportion of lakes in New York with invasive species different from the proporti... |
Any pure strategy Nash equilibrium is implicitly a mixed-strategies Nash equilibrium. Since the valuations vary, it's a good indicator we want to consider mixed-strategies. The fact that the problem tells us this is a stronger indicator, though I'm sure not the axiomatic justification you are seeking. :-)
Consider play... |
Preprints (rote Reihe) des Fachbereich Mathematik Refine Keywords average density (3) (remove)
296
We show that the occupation measure on the path of a planar Brownian motion run for an arbitrary finite time intervalhas an average density of order three with respect to thegauge function t^2 log(1/t). This is a surprisi... |
Shapes appearing stretched in the periphery is a consequence of perspective projection. The wider the field of view (FOV) is, the stronger the stretching effect gets.To demonstrate the effect I wrote a quick example on ShaderToy: https://www.shadertoy.com/view/MltBW2As you can see on the images below (corresponding to ... |
Notice:
If you happen to see a question you know the answer to, please do chime in and help your fellow community members. We encourage our fourm members to be more involved, jump in and help out your fellow researchers with their questions. GATK forum is a community forum and helping each other with using GATK tools a... |
Let $(X_i,Y_i)_{i\in\mathbb{Z}}$ be a finite-valued stationary process whose $\sigma$-algebra of tail events is trivial. Let $\mathcal{F}_n^m$ be the $\sigma$-algebra generated by $X_n,\dots,X_m$ ($n,m\in\mathbb{Z}$) and define $\mathcal{G}_n^m$ similarly for $Y_i$. Let $a$ be some fixed state of $X$ and consider the r... |
Recent Posts Recent Comments Archives Categories Meta Author Archives: res65
This course was eye-opening in the sense that sustainability is in all aspects of life. I never thought about all the ways it can be improved and actually how significant the impacts can be to little changes over the course … Continue reading
... |
Search
Now showing items 1-1 of 1
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 ... |
Search
Now showing items 1-5 of 5
Measurement of electrons from beauty hadron decays in pp collisions at root √s=7 TeV
(Elsevier, 2013-04-10)
The production cross section of electrons from semileptonic decays of beauty hadrons was measured at mid-rapidity (|y| < 0.8) in the transverse momentum range 1 < pT <8 GeV/c wit... |
Search
Now showing items 1-10 of 55
J/Ψ production and nuclear effects in p-Pb collisions at √sNN=5.02 TeV
(Springer, 2014-02)
Inclusive J/ψ production has been studied with the ALICE detector in p-Pb collisions at the nucleon–nucleon center of mass energy √sNN = 5.02TeV at the CERN LHC. The measurement is performed in... |
A particle moves along the x-axis so that at time t its position is given by $x(t) = t^3-6t^2+9t+11$ during what time intervals is the particle moving to the left? so I know that we need the velocity for that and we can get that after taking the derivative but I don't know what to do after that the velocity would than ... |
Details
For Math equations in entries - compose posts in itex, and converts them to XHTML+MathML, which advanced browsers like Mozilla can render.
$\sin(\theta)\cos(\theta)= \frac{1}{2}\sin(2\theta)$
is an inline equation.
\[\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}\]
is a display equation. |
Signal-to-Noise Ratio
Don H. Johnson (2006), Scholarpedia, 1(12):2088. doi:10.4249/scholarpedia.2088 revision #126771 [link to/cite this article] Signal-to-noise ratio generically means the dimensionless ratio of the signal power to the noise power contained in a recording.Abbreviated SNR by engineers and scientists, t... |
Defining parameters
Level: \( N \) = \( 30 = 2 \cdot 3 \cdot 5 \) Weight: \( k \) = \( 2 \) Nonzero newspaces: \( 3 \) Newforms: \( 3 \) Sturm bound: \(96\) Trace bound: \(1\) Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(30))\).
Total New Old Modular forms 40 7 33 Cusp fo... |
07/16/19
No Comments
Introduction
In this post I will discuss building a simple recommender system for a movie database which will be able to:
– suggest top N movies similar to a given movie title to users, and – predict user votes for the movies they have not voted for. In the next part of this article I will show how... |
Yes, $Z$ is a proper martingale. However, $\int_0^T(Z_sW_s)^2\,ds$ is
not integrable for large $T$. As the quadratic variation of $Z$ is $[Z]_t=4\int_0^t(Z_sW_s)^2\,ds$, Ito's isometry says that this is integrable if and only if $Z$ is a square-integrable martingale, and you can show that $Z$ is not square integrable a... |
its a famous equation $$\Delta s^2=-(c\Delta t)^2+(\Delta x)^2$$ but why do we put the minus sign i heard its there because of that space is ruled by non-Euclidean geometry rules and if that was true what is the difference between a Euclidean and non-Euclidean geometry?
[I will work in natural units where $c=1$. I will... |
Tracking and forecasting epidemic spread through viral genome sequencing
Trevor Bedford (@trvrb)
9 Oct 2019 EPPIcenter Seminar Series UCSF Slides at: bedford.io/talks We work at the interface of virology, evolution and epidemiology Sequencing to reconstruct pathogen spread Epidemic process Sample some individuals Seque... |
I am in my 4th year (3 semesters left including the current one), taking mechanics, E&M, quantum mechanics, and a lab course. For each of the three main courses, we get one problem set per week that's around 5-8 questions. In addition to that there's a lab report due every 1-2 weeks.It really...
This is a random proble... |
I don't think there is a specific name for the coarsest topology on $X \times X$ for which $d : X \times X \to \mathbb{R}$ is continuous. In general if $f$ is a function from a set $Y$ to a topological space $Z$, the coarsest topology on $Y$ for which $f$ is continuous is called the
topology on $X$ generated by $f$. Th... |
To do Hartree-Fock to Helium atom, you just need to calculate one orbital, which for helium is spherically symmetric. The Hartree-Fock 'integro-differential' equation for spherically symmetric atom with one eigenstate can be written as
$$\left(-\frac{1}{2}\nabla^2 - \frac{2}{r} + V_{Hx}(r) \right) u(r) = \epsilon u(r),... |
We will consider the case of real transport with a given flow rate $J=\rho u$. We assume that all compressors are identical, capable of maintaining a given air flow. Specifications: the flow velocity is limited by the condition $1\le u\le 10$ m/s. It is necessary to determine how many compressors are needed and how to ... |
Abbreviation:
MultSlat
A
(or multiplicative semilattice ) is a structure $\mathbf{A}=\langle A,\vee,\cdot\rangle$ of type $\langle 2,2\rangle$ such that $m$-semilattice
$\langle A,\vee\rangle$ is a semilattice
$\cdot$ distributes over $\vee$: $x(y\vee z)=xy\vee xz$, $(x\vee y)z=xz\vee yz$
Remark: This is a template. If... |
Wrinklers are twitchy leech-like creatures that, in normal gameplay, only start appearing during the Grandmapocalypse. While they at first appear to reduce CpS (cookies per second), they actually provide a massive boost to cookie production in the long run. There is a 0.01% chance a Shiny wrinkler will spawn instead of... |
Be $U\subseteq \mathbb{C}$ simply connected region with $U\neq\mathbb{C}$ and $a,b\in U$, $a\neq b$. Is there an biholomorphism $f:U\longrightarrow U$ with $f(a)=b$ and $f(b)=a$?
I know that, by the Riemann mapping theorem, there are unique isomorphisms $h:U\longrightarrow D(0,1)$ with $h(a)=0$, and $g:U\longrightarrow... |
Show that $\sqrt{13}$ is an irrational number.
How to direct proof that number is irrational number. So what is the first step.....
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It only takes a minute to sign up.Sign up to join this c... |
We can look at this in the following way:
Suppose we are doing an experiment where we need to toss an unbiased coin $n$ times. The overall outcome of the experiment is $Y$ which is the summation of individual tosses (say, head as 1 and tail as 0). So, for this experiment, $Y = \sum_{i=1}^n X_i$, where $X_i$ are outcome... |
I am tired of fractions, you too? Well let’s switch gears and talk about the roots of numbers. This is preparing you for a post or posts on the rules of exponents.
So before, I introduced the concept of the square root and how it is the reverse operation of squaring a number:
\[
\sqrt{25}\hspace{0.33em}{=}\hspace{0.33e... |
Let $c$ be an irrational real number. Let $\{\cdot\}$ be the fractional part operator. I would like to get some sense of how in-the-dark we are about the distribution of values of $\{cn!\}$, for familiar values of $c$. This is related to a previous post which (essentially) asks the question "Does $n!/(2\pi)$ tend to a ... |
Sparsity is an important topic in machine learning. When we build a model, the simplest approach is usually to make no assumptions about its internal structure, and to connect every possible input to every possible output, perhaps with some intermediate representations. This is, for instance, how we ended up with the f... |
In have a matrix function $A$ (size 3x3) and a vector function $v$ (size 3x1) that I calculate with a matrix-vector multiplication $B(x)e(x)$, $B(x)$ a 3x3 matrix function and $e(x)$ a 3x1 vector function. Applying convolution $A*v$ involves many operatons:
$$ (A(x)*\underbrace{(B(x)e(x))}_{ = v(x)})_{ij} = \begin{bmat... |
If a Half of a Group are Elements of Order 2, then the Rest form an Abelian Normal Subgroup of Odd Order
Problem 575
Let $G$ be a finite group of order $2n$.Suppose that exactly a half of $G$ consists of elements of order $2$ and the rest forms a subgroup.Namely, suppose that $G=S\sqcup H$, where $S$ is the set of all ... |
Let $ f$ be an irreducible polynomial of degree $q$ over $\mathbb{F}_p$. Let ${\bf F}=\frac{\mathbb{F}_p[x]}{f}$ be the finite field which contain $p^q$ elements. Assume $k>1$ is an integer and suppose that ${\bf R}=\frac{\mathbb{F}_p[x]}{f^k}$ is the quotient ring such that the coefficients come from $\mathbb{F}_p$ an... |
Fluid Mechanics - Dec 2016
Mechanical Engg (Semester 3)
TOTAL MARKS: 100
TOTAL TIME: 3 HOURS (1) Question 1 is compulsory. (2) Attempt any four from the remaining questions. (3) Assume data wherever required. (4) Figures to the right indicate full marks.
Solve any one question fromQ.1(a,b) and Q.2(a,b) 1(a) Distinguish... |
I need to prove that
every compact metric space is complete. I think I need to use the following two facts: A set $K$ is compact if and only if every collection $\mathcal{F}$ of closed subsets with finite intersection property has $\bigcap\{F:F\in\mathcal{F}\}\neq\emptyset$. A metric space $(X,d)$ is complete if and on... |
User:Andrey Shilnikov/Proposed/Multi-stability in neuronal models
In preparation
The ability of distinct anatomical circuits to generate multiple patterns of rhythmic activity is widespread among vertebrate and invertebrate species. These patterns correspond to different locomotor behaviours. For example, swimming and ... |
This article presents a simple tutorial code from SDALGCP package to make inference on spatially aggregated disease count data when one assume that the disease risk is spatially continious. There are two main functions provided by the package, for parameter estimation and for prediction.
where \(y_{i}\) and \(d_{i}\) a... |
If the Images of Vectors are Linearly Independent, then They Are Linearly Independent
Problem 62
Let $T: \R^n \to \R^m$ be a linear transformation.Suppose that $S=\{\mathbf{x}_1, \mathbf{x}_2,\dots, \mathbf{x}_k\}$ is a subset of $\R^n$ such that $\{T(\mathbf{x}_1), T(\mathbf{x}_2), \dots, T(\mathbf{x}_k) \}$ is a line... |
Reynolds number, abbreviated as Re, is a dimensionless number that measures the ratio of inertial forces (forces that remain at rest or in uniform motion) to viscosity forces (the resistance to flow).
Reynolds Number formula
\(\large{ Re = \frac{ \rho \; v \; l_c }{ \mu } }\)
\(\large{ Re = \frac{ v \; l_c }{ \nu } }\)... |
I would like a clarification on bank angle and how its different from roll angle with respect to to fixed wing aircraft. It is my understanding that the bank angle is a result of rotating the aircraft body to the stability frame, implying that if the angle of attack $\alpha$ and the side slip angle $\beta$ are zero the... |
Let $\Sigma$ be an alphabet, ie a nonempty finite set. A string is any finite sequence of elements (characters) from $\Sigma$. As an example, $ \{0, 1\}$ is the binary alphabet and $0110$ is a string for this alphabet.
Usually, as long as $\Sigma$ contains more than 1 element, the exact number of elements in $\Sigma$ d... |
3 0
Some friend asked me the following question:
For a real scalar field \phi, assume that H = H_free - \int d^3 x\ J \phi. J(x, t) is just some real number, source, or background field, without second quantization. Now, what is the amplitude \psi(x, t) for finding a particle at time t(before, during, or after source i... |
The question as asked is open to interpretation, so I will first rephrase it to have a basis to build upon. Your last paragraph tells me that you want to know the optimum bank angle to get the highest ratio of turn rate to altitude loss in a glide at a given airspeed.
Spoiler: Since steeper bank angles require more lif... |
Differential and Integral Equations Differential Integral Equations Volume 31, Number 9/10 (2018), 685-700. A sharp lower bound for the lifespan of small solutions to the Schrödinger equation with a subcritical power nonlinearity Abstract
Let $T_{\varepsilon}$ be the lifespan for the solution to the Schrödinger equatio... |
The "left to right" of the biconditional is true. As noted in another answer, we can use L'hopital. But I will utilize a direct approach. We need to show that for arbitrarily large $M$, we have for sufficiently large $x$ the inequality $\frac{f(x)}{x} > M$.
By assumption, for any arbitrarily large $M$ we have $f'(x) > ... |
This answer is a response to a comment by the OP on on yoda's answer.
Suppose that $h(t)$, the impulse response of a continuous-time linear time-invariant system, has the property that $$\int_{-\infty}^{\infty} |h(t)| \mathrm dt = M$$ forsome finite number $M$. Then, for
each and every bounded input $x(t)$, the output ... |
Defining parameters
Level: \( N \) = \( 63 = 3^{2} \cdot 7 \) Weight: \( k \) = \( 2 \) Nonzero newspaces: \( 10 \) Newforms: \( 17 \) Sturm bound: \(576\) Trace bound: \(4\) Dimensions
The following table gives the dimensions of various subspaces of \(M_{2}(\Gamma_1(63))\).
Total New Old Modular forms 192 131 61 Cusp ... |
Basically 2 strings, $a>b$, which go into the first box and do division to output $b,r$ such that $a = bq + r$ and $r<b$, then you have to check for $r=0$ which returns $b$ if we are done, otherwise inputs $r,q$ into the division box..
There was a guy at my university who was convinced he had proven the Collatz Conject... |
I am interested in the early proofs of the theorem. It is often called Cauchy mean value theorem, so perhaps Cauchy proved it first. In all the proofs that I have seen we construct a contrived function, applying Rolle's theorem to which works out just right. It seems like a miracle that one would come up with such a fu... |
In this chapter we turn to the important question of determining the distribution of a sum of independent random variables in terms of the distributions of the individual constituents. In this section we consider only sums of discrete random variables, reserving the case of continuous random variables for the next sect... |
Mathematics - Functional Analysis and Mathematics - Metric Geometry
Abstract
The following strengthening of the Elton-Odell theorem on the existence of a $(1+\epsilon)-$separated sequences in the unit sphere $S_X$ of an infinite dimensional Banach space $X$ is proved: There exists an infinite subset $S\subseteq S_X$ an... |
Bunuel wrote:
In the figure above, if isosceles right triangle PQR has an area of 4, what is the area of the shaded portion of the figure?
(A) \(\pi\)
(B) \(2\pi\)
(C) \(2\sqrt{2}\pi\)
(D) \(4\pi\)
(E) \(8\pi\)
Attachment:
The attachment
2018-02-05_0842.png is no longer available
Attachment:
2018-02-05_0842ed.png [ 19.... |
Question
A beam is supported at the two end and is uniformly loaded. The bending moment M at a distance x from one end is given by \[M = \frac{WL}{2}x - \frac{W}{2} x^2\] .
Find the point at which M is maximum in a given case.
Solution
\[\text { Given }: \hspace{0.167em} M = \frac{WL}{2}x - \frac{W}{2} x^2 \]
\[ \Right... |
Subsets and Splits
No community queries yet
The top public SQL queries from the community will appear here once available.