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This was too long to be a comment, my apologies:
Further to Tim Gowers' comment and the following discussion, Chapter 6 of Bollobas' lovely white book "Combinatorics - set systems hypergraphs, families of vectors, and combinatorial probability" studies exactly this kind of question,.
In fact Tim's comment corresponds t... |
Hi, I'm aware of a typical example of injective immersion that is not a topological embedding: figure 8##\beta: (-\pi, \pi) \to \mathbb R^2##, with ##\beta(t)=(\sin 2t,\sin t)##As explained here an-injective-immersion-that-is-not-a-topological-embedding the image of ##\beta## is compact in...
I have a hypothetical univ... |
LaTeX typesetting is made by using special tags or commands that provide a handful of ways to format your document. Sometimes standard commands are not enough to fulfil some specific needs, in such cases new commands can be defined and this article explains how.
Contents
Most of the LaTeX commands are simple words prec... |
% Note: replace “Template” with Name_of_class in previous line
Abbreviation:
CReg
A
is a Hausdorff space $\mathbf{X}=\langle X,\Omega\rangle$ that is completely regular Hausdorff space : $...$ completely regular
Remark: This is a template. If you know something about this class, click on the 'Edit text of this page' li... |
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In Chapter 4 of
Seven Sketches, Fong and Spivak introduce 'enriched profunctors' as a way to study collaborative design, where different teams are working together to make a product. An enriched profunctor can be used to answer the ... |
No-ones showing the second quotient:
a) $f(x) = x^2 - 2x$
So
\begin{align}\frac{f(x+h) - f(x)}{h} &= \frac{(x +h)^2 - 2(x-h) - x^2 + 2x}{h} \\&= \frac{x^2 + 2hx + h^2 - 2x - 2h - x^2 + 2x}h \\&= \frac{2hx + h^2 - 2h}h \\&= 2x +h - 2\end{align}
And for the other
\begin{align}\frac{f(x) -f(a)}{x-a} &= \frac{x^2 -2x -a^2 ... |
Makkai and Paré introduced the following binary relation on regular cardinals: given $\kappa$ and $\lambda$, $\kappa \vartriangleleft \lambda$ (read, $\kappa$ is
sharply less than $\lambda$) when $\kappa < \lambda$ and, for every set $X$ of cardinality $< \lambda$, the set $P_\kappa (X)$ of all subsets of $X$ of cardin... |
If $k \leq (1-\epsilon) N$, where $N$ is the total number of subtrees, then the following approach would work:
Start with the empty list $L$.
Repeat $k$ times:
Pick a random subtree $T'$. If $T' \notin L$, add it to $L$; otherwise, go back to the previous step.
Since $k \leq (1-\epsilon) N$, the expected number of time... |
The answer is $m/n$. The reason is that
$$f(n,x) = \sum_{j=0}^{\infty} \frac{x^{j n}}{(j n)!} = \frac1{n} \sum_{k=0}^{n-1} \exp{\left ( e^{i 2 \pi k/n} x\right )} $$
The sum is dominated by the $k=0$ term as $x \to \infty$. The ratio of such terms is thus $m/n$.
ADDENDUM
Proof of the above assertion is straightforward.... |
How many subgroups $K \le \mathbb{Z}_n$ are there with $K =\ker(\phi)$ for some homomorphism $\phi\colon\mathbb{Z}_n \rightarrow \mathbb{Z}_m$?
Stuck and need a hint. Have so far that there are $\gcd(n,m)$ such homomorphisms. Also that all such maps are of the form $\phi_a(k)= ak$ for $a \in \mathbb{Z}_m$ satisfying $n... |
For a simple elementary reaction on electrode
\begin{equation} O+e^-\rightleftharpoons R \end{equation}
We can derive the Butler-Volmer equation. But it seems that the formula found on John Newman's Electrochemical System seems to be different from the one found on Allen Bard's Electrochemical Methods, both of which ar... |
On general super-target spaces the $\kappa$-symmetry of the Green-Schwarz action functional is indeed a bit, say, in-elegant. But a miracle happens as soon as the target space has the structure of a super-group (notably if it is just super-Minkowski spacetime with its canonical structure of the super-translation group ... |
I have a CO
2 sensor that output signal values 30-50 mV. I need to translate these voltages to 0-5 V for my microcontroller with the highest resolution. I understand that I can amplify the voltage using a non-inverting op-amp circuit, as shown, to a range of 3-5 V, but is it possible to expand that range to 0-5 V in or... |
I've bee given 2 equations in spherical form. One of a sphere $(s_1)$ and the other of a cylinder $(s_2)$.
$$S_1 : \rho = 4\cos \phi \text{ and } S_2 : \rho \sin \phi = 1$$
I need to find the volume inside the sphere and inside the cylinder using both spherical and cylindrical coordinates.
So far I was able to convert ... |
I'm struggling with this problem, I'm still only on part (a). I tried X=rcos(theta) Y=rsin(theta) but I don't think I'm doing it right.
Curve C has polar equation r=sin(${\theta}$)+cos(${\theta}$).
(a) Write parametric equations for the curve C.
$\left\{\begin{matrix} x= \\ y= \end{matrix}\right.$
(b) Find the slope of... |
Abbreviation:
DCPO
A
is a poset $\mathbf{P}=\langle P,\leq \rangle $such that every directed subset of $P$ has a least upper bound: $\forall D\subseteq P\ (D\ne\emptyset\mbox{and}\forall x,y\in D\ \exists z\in D(x,y\le z)\Longrightarrow \exists z\in P(z=\bigvee D))$. directed complete partial order
Let $\mathbf{P}$ and... |
Hi, Can someone provide me some self reading material for Condensed matter theory? I've done QFT previously for which I could happily read Peskin supplemented with David Tong. Can you please suggest some references along those lines? Thanks
@skullpatrol The second one was in my MSc and covered considerably less than my... |
Let $X_{1},X_{2},\ldots,X_{n}$ be a random sample whose distribution is given by $\mathcal{N}(\mu,\sigma^{2})$, where both parameters are unknown.
(a) Prove the normal probability density function satisfies the Cramer-Rao theorem hypothesis.
(b) Prove that $T(\textbf{X}) = \hat{\sigma}^{2}$ reaches the Cramer-Rao bound... |
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Search for new resonances in $W\gamma$ and $Z\gamma$ Final States in $pp$ Collisions at $\sqrt{s}=8\,\mathrm{TeV}$ with the ATLAS Detector
(Elsevier, 2014-11-10)
This letter presents a search for new resonances decaying to final states with a vector boson produced in association with a... |
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Higher harmonic flow coefficients of identified hadrons in Pb-Pb collisions at $\sqrt{s_{\rm NN}}$ = 2.76 TeV
(Springer, 2016-09)
The elliptic, triangular, quadrangular and pentagonal anisotropic flow coefficients for $\pi^{\pm}$, $\mathrm{K}^{\pm}$ and p+$\overline{\mathrm{p}}$ in Pb-... |
A good way to think about these equations is to imagine them as sets over valid words. Say I have an alphabet $\Sigma = \{a, b\}$, then the rule$$A \leftarrow A a \mid b$$
says that there's some set $A$ that is isomorphic to the set $(A * \{a\}) \cup \{b\}$. Here the $*$ operation is the product/concatenation operation... |
A remark on an eigenvalue condition for the global injectivity of differentiable maps of $R^2$
1.
Instituto de Ciências Matemáticas e de Computa¸cão - USP, Cx. Postal 668, CEP 13560–970, São Carlos, SP, Brazil
2.
Institute of Mathematics, P.O. Box 1078, Hanoi, Vietnam
There does not exist a sequence $R^2$ ∋ $x_i\righta... |
The motivation and previous discussion of some related ideas can be seen here.
My question: given a sequence $u_n\in u_0+H^1_0(\Omega)$ where $u_0\in H^1(\Omega)$ and $\Omega\subset \mathbb R^N$ is open bounded lipschitz boundary.
Assume $u_n\to u\in u_0+H^1_0(\Omega)$ weakly in $H^1$, I want to obtain a sequence of fu... |
Let $X$ be a topological space.
Definitions:
$X$ is countably compact if every countable open cover of $X$ has a finite subcover or equivalently, every sequence in $X$ has a cluster point. $X$ is sequentially compact if every sequence in $X$ has a convergent subsequence $X$ is sequential if every sequentially closed se... |
I am studying differential geometry I am trying to proof the expression below.
Given that for a map $\phi$ : $M$ $\to$ $M$ the pull-back $\phi$*$\omega$ $\in$ $T^\ast_p M$ of a 1-form $\omega $ $ \in$ $T^\ast_p M$ is defined by :
($\phi$*$\omega$)$(v)$ = $\omega$($\phi_{*}v$) where $v$ $\in$ $T_{p}M$.
How would we proo... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
The
amsmath package provides a handful of options for displaying equations. You can choose the layout that better suits your document, even if the equations are really long, or if you have to include several equations in the same line.
Contents
The standard LaTeX tools for equations may lack some flexibility, causing o... |
Abbreviation:
PoGrp
A
is a structure $\mathbf{G}=\langle G,\cdot,^{-1},1,\le\rangle$ such that partially ordered group
$\langle G,\cdot,^{-1},1\rangle$ is a group
$\langle G,\le\rangle$ is a partially ordered set
$\cdot$ is
: $x\le y\Longrightarrow wxz\le wyz$ orderpreserving
Let $\mathbf{A}$ and $\mathbf{B}$ be partia... |
Abbreviation:
Sfld
A
is a semiring with identity $\mathbf{S}=\langle S,+,\cdot, 1\rangle $ such that semifield
$\langle S^*,\cdot,1\rangle$ is a group, where $S^*=S-\{0\}$ if $S$ has an absorbtive $0$, and $S=S^*$ otherwise.
Let $\mathbf{S}$ and $\mathbf{T}$ be semifields. A morphism from $\mathbf{S}$ to $\mathbf{T}$ i... |
Can you help me evaluating the following indefinite integral?
$$ \int \sqrt{{x}^{2} + 3} \; dx $$
Please, don't give a full solution, just some hint on which method to use...
** UPDATE **
Thank you very much to everybody for the useful comments and suggestions. I'm sorry for the delay with my reply, unfortunately do so... |
I will first state Fatou's lemma and provide a proof, then I will present the corollary I am trying to prove. I am a little lost on the proof so I to assist in the reader's help I will provide what Folland suggests to do to prove it.
If $\{f_n\}$ is any sequence in $L^{+}$, then $$\int(\lim\inf f_n)\leq \lim\inf\int f_... |
Let $L/K$ be a Galois extension of number fields with Galois group $G$. Let $O_K$ and $O_L$ be the ring of algebraic integers of $K$ and $L$ respectively. Let $P\subseteq O_K$ be a prime. Let $Q\subseteq O_L$ be a prime lying over $P$.
The decomposition group is defined as $$D(Q|P)=\lbrace \sigma\in G\text{ }|\text{ }\... |
On multi-trial Forney-Kovalev decoding of concatenated codes
1.
DCS, Ruhr-Universität Bochum, Universitätsstraße 150, 44780 Bochum, Germany
2.
TAIT, Ulm University, Albert-Einstein-Allee 43, 89081, Ulm
3.
ECE, University of Toronto, 10 King's College Road, Toronto M5S 3G4, ON, Canada
Our approach extends results of For... |
Suppose we have a signal $y(t)$. For sampling we use a Dirac $\delta$ function. The sampled function is $\widetilde{y}(t)$. So $$\widetilde{y}(t) = y(t)\cdot\sum_{n=-\infty}^{\infty}\delta(t-nT).$$ The Fourier transformation is $$\widetilde{Y}(\omega)=\mathcal{F\{\widetilde{y}(t)\}} = \sum_{n=-\infty}^{\infty}y(nT)e^{-... |
Consider the space of all bounded continuous real-valued functions of $\mathbb{R}$. I am having trouble understanding how to find the closed subalgebra generated by sine and cosine.
Denote $\mathcal A$ the subalgebra generated by $x\mapsto \cos x$ and $x\mapsto \sin x$. $\mathcal A$ contains all the maps $\cos(nx)$ and... |
Evaluate $$\int\sqrt{x^3+x^2}\;dx$$
What I have tried
Using substitution (which I believe was applied incorrectly) I get: $$\frac{(x+2)\sqrt{4x+4}}{4x+4}$$
How can this integral be evaluated?
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fiel... |
Definition:Disjoint Union (Set Theory) Definition
Let $\family {S_i}_{i \mathop \in I}$ be an $I$-indexed family of sets.
The disjoint union of $\family {S_i}_{i \mathop \in I}$ is defined as the set: $\displaystyle \bigsqcup_{i \mathop \in I} S_i = \bigcup_{i \mathop \in I} \set {\tuple {x, i}: x \in S_i}$
where $\big... |
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Anisotropic flow of inclusive and identified particles in Pb–Pb collisions at $\sqrt{{s}_{NN}}=$ 5.02 TeV with ALICE
(Elsevier, 2017-11)
Anisotropic flow measurements constrain the shear $(\eta/s)$ and bulk ($\zeta/s$) viscosity of the quark-gluon plasma created in heavy-ion collisions... |
65th SSC CGL level Question Set, topic Trigonometry 6
This is the 65th question set for the 10 practice problem exercise for SSC CGL exam and 6th on topic Trigonometry. You will find the answers to the questions along with list of related readings including the detailed conceptual solutions after the questions.
Before ... |
Abbreviation:
TA
A
is a structure $\mathbf{A}=\langle A,\vee,0,\wedge,1,\neg,\diamond_f, \diamond_p\rangle$ such that both tense algebra
$\langle A,\vee,0,\wedge,1,\neg,\diamond_f\rangle$ and $\langle A,\vee,0,\wedge,1,\neg,\diamond_p\rangle$ are Modal algebras
$\diamond_p$ and $\diamond_f$ are
: $x\wedge\diamond_py = ... |
Working with the bosonic string in a background space-time with one compact dimension, i.e.: $$ R^{1,24}\times S^1 $$ I have been able to calculate the mass-squared: $$ M^2 = \frac{n^2}{R^2} + \frac{m^2R^2}{\alpha^{'2}} + \frac{2}{\alpha'}\left( N + \bar{N} - 2\right) $$ Here n and m are integers related to the quantis... |
I would like to derive the Fourier transform of $f(x)=\ln(x^2+a^2)$, where $a\in \mathbb{R}^+$ by making use of the properties:
\begin{equation} \mathcal{F}[f'(x)]=(ik)\hat{f}(k)\\ \mathcal{F}[-ixf(x)]=\hat{f}'(k) \end{equation} For the Fourier transform I use the definition given by:
\begin{equation} \hat{f}(k)=\frac{... |
6. Series 32. Year Post deadline: 29th April 2019 Upload deadline: 30th April 2019 11:59:59 PM CET
(3 points)1. selfenlightment
We illuminate a mirror at an angle of $\alpha = 15\mathrm{\dg }$ with respect to the normal. We want the light to travel directly back to the source. For doing so, we can use a glass prism wit... |
I realize that the Maclaurin Series is a special form of the Taylor Series where the series is centered at $x=0$, but I have to wonder what's special about it such that it deserves its own special designation? On that point, how would you know (or care) which point to choose as the center of a Taylor Series?
Expanding ... |
Usually a simple P,PI loop is better than bad PID loop. You can put 2 PI controlers for speed, for each wheel it own PI controller. Then you just control the speed of each wheel separately. Here is a small pseudo algorithm of PI controller with trap integration method:\$ u(k) = K_p \bigg[ e(k)-e(k-1)+\dfrac{T_s}{2T_i}\... |
Let $X$ be a projective variety over an algebraically closed field of characteristic zero. Let $\eta$ be a generic point of $X$ and $x$ be a closed point. By http://stacks.math.columbia.edu/tag/054F there exists a discrete valuation ring $R$ and a morphism $\mbox{Spec}(R) \to X$ such that the fraction field of $R$ maps... |
Let's say we've got a fluid of heavy and light particles inside a cubical flask, which is initially shaken up so that the density of heavy particles is uniform everywhere. Let's also say that these molecules interact identically whether in contact with like or opposite particles (i.e. they don't naturally separate, lik... |
Answer
$x^2+12x+36 \Rightarrow (x+6)^2 $
Work Step by Step
The third term of a perfect square trinomial is equal to the square of half the coefficient of the middle term. Hence, to complete the square of the given expression $ x^2+12x ,$ the third term must be \begin{array}{l}\require{cancel}\left( \dfrac{12}{2} \right... |
Answer
Two vectors are orthogonal if the dot product of both the vectors is 0.
Work Step by Step
If $v$ and $w$ are non-zero vectors and $\theta $ is the smallest non-negative angle between $\mathbf{u}$ and $\mathbf{w}$, Then the angle between two vectors can be calculated as: $\begin{align} & \cos \theta =\frac{\mathb... |
I have a question that reads:
A full-wave controlled bridge rectifier is considered, shown below. Vs = 230V. Load is represented by \$i_o = 10\$ A. Frequency is 50 Hz and the delay angle is 45\$^{\circ}\$.
(a) Sketch \$V_{o(avg)}\$, \$V_{SCR1}\$ and \$i_s\$
(b) Derive the formula for calculating the average value and R... |
This paper is one in a series of papers in which du Bois Reymond studied functions on the positive real line ordered by the "order of infinity" (order of growth at infinity), what he later called infinitary pantachy. This was motivated by attempts to find "ideal boundary" between converging and diverging series in term... |
Solve the following system of equations: $\left\{\begin{matrix} x^3(1-x)+y^3(1-y)=12xy+18\\ \left | 3x-2y+10 \right |+\left | 2x-3y \right |=10 \end{matrix}\right.$
closed as too localized by Gerry Myerson, Amzoti, Lord_Farin, Micah, Asaf Karagila♦ May 28 '13 at 13:20
This question is unlikely to help any future visito... |
If we have a two dimensional measurementbasis, then we have two possible outcomes of the measurement. Now I figured: considering the law of conservation of energy, if one particle goes in, one and only one can come out. So outcome "both results simultaneously" cannot happen, for that would...
Summary: If a measurement ... |
One disadvantage of the fact that you have posted 5 identical answers (1, 2, 3, 4, 5) is that if other users have some comments about the website you created, they will post them in all these place. If you have some place online where you would like to receive feedback, you should probably also add link to that. — Mart... |
An example of methylation analysis with simulated datasets
Part 2: Potential DMPs from the methylation signal
Methylation analysis with Methyl-IT is illustrated on simulated datasets of methylated and unmethylated read counts with relatively high average of methylation levels: 0.15 and 0.286 for control and treatment g... |
I'm having trouble with this problem in Ahlfors' Complex Analysis (page 238):
If a vertex of the polygon is allowed to be at $\infty$, what modification does the formula undergo? If in this context $\beta_k = 1$, what is the polygon like?
The formula he is referring to is (probably) $$F(w) = C \int_0^w \prod_{k=1}^n ( ... |
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1. Measurement of the ZZ production cross section in proton-proton collisions at √s = 8 TeV using the ZZ → ℓ−ℓ+ℓ′−ℓ′+ and ZZ→ℓ−ℓ+νν¯¯¯ decay channels with the ATLAS detec... |
As @DavidRicherby already points out, the confusion arises because different measures of complexity are getting mixed up.But let me elaborate a bit.
Usually, when studying algorithms for polynomial multiplication over arbitrary rings, one is interested in the number of arithmetic operations in the ring that an algorith... |
Here are a few trivial lemmas. I won't use anything about the rolling motion, just that the distance is defined by gluing pentagons edge-to-edge:
The $dd$-circle of radius $k$, which I'll call $C_k$, is a closed polygonal curve. Let $D_k$ be the closed $dd$-disk of radius $k$; note that $D_k$ may contain holes and $C_k... |
Radiation will kill you on the surface
Several other posts hit the same point, but to summarize briefly, Europa's surface receives 540 rem per day, which is probably a fatal dose. However, the 1080 rem you get in two days is definitely a fatal dose. You need shielding, water (and ice) are great shielding, there you go.... |
I'm a little late to this party, but here is the illustration of the method so many seem to suggest:
$$\cos(\theta) -\sin(\theta) = 1 \\(\cos(\theta)-\sin(\theta))^2 = 1^2 \\\cos^2(\theta) - 2\sin(\theta)\cos(\theta) + \sin^2(\theta) = 1 \\-2\sin(\theta)\cos(\theta) + [\cos^2(\theta) + \sin^2(\theta)] = 1 \\-2\sin(\the... |
The title of your question asks for techniques that are impossible to break, to which the One Time Pad (OTP) is the correct answer, as pointed out in the other answers. The OTP is information-theoretically secure, which means that an adversaries computational abilities are inapplicable when it comes to finding the mess... |
This is very much an open question, but yes, there is a considerable amount of work that is being done on this front.Some clarificationsIt is, first of all, to be noted that there are two major ways to merge machine learning (and deep learning in particular) with quantum mechanics/quantum computing:1) ML $\to$ QMApply ... |
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1. J-aggregates
2012, ISBN 9814365742, viii, 520
Book
3. Earthquake rupture properties of the 2016 Kumamoto earthquake foreshocks (M j 6.5 and M j 6.4) revealed by conven... |
Abbreviation:
FL$_{ew}$
A
$_{ew}$ FL is a FLe-algebra $\mathbf{A}=\langle A, \vee, \wedge, \cdot, 1, \backslash, /, 0\rangle$ that is -algebra (i.e. satisfies the weakening rules): $0\le x\le 1$ integral
Remark: This is a template. If you know something about this class, click on the 'Edit text of this page' link at th... |
Abbreviation:
Grp
A
is a structure $\mathbf{G}=\langle G,\cdot,^{-1},e\rangle $, where $\cdot $ is an infix binary operation, calledthe group , $^{-1}$ is a postfix unary operation, called the group product and $e$ is a constant (nullary operation), called the group inverse , such that identity element
$\cdot $ is asso... |
Interested in the following function:$$ \Psi(s)=\sum_{n=2}^\infty \frac{1}{\pi(n)^s}, $$where $\pi(n)$ is the prime counting function.When $s=2$ the sum becomes the following:$$ \Psi(2)=\sum_{n=2}^\infty \frac{1}{\pi(n)^2}=1+\frac{1}{2^2}+\frac{1}{2^2}+\frac{1}{3^2}+\frac{1}{3^2}+\frac{1...
Consider a random binary str... |
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... |
Let us consider the set of complex numbers and the binary operation $\circ$ defined by
$z_a\circ z_b=|z_a|e^{\Theta(z_b)}$,
where $\Theta(z_b)$ is the argument of the complex number $z_b$.
Explain whether the set of complex numbers together with the binary operation $\circ$ forms a monoid.
I know I need to prove whethe... |
below is an exercise that is really giving me a hard time, I believe that there is a simple way around it but I can not find it:
Assume the correct regression model is Y = X$\beta$ + $\epsilon$ for E($\epsilon$) = 0 and var($\epsilon$) = $\sigma^2$I.
Assume the matrix X of dimensions n × m with m < n has full rank. Den... |
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... |
Leaving it on would use more energy, absolutely. Sometimes, people try to convince themselves that turning a light on and off uses more energy because there is some high inrush current, or some such thing.Firstly, incandescent lights hardly have any inrush current, because they don't have any capacitors to charge, and ... |
ISSN:
1930-8337
eISSN:
1930-8345
All Issues
Inverse Problems & Imaging
August 2011 , Volume 5 , Issue 3
Select all articles
Export/Reference:
Abstract:
A new reconstruction algorithm is presented for eit in dimension two, based on the constructive uniqueness proof given by Astala and Päivärinta in [
Ann. of Math. 163(2... |
How to Couple a Full-Wave Simulation to a Ray Tracing Simulation
Welcome back to our discussion on multiscale modeling in high-frequency electromagnetics. Multiscale modeling is a simulation challenge that arises when there are vastly different scales in a single simulation, such as the size of an antenna compared to t... |
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... |
$$\text{maximize } f(\mathbf{x}) \quad\text{subject to } \mathbf{Ax} = \mathbf{b}$$
where
$$f(\mathbf{x}) = \sum_{i=1}^N\sqrt{1+\frac{x_i^4}{\left(\sum_{i=1}^{N}x_i^2\right)^2}},$$
$\mathbf{x} = [x_1,x_2,...,x_N]^T \in \mathbb{R}^{N\times 1}$ and $\mathbf{A} \in \mathbb{R}^{M\times N}$.
We can see that $f$ is convex an... |
I was working through this z-test of proportions example I found online. The online example solutions says that the difference between the groups is statistically significant, whereas I concluded it was not.
Problem:
Suppose the Acme Drug Company develops a new drug, designed to prevent colds. The company states that t... |
257 23 Homework Statement Two identical uniform triangular metal played held together by light rods. Caluclate the x coordinate of centre of mass of the two mass object. Give that mass per unit area of plate is 1.4g/cm square and total mass = 25.2g Homework Equations -
Not sure what I went wrong here, anyone can help m... |
On the DNA Computer Binary Code
In any finite set we can define a
, a partial order in different ways. But here, a partial order is defined in the set of four DNA bases in such a manner that a Boolean lattice structure is obtained. A Boolean lattice is an algebraic structure that captures essential properties of both s... |
This answer focuses more on minimalizing the code, rather than finding the source of the problem, as the top-voted answer does. It is intended to be concise and hands-on, but digestible rather than exhaustive. Suggestions for improvement welcome!
Here are some strategies for reducing your code, which will help you get ... |
I want to implement the EM algorithm manually and then compare it to the results of the
normalmixEM of
mixtools package. Of course, I would be happy if they both lead to the same results. The main reference is Geoffrey McLachlan (2000),
Finite Mixture Models.
I have a mixture density of two Gaussians, in general form, ... |
For the sake of completeness, here are more general statements:
1) Every separable type I factor is singly generated. You take the weighted shift $S=\sum_j 2^{-j}E_{j,j+1}$. Then $W^*(S)$ contains $(S^*S)^{1/2}=\sum_j2^{-j}E_{jj}$ and now by using the characteristic function of $\{2^{-j}\}$ we obtain $E_{jj}\in W^*(S)$... |
Digital PLL's -- Part 2
In Part 1, we found the time response of a 2
nd order PLL with a proportional + integral (lead-lag) loop filter. Now let’s look at this PLL in the Z-domain [1, 2]. We will find that the response is characterized by a loop natural frequency ω n and damping coefficient ζ.
Having a Z-domain model o... |
Title Picard and Chazy solutions to the Painlevé VI equation Publication Type Journal Article Year of Publication 2001 Authors Mazzocco, M Journal Math. Ann. 321 (2001) 157-195 Abstract
I study the solutions of a particular family of Painlevé VI equations with the parameters $\beta=\gamma=0, \delta=1/2$ and $2\alpha=(2... |
Consider elastic net regression with
glmnet-like parametrization of the loss function$$\mathcal L = \frac{1}{2n}\big\lVert y - \beta_0-X\beta\big\rVert^2 + \lambda\big(\alpha\lVert \beta\rVert_1 + (1-\alpha) \lVert \beta\rVert^2_2/2\big).$$ I have a data set with $n\ll p$ (44 and 3000 respectively) and I am using repea... |
Let $BG$ is classifying space of $G$ topological group.
If $G$ is any compact group and $H$ is a closed subgroup of $G$, then the inclusion map $i:H\rightarrow G$ induces \begin{equation*} G/H\rightarrow BH\rightarrow BG \end{equation*} a fiber bundle?
If $G$ is any compact group and $H$ is a closed subgroup of $G$, th... |
Context:
On the 5th page of the paper Quantum circuit design for solving linear systems of equations (Cao et al, 2012) there's this circuit:
Schematic:
A brief schematic of what's actually happening in the circuit is:
Question:
Cao et al.'s circuit (in Figure 4) is specifically made for the matrix:
$$A = \frac{1}{4} \l... |
RF Signal Transformation Between the Time and Frequency Domains
When we analyze high-frequency electromagnetics problems using the finite element method (FEM), we often compute S-parameters in the frequency domain without reviewing the results in the complementary domain; that is, the time domain. The time domain is wh... |
I'm trying to solve this problem that was given for my homework assignment, but I cannot figure out how to actually finish the problem in a way that makes sense to me. I've gotten as far as finding $\text{curl }\textbf{F} = \langle1, 1, 1\rangle$ from the original integral $\oint_C z dx + x dy + y dz $. (I believe that... |
Goodness-of-fit statistic. Suppose you want to test whether a die is fair by rolling it 600 times.Then you would expect, on average, to see each face $E = 100$ times. If the observedcounts for faces $i = 1, \dots, 6$ are $X_i,$ then the chi-squaredstatistic is
$$Q = \sum_{i=1}^6 \frac{(X_i - E)^2}{E} \stackrel{aprx}{\s... |
There are many examples of gauge theories with disconnected gauge groups, but as far as I know, the non-trivial topological sectors of these theories are beyond the current experimental capabilities.
In order for large gauge transformations to act nontrivially on the states, it must be a symmetry of the Hamiltonian. Fo... |
The Annals of Probability Ann. Probab. Volume 46, Number 1 (2018), 456-490. Random walks on the random graph Abstract
We study random walks on the giant component of the Erdős–Rényi random graph $\mathcal{G}(n,p)$ where $p=\lambda/n$ for $\lambda>1$ fixed. The mixing time from a worst starting point was shown by Founto... |
26 0
One thing that always bothered me in Chemistry is how the equilibrium constant is written. It never made sense to me.
If I take a simple bimolecular reaction approaching equilibrium :
[tex] aA + bB \mathop{\rightleftharpoons}^{k_1}_{k_{-1}} cC + dD [/tex]
From ART ,
[tex] r_1 = k_1 [A]^ \alpha
If I take a simple b... |
You are correct. Estimating the instantaneous phase of a noisy sinusoid is NOT easy. I suggest you design a narrow bandpass filter such that your sinusoid-of-interest is in the filter's passband. (The better the filter the more noise that will be eliminated.) Pass your two signals through the bandpass filter to generat... |
Difference between revisions of "Group cohomology of elementary abelian group of prime-square order"
(→Over an abelian group)
(→Over an abelian group)
Line 35: Line 35:
The homology groups with coefficients in an abelian group <math>M</math> are given as follows:
The homology groups with coefficients in an abelian grou... |
While trying to solve the exercise below, I came up with a wrong conclusion, but I can't see why it's wrong. Also I'm accepting suggestions to get the right solution. This is the problem 17 from chapter 10 of Rudin's Functional Analysis.
Let $A$ be a Banach algebra. Suppose that the spectrum of $x\in A$ is not connecte... |
Minhash is said to estimate the Jaccard coefficient - supposedly because it's faster to compute. Given two sets $A$ and $B$, minhash (with k hash functions) takes $O(k*(|A|+|B|))$ time to compute.
But isn't it possible to also compute the Jaccard coefficient $\frac {|A \cap B|} {|A \cup B|} $ in $O(|A|+|B|)$ time by si... |
Suppose $f$ is continuous on $[a, b]$, if for every continuous function $g$ on $[a, b]$ with $g(a) = g(b) = 0, \int_{a}^{b}f(x)g(x) dx = 0$, Show $f(x) = 0, \forall x \in [a, b]$,
I want to prove by contradiction, and then find a continuous $g$ such that $g(a) = g(b) = 0$ but $\int_{a}^{b}f(x)g(x) dx \neq 0$
Proof: Sup... |
From Artin:
When $d$ is congruent $2$ or $3$ modulo $4$, an integer prime $p$ remains prime in the ring of integers of $\Bbb{Q}[$$\sqrt{d}]$ if the polynomial $x^2-d$ is irreducible modulo $p$.
a) Prove that this is also true when $d \equiv 1$ modulo $4$ and $p\neq 2$
b) What happens to $p=2$ when $d \equiv 1$ modulo $... |
ISSN:
1930-5346
eISSN:
1930-5338
All Issues
Advances in Mathematics of Communications
November 2013 , Volume 7 , Issue 4
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Abstract:
We enumerate $H$-phase Golay sequences for $H\le 36$ and lengths up to 33. Our enumeration method is based on filtering by the power spectra. Some of t... |
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