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For those that haven't seen this link - please have a look as it's a an awe-inspiring 360 interactive panormic image of the milky way (may need a bit of time to load though!). I've found myself idly browsing it several times and as an astronomy layman I wondered if anyone could help me navigate what I'm looking at.
Whi... | CommonCrawl |
Volume 23, Number 2 (1995), 852-878.
We consider the concentration of measure for $n$ i.i.d., two-dimensional random variables under the conditioning that they form a record. Under mild conditions, we show that all random variables tend to concentrate, as $n \rightarrow \infty$, around limiting curves, which are the so... | CommonCrawl |
What does it take to design a 4th order band-pass filter with -24dB/Octave?
Is it accurate to say in digital audio that, when a fader is down, then its value is "-$\infty$"?
Detecting a whistle in audio clip or stream?
Given a log-plot of frequency-magnitude-phase how to apply it as an EQ curve to a signal?
I found the... | CommonCrawl |
Zhihui Yang, Fan Lin, Claudia S Robertson and Kevin K W Wang.
Dual vulnerability of TDP-43 to calpain and caspase-3 proteolysis after neurotoxic conditions and traumatic brain injury.. Journal of cerebral blood flow and metabolism : official journal of the International Society of Cerebral Blood Flow and Metabolism, 20... | CommonCrawl |
That's all equivalences I can see so far. But they all seem so similar. Are they all equivalent? If not, is there a subset of the set of the above theorems the elements of which are pairwise equivalent?
Browse other questions tagged real-analysis linear-algebra differential-geometry differential-topology multilinear-al... | CommonCrawl |
Volume 7, Number 10 (2002), 1193-1214.
We consider a semilinear problem of the type $Lu=f(b,u),$ where $f(b,u)\simeq bu$ as $u\to 0$ and $f(b,u)\simeq b_\infty u$ as $\|u \| \to\infty$ assuming that there exist a finite number of eigenvalues of the linear operator $L$ between $b$ and $b_\infty$. Under suitable assumpti... | CommonCrawl |
The spin-Hall effect (SHE) and its reciprocal, the inverse spin-Hall effect (ISHE), are of great importance in spintronics since they enable, respectively, the conversion of a longitudinal charge current to a transverse spin current and the reverse process. Here we will report on a ferromagnetic resonance (FMR) study o... | CommonCrawl |
Theorem 1: Let $A$ and $B$ be countable sets. Then the cartesian product $A \times B$ is countable.
Proof: There are three cases to consider.
Case 1: If both $A$ and $B$ are finite with $|A| = m$ and $|B| = n$ then it is easy to show that $|A \times B| = mn$ and hence $A \times B$ is finite and so it is countable.
Then... | CommonCrawl |
Move $1$ match and make this correct.
You can't break the match.
You can't make an inequality sign, just change numbers and/or operators.
moving the cross stick in the plus sign to go diagonally across the equals sign.
And there were no matches (hehe).
just change the equals sign to a more than sign!
If only the first ... | CommonCrawl |
Abstract: We prove that the metric projection onto a finite-dimensional subspace $Y\subset L_p$, $p\in(1,2)\cup(2,\infty)$, satisfies the Lipschitz condition if and only if every function in $Y$ is supported on finitely many atoms. We estimate the Lipschitz constant of such a projection for the case in which the subspa... | CommonCrawl |
Statistical analysis of familial correlations.
Inferences for familial (intraclass and interclass) correlations are considered for unbalanced familial data from multivariate normal populations. The most commonly used familial correlation is that between siblings (without regard to gender), called intraclass or sib-sib ... | CommonCrawl |
Is it appropriate to use a Bonferroni adjustment in all cases of multiple testing?
If one performs a test on a data set, then one splits that data set into finer levels (e.g. split the data by gender) and performs the same tests, how might this affect the number of individual tests that are perceived? That is, if X hyp... | CommonCrawl |
This is the third post on my Hexapod Project series. The point of this project is to build a robot that allows me to try out a few robotics concepts. For a listing of each post in this series, click here. In this post, I'll talk about using laser ranging to let the hexapod keep track of where it is relative to its envi... | CommonCrawl |
Supported by Global COE Program "The Research and Training Center for New Development in Mathematics", Graduate School of Mathematical Sciences, the University of Tokyo.
Abstract: Kazhdan's property (T) is one of the most important properties in the analytic group theory, and has a numerous applications to many other f... | CommonCrawl |
In the fundamental works on the theory of Lie groups (S. Lie, H. Poincaré, E. Cartan, H. Weyl, and others) it is a group of smooth or analytic transformations of the space $\mathbf R^n$ or $\mathbf C^n$, depending smoothly or analytically on parameters. When there are finitely many numerical parameters, a continuous gr... | CommonCrawl |
A Dirichlet character $\chi: \Z\to \C$ has a modulus $n$ such that $\chi$ is induced from a function $\chi:\Z/n\Z\to \C$. It gives a homomorphism $(\Z/n\Z)^\times\to \C^\times$. The underlying unit group is $(\Z/n\Z)^\times$, the group of units of the ring $\Z/n\Z$.
Not referenced anywhere at the moment. | CommonCrawl |
"The P2NFFT method for mixed charge-dipole systems"
We consider a typical $N$-body problem in order to compute electrostatic interactions in particle systems containing a mixture of charges and dipoles. Classical particle-mesh methods make use of the fast Fourier transform (FFT) to compute the interactions in pure char... | CommonCrawl |
It looks very similar indeed, except for a rotation of each velocity by 90° (in the complex plane) and complex conjugation. Namely, the vortices tend to swirl around one another, not collide as the polynomial zeros tend to do under heat flow. In fact, the motion of vortices is described by a Hamiltonian dynamical syste... | CommonCrawl |
We know that the consistency of ZFC+"Exists an inaccessible cardinal" implies the consistency of ZF+DC+"All sets are Lebesgue measurable"; and DC proves the existence of non-Borel sets.
J. Truss proved that repeating Solovay's construction by collapsing any limit cardinal to be $\aleph_1$ we obtain a model of ZF+"All s... | CommonCrawl |
Journal: J. London Math. Soc.
We establish existence and non-existence results for entire solutions to the fractional Allen-Cahn equation in $\mathbb R^3$, which vanish on helicoids and are invariant under screw-motion. In addition, we prove that helicoids are surfaces with vanishing nonlocal mean curvature. | CommonCrawl |
Department of Mathematics, Shimane University, Matsue, Japan.
On the set $\mathbb R$ of real numbers we consider a poset $\mathcal P_\tau(\mathbb R)$ (by inclusion) of topologies $\tau(A)$, where $A\subseteq \mathbb R$, such that $A_1\supseteq A_2$ iff $\tau(A_1)\subseteq \tau(A_2)$. The poset has the minimal element $... | CommonCrawl |
I was reading a paper in which the authors use the fact that any compact simply-connected homogeneous symplectic manifold has non-zero Euler characteristic. They prove it by quoting a theorem by Kostant which implies that the manifold is symplectomorphic to a coadjoint orbit of a semisimple group, then state that compa... | CommonCrawl |
I am trying to figure out why the answer is T>W. Do you have any idea why? If so could you please explain. Thank you.
There is an explanation in the diagram. What don't you like about this explanation?
So the denominator $2\sin\theta\cong0$ and therefore $T\to\infty$. As $W=mg$, clearly $W$ is a finite value (making th... | CommonCrawl |
For puzzles based on the movements of a knight piece in chess.
On a $3\times3$ grid we have: with $8$ moves needed to swap the red and blue knights. What is the minimum numbers of moves to swap the knights on a $4\times4$ grid?
A knight is placed on an infinitely large chess board with no edges. It can only visit each ... | CommonCrawl |
Let $R_1,\ldots,R_n$ and $C_1,\ldots,C_n$ be sets of size n.
When does there exist an $n \times n$ matrix in which the $i$-th row is a permutation of $R_i$, for all $1 \leq i \leq n$, and the $j$-th column is a permutation of $C_j$, for all $1 \leq j \leq n$?
The multiset $\cup R_i$ equals the multiset $\cup C_i$.
wher... | CommonCrawl |
In this article, I will talk about how to write Monte Carlo simulations in CUDA. More specifically, I will explain how to carry it out step-by -step while writing the code for pricing a down-and-out barrier option, as its path dependency will make it a perfect example for us to learn Monte Carlo in CUDA. Also, I will s... | CommonCrawl |
To find the trajectory of anything in General Relativity, usually you only need the metric tensor, from which you can obtain the geodesic equations. Nevertheless, a common problem that arises in cosmology is that as soon as we depart from the simplest homogeneous models, the task of finding solutions to the geodesic eq... | CommonCrawl |
Multivariate clustering in astrophysics is a recent development justified by the bigger and bigger surveys of the sky. The phylogenetic approach is probably the most unexpected technique that has appeared for the unsupervised classification of galaxies, stellar populations or globular clusters. On one side, this is a s... | CommonCrawl |
Suppose Ivica's message consists of $N$ characters.
Ivica must first find a matrix consisting of $R$ rows and $C$ columns such that $R \le C$ and $R \cdot C = N$. If there is more than one such matrix, Ivica chooses the one with the most rows.
Ivica writes his message into the matrix in row-major order. In other words,... | CommonCrawl |
The Hodge-Deligne polynomials of some moduli spaces of coherent systems.
A coherent system on a smooth projective curve C consists of a pair (E,V) where E is a vector bundle on C (of rank n and degree d) and V is a subspace (of dimension k) of $H^0(C,E)$. For each triple (n,d,k) there is a family of moduli spaces of co... | CommonCrawl |
Lets first define a few terms.
Discrete Random Variable - This is a variable that can only take on particular values. For example heads or tails of a coin, it makes no sense to talk about 3/4's heads or 1/8 tails. Another example, the integers 1 through 6 are possible values when rolling a die. There is no way to get 4... | CommonCrawl |
This paper proposes the novel Pose Guided Person Generation Network (PG$^2$) that allows to synthesize person images in arbitrary poses, based on an image of that person and a novel pose. Our generation framework PG$^2$ utilizes the pose information explicitly and consists of two key stages: pose integration and image ... | CommonCrawl |
Let $T$ be a random variable, and let $S$ be a random variable defined on the same space as $T$. As we have seen, conditioning on $S$ might be a good way to find probabilities for $T$ if $S$ and $T$ are related. In this section we will see that conditioning on $S$ can also be a good way to find the expectation of $T$.
... | CommonCrawl |
Kindly organised by Jonas Azzam, this short mini course will be an insight into Cheeger's Theorem in Geometric Measure Theory.
Venue: 5.20 ICMS Lecture Theatre, 5th Floor, 47 Potterow, Edinburgh EH8 9BT.
Abstract: Rademacher's theorem states that any Lipschitz $f \colon \mathbb R^n \to \mathbb R$ is differentiable Lebe... | CommonCrawl |
We have implemented a certified Wang tiling program for tiling a rectangle region using a brick corner Wang tile set. A brick corner Wang tile set is a special Wang tile set introduced by A. Derouet-Jourdan et al. in computer graphics in 2015 to model wall patterns texture. We have implemented a tiling algorithm using ... | CommonCrawl |
Abstract: In this paper we show how the complexity of performing nearest neighbor (NNS) search on a metric space is related to the expansion of the metric space. Given a metric space we look at the graph obtained by connecting every pair of points within a certain distance $r$ . We then look at various notions of expan... | CommonCrawl |
whether the project is a part of a broader collaboration.
Application deadline for the year 2019 is December 31, 2018.
If you have a project that you believe is eligible for support from Votruba-Blokhintsev program, please submit your details below.
The application will be considered at the next meeting of Votruba-Blok... | CommonCrawl |
Abstract: Let $\Omega$ be a convex domain in the complex plane $\mathbb C$ and $H$ the space of holomorphic functions in $\Omega$ with the topology of uniform convergence on compact subsets of $\Omega$. Let $W_1$ and $W_2$ be a pair of (differentiation) invariant subspaces of $H$ admitting spectral synthesis. Condition... | CommonCrawl |
Citation: Quantum 2, 81 (2018).
We provide a fine-grained definition for monogamous measure of entanglement that does not invoke any particular monogamy relation. Our definition is given in terms an equality, as oppose to inequality, that we call the "disentangling condition". We relate our definition to the more tradi... | CommonCrawl |
Here is the problem which I thought was simple dynamic programming, which is however not the case.
Given an $N \times M$ matrix of numbers from 1 to $NM$ (each number occurs only once), find a path from top left to right bottom while moving right or down only. If we sort all values visited in this path it should be lex... | CommonCrawl |
If we look at Euclidean and Manhattan distances, these are both just specific instances of $p = 2$ and $p=1$, respectively.
For $p < 1$ this distance measure is not actually a metric, but it may still be interesting sometimes. For this problem, write a program to compute the $p$-norm distance between pairs of points, f... | CommonCrawl |
Abstract: We consider the real part $\Re(\zeta(s))$ of the Riemann zeta-function $\zeta(s)$ in the half-plane $\Re(s) \ge 1$. We show how to compute accurately the constant $\sigma_0 = 1.19\ldots$ which is defined to be the supremum of $\sigma$ such that $\Re(\zeta(\sigma+it))$ can be negative (or zero) for some real $... | CommonCrawl |
Abstract: High dimensional data and systems with many degrees of freedom are often characterized by covariance matrices. In this paper, we consider the problem of simultaneously estimating the dimension of the principal (dominant) subspace of these covariance matrices and obtaining an approximation to the subspace. Thi... | CommonCrawl |
The retailer should charge 5 dollars for the candy.
Let s represent the selling price. We can use the following guideline to solve this problem: Selling price = Cost + Profit So: s = 2.5 + 50% $\times$ s s = 2.5 + 0.5 $\times$ s s = 2.5 + 0.5s 0.5s = 2.5 Divide both sides by 0.5: s = 5 The retailer should charge 5 doll... | CommonCrawl |
Octonion algebras are non-associative algebras endowed with a non-degenerate multiplicative quadratic form, which over fields determines the algebra completely, but not over rings in general. Connecting to the talk given by P. Gille, and reporting on a joint work with him, I will show how to construct all octonion alge... | CommonCrawl |
$cl:2^X\to 2^X$ satisfying $A\subset cl(A)$ for all $A\subset X$. That's a good way to summarize Kuratowski's closure operator.
Basic geometry on a set $X$ is a dot product $\cdot:2^X\times 2^X\to 2^Y$. Its equivalent form is an orthogonality relation on subsets of $X$. The optimal case is if the orthogonality relation... | CommonCrawl |
How can I make large curly brackets spanning multiple lines?
Brackets and Parentheses Parentheses and brackets are very common in mathematical formulas. You can easily control the size and style of brackets in L a T e X ; this article explains how.
How do I add brackets to the beginning of every line?
Put multiple line... | CommonCrawl |
In the above calculation, we calculated the determinant of the $3\times 3$ matrix by expanding along the third row. From the above equation, we can conclude that the eigenvalues of $A$ are $\lambda=3,1,-4$.
Previous story Find All Values of $a$ which Will Guarantee that $A$ Has Eigenvalues 0, 3, and -3. | CommonCrawl |
Logic is a part of the study of human reason, the ability we have to think abstractly, solve problems, explain the things that we know, and infer new knowledge on the basis of evidence. Traditionally, logic has focused on the last of these items, the ability to make inferences on the basis of evidence, by evaluating th... | CommonCrawl |
Abstract: We study the asymptotic consistency properties of $\alpha$-Rényi approximate posteriors, a class of variational Bayesian methods that approximate an intractable Bayesian posterior with a member of a tractable family of distributions, the member chosen to minimize the $\alpha$-Rényi divergence from the true po... | CommonCrawl |
This is an initiation project to introduce RAMP and get you to know how it works.
The goal is to develop prediction models able to identify which news is fake.
You goal is to classify each statement (+ metadata) into one of the categories.
The original training data frame has 13000+ instances. In the starting kit, we g... | CommonCrawl |
What is the difference between a qubit and classical bit?
As I understand it, the main difference between quantum and non-quantum computers is that quantum computers use qubits while non-quantum computers use (classical) bits.
What is the difference between qubits and classical bits?
A bit is a binary unit of informati... | CommonCrawl |
We introduce a new online deadlock-avoidance policy, Transitive Joins (TJ), that targets programs with dynamic task parallelism and arbitrary join operations. In this model, a computation task can asynchronously spawn new tasks and selectively join (block) on any task for which it has a handle. We prove that TJ soundly... | CommonCrawl |
Aims. Photodissociation by UV light is an important destruction mechanism for carbon monoxide (CO) in many astrophysical environments, ranging from interstellar clouds to protoplanetary disks. The aim of this work is to gain a better understanding of the depth dependence and isotope-selective nature of this process. Me... | CommonCrawl |
2018 ⋆ 100% Private Proxies - Fast, Anonymous, Quality, Unlimited USA Private Proxy!
A couple of days ago, I received the following email from Home office(UK) for my spouse visa. I have deposited my IHS fee and it's been a week since I submitted my passport. Is there any chance where they can still refuse my visa? Addi... | CommonCrawl |
Abstract: We study the fluctuations of the spin per site around the thermodynamic magnetization in the mean-field Blume-Capel model. Our main theorem generalizes the main result in a previous paper (Ellis, Machta, and Otto) in which the first rigorous confirmation of the statistical mechanical theory of finite-size sca... | CommonCrawl |
Now we don't need to consider $1\times 1$ any longer as we have found the smallest rectangle tilable with copies of U plus copies of $1\times 1$.
There are at least 6 more solutions. I tagged it 'computer-puzzle' but you can certainly work some of these out by hand. The larger ones might be a bit challenging. | CommonCrawl |
Say I fit a multiple regression of p explanatory variables. The t-test will allow me to check if any single one of those is significant ($H_0: \beta_i = 0$). I can do a partial F-test to check if some subset of them is significant ($H_0: \beta_i=\beta_j=...=\beta_k=0$).
What I often see though is that someone gets 5 p-... | CommonCrawl |
There's a nice paper by Menon and Elkan about dyadic prediction with latent features. It cares about the right things: ease of implementation, ability to incorporate multiple sources of information, and scalability. The model can be thought of as a mash-up of multinomial logit and matrix factorization.
\] where $\alpha... | CommonCrawl |
What's the point of Pauli's Exclusion Principle if time and space are continuous?
What does the Pauli Exclusion Principle mean if time and space are continuous?
If time and space are continuous then identical quantum states are impossible to begin with. in the question.
This assertion is just plainly false. A quantum s... | CommonCrawl |
In general, if given equation of any two curves, how to find the shortest distance?
According to me, finding common normal won't work as it isn't necessary for both of them to have one like in case of domain bounded functions.
We can take a more general approach i.e. by assuming points on both the curves, forming the e... | CommonCrawl |
Machine Learning has become a big topic in the IT world nowadays. There are thousands of articles about how ML is changing the way big data is analyzed. High level business decisions are taking place using ML algorithms to make accurate predictions and visualizing trends in the market.
Now, let's ask our selves what ex... | CommonCrawl |
Consider the following expression grammar. The semantic rules for expression evaluation are stated next to each grammar production.
Assume the conflicts of this question are resolved using yacc tool and an LALR(1) parser is generated for parsing arithmetic expressions as per the given grammar. Consider an expression $3... | CommonCrawl |
Using quantum Monte Carlo simulations, we compute the participation (Shannon-R\'enyi) entropies for groundstate wave functions of Heisenberg antiferromagnets for one-dimensional (line) subsystems of length $L$ embedded in two-dimensional ($L\times L$) square lattices. We also study the line entropy at finite temperatur... | CommonCrawl |
Informally, the term infinity is used to mean some infinite number, but this concept falls very far short of a usable definition.
The symbol $\infty$ (supposedly invented by John Wallis) is often used in this context to mean an infinite number.
However, outside of its formal use in the definition of limits its use is s... | CommonCrawl |
Abstract: Consider the relativistic Vlasov-Maxwell system with initial data of unrestricted size. In the two dimensional and the two and a half dimensional cases, Glassey-Schaeffer (1997, 1998, 1998) proved that for regular initial data with compact momentum support this system has unique global in time classical solut... | CommonCrawl |
At the beginning of this section, we claimed that breadth-first search finds the distance to each reachable vertex in a graph $G=(V,E)$ from a given source vertex $s \in V$ . Define the shortest-path distance $\delta(s,v)$ from $s$ to $v$ as the minimum number of edges in any path from vertex $s$ to vertex $v$; if ther... | CommonCrawl |
Abstract : For a real number $0<\lambda<2$, we introduce a transformation $T_\lambda$ naturally associated to expansion in $\lambda$-continued fraction, for which we also give a geometrical interpretation. The symbolic coding of the orbits of $T_\lambda$ provides an algorithm to expand any positive real number in lambd... | CommonCrawl |
You are on an $n \times m$ grid where each square on the grid has a digit on it. From a given square that has digit $k$ on it, a Move consists of jumping exactly $k$ squares in one of the four cardinal directions. A move cannot go beyond the edges of the grid; it does not wrap. What is the minimum number of moves requi... | CommonCrawl |
For questions about mathematical induction, a method of mathematical proof. Mathematical induction generally proceeds by proving a statement for some integer, called the base case, and then proving that if it holds for one integer then it holds for the next integer. This tag is primarily meant for questions about induc... | CommonCrawl |
Our sad tale begins with a tight clique of friends. Together they went on a trip to the picturesque country of Molvania. During their stay, various events which are too horrible to mention occurred. The net result was that the last evening of the trip ended with a momentous exchange of "I never want to see you again!"s... | CommonCrawl |
If twice the son's age in years is added to the father's age, the sum is 70. But if the twice the father's age is added to the son's age, the sum is 95. Find the ages of father and son.
Strategy : Given word problem can be solved by converting it into a set of simultaneous equations. Solution : Let the age of son be X ... | CommonCrawl |
In a previous question (Calabi-Yau manifolds and compactification of extra dimensions in M-theory), I was told that the $G(2)$ lattice can be used to compactify the extra 7 dimensions of M-theory and preserve exactly $\mathcal N=1$ supersymmetry.
However, since there is only 1 $G(2)$ lattice, there should be only 1 4-d... | CommonCrawl |
number of orbits of a group: is map well-defined and surjective?
Let $G$ be a finite group acting on a finite set $X$. Let $m$ be a number of orbits of $G$ on $X$ and $M$ be the number of orbits of $G$ on $X\times X$. Show that $m^2\le M$ with equality if and only if G acts trivialy on $X$.
I need your help to solve th... | CommonCrawl |
We show that the Novikov–Shubin invariant of an element of the integral group ring of the lamplighter group $\mathbf Z_2 \wr \mathbf Z$ can be irrational. This disproves a conjecture of Lott and Lück. Furthermore we show that every positive real number is equal to the Novikov–Shubin invariant of some element of the rea... | CommonCrawl |
Abstract: Eilenberg-type correspondences, relating varieties of languages (e.g. of finite words, infinite words, or trees) to pseudovarieties of finite algebras, form the backbone of algebraic language theory. Numerous such correspondences are known in the literature. We demonstrate that they all arise from the same re... | CommonCrawl |
Given an $n$-vertex weighted tree with structural diameter $S$ and a subset of $m$ vertices, we present a technique to compute a corresponding $m \times m$ Gram matrix of the pseudoinverse of the graph Laplacian in $O(n+ m^2 + m S)$ time. We discuss the application of this technique to fast label prediction on a generi... | CommonCrawl |
I have an integer linear program (ILP) with some variables $x_i$ that are intended to represent boolean values. The $x_i$'s are constrained to be integers and to hold either 0 or 1 ($0 \le x_i \le 1$).
I want to express boolean operations on these 0/1-valued variables, using linear constraints. How can I do this?
More ... | CommonCrawl |
We find the capacity pre-log of a temporally correlated Rayleigh block-fading single-input multiple-output (SIMO) channel in the noncoherent setting. It is well known that for blocklength $L$ and rank of the channel covariance matrix equal to $Q$, the capacity pre-log in the single-input single-output (SISO) case is gi... | CommonCrawl |
Recall from The Squares of Riemann-Stieltjes Integrable Functions with Increasing Integrators page that if $f$ is a function defined on $[a, b]$ and $\alpha$ is an increasing function on $[a, b]$ then if $f$ is Riemann-Stieltjes integrable with respect to $\alpha$ on $[a, b]$ then $f^2$ is also Riemann-Stieltjes integr... | CommonCrawl |
This is a short guide how to format citations and the bibliography in a manuscript for Progress in Disaster Science. For a complete guide how to prepare your manuscript refer to the journal's instructions to authors.
McDonald F. Watching the players at the climate poker table. Nature 2011;480:293.
Turecek R, Trussell L... | CommonCrawl |
Calculates the scattering from a barbell-shaped cylinder. Like `capped-cylinder`, this is a sphereocylinder with spherical end caps that have a radius larger than that of the cylinder, but with the center of the end cap radius lying outside of the cylinder. See the diagram for the details of the geometry and restrictio... | CommonCrawl |
Abstract: We address the Riemann and Cauchy problems for systems of $n$ conservation laws in $m$ unknowns which are subject to $m-n$ constraints ($m\geq n$). Such constrained systems generalize systems of conservation laws in standard form to include various examples of conservation laws in Physics and Engineering beyo... | CommonCrawl |
of $f$ at $x_0 \in [0,1]$ .
For any $\epsilon \gt 0$,for any $\delta \gt 0$ such that for all $x \in (0,1)$ and $0 \lt|x-x_0| \lt \delta$, one has $|f(x) - L| \lt \epsilon$ .
This definition is incorrect because for any $\epsilon \gt 0$ there exists some $\delta \gt 0$ that is small enough. It can't be any delta. Is th... | CommonCrawl |
Аннотация: The paper is concerned with the large time behavior of solutions of the heat equation on a thin two-layer domain. Such systems may arise from modeling thermal emission (as a result of chemical reaction) and heat transfer between two thin films. It is shown that every solution converges as $t\to+\infty$ to a ... | CommonCrawl |
Abstract: We consider the problem of the reduction of unitary irreducible representations of the generalized Poincaré groups $\mathscr P(1,n)$ with respect to their subgroups $\mathscr P(1, n-k)$. We find the explicit form of the unitary operator that relates the canonical basis of the representation to the $\mathscr P... | CommonCrawl |
A maximal subgroup of $\GL(2,\F_p)$ that fixes a one-dimensional subspace of $\F_p^2$ is called a Borel subgroup. Every Borel subgroup is conjugate to the subgroup of upper triangular matrices.
Subgroup labels containing the letter B identify a subgroup of $\GL(2,\F_p)$ that lies in the Borel subgroup of upper triangul... | CommonCrawl |
Abstract: We consider the problem of decomposing a real-valued symmetric tensor as the sum of outer products of real-valued, pairwise orthogonal vectors. Such decompositions do not generally exist, but we show that some symmetric tensor decomposition problems can be converted to orthogonal problems following the whiten... | CommonCrawl |
I'm running an experiment and am suspecting that competitive people may respond differently to experimental treatments compared to non-competitive people.
"My friends would describe me as a competitive person."
"I would describe myself as a competitive person."
"Even when there is no monetary reward, I will seek to sur... | CommonCrawl |
Zarebnia, M., Aghili, M. (2017). An approximation to the solution of Benjamin-Bona-Mahony-Burgers equation. Computational Methods for Differential Equations, 5(4), 301-309.
Mohammad Zarebnia; Maryam Aghili. "An approximation to the solution of Benjamin-Bona-Mahony-Burgers equation". Computational Methods for Differenti... | CommonCrawl |
Add up all the numbers from 1 to 100.
The class got busy calculating. But not Gauss. After a few minutes, while most students were just beginning to struggle with the teens, Gauss was just finishing with writing down his final answer.
When he brought it to submit it, his teacher was furious with him for not taking the ... | CommonCrawl |
I've recently stumbled upon this very nice interactive visualization of eigenvectors of two-dimensional matrices, and how powers $A^k$ act on various vectors.
How can this sort of visualization be realized with Mathematica, leveraging its dynamical capabilities?
The following is an attempt to recreate a similar sort of... | CommonCrawl |
Iron carbonyl-mediated Michael homologous reactions of gamma-alkoxy alkenones.
The reaction of $\gamma$-benzyloxy-$\alpha,\beta$-unsaturated ketones with diiron nonacarbonyl afforded the corresponding $\eta\sp2$-iron tetracarbonyl alkene complexes selectively, without perceptible formation of $\eta\sp4$-iron tricarbony... | CommonCrawl |
You are given an array that contains $n$ positive integers.
Your task is to divide the array into $k$ subarrays so that the maximum sum in a subarray is a small as possible.
The first input line contains two integers $n$ and $k$: the size of the array and the number of subarrays in the division.
The next line contains ... | CommonCrawl |
In the path integral approach to gauge theory, observables are gauge invariant functions on the space $\mathcal A$ of a $G$-connections on $E$, where $G$ denotes the structure group and $E$ the fiber bundle. Therefore, an observable $f$ is a function on the space $\mathcal A / \mathcal G$, of connections modulo gauge t... | CommonCrawl |
Pyramidal Cells are present in the cerebral cortex and the hippocampus. They exhibit non linear summation of inputs, with dendritic compartments acting as individual subunits capable of producing their own spikes. These dendrites then project to the cell body, where all dendritic signals are summed and integrated to de... | CommonCrawl |
Семинар Теорија вероватноћа и математичка статистика, 9, 10. и 11. јул 2018.
Апстракт: We investigate the randomized Karlin model with parameter $\beta\in(0,1)$, which is based on an infinite urn scheme. It has been shown before that when the randomization is bounded, the so-called odd-occupancy process scales to a fra... | CommonCrawl |
This article describes the extension of recent methods for a posteriori error estimation such as dual-weighted residual methods to node-centered finite volume discretizations of second order elliptic boundary value problems including upwind discretizations. It is shown how different sources of errors, in particular mod... | CommonCrawl |
In his text Unreasonably Big Physics, Tetragraviton classifies the Texan SSC collider as marginally reasonable but other proposed projects are said to be unreasonable.
They include a wonderful 2017 collider proposal in the Gulf of Mexico. The structure would host some new, potentially clever 4-tesla dipoles and would b... | CommonCrawl |
I do not know any multimodal distributions.
Why are all known distributions unimodal? Is there any "famous" distribution that have more than one mode?
Of course, mixtures of distributions are often multimodal, but I would like to know whether there exist any "non-mixture" distributions that have more than one mode.
The... | CommonCrawl |
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