All posts under tag "Mathematics"
We construct a new family of quantum MDS codes from classical generalized Reed-Solomon codes and derive the necessary and sufficient condition under which these quantum codes exist. We also give code bounds and show how to construct them analytically. We find that existing quantum MDS codes can be u
In this paper we construct integrable three-dimensional quantum-mechanical systems with magnetic fields, admitting pairs of commuting second-order integrals of motion. The case of Cartesian coordinates is considered. Most of the systems obtained are new and not related to the separation of variables
Recent attention in quickest change detection in the multi-sensor setting has been on the case where the densities of the observations change at the same instant at all the sensors due to the disruption. In this work, a more general scenario is considered where the change propagates across the senso
The downlink transmission in multi-user multiple-input multiple-output (MIMO) systems has been extensively studied from both communication-theoretic and information-theoretic perspectives. Most of these papers assume perfect/imperfect channel knowledge. In general, the problem of channel training an
In this paper, we mainly study the robust stability of linear continuous systems with parameter uncertainties, a more general kind of uncertainties for system matrices is considered, i.e., entries of system matrices are rational functions of uncertain parameters which are varying in intervals. we pr
We consider an ultracold rotating Bose gas in a harmonic trap close to the critical angular velocity so that the system can be considered to be confined to the lowest Landau level. With this assumption we prove that the Gross-Pitaevskii energy functional accurately describes the ground state energy
In this work, we suggest a parameterized statistical model (the gamma distribution) for the frequency of word occurrences in long strings of English text and use this model to build a corresponding thermodynamic picture by constructing the partition function. We then use our partition function to co
Let H be a Haar distributed random matrix on the group of pxp real orthogonal matrices. Partition H into four blocks: (1) the (1,1) element, (2)the rest of the first row, (3) the rest of the first column, and (4)the remaining (p-1)x(p-1) matrix. The marginal distribution of (1) is well known. In thi
The study of high-dimensional differential equations is challenging and difficult due to the analytical and computational intractability. Here, we improve the speed of waveform relaxation (WR), a method to simulate high-dimensional differential-algebraic equations. This new method termed adaptive wa
If b^2 + 1 is prime then b must be even, hence we examine the form 4u^2 + 1. Rather than study primes of this form we study composites where the main theorem of this paper establishes that if 4u^2 + 1 is composite, then u belongs to a set whose elements are those u such that u^2 + t^2 = n(n + 1), wh
We give a characterization of Maximum Entropy/Minimum Relative Entropy inference by providing two `strong entropy concentration' theorems. These theorems unify and generalize Jaynes' `concentration phenomenon' and Van Campenhout and Cover's `conditional limit theorem'. The theorems characterize exac
One of the main problems that emerges in the classic approach to semantics is the difficulty in acquisition and maintenance of ontologies and semantic annotations. On the other hand, the Internet explosion and the massive diffusion of mobile smart devices lead to the creation of a worldwide system,
Compared with classical process-based models, the functional-structural plant models provide more efficient tools to explore the impact of changes in plant structures on plant functioning. In this paper we investigated the effects of branches on the sourcesink interaction for the cotton plant (Gossy
A noncolliding diffusion process is a conditional process of $N$ independent one-dimensional diffusion processes such that the particles never collide with each other. This process realizes an interacting particle system with long-ranged strong repulsive forces acting between any pair of particles.
Motivated by various results on homogeneous geodesics of Riemannian spaces, we study homogeneous trajectories, i.e. trajectories which are orbits of a one-parameter symmetry group, of Lagrangian and Hamiltonian systems. We present criteria under which an orbit of a one-parameter subgroup of a symmet
The emph{index coding} problem has recently attracted a significant attention from the research community due to its theoretical significance and applications in wireless ad-hoc networks. An instance of the index coding problem includes a sender that holds a set of information messages $X={x_1,...,x
Sudoku grids can be thought of as graphs where the vertices are the squares of the grid, and edges join vertices in the same row, column, or sub-grid. A Sudoku puzzle corresponds to a partial proper coloring of the Sudoku graph. We provide a new and simpler proof of the theorem which states that the
Polar codes are novel and efficient error correcting codes with low encoding and decoding complexities. These codes have a channel dependent generator matrix which is determined by the code dimension, code length and transmission channel parameters. This paper studies a variant of the McEliece publi
Let S1(Gamma,Gamma) be the statement: For each sequence of point-cofinite open covers, one can pick one element from each cover and obtain a point-cofinite cover. b is the minimal cardinality of a set of reals not satisfying S1(Gamma,Gamma). We prove the following assertions: (1) If there is an un
Superfilters are generalized ultrafilters, which capture the underlying concept in Ramsey theoretic theorems such as van der Waerden's Theorem. We establish several properties of superfilters, which generalize both Ramsey's Theorem and its variant for ultrafilters on the natural numbers. We use them
There is an increasing demand for controller design techniques capable of addressing the complex requirements of todays embedded applications. This demand has sparked the interest in symbolic control where lower complexity models of control systems are used to cater for complex specifications given
We develop a maximum relative entropy formalism to generate optimal approximations to probability distributions. The central results consist in (a) justifying the use of relative entropy as the uniquely natural criterion to select a preferred approximation from within a family of trial parameterized
We prove an extension of the Quillen Theorem Bn for homotopy fibres to a similar result for homotopy pullbacks and use this to obtain sufficient conditions on a pullback diagram of categories to guarantee that it be a homotopy pullback.
In this note, we give a probabilistic interpretation of the Central Limit Theorem used for approximating isotropic Gaussians in [1].
At some places (see the references) Martin Erickson describes a certain game: 'Two players alternately write O's (first player) and X's (second player) in the unoccupied cells of an n x n grid. The first player (if any) to occupy four cells at the vertices of a square with horizontal and vertical
The spaces D, S and E' over mathbb{R}^(n) are known to be flat modules over A=mathbb{C}[partial_{1},...,partial_{n}], whereas their duals D', S' and E are known to be injective modules over the same ring. Let A be a Noetherian k-algebra (k=mathbb{R} or mathbb{C}). The above observation leads us to s
We contribute some information towards finding a general algorithm for constructing, for a given profinite group, $G$, a compact connected space, $X$, such that the full homeomorphism group, $H(X)$, with the compact-open topology is isomorphic to $G$ as a topological group. It is proposed that one s
In this paper, by using hardy inequality, we establish some new integral inequalities of Hardy-Hilbert type with general kernel. As applications, equivalent forms and some particular results are built; the corresponding to the double series inequalities are given.reverse forms are considered also.
The proof of cite[Proposition 2.1]{DKS}[arXiv:1104.0232] is partially incorrect. In this short note, we provide a new proof, which requires an additional hypothesis. A modification of this new proof also corrects the proof of cite[Proposition 2.1]{Ch}[arXiv:2310.17456], where the incorrect argument
An approach based on the spectral and Lie - algebraic techniques for constructing vertex operator representation for solutions to a Riemann type Gurevicz-Zybin hydrodynamical hierarchy is devised. A functional representation generating an infinite hirerachy of dispersive Lax type integrable flows is
In this paper we extend the Dirichlet integral formula of Lobachevsky. Let $f(x)$ be a continuous function and satisfy in the $pi$-periodic assumption $f(x+pi)=f(x)$, and $f(pi-x)=f(x)$, $0leq x<infty $. If the integral $int_0^infty frac{sin^4x}{x^4}f(x)dx$ defined in the sense of the improper Riema
We give the first elementary construction of equivalent formulas in Hanf normal form. The triply exponential upper bound is complemented by a matching lower bound.
An outer bound to the two-receiver discrete memoryless broadcast channel is presented. We compare it to the known outer bounds and show that the outer bound presented is at least as tight as the existing bounds.
For a commutative ring $R$ and a weakly proregular ideal $I$, we prove a simple universal property of the category of $L_0$-complete $R$-modules: it is the smallest replete exact abelian subcategory of the category of $R$-modules which contains all the $I$-adically complete $R$-modules.
We study the effective behavior of heterogeneous energies arising in the modeling of material voids in geometrically linear elastic materials. Specifically, we consider functionals featuring bulk terms depending on the symmetrized gradient of the displacement and terms comparable to the surface area
This paper studies a class of rank-based inequality measures built from linear combinations of expected order statistics. The proposed framework unifies several well-known indices, including the classical Gini coefficient, the $m$th Gini index, extended $m$th Gini index and $S$-Gini index, and also
This paper enhances the result of the work [G. Kozma, B. Tóth, Ann. Probab. vol. 45 (2017) 4307-4347] . We prove the central limit theorem (in probability w.r.t. the environment) for the displacement of a random walker in divergence-free (or, doubly stochastic) random environment, with substantially
We show that character analysis using Fourier series is possible, at least when a mathematical character is considered. Previous approaches to character analysis are somewhat not in the spirit of harmonic analysis.
We give a necessary and sufficient condition so that a pair of disjoint Jordan regions in the sphere can be quasiconformally mapped to a pair of disks. As a consequence, we obtain a simple characterization that involves Lipschitz functions for the case that one of the Jordan regions is a half-plane.
This correction article is actually unnecessary. The proof of Theorem 1.2, concerning commutative HQ-algebra spectra and commutative differential graded algebras, in the author's paper [American Journal of Mathematics vol. 129 (2007) 351-379 (arxiv:math/0209215v4)] is correct as originally stated.
In this paper we provide a framework for quantitative statements on distances and measures when studying algebraic varieties and morphisms of algebraic varieties over local fields. We will concentrate on local fields of the type $mathbb{F}_ell((t))$ and work uniformly with respect to finite extens
Systems of instantaneously annihilating or coalescing Brownian motions on the line are considered. The extreme points of the set of entrance laws for this process are shown to be Pfaffian point processes at all times and their kernels are identified.
Let p>2 be prime, and let n,m be positive integers. For cyclic field extensions E/F of degree p^n that contain a primitive pth root of unity, we show that the associated F_p[Gal(E/F)]-modules H^m(G_E,mu_p) have a sparse decomposition. When E/F is additionally a subextension of a cyclic, degree p^{n+
We outline an extension of paraproduct decompositions for compositions of the form $A(f)$ where $A in C^{d}(mathbb{R}), f in Λ_α([0,1]^d)$ developed in [arXiv:2503.12629] and [arXiv:2508.13322] to settings where $(A in C^1(mathbb{R}),f in Λ_α(X))$ and $ (A in C^2(mathbb{R}),f in Λ_α(X times Y))$. To
The groupoid attached to the action of PSL(2,Z) on the irrational reals by linear fractional transformations is free.
Let $mathcal R_{n}$ be the set of all rational functions of the type $r(z) = f(z)/w(z)$, where $f(z)$ is a polynomial of degree at most $n$ and $w(z) = prod_{j=1}^{n}(z-β_j)$, $|β_j|>1$ for $1leq jleq n$. In this work, we investigate the growth behavior of rational functions with prescribed poles by
We present a new complex non-stationary particle-like solution of the non-linear Klein-Gordon equation with several spatial variables. The construction is based on reduction to an ordinary differential equation.
We introduce new logarithmic Hurwitz spaces $mathcal{LH}^{mathbb{Z}_{(p)}}_A$ and $mathcal{LH}^{mathbb{F}_{p}}_{A,Ξ}$ over $mathbb{Z}_{(p)}$ and $mathbb{F}_p$ respectively that in the mixed characteristic case can be considered as a compactification of the admissible cover stack parametrizing ramifi
The notion of the Fibonacci cobweb poset from [1] has been naturally extended to any admissible sequence $F$ in [2] where it was also recognized that the celebrated prefab notion of Bender and Goldman [3] - (see also [4,5]) - admits such an extension so as to encompass the new type combinatorial obj
Michael Kinyon's 2005 open problem, based on the universality of Osborn loops is solved. It is shown that not every Osborn loop is universal.
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