Related papers: Extraction Theorems With Small Extraction Numbers
Let $A_q(n,d)$ be the maximum order (maximum number of codewords) of a $q$-ary code of length $n$ and Hamming distance at least $d$. And let $A(n,d,w)$ that of a binary code of constant weight $w$. Building on results from algebraic graph…
We derive a Liouville type result for special Lagrangian equations with certain "convexity" and restricted linear growth assumptions on the solutions.
In this paper, we introduce a new subclass of close-to-convex harmonic functions. We present a sufficient coefficient condition for a function to be a member of this class. Furthermore, we establish a distortion theorem. These results lay…
We present some results about the irreducible representations appearing in the exterior algebra $\Lambda \mathfrak{g}$, where $ \mathfrak{g}$ is a simple Lie algebra over $\mathbb{C}$. For Lie algebras of type $B$, $C$ or $D$ we prove that…
This paper is a continuation of the investigation of resolvents of elliptic operators on conic manifolds from math.AP/0410178 and math.AP/0410176 to the case of manifolds with boundary and realizations of operators under boundary…
In a recent article by Farah and the authors, a strong lifting theorem was proved for a class of coordinate-respecting maps between reduced products of discrete structures, hereby working under mild Forcing Axioms. We generalise this…
In "Octonion Algebra and its Connection to Physics" [16] an algorithm on octonions is brought forward for description of physical law, the "octonion variance sieve process". This paper expresses the used algorithm in symbolic form, and…
We introduce a cohomology theory that classifies differential objects that arise from Picard-Vessiot theory, using the differential Hopf-Galois descent. To do this, we provide an explicit description of Picard-Vessiot theory in terms of…
In this paper, we introduce a family of topological spaces that captures the existence of preservation theorems. The structure of those spaces allows us to study the relativisation of preservation theorems under suitable definitions of…
In this letter we consider the ensemble of codes formed by the serial concatenation of a Hamming code and two accumulate codes. We show that this ensemble is asymptotically good, in the sense that most codes in the ensemble have minimum…
Using class field theory, we prove a restriction on the intersection of the maximal abelian extensions associated with different number fields. This restriction is then used to improve a result of Rosen and Silverman about the linear…
Our main interest in this paper is chiefly concerned with the conditions characterizing \textit{orthogonal and symplectic abstract differential geometries}. A detailed account about the sheaf-theoretic version of the \textit{symplectic…
We introduce two families of inequalities. Large ensemble decoupling is connected to the continuous restriction phenomenon. Tight decoupling is connected to the discrete Restriction conjecture for the sphere. Our investigation opens new…
In many everyday categories (sets, spaces, modules, ...) objects can be both added and multiplied. The arithmetic of such objects is a challenge because there is usually no subtraction. We prove a family of cases of the following principle:…
In this article, we derive better results concerning powered numbers in short intervals, both unconditionally and conditionally on the $abc$-conjecture. We make use of sieve method, a polynomial identity, and a recent breakthrough result on…
Our aim is to give for some classes non-additive measures some limit theorems. For balanced games we obtain a weak and strong law of large numbers for bounded random variables, a sharper conclusion is obtain with exact games. We provide an…
The divergence minimization problem plays an important role in various fields. In this note, we focus on differentiable and strictly convex divergences. For some minimization problems, we show the minimizer conditions and the uniqueness of…
We prove lower bounds for the Dirichlet Laplacian on possibly unbounded domains in terms of natural geometric conditions. This is used to derive uncertainty principles for low energy functions of general elliptic second order divergence…
We derive a new estimate of the size of finite sets of points in metric spaces with few distances. The following applications are considered: (1) we improve the Ray-Chaudhuri--Wilson bound of the size of uniform intersecting families of…
In this note, we generalise two results on prime numbers in short intervals. The first result is Ingham's theorem which connects the zero-density estimates with short intervals where the prime number theorem holds, and the second result is…