Related papers: Completely strong superadditivity of generalized m…
This paper presents generalizations of semidefinite programming formulations of 1-norm optimization problems over infinite dictionaries of vectors of complex exponentials, which were recently proposed for superresolution, gridless…
We study the power mean inequality of the generalized trigonometric and hyperbolic functions with two parameters. The generalized $p$-trigonometric and $(p, q)$-trigonometric functions were introduced by P. Lindqvist and S. Takeuchi,…
We prove a matrix inequality for matrix monotone functions, and apply it to prove a singular value inequality for Heinz means recently conjectured by X. Zhan.
A notion of generalized $n$-semimodularity is introduced, which extends that of (sub/super)mod\-ularity in four ways at once. The main result of this paper, stating that every generalized $(n\colon\!2)$-semimodular function on the $n$th…
We give an alternative proof of a sharp generalization of an integral inequality for the dyadic maximal operator due to which the evaluation of the Bellman function of this operator with respect to two variables, is possible. This last…
This paper studies the equivalence between generalized holomorphic functions (GHF) and complex analytic functions in the framework of Robinson-Colombeau generalized numbers. In every non-Archimedean ring, the use of ordinary series is…
In this work we compute the Stokes matrices of the ordinary differential equation satisfied by the hypergeometric integrals associated to an arrangement of hyperplanes in generic position. This generalizes the computation done by Ramis and…
The generalized $p$-trigonometric and ($p,q$)-trigonometric functions were introduced by P. Lindqvist and S. Takeuchi, respectively. We prove some inequalities and present a few conjectures for the ($p,q$)-functions.
We give some statements that are equivalent to the existence of group inverses of Peirce corner matrices of a $2 \times 2$ block matrix and its generalized Schur complements. As applications, several new results for the Drazin inverses of…
We show that the weak and strong forms of the Generalized Spectral Conjecture (GSC) of Boyle and Handelman are equivalent. The GSC asserts that well understood necessary spectral conditions on a square matrix A over a subring S of the reals…
We study the existence of formal Taylor expansions for functions defined on fields of generalised series. We prove a general result for the existence and convergence of those expansions for fields equipped with a derivation and an…
Submodular functions are known to satisfy various forms of fractional subadditivity. This work investigates the conditions for equality to hold exactly or approximately in the fractional subadditivity of submodular functions. We establish…
For any block of a finite group over an algebraically closed field of characteristic $2$ which has dihedral, semidihedral, or generalized quaternion defect groups, we determine explicitly the decomposition of the associated diagonal…
We obtain new results on the existence and multiplicity of fixed points of Hammerstein equations in very general cones. In order to achieve this, we combine a new formulation of cones in terms of continuous functionals with fixed point…
Dembo, Cover, and Thomas (1991) developed an elegant information-theoretic framework for proving determinantal inequalities for positive definite matrices, which relies on the structural inequalities of differential entropy. Submodular…
It is established that general s-convex functions are a new class of generalized convex functions. In a similar vein, a new class of general s-convex sets is introduced, which are generalizations of s-convex sets. Additionally, certain…
We present a conjecture for expressing the coefficients in the Cayley-Hamilton theorem for supermatrices in terms of supertraces. The conjecture is tested for several supermatrix dimensions and unique results are obtained. Generating…
By universal formulas we understand parameterized analytic expressions that have a fixed complexity, but nevertheless can approximate any continuous function on a compact set. There exist various examples of such formulas, including some in…
We extend Makkai duality between coherent toposes and ultracategories to a duality between toposes with enough points and ultraconvergence spaces. Our proof generalizes and simplifies Makkai's original proof. Our main result can also be…
We prove a generalisation to any characteristic of a result of Macdonald that describes strict polynomial functors in characteristic zero in terms of representations of the groupoid of finite sets and bijections. Our result will give an…