Related papers: Remarks on some majorization inequalities
We use the definition of a fractional integral, recently proposed by Katugampola, to establish a generalization of the reverse Minkowski's inequality. We show two new theorems associated with this inequality, as well as state and show other…
We consider an elliptic operator in which the second-order term is very small in one direction. In this regime, we study the behaviour of the principal eigenfunction and of the principal eigenvalue. Our first result deals with the limit of…
Majorization is a basic concept in matrix theory that has found applications in numerous settings over the past century. Power majorization is a more specialized notion that has been studied in the theory of inequalities. On the other hand,…
We generalize Araki's log-majorization to the log-convexity theorem for the eigenvalues of $\Phi(A^p)^{1/2}\Psi(B^p)\Phi(A^p)^{1/2}$ as a function of $p\ge0$, where $A,B$ are positive semidefinite matrices and $\Phi,\Psi$ are positive…
We develop an extension of valuations theorem for suitable extensions of idempotent semirings. As an application, we give a new proof for the classical case of fields. Along the way, we develop characteristic one analogues of some central…
The notes contain a streamlined account on stability of univariate polynomials and related problems
In this paper, we explain how some basic facts about valuation can help clarify many questions about divisibility in integral domains.
In these notes we focus a bit on the complex case for some families of matrices and equivalences between them.
In this paper we give refinements of some convex and log-convex moment inequalities of the first and second order using a special kind of positive semi-definite form. An open problem concerning eight parameter refinement of second order is…
In this note, we study a certain class of trigonometric series which is important in many problems. An unproved statement in Zygmund's book [5] will be proved and generalized. Further discussions based on this problem will also be made…
In this note we establish some appropriate conditions for stochastic equality of two random variables/vectors which are ordered with respect to convex ordering or with respect to supermodular ordering. Multivariate extensions of this result…
In this short note we use the umbral formalism to derive the Ramanujan Master Theorem and discuss its extension to more general cases.
This paper is the extended introduction of a serie of papers about modelling T-homotopy by refinement of observation. The notion of T-homotopy equivalence is discussed. A new one is proposed and its behaviour with respect to other…
In the present paper a new mean value theorem for polynomials of special form is obtained. The case of sums on vertices of a regular polygon is studied. A criterion for a certain equation to be satisfied is obtained.
We describe the inequalities on the possible eigenvalues of products of unitary matrices in terms of quantum Schubert calculus. Related problems are the existence of flat connections on the punctured two-sphere with prescribed holonomies,…
A short account of recent existence and multiplicity theorems on the Dirichlet problem for an elliptic equation with $(p,q)$-Laplacian in a bounded domain is performed. Both eigenvalue problems and different types of perturbation terms are…
A short note that contains some Cliff's notes of the general theory (see math.AG/9905103) but concentrates on one of the stranger aspects of it - existence of other irreducible components.
The article introduces Ahlfors' generalization of the Schwarz lemma. With this powerful geometric tool of complex functions in one variable, we are able to prove some theorems concerning the size of images under holomorphic mappings,…
These notes deal with a few properties of convolutions in the role of approximations to the identity.
In the paper, the idea of describing not-yet-verified properties of quantum objects with logical many-valuedness is scrutinized. As it is argued, to promote such an idea, the following two foundational problems of many-valued quantum logic…