Related papers: On expected and von Neumann-Morgenstern utility fu…
In this article, we investigate some of the fine properties of the value function associated to an optimal control problem in the Wasserstein space of probability measures. Building on new interpolation and linearisation formulas for…
New recursion relations for the Riemann zeta function are introduced. Their derivation started from the standard functional equation. The new functional equations have both real and imaginary increment versions and can be applied over the…
In this article we give some improvements and generalizations of the famous Jensen's and Jensen-Mercer inequalities for twice differentiable functions, where convexity property of the target function is not assumed in advance. They…
Generalized Bargmann representations which are based on generalized coherent states are considered. The growth of the corresponding analytic functions in the complex plane is studied. Results about the overcompleteness or undercompleteness…
Sequences of experimental ground-state energies for both odd and even $A$ are mapped onto concave patterns cured from convexities due to pairing and/or shell effects. The same patterns, completed by a list of excitation energies, give…
The classes of n-Wright-convex functions and n-Jensen-convex functions are compared with each other. It is shown that for any odd natural number $n$ the first one is the proper subclass of the second one. To reach this aim new tools…
The paper is concerned with proving the equivalence of convexity or concavity properties of thermodynamic functions, such as energy and entropy, depending on different sets of variables. These variables are the basic thermodynamic state…
We give a distribution-dependent concentration inequality for functions of independent variables. The result extends Bernstein's inequality from sums to more general functions, whose variation in any argument does not depend too much on the…
We introduce a new Tauberian framework through the theory of "regular arithmetic functions". This allows us to establish a characterization of the Riemann hypothesis by linking the floor function to the distribution of nontrivial zeros of…
In this note we offer some log-concavity properties of certain functions related to Bessel functions of the first kind and modified Bessel functions of the first and second kind, by solving partially a recent conjecture on the…
We consider a certain class of Herglotz-Nevanlinna matrix-valued functions which can be realized as the Weyl-Titchmarsh matrix-valued function of some symmetric operator and its self-adjoint extension. New properties of Weyl -Titchmarsh…
Riemannian Geometry, Topology and Dynamics permit to introduce partially defined holomorphic functions on the variety of representations of the fundamental group of a manifold. The functions we consider are the complex valued Ray-Singer…
The comonotonic maxitivity property of functionals frequently appears in the characterization of fuzzy integrals based on the maximum operation. In some special cases, comonotonic maxitivity implies monotonicity of functionals. The question…
We give necessary and sufficient criteria for a distribution to be smooth or uniformly H\"{o}lder continuous in terms of approximation sequences by smooth functions; in particular, in terms of those arising as regularizations…
Recently, authors have studied inequalities involving expectations of selected functions viz. failure rate, mean residual life, aging intensity function and log-odds rate which are defined for left truncated random variables in reliability…
Many different rules for decision making have been introduced in the literature. We show that a notion of generalized expected utility proposed in Part I of this paper is a universal decision rule, in the sense that it can represent…
In operator algebra theory, a conditional expectation is usually assumed to be a projection map onto a sub-algebra. In the paper, a further type of conditional expectation and an extension of the Lueders - von Neumann measurement to…
Functions satisfying the functional equation \begin{align*} \sum_{r=0}^{n-1} (-1)^r f(x+ry, ny) = f(x,y), \quad \text{for any positive odd integer $n$}, \end{align*} are named the alternating invariant functions. Examples of such functions…
We propose analogs of the classical Generalized Riemann Hypothesis and the Generalized Simplicity Conjecture for the characteristic p L-series associated to function fields over a finite field. These analogs are based on the use of absolute…
We give the definition of uniform symmetric continuity for functions defined on a nonempty subset of the real line. Then we investigate the properties of uniformly symmetrically continuous functions and compare them with those of…