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Multimodular functions, primarily used in the literature of queueing theory, discrete-event systems, and operations research, constitute a fundamental function class in discrete convex analysis. The objective of this paper is to clarify the…
We obtain sufficient conditions for an exponential type entire function not to have zeros in the open lower half-plane. An exact inequality containing the real and imaginary parts of such functions and their derivatives restricted to the…
In various economic applications, people want to compare $n$ units with respect to certain quantities $Y_1, Y_2, \ldots, Y_n$ measuring their performance. The latter, however, is often influenced by certain factors which are beyond control…
Submodular functions are discrete functions that model laws of diminishing returns and enjoy numerous algorithmic applications. They have been used in many areas, including combinatorial optimization, machine learning, and economics. In…
Companions of Ostrowski's integral ineqaulity for absolutely continuous functions and applications for composite quadrature rules and for p.d.f.'s are provided.
A fascinating inverse problem that has been receiving considerable attention is the construction of realizations of random two-phase heterogeneous media with a target two-point correlation function. However, not every hypothetical two-point…
The present research deals with generalizations of the Salem function with arguments defined in terms of certain alternating expansions of real numbers. The special attention is given to modelling such functions by systems of functional…
Given a function $f:(0,\infty)\rightarrow\RR$ and a positive semidefinite $n\times n$ matrix $P$, one may define a trace functional on positive definite $n\times n$ matrices as $A\mapsto \Tr(Pf(A))$. For differentiable functions $f$, the…
A new necessary and sufficient stability test in a tractable number of operations for linear neutral-type delay systems is introduced. It is developed in the Lyapunov-Krasovskii framework via functionals with prescribed derivatives. The…
We consider general subordination and obtain the formula of the subordinated predictable compensator. An example of application is given.
Using simple operator-valued analytic function considerations several general analytic subordination results for a freely Markovian triple of operator algebras are derived from the analytic subordination result for generalized resolvents in…
The two-functional conjecture says that if a function f analytic and univalent in the unit disk maximizes Re{L} and Re{M} for two continuous linear functionals L and M, L is not equal to cM for any c>0, then f is a rotation of the Koebe…
Let g be a (say, sufficiently differentiable) function on the reals. One knows how to apply g to Hermitian elements A of a C* algebra. Yet the question of differentiability of the mapping A to g(A) is not trivial, since in general "A and dA…
We consider general convolutional derivatives and related fractional statistical dynamics of continuous interacting particle systems. We apply the subordination principle to construct kinetic fractional statistical dynamics in the continuum…
The extensions of the classical Debye model of susceptibility of dielectric materials to the well-known Cole-Cole, Davidson- Cole, or the Havriliak-Negami models is done by introducing non-integer power parameters to the frequency-domain…
In this paper we focus on providing sufficient conditions for some well-known stochastic orders in reliability but dealing with the discrete versions of them, filling a gap in the literature. In particular, we find conditions based on the…
A function in a class $\mathcal{F}(X)$ is said to be subdifferentially determined in $\mathcal{F}(X)$ if it is equal up to an additive constant to any function in $\mathcal{F}(X)$ with the same subdifferential. A function is said to be…
We derive the necessary and sufficient conditions for the simple eigenvalues of rational matrix functions with symmetry structure to have the same normwise condition number with respect to arbitrary and structure-preserving perturbations.…
The weighted star-discrepancy has been introduced by Sloan and Wo{\'z}niakowski to reflect the fact that in multidimensional integration problems some coordinates of a function may be more important than others. It provides upper bounds for…
Let $p(z)=zf'(z)/f(z)$ for a function $f(z)$ analytic on the unit disk $|z|<1$ in the complex plane and normalized by $f(0)=0, f'(0)=1.$ We will provide lower and upper bounds for the best constants $\delta_0$ and $\delta_1$ such that the…