Related papers: Remarks on the Sibony functions and pseudometrics

We study pseudo-Riemannian invariant metrics on bicovariant bimodules over Hopf algebras. We clarify some properties of such metrics and prove that pseudo-Riemannian invariant metrics on a bicovariant bimodule and its cocycle deformations…

This paper deals with some inequalities for trigonometric and hyperbolic functions such as the Jordan inequality and its generalizations. In particular, lower and upper bounds for functions such as (sin x)/x and x/(sinh x) are proved.

Short remarks on the problem of assigning frequency spectra to Casimir, sonoluminescence, Hawking, Unruh, and quantum optical squeezing effects are presented

This is a review of some of the interesting properties of the Riemann Zeta Function.

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis…

Results involving various mean value properties are reviewed for harmonic, biharmonic and metaharmonic functions. It is also considered how the standard mean value property can be weakened to imply harmonicity and belonging to other classes…

Experimental results on hadronic structures are discussed in view of our physics understanding. Achievements and challenges are noted.

Some formulas and speculations are presented relative to integrable systems and quantum mechanics.

Structures of commuting semigroups of isometries under certain additional assumptions like double commutativity or dual double commutativity are found.

In this survey paper, I first review the history of Bernoulli numbers, then examine the modern definition of Bernoulli numbers and the appearance of Bernoulli numbers in expansion of functions. I revisit some properties of Bernoulli numbers…

A characterization of multiplicative (and additive) arithmetical functions is given. Using this characterization, we show that the group of multiplicative arithmetical functions is isomorphic to the group of additive arithmetical functions.

This is a brief introduction to the basic concepts of topology. It includes the basic constructions, discusses separation properties, metric and pseudometric spaces, and gives some applications arising from the use of topology in computing.

We introduce the central Fubini-like numbers and polynomials using Rota approach. Several identities and properties are established as generating functions, recurrences, explicit formulas, parity, asymptotics and determinantal…

In this paper, we mainly discuss some generalized metric properties and the character of the free paratopological groups, and extend several results valid for free topological groups to free paratopological groups.

In this paper, we find several determinants expressing the Fibonomial coefficients. We also give the generating functions, Vandermonde identity, and continued fractions about Fibonomial coefficients.

An overview of the cosmological models with expansion, shear and rotation is presented. Problems of the rotating models are discussed, their general kinematic properties and dynamical realizations are described. A particular attention is…

In the abstract of [1] we read: "We obtain so far unproved properties of a ratio involving a classof Hermite and parabolic cylinder functions." However, we explain how some of the main results in that paper were already proved in [2],…

We review some basic definitions and few facts recently established for $\D$-pseudo bosons and for pseudo-fermions. We also discuss an extended version of these latter, based on biorthogonal bases, which lives in a finite dimensional…

In this paper, approximate convexity and approximate midconvexity properties, called $\varphi$-convexity and $\varphi$-midconvexity, of real valued function are investigated. Various characterizations of $\varphi$-convex and…

In a series of recent papers the author has introduced the notion of (regular) pseudo-bosons showing, in particular, that two number-like operators, whose spectra are ${\Bbb N}_0:={\Bbb N}\cup\{0\}$, can be naturally introduced. Here we…