Related papers: Remarks on the Sibony functions and pseudometrics

We make an asymptotic analysis via singularity analysis of generating functions of a number sequence that involves the Fibonacci numbers and generalizes the binomial coefficients.

The notions of quasiconvexity, Wright convexity and convexity for functions defined on a metric Abelian group are introduced. Various characterizations of such functions, the structural properties of the functions classes so obtained are…

In this paper, we gave some properties of binomial coefficient.

We construct local normal forms of pseudo-Riemannian projectively equivalent 2-dimensional metrics.

We derive a general recurrence relation for squares of Fibonacci-like numbers. Various properties are developed, including double binomial summation identites.

We show some lower estimates for the Kobayashi-Royden metric on a class of smooth bounded pseudoconvex domains.

Some properties of integral averages of functions on intervals and their asymptotic behavior are investigated. The results are aimed at applications to entire and subharmonic functions.

We introduce sequences of functions orthogonal on a finite interval: proper orthogonal rational functions, orthogonal exponential functions, orthogonal logarithmic functions, and transmuted orthogonal polynomials

We propose to study deformation quantizations of Whitney functions. To this end, we extend the notion of a deformation quantization to algebras of Whitney functions over a singular set, and show the existence of a deformation quantization…

This note establishes several integral identities relating certain metric properties of level hypersurfaces of Morse functions.

A direct proof of Oka's lemma on the relation of holomorphic convexity and the properties of the distance to the boundary function is provided. Some related problems for subharmonicity properties of this function are also studied. A new…

We study the measure theoretic properties of typical C 0 maps of the interval. We prove that any ergodic measure is pseudo-physical, and conversely, any pseudo-physical measure is in the closure of the ergodic measures, as well as in the…

These lectures are a brief introduction to supersymmetry.

We study some basic properties and examples of Hermitian metrics on complex manifolds whose traces of the curvature of the Chern connection are proportional to the metric itself.

We show that the metric operator for a pseudo-supersymmetric Hamiltonian that has at least one negative real eigenvalue is necessarily indefinite. We introduce pseudo-Hermitian fermion (phermion) and abnormal phermion algebras and provide a…

We discuss some properties of the distance functions on Riemannian manifolds and we relate their behavior to the geometry of the manifolds. This leads to alternative proofs of some "classical" theorems connecting curvature and topology.

Characterizations of pseudoultrametric-preserving functions and semimetric-preserving functions are found. The structural properties of pseudoultrametrics which can be represented as a composition of an ultrametric and…

These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.

We will give a summary about the relations between the spectra of the Perron--Frobenius operator and pseudo random sequences for 1-dimensional cases.

We discuss in which sense the so-called {\em regular pseudo-bosons}, recently introduced by Trifonov and analyzed in some details by the author, are related to ordinary bosons. We repeat the same analysis also for {\em pseudo-bosons}, and…