Related papers: Remarks on Uniformly Symmetrically Continuous Func…
Connectedness, path connectedness, and uniform connectedness are well-known concepts. In the traditional presentation of these concepts there is a substantial difference between connectedness and the other two notions, namely connectedness…
We do further investigation in a certain cosine function defined for smooth Minkowski spaces. We prove that such function is symmetric if and only if the referred space is Euclidean, and also that it can be given in terms of the Gateaux…
We study the symmetry properties of autonomous integrating factors from an algebraic point of view. The symmetries are delineated for the resulting integrals treated as equations and symmetries of the integrals treated as functions or…
We introduce characteristic functions for certain contractive liftings of row contractions. These are multi-analytic operators which classify the liftings up to unitary equivalence and provide a kind of functional model. The most important…
We define an equivalence relation on integer compositions and show that two ribbon Schur functions are identical if and only if their defining compositions are equivalent in this sense. This equivalence is completely determined by means of…
We consider the space of convex functions defined in the Euclidean $n$-dimensional space, which are lower semi-continuous and tend to infinity at infinity. We study real-valued valuations defined on this space of functions, which are…
Spontaneous synchronization has long served as a paradigm for behavioral uniformity that can emerge from interactions in complex systems. When the interacting entities are identical and their coupling patterns are also identical, the…
We investigate in which cases the boundary of a multiply connected wandering domain of an entire function is uniformly perfect. We give a general criterion implying that it is not uniformly perfect. This criterion applies in particular to…
Generalised definitions of exponential, trigonometric sine and cosine and hyperbolic sine and cosine functions are given. In the lowest order, these functions correspond to ordinary exponential, trigonometric sine etc. Some of the…
The aim of this paper is to introduce and study the concept of a contra-semicontinuous function and further investigate the class of strongly $S$-closed spaces. We obtain some new decompositions of generalized continuous functions.
We present a versatile construction allowing one to obtain pairs of integer sets with infinite symmetric difference, infinite intersection, and identical representation functions.
Diversities have recently been developed as multiway metrics admitting clear and useful notions of hyperconvexity and tight span. In this note we consider the analytic properties of diversities, in particular the generalizations of uniform…
We construct a monotone, continuous, but not absolutely continuous function whose minimal modulus of continuity is absolutely continuous. In particular, we establish that there is no equivalence between the absolute continuity of a function…
Let $\A$ be the operator which assigns to each $m \times n$ matrix-valued function on the unit circle with entries in $H^\infty + C$ its unique superoptimal approximant in the space of bounded analytic $m \times n$ matrix-valued functions…
Morphic sequences form a natural class of infinite sequences, extending the well-studied class of automatic sequences. Where automatic sequences are known to have several equivalent characterizations and the class of automatic sequences is…
We consider several coding discretizations of continuous functions which reflect their variation at some given precision. We study certain statistical and combinatorial properties of the sequence of finite words obtained by coding a typical…
Various versions of the definition of nonclassical symmetries existing in the literature are analyzed. Comparing properties of Lie and nonclassical symmetries leads to the conclusion that in fact a nonclassical symmetry is not a symmetry in…
The paper considers a universal approach that allows one to quite simply obtain nonlinear asymptotic estimates of various summation functions. It is shown the application of this approach to the asymptotic estimation of divergent Dirichlet…
Recent advances in the theory of complex symmetric operators are presented and related to current studies in non-hermitian quantum mechanics. The main themes of the survey are: the structure of complex symmetric operators, $C$-selfadjoint…
We define positive and strictly positive definite functions on a domain and study these functions on a list of regular domains. The list includes the unit ball, conic surface, hyperbolic surface, solid hyperboloid, and simplex. Each of…