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By designating vertices with variables, a simple undirected graph can be augmented to have an associated representing rational function in two variables taking the complex bi-upper halfplane to itself. We give relations between representing…
We show that some singular maximal functions and singular Radon transforms satisfy a weak type $L\log\log L$ inequality. Examples include the maximal function and Hilbert transform associated to averages along a parabola. The weak type…
We prove that every bounded finely plurisubharmonic function can be locally (in the pluri-fine topology) written as the difference of two usual plurisubharmonic functions. As a consequence finely plurisubharmonic functions are continuous…
We give several unequivalent notions of convergency of meromorphic functions and more generally meromorphic mappings (strong, weak, $\Gamma $-convergency and some others). Relations between them are investigated. A version of Rouche theorem…
This paper is an introduction to the theory of multivector functions of a real variable. The notions of limit, continuity and derivative for these objects are given. The theory of multivector functions of a real variable, even being similar…
The main purpose of this note is to provide a topological approach to defining additive functions on Riemannian co-compact normal coverings.
We consider continuous functions f : [0,1] \to R that cut the real axis at every point of a measurable set of positive measure and we construct examples where f fails to have bounded variation, and at the opposite end, where f admits…
In this paper, we generalize the construction of strongly regular graphs in [Y. Tan et al., Strongly regular graphs associated with ternary bent functions, J. Combin.Theory Ser. A (2010), 117, 668-682] from ternary bent functions to $p$-ary…
In this paper, we establish some new inequalities for class of SX(h,I) convex functions which are supermultiplicative or superadditive and nonnegative. And we also give some applications for special means.
In this paper, we construct a digraph structure on $p$-adic dynamical systems defined by rational functions. We study the conditions under which the functions are measure-preserving, invertible and isometric, ergodic, and minimal on…
We extend P\'olya's indicator diagram theory to encompass entire functions of order at most 1, allowing functions of maximal type. To do so, we introduce an extension of the complex plane in which indicator diagrams may be unbounded or even…
Fracture functions and their evolution equations are reviewed. Some phenomenological applications are briefly discussed.
In this article, we further explore convex functions by revealing new bounds, resulting from stronger convexity behavior. In particular, we define the so called radical convex functions and study their properties. We will see that such…
This paper presents sufficient graph-theoretic conditions for injectivity of collections of differentiable functions on rectangular subsets of R^n. The results have implications for the possibility of multiple fixed points of maps and…
These informal notes are concerned with spaces of functions in various situations, including continuous functions on topological spaces, holomorphic functions of one or more complex variables, and so on.
On Riemann surfaces $M$, there exists a canonical correspondence between a possibly multivalued function $\Psi_X$ whose differential is single valued ($i.e.$ an additively automorphic singular complex analytic function) and a vector field…
We examine Bourbaki's function, an easily-constructed continuous but nowhere-differentiable function, and explore properties including functional identities, the antiderivative, and the box and Hausdorff dimensions of the graph.
The main purpose of this work is to characterize derivations through functional equations. This work consists of five chapters. In the first one, we summarize the most important notions and results from the theory of functional equations.…
In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…
The paper provides the first constructions of strongly regular graphs and association schemes from weakly regular plateaued functions over finite fields of odd characteristic. We generalize the construction method of strongly regular graphs…