Related papers: A Generalization of the arctg function

In this paper, we give an elementary proof of the additivity of the functional inverses of the resolvents of large $N$ random matrices, using recently developed matrix model techniques. This proof also gives a very natural generalization of…

In this paper, we sharpen and generalize Shafer's inequality for the arc tangent function. From this, some known results are refined.

We give some conditions under which (uniform) convergence of a family of Dirichlet series to another Dirichlet series implies the convergence of their individual coefficients and/or exponents. We give some applications to some spectral zeta…

Family of equations, which is the generalization of the $K(m,m)$ equation, is considered. Periodic wave solutions for the family of nonlinear equations are constructed.

We introduce generalized notions of a divergence function and a Fisher information matrix. We propose to generalize the notion of an exponential family of models by reformulating it in terms of the Fisher information matrix. Our methods are…

We study a family of generalized continued fractions, which are defined by a pair of substitution sequences in a finite alphabet. We prove that they are stammering sequences, in the sense of Adamczewski and Bugeaud. We also prove that this…

We describe the geometric structures involved in the variational formulation of physical theories. In presence of these structures, the constitutive set of a physical system can be generated by a family of functions. We discuss conditions,…

We present an asymptotic expansion for a family of multiple integrals connected with relatives of the Dickman function. The coefficients of this expansion have a similar arithmetic structure as those appearing in work of Soundararajan on an…

We present an infinite family of quadratic APN functions on a finite field of dimension over GF(2) divisible by 3.

We present an algebraic theory of orthogonal polynomials in several variables that includes classical orthogonal polynomials as a special case. Our bottom line is a straightforward connection between apolarity of binary forms and the inner…

A resonance theorem providing existence of functions that are counterexamples for all members of a given family of translation invariant differentiation bases is proved. Applications of the theorem to Zygmund problem on a choice of…

We introduce and study a mathematical framework for a broad class of regularization functionals for ill-posed inverse problems: Regularization Graphs. Regularization graphs allow to construct functionals using as building blocks linear…

We study the arity gap of functions of several variables defined on an arbitrary set A and valued in another set B. The arity gap of such a function is the minimum decrease in the number of essential variables when variables are identified.…

We define the Schur-Agler class in infinite variables to consist of functions whose restrictions to finite dimensional polydisks belong to the Schur-Agler class. We show that a natural generalization of an Agler decomposition holds and the…

Let A denote the ring of arithmetical functions with unitary convolution, and let V be a finite subset of the positive integers having the property that for every v in V, all unitary divisors of v lie in V. We study the truncation A_V, an…

We develop a theory of multiplicative functions (with values inside or on the unit circle) in arithmetic progressions analogous to the well-known theory of primes in arithmetic progressions.

In this paper, we show that for a broad class of pseudoconvex formal-analytic arithmetic surfaces over $\text{Spec}(\mathbb{Z})$, those which admit a nonconstant monic such regular function, that a conjecture of Bost-Charles that the ring…

In this paper we generalize notions of iterated integral with regard to an unpredictable process. We establish a formula of integration by parts, the existence of a continuous modification and give an expression of the increasing process.

The Lambert W function gives the solutions of a simple exponential polynomial. The generalized Lambert W function was defined by Mez\"{o} and Baricz, and has found applications in delay differential equations and physics. In this article we…

We have established various criteria for the topological transitivity of families of continuous (holomorphic) functions. Furthermore, by leveraging the properties of expanding families of meromorphic functions, we offer an alternative proof…