Related papers: On Some Classes of Functions and Hypercubes
Functional dynamics, introduced in a previous paper, is analyzed, focusing on the formation of a hierarchical rule to determine the dynamics of the functional value. To study the periodic (or non-fixed) solution, the functional dynamics is…
Mathematical models are sometime given as functions of independent input variables and equations or inequations connecting the input variables. A probabilistic characterization of such models results in treating them as functions with…
In this article, a class of analytic functions is investigated and their some properties are established. Several recurrence relations and various classes of bilinear and bilateral generating functions for these analytic functions are also…
The idea of using unfolding as a way of computing a program semantics has been applied successfully to logic programs and has shown itself a powerful tool that provides concrete, implementable results, as its outcome is actually source…
Existence results for Hilbert's problem 13th mean that any equation constructed by continue functions can be given solution represented as a superposition of continue functions of one variable or of continue functions of two variables.…
The proposed system of integer functions is logically fully independent from the traditional mathematical analysis of the real functions, but there is a well-defined mutual correspondence between the two disciplines. The system of integer…
Deontic logic is a very well researched branch of mathematical logic and philosophy. Various kinds of deontic logics are discussed for different application domains like argumentation theory, legal reasoning, and acts in multi-agent…
Logics closed under classes of substitutions broader than class of uniform substitutions are known as hyperformal logics. This paper extends known results about hyperformal logics in two ways. First: we examine a very powerful form of…
For a rational function of several variables with nonnegative imaginary part on the upper poly-half-plane, the matrix representations are obtained.
This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations…
This is an anthology of series involving rational, factorial, and power functions expressed in terms of special functions. New finite expansions involving quotient functions expressed in terms of the Hurwitz-Lerch zeta function are given.…
Closed classes of three-valued logic generated by symmetric funtions that equal $1$ in almost all tuples from $\{1,2\}^n$ and equal $0$ on the rest tuples are considered. Criteria for bases existence for these classes is obtained.
In this note I present a readable version of the proof of my 2001 result, giving a sufficient and necessary condition for a function on a combinatorial cube to essentially (locally) depend on at most one variable (see the end of the paper…
In this article we give evaluations of certain series of hyperbolic functions using Jacobi elliptic functions theory. We also define some new functions that enable us to give characterization of not solvable class of series.
Functions of several octonion variables are investigated and integral representation theorems for them are proved. With the help of them solutions of the ${\tilde {\partial}}$-equations are studied. More generally functions of several…
By means of the contour integration method, we evaluate, in closed form, a class of definite integrals involving hyperbolic tangent function.
Classes of functions of several variables on arbitrary non-empty domains that are closed under permutation of variables and addition of dummy variables are characterized in terms of generalized constraints, and hereby Hellerstein's Galois…
Rectangular designs are classified as regular, Latin regular, semiregular, Latin semiregular and singular designs. Some series of selfdual as well as alpharesolvable designs are obtained using matrix approaches which belong to the above…
We derive explicit formulae for the subalgebra zeta functions of all higher Heisenberg Lie algebras over an arbitrary compact discrete valuation ring $\mathfrak{o}$. To this end, we develop Hecke-theoretic techniques for the enumeration, by…
In this manuscript, the authors derive closed formula for definite integrals of combinations of powers and logarithmic functions of complicated arguments and express these integrals in terms of the Hurwitz zeta. These derivations are then…