Related papers: $\sigma$-Relations, $\sigma$-functions and $\sigma…
A correlation function of the classical orthogonal polynomials is defined and determined. The correlation function obeys a second order difference equation in two variables. The correlation function for the Gegenbauer, Chebyshev and…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
We list the so-called Askey-scheme of hypergeometric orthogonal polynomials. In chapter 1 we give the definition, the orthogonality relation, the three term recurrence relation and generating functions of all classes of orthogonal…
In this paper, we first give the cartesian product of two neutrosophic multi sets(NMS). Then, we define relations on neutrosophic multi sets to extend the intuitionistic fuzzy multi relations to neutrosophic multi relations. The relations…
It is well-known fact that there exists 1-1 correspondence between so-called double (or flou) sets and intuitionistic sets (also known as orthopairs). At first glance, these two concepts seem to be irreconcilable. However, one must remember…
In 1958, Helson and Lowdenslager extended the theory of analytic functions to a general class of groups with ordered duals. In this context, analytic functions on such a group $G$ are defined as the integrable functions whose Fourier…
We introduce a notion of positive definiteness for functions $f\!:P\to\mathbb{R}$ defined on meet semilattices $(P,\preceq,\wedge)$ and prove several properties for these functions. In addition, we utilize the $LDL^{\rm T}$ decomposition of…
A function in a class $\mathcal{F}(X)$ is said to be subdifferentially determined in $\mathcal{F}(X)$ if it is equal up to an additive constant to any function in $\mathcal{F}(X)$ with the same subdifferential. A function is said to be…
In this short note we use ideas from systems theory to define a functional calculus for infinitesimal generators of strongly continuous semigroups on a Hilbert space. Among others, we show how this leads to new proofs of (known) results in…
In this paper, we introduce and share the new concept of $\mathcal{MT}(\lambda )$-functions and its some characterizations.
Four families of special functions, depending on n variables, are studied. We call them symmetric and antisymmetric multivariate sine and cosine functions. They are given as determinants or antideterminants of matrices, whose matrix…
This paper introduces function alignment, a novel theory of mind and intelligence that is both intuitively compelling and structurally grounded. It explicitly models how meaning, interpretation, and analogy emerge from interactions among…
We introduce the notion of relational symplectic groupoid as a way to integrate Poisson manifolds in general, following the construction through the Poisson sigma model (PSM) given by Cattaneo and Felder. We extend such construction to the…
Classical Schur analysis is intimately connected to the theory of orthogonal polynomials on the circle [Simon, 2005]. We investigate here the connection between multipoint Schur analysis and orthogonal rational functions. Specifically, we…
In 1997 the present authors published a review (Ref. BEL97 in the present manuscript) that recapitulated and developed classical theory of Abelian functions realized in terms of multi-dimensional sigma-functions. This approach originated by…
We produce explicit formulae for various ideal zeta functions associated to the members of an infinite family of class-$2$-nilpotent Lie rings, introduced in [1], in terms of Igusa functions. As corollaries we obtain information about…
Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between…
Analogical reasoning depends fundamentally on the ability to learn and generalize about relations between objects. We develop an approach to relational learning which, given a set of pairs of objects…
Topological Recursion generates a family of symmetric differential forms (correlators) from some initial data $(\Sigma,x,y,B)$. We give a functional relation between the correlators of genus $g=0$ generated by the initial data…
The series of papers is devoted to the study of convergence for pairs of surfaces and smooth functions thereon. We model such pairs with varifolds and multiple-valued functions to capture their limits. In the present paper, we study Young…