相关论文: Some Problems in Defining Functional Integration o…
The question in the title is ambiguous. At least the understanding of words essentially different and function theory should be clarified. We discuss approaches to do that. We also present a new framework for analytic function theories…
We investigate functionals defined on manifolds through parameterizations. If they are to be meaningful, from a geometrical viewpoint, they ought to be invariant under reparameterizations. Standard, local, integral functionals with this…
The problem of synthesis of gate-level descriptions of digital circuits from behavioural specifications written in higher-level programming languages (hardware compilation) has been studied for a long time yet a definitive solution has not…
Evaluation of basic integrals over Gaussian functions, traditionally utilized for electronic structure computations on molecules and solids, is discussed in a pedagogical form.
We develop notions of integrable functions within the theory of schemic motivic integration.
Fractal percolation exhibits a dramatic topological phase transition, changing abruptly from a dust-like set to a system spanning cluster. The transition points are unknown and difficult to estimate. In many classical percolation models the…
This paper is devoted for the study of a new generalization of Struve function type. In this paper , We establish four new integral formulas involving the Galue type Struve function, which are express in term of the generalized (Wright)…
This chapter serves as an introduction to systems engineering focused on the broad issues surrounding realizing complex integrated systems. What is a system? We pose a number of possible definitions and perspectives, but leave open the…
We consider the problem of clustering functional data while jointly selecting the most relevant features for classification. This problem has never been tackled before in the functional data context, and it requires a proper definition of…
Without an agreed-upon definition of intelligence, asking "is this system intelligent?"" is an untestable question. This lack of consensus hinders research, and public perception, on Artificial Intelligence (AI), particularly since the rise…
We consider some possible approaches to the fractional-order generalization of definition of variation (functional) derivative. Some problems of formulation of a fractional-order variational derivative are discussed. To give a consistent…
The aim of the present article is to establish the connection between the existence of the limit along the normal and an admissible limit at a fixed boundary point for holomorphic functions of several complex variables.
We discuss the inequalities for $q$-integrals because of the fact that the inequalities can be very useful in the future mathematical research. Since $q$-integral of a function over an interval $[a,b]$ is defined by the difference of two…
We extend the theory of Euler integration from the class of constructible functions to that of "tame" real-valued functions (definable with respect to an o-minimal structure). The corresponding integral operator has some unusual defects (it…
In this article, it is analyzed a problem of existence of a function which is able to transform electromagnetic potentials defined in one gauge to corresponding potentials defined in the other gauge. It is shown that such a function cannot…
Gauge fixing is interpreted in BV formalism as a choice of Lagrangian submanifold in an odd symplectic manifold. A natural construction defines an integration procedure on families of Lagrangian submanifolds. In string perturbation theory,…
In this papaer, we put forward some new definitions and integral inequalities by using fairly elementary analysis.
The problem of determining gauge and monoidal equivalence classes of fusion categories is considered from the perspective of geometric invariant theory. It is shown that the gauge (or monoidal) class of a fusion category is determined by…
This paper provides a precise and scientific definition of complexity and coupling, grounded in the functional domain, particularly within industrial control and automation systems (iCAS). We highlight the widespread ambiguity in defining…
The relation between representations and positive definite functions is a key concept in harmonic analysis on topological groups. Recently this relation has been studied on topological groupoids. This is the second in a series of papers in…