Related papers: On a New Type $pq$-Calculus

We introduce perturbative Feynman integrals in the context of q-calculus generalizing the Gaussian q-integrals introduced by Diaz and Teruel. We provide analytic as well as combinatorial interpretations for the Feynman-Jackson integrals.

A brief review of the construction and classifiaction of the bicovariant differential calculi on quantum groups is given.

In the recent p-adic q-integral on the p-adic integers' rings was constructed >. The purpose of this paper is to give several interesting integral equation for the p-adic q-integerals on the rings of p-adic integers. As an integral…

This paper describes the classification of analytic $q$-difference equations. The difference Galois groups are computed. A tentative description of the universal difference Galois group is given.

We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses different forms of integral operators that generalizes the…

Algebraic lambda-calculi have been studied in various ways, but their semantics remain mostly untouched. In this paper we propose a semantic analysis of a general simply-typed lambda-calculus endowed with a structure of vector space. We…

In this paper we derive a sufficient condition for the existence of a unique solution of a Cauchy type q-fractional problem (involving the fractional q-derivative of Riemann-Liouville type) for some nonlinear differential equations. The key…

We present a systematic study of integrals over [0,1] where the integrand is of the form Q(x) log log 1/x. Here Q is a rational function.

In this research, Minkowski type functions which are constructed on certain probability distributions, are introduced. There are investigated differential, integral, and other properties of these functions.

Motivated by extending the functional stochastic calculus, to important functionals to which it does not apply, a notion of functional derivative along a curve is introduced. This new setting is developed by incorporating path-dependent…

In this paper, we prove several Poincar\'e inequalities of fractional type on conformally flat manifolds with finite total Q-curvature. This shows a new aspect of the $Q$-curvature on noncompact complete manifolds.

An analytical approach to convolution of functions, which appear in perturbative calculations, is discussed. An extended list of integrals is presented.

Quantum computing exposes the brilliance of quantum mechanics through computer science and, as such, gives oneself a marvelous and exhilarating journey to go through. This article leads along that journey with a historical and current…

Information-theoretic derivations of the formalism of quantum theory have recently attracted much attention. We analyze the axioms underlying a few such derivations and propose a conceptual framework in which, by combining several…

Main purposes of the paper are followings: 1) To show examples of the calculations in domain of QFT via ``derivative rules'' of an expert system; 2) To consider advantages and disadvantage that technology of the calculations; 3) To reflect…

Fractional calculus and q-deformed Lie algebras are closely related. Both concepts expand the scope of standard Lie algebras to describe generalized symmetries. A new class of fractional q-deformed Lie algebras is proposed, which for the…

We introduce a construction of the differential calculus on the quantum supergroup GL$_{p,q}(1| 1)$. We obtain two differential calculi, respectively, associated with the left and right Cartan-Maurer one-forms. We also obtain the quantum…

The ZX-calculus is a powerful framework for reasoning in quantum computing. It provides in particular a compact representation of matrices of interests. A peculiar property of the ZX-calculus is the absence of a formal sum allowing the…

R. B. Melrose's b-calculus provides a framework for dealing with problems of partial differential equations that arise in singular or degenerate geometric situations. This article is a somewhat informal short course introducing many of the…

The review of modern study of algebraic, geometric and differential properties of quaternionic (Q) numbers with their applications. Traditional and "tensor" formulation of Q-units with their possible representations are discussed and groups…