Related papers: A Generalization of Calculus for Use with Continuo…
Path integrals are a central tool when it comes to describing quantum or thermal fluctuations of particles or fields. Their success dates back to Feynman who showed how to use them within the framework of quantum mechanics. Since then, path…
The extensive deployment of probabilistic algorithms has radically changed our perspective on several well-established computational notions. Correctness is probably the most basic one. While a typical probabilistic program cannot be said…
We study operators that are generalizations of the classical Riemann-Liouville fractional integral, and of the Riemann-Liouville and Caputo fractional derivatives. A useful formula relating the generalized fractional derivatives is proved,…
A differential calculus on an associative algebra A is an algebraic analogue of the calculus of differential forms on a smooth manifold. It supplies A with a structure on which dynamics and field theory can be formulated to some extent in…
In the paper we consider models of generalized counting processes time-changed by a general inverse subordinator, we characterize their distributions and present governing equations for them. The equations are given in terms of the…
This note describes how the the scalable ZXH calculus can be used to represent in a compact way the quantum gates that are diagonal in the computational basis. This includes controlled and multi-controlled Z gates, their generalizations,…
We define an extension of lambda-calculus with dependents types that enables us to encode transparent and opaque probabilistic programs and prove a strong normalisation result for it by a reducibility technique. While transparent…
Neutrosophic Analysis is a generalization of Set Analysis, which in its turn is a generalization of Interval Analysis. Neutrosophic Precalculus is referred to indeterminate staticity, while Neutrosophic Calculus is the mathematics of…
In this paper we present the first steps for obtaining a discrete Quantum Mechanics making use of the Umbral Calculus. The idea is to discretize the continuous Schroedinger equation substituting the continuous derivatives by discrete ones…
We exploit transformations relating generalized $q$-series, infinite products, sums over integer partitions, and continued fractions, to find partition-theoretic formulas to compute the values of constants such as $\pi$, and to connect sums…
This note tries to show that a re-examination of a first course in analysis, using the more sophisticated tools and approaches obtained in later stages, can be a real fun for experts, advanced students, etc. We start by going to the…
In this paper, a new calculus on sequences is defined. Also, the $\lambda$-derivative and the $\lambda$-integration are investigated. The fundamental theorem of $\lambda$-calculus is included. A suitable function basis for the…
We establish two types of estimates for generalized derivatives of set-valued mappings which carry the essence of two basic patterns observed troughout the pile of calculus rules. These estimates also illustrate the role of the essential…
The attempt to unify the laws of physics is approached from a discrete vision of space and time, abandoning the continuous medium paradigm that presided over the derivation of certain equations of physics-Navier-Stokes., Navier-Lam{\'e},…
The purpose of this article is twofold. First, we introduce the constants $\zeta_k(\alpha,r,q)$ where $\alpha \in (0,1)$ and study them along the lines of work done on Euler constant in arithmetic progression $\gamma(r,q)$ by Briggs,…
A notion of probabilistic lambda-calculus usually comes with a prescribed reduction strategy, typically call-by-name or call-by-value, as the calculus is non-confluent and these strategies yield different results. This is a break with one…
The lambda calculus is a universal programming language. It can represent the computable functions, and such offers a formal counterpart to the point of view of functions as rules. Terms represent functions and this allows for the…
Fractional calculus generalizes the derivative and antiderivative operations of differential and integral calculus from integer orders to the entire complex plane. Methods are presented for using this generalized calculus with Laplace…
Although being powerful, the differential transform method yet suffers from a drawback which is how to compute the differential transform of nonlinear non-autonomous functions that can limit its applicability. In order to overcome this…
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…