Related papers: A Tasty Combination: Multivariable Calculus and Di…
We exploit the link between the transport equation and derivatives of expectations to construct efficient pathwise gradient estimators for multivariate distributions. We focus on two main threads. First, we use null solutions of the…
In numerous applicative contexts, data are too rich and too complex to be represented by numerical vectors. A general approach to extend machine learning and data mining techniques to such data is to really on a dissimilarity or on a kernel…
When students are learning to use math in physics, one of the most important ideas they need to learn is that equations are not just calculational tools; they represent relationships between physical variables that change together (covary).…
How to select variables and identify functional forms for continuous variables is a key concern when creating a multivariable model. Ad hoc 'traditional' approaches to variable selection have been in use for at least 50 years. Similarly,…
In the present work, an attempted was made to develop a numerical algorithm by the use of new orthogonal hybrid functions formed from hybrid of piecewise constant orthogonal sample-and-hold functions and piecewise linear orthogonal…
This paper is concerned with the derivation and properties of differential complexes arising from a variety of problems in differential equations, with applications in continuum mechanics, relativity, and other fields. We present a…
We construct a two-parameter covariant differential calculus on the quantum $h$-exterior plane. We also give a deformation of the two-dimensional fermionic phase space.
Explicit general constructions of paragrassmann calculus with one and many variables are given. Relations of the paragrassmann calculus to quantum groups are outlined and possible physics applications are briefly discussed. This paper is…
Fractional calculus is a powerful and effective tool for modelling nonlinear systems. The M derivative is the generalization of alternative fractional derivative. This M derivative obey the properties of integer calculus. In this paper, we…
In one variable, there exists a satisfactory classification of commutative rings of differential operators. In several variables, even the simplest generalizations seem to be unknown and in this report we give examples and pose questions…
Most of theoretical physics is based on the mathematics of functions of a real or a complex variable; yet we frequently are drawn to try extending our reach to include quaternions. The non-commutativity of the quaternion algebra poses…
Noncommutative rational functions appeared in many contexts in system theory and control, from the theory of finite automata and formal languages to robust control and LMIs. We survey the construction of noncommutative rational functions,…
Quantum computing has traditionally centered around the discrete variable paradigm. A new direction is the inclusion of continuous variable modes and the consideration of a hybrid continuous-discrete approach to quantum computing. In this…
We construct the generalized version of covariant Z_3-graded differential calculus introduced by one of us (R.K.), and then extended to the case of arbitrary Z_N grading. Here our main purpose is to establish the recurrence formulae for the…
Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rules and matrix realizations of dual numbers, we will present a…
We build a differential calculus for subalgebras of the Moyal algebra on R^4 starting from a redundant differential calculus on the Moyal algebra, which is suitable for reduction. In some cases we find a frame of 1-forms which allows to…
Motivated by the general problem of extending the classical theory of holomorphic functions of a complex variable to the case of quater- nion functions, we give a notion of an H-derivative for functions of one quaternion variable. We show…
Differintegral methods, currently exploited in calculus, provide a fairly unexhausted source of tools to be applied to a wide class of problems involving the theory of special functions and not only. The use of integral transforms of Borel…
Binomial coefficients have been used for centuries in a variety of fields and have accumulated numerous definitions. In this paper, we introduce a new way of defining binomial coefficients as repeated sums of ones. A multitude of binomial…
Fractional dissipation is a powerful tool to study non-local physical phenomena such as damping models. The design of geometric, in particular, variational integrators for the numerical simulation of such systems relies on a variational…