Related papers: Integration in Finite Terms: Dilogarithmic Integra…

Integration at a point is a new kind of integration derived from integration over an interval in infinitesimal and infinity domains which are spaces larger than the reals. Consider a continuous monotonic divergent function that is…

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors,…

We develop Kummer theory for algebraic function fields in finitely many transcendental variables. We consider any finitely generated Kummer extension (possibly, over a cyclotomic extension) of an algebraic function field, and describe the…

We give a necessary and sufficient condition for the integrality of the Taylor coefficients of mirror maps at the origin. By mirror maps, we mean formal power series z.exp(G(z)/F(z)), where F(z) and G(z)+log(z)F(z) are particular solutions…

One of the most challenging problems in the domain of 2-D image or 3-D shape is to handle the non-rigid deformation. From the perspective of transformation groups, the conformal transformation is a key part of the diffeomorphism. According…

An integro-differential ring is a differential ring that is closed under an integration operation satisfying the fundamental theorem of calculus. Via the Newton--Leibniz formula, a generalized evaluation is defined in terms of integration…

Index transforms with the product of the associated Legendre functions are introduced. Mapping properties are investigated in the Lebesgue spaces. Inversion formulas are proved. The results are applied to solve a boundary value problem in a…

We obtain a new decomposition of the Riemann-Liouville operators of fractional integration as a series involving derivatives (of integer order). The new formulas are valid for functions of class $C^n$, $n \in \mathbb{N}$, and allow us to…

We show that the module of integral points on a Drinfeld module satisfies a an analogue of Dirichlet's unit theorem, despite its failure to be finitely generated. As a consequence, we obtain a construction of a canonical finitely generated…

This paper introduces and investigates some properties of algebras constructed from the algebra of polynomials via derivation and integration operators using a process presented by Dzhumadildaev in a previous work. In particular, we…

Let F be a characteristic zero differential field with an algebraically closed field of constants, E be a no-new-constant extension of F by antiderivatives of F and let y1, ..., yn be antiderivatives of E. The antiderivatives y1, ..., yn of…

We study certain modules over the algebra of a Cartier divisor on a scheme. Using these modules, we present an inductive method for studying finite generation properties of algebras and modules. In the context of the minimal model program,…

We develop a theory of parafree augmented algebras similar to the theory of parafree groups and explore some questions related to the Parafree Conjecture. We provide an example of finitely generated parafree augmented algebra of infinite…

We develop a theory of integration over valued fields of residue characteristic zero. In particular we obtain new and base-field independent foundations for integration over local fields of large residue characteristic, extending results of…

We introduce and study algebraic dynamical systems generated by triangular systems of rational functions. We obtain several results about the degree growth and linear independence of iterates as well as about possible lengths of…

We prove, using a fixed point theorem in a Banach algebra, an existence result for a fractional functional differential equation in the Riemann-Liouville sense. Dependence of solutions with respect to initial data and an uniqueness result…

There has been a growing need to devise processes that can create comprehensive datasets in the world of Computer Algebra, both for accurate benchmarking and for new intersections with machine learning technology. We present here a method…

Using the example of Liouville theory, we show how the separation into left- and rightmoving degrees of freedom of a nonrational conformal field theory can be made explicit in terms of its integrable structure. The key observation is that…

This note presents techniques to analytically solve double integrals of the dilogarithmic type which are of great importance in the perturbative treatment of quantum field theory. In our approach divergent integrals can be calculated…

The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. The motivation to write this paper is an unpublished yet result of J.R.Gomez, B.A.Omirov on necessary and sufficient conditions…