Search

Abstract In this paper we briefly discuss Rings — an efficient lightweight library for commutative algebra. Polynomial arithmetic, GCDs, polynomial factorization and Gröbner bases are implemented with the use of modern asymptotically fast algorithms. Rings can be easily interacted or embedded in applications in high-energy physics and other research areas via a simple API with fully typed hierarchy of algebraic structures and algorithms for commutative algebra. The use of the Scala language brings a quite novel powerful, strongly typed functional programming model allowing to write short, expressive, and fast code for applications. At the same time Rings shows one of the best performances among existing software for algebraic calculations. Program summary Program Title: Rings Program Files doi: http://dx.doi.org/10.17632/2k79hftjy9.1 Licensing provisions: Apache 2.0 Programming language: Java, Scala Nature of problem: Fast methods for rational function arithmetic, simplification of polynomial expressions, Gröbner bases and other related computer algebra methods naturally arising in physical applications Solution method: Efficient implementation of modern asymptotically fast algorithms in Java language External routines: Java 8 and higher, Scala 2.11 or 2.12 Additional comments: project page: https://github.com/PoslavskySV/rings , documentation: http://rings.readthedocs.io/en/latest/ [ABSTRACT FROM AUTHOR]

A computation-oriented representation of uncertain kinetic systems is introduced and analysed in this paper. It is assumed that the monomial coefficients of the ODEs belong to a polytopic set, which defines a set of dynamical systems for an uncertain model. An optimization-based computation model is proposed for the structural analysis of uncertain models. It is shown that the so-called dense realization containing the maximal number of reactions (directed edges) is computable in polynomial time, and it forms a superstructure among all the possible reaction graphs corresponding to an uncertain kinetic model, assuming a fixed set of complexes. The set of core reactions present in all reaction graphs of an uncertain model is also studied. Most importantly, an algorithm is proposed to compute all possible reaction graph structures for an uncertain kinetic model. [ABSTRACT FROM AUTHOR]

Abstract: This work suggests a new analytical technique called the fractional homotopy analysis transform method (FHATM) for solving nonlinear homogeneous and nonhomogeneous time-fractional gas dynamics equations. The FHATM is an innovative adjustment in Laplace transform algorithm (LTA) and makes the calculation much simpler. The proposed technique solves the nonlinear problems without using Adomian polynomials and He’s polynomials which can be considered as a clear advantage of this new algorithm over decomposition and the homotopy perturbation transform method. In this paper, it can be observed that the auxiliary parameter , which controls the convergence of the HATM approximate series solutions, also can be used in predicting and calculating multiple solutions. This is a basic and more qualitative difference in analysis between HATM and other methods. The solutions obtained by the proposed method indicate that the approach is easy to implement and computationally very attractive. The proposed method is illustrated by solving some numerical examples. [Copyright &y& Elsevier]