Mathematics in Computer Science
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Papers 713
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#1Amir Hashemi (IUT: Isfahan University of Technology)H-Index: 9
#2Matthias Orth (University of Kassel)
Last. Werner M. Seiler (University of Kassel)H-Index: 14
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We extend the concept of Grobner bases to relative Grobner bases for ideals in and modules over quotient rings of a polynomial ring over a field. We develop a “relative” variant of both Buchberger’s criteria for avoiding reductions to zero and Schreyer’s theorem for a Grobner basis of the syzygy module. As main contribution, we then introduce the novel notion of relative involutive bases and present an algorithm for their explicit construction. Finally, we define the new notion of relatively qua...
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#1Niclas Kruff (RWTH Aachen University)H-Index: 2
#2Christoph Lüders (University of Bonn)H-Index: 2
Last. Sebastian Walcher (RWTH Aachen University)H-Index: 21
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We present a symbolic algorithmic approach that allows to compute invariant manifolds and corresponding reduced systems for differential equations modeling biological networks which comprise chemical reaction networks for cellular biochemistry, and compartmental models for pharmacology, epidemiology and ecology. Multiple time scales of a given network are obtained by scaling, based on tropical geometry. Our reduction is mathematically justified within a singular perturbation setting using a rece...
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The computing Grid has emerged as a platform to solve the complex and ever-increasing processing need of man and advances in computing technology have birthed the multicore era aimed for high throughput and efficient parallel computing. However, most systems still rely on the underlying hardware for parallelism despite the hard evidence that sequential algorithms do not optimally exploit parallel systems. This research seeks to harness the benefits of multicore systems using job and machine grou...
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#1Dimitrios Vlachakis (UoA: National and Kapodistrian University of Athens)H-Index: 19
#2Panayiotis Vlamos (Ionian University)H-Index: 11
COVID19 is the most impactful pandemic of recent times worldwide. It is a highly infectious disease that is caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2 virus), To date there is specific drug nor vaccination against COVID19. Therefor the need for novel and pioneering anti-COVID19 is of paramount importance. In this direction, computer-aided drug design constitutes a very promising antiviral approach for the discovery and analysis of drugs and molecules with biological ac...
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In the recent past, results have shown that Nilpotent groups such as p-groups, have normal series of finite length. Any finite p-group has many normal subgroups and consequently, the phenomenon of large number of non-isomorphic subgroups of a given order. This makes it an ideal object for combinatorial and cohomological investigations. Cartesian product (otherwise known as the product set) plays vital roles in the course of synthesizing the abstract groups. Previous studies have determined the n...
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#1José Cano (University of Valladolid)H-Index: 2
#1José Miguel García Cano (University of Valladolid)H-Index: 35
Last. J. Rafael SendraH-Index: 22
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In this paper, we study the algebraic, rational and formal Puiseux series solutions of certain type of systems of autonomous ordinary differential equations. More precisely, we deal with systems which associated algebraic set is of dimension one. We establish a relationship between the solutions of the system and the solutions of an associated first order autonomous ordinary differential equation, that we call the reduced differential equation. Using results on such equations, we prove the conve...
1 CitationsSource
#1François BoulierH-Index: 13
#2François Lemaire (Laboratoire d'Informatique Fondamentale de Lille)H-Index: 12
Last. Adrien Poteaux (IRIA: French Institute for Research in Computer Science and Automation)H-Index: 9
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This paper contains short contributions to the theory of regular chains which follow a recent JSC paper by the same authors. These contributions apply to both the nondifferential and the differential context. They deal with the computation of normal forms and with the membership problem to ideals defined by regular chains.
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#1Youren Hu (CAS: Chinese Academy of Sciences)
#2Xiao-Shan Gao (CAS: Chinese Academy of Sciences)H-Index: 29
In this paper, the concept of tropical differential Grobner basis is introduced, which is a natural generalization of the tropical Grobner basis to the recently introduced tropical differential algebra. Like the differential Grobner basis, the tropical differential Grobner basis generally contains an infinite number of elements. We give a Buchberger style criterion for the tropical differential Grobner basis. For differential ideals generated by homogeneous linear differential polynomials with c...
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#1Shinichi Tajima (Niigata University)H-Index: 9
#2Katsusuke Nabeshima (University of Tokushima)H-Index: 7
The torsion module of Kahler differential forms is considered in the context of symbolic computation. Relations between logarithmic differential forms and logarithmic vector fields are investigated. As an application, an effective method is proposed for computing torsion differential forms associated with a hypersurface with an isolated singularity. The main ingredients of the proposed method are logarithmic vector fields and local cohomology.
1 CitationsSource
#1Dima Grigoriev (university of lille)H-Index: 28
#2Alexandru Iosif (RWTH Aachen University)H-Index: 3
Last. Andreas Weber (University of Bonn)H-Index: 36
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We consider the problem of testing whether the points in a complex or real variety with non-zero coordinates form a multiplicative group or, more generally, a coset of a multiplicative group. For the coset case, we study the notion of shifted toric varieties which generalizes the notion of toric varieties. This requires a geometric view on the varieties rather than an algebraic view on the ideals. We present algorithms and computations on 129 models from the BioModels repository testing for grou...
8 CitationsSource
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