Article
Mathematics, Applied
F. Guillen-Gonzalez, G. Tierra
Summary: This work focuses on designing and studying efficient and accurate numerical schemes to approximate a chemo-attraction model with consumption effects. Various finite element schemes are presented and their properties, such as cell conservation, energy-stability, and approximated positivity, are detailed. Numerical simulations are conducted to study the efficiency of each scheme and compare them with other classical schemes.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Bingru Huang, Falai Chen
Summary: This paper studies the stability of the dimension of the Sd(J) spline space with bi-degree (d, d) over a T-mesh J. The stability of the dimension is shown to depend on the rank stability of a matrix M corresponding to the multi-vertices of the non-diagonalizable component of J. Due to its smaller size, the stability of M is easier to verify compared to the conformality matrix associated with the T-connected component. As an application, the stability of the spline space S3(J) dimension is re-proven for a T-mesh generated by subdividing a collection of 2 x 2 submeshes of a tensor product mesh under cross subdivision.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Zahid Rasheed, Hongying Zhang, Syed Masroor Anwar, Muhammad Noor-ul-Amin, Nurudeen A. Adegoke, Saddam Akber Abbasi
Summary: This study evaluates fourteen distinct ranked-set sampling methodologies and finds that modified neoteric ranked-set sampling consistently outperforms other techniques in all tested scenarios. The results suggest the potential of ranked-set sampling approaches for enhancing process monitoring mechanisms.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Jing Zhang, Hongxing Rui
Summary: A combined Galerkin and mixed finite element method is proposed to analyze fully coupled nonlinear thermo-poroelastic model problems. The method utilizes Galerkin finite element method for temperature, mixed finite element method for pressure, and Galerkin finite element method for elastic displacement. The stability and convergence of the method are obtained, and optimal error estimates are proved without certain extra restrictions on both time step and spatial meshes.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Marjeta Knez, Francesca Pelosi, Maria Lucia Sampoli
Summary: This paper addresses the problem of constructing spatial G2 continuous Pythagorean-hodograph (PH) spline curves that interpolate points and frame data with the prescribed arc length. The proposed interpolation scheme is completely local and suitable for motion design applications. The paper presents a direct generalization of the construction done for planar curves to spatial ones by using an automatic procedure for computing the frame and velocity quaternions. Several numerical examples are provided to demonstrate the effectiveness of the proposed method.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS
(2024)
Article
Mathematics, Applied
Yves Baudelaire Fomatati
Summary: This paper improves the algorithm for matrix factorization of polynomials, obtaining better results by refining the construction of one of the main ingredients of the algorithm.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Computer Science, Theory & Methods
Yulia Alexandr, Serkan Hosten
Summary: In this study, the theory of logarithmic Voronoi cells is extended to Gaussian statistical models. The properties of logarithmic Voronoi cells are analyzed for models of ML degree one and linear covariance models. The decomposition theory of logarithmic Voronoi cells is introduced for the latter family. The characteristics of logarithmic Voronoi cells in covariance models are also studied.
JOURNAL OF SYMBOLIC COMPUTATION
(2024)
Article
Mathematics, Applied
Mikhailo Dokuchaev, Itailma Rocha
Summary: In this study, we construct an abelian group C(Theta/R) formed by the isomorphism classes of partial generalized crossed products related to a unital partial representation Theta of a group G into the Picard semigroup PicS(R) of a non-necessarily commutative unital ring R. We identify an appropriate second partial cohomology group of G with a naturally defined subgroup C0(Theta/R) of C(Theta/R). Using these results, we generalize the works by Kanzaki and Miyashita by giving an analogue of the Chase-Harrison-Rosenberg exact sequence associated with an extension of rings and a unital partial representation of an arbitrary group into the monoid of R-subbimodules.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Alexei Entin, Noam Pirani
Summary: This paper proves the existence of a Galois extension with ramification only at infinity for symmetric and alternating groups over finite fields of odd characteristic.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Computer Science, Theory & Methods
Elisa Gorla, Flavio Salizzoni
Summary: The MacWilliams' Extension Theorem, proposed by Florence Jessie MacWilliams, investigates the extension of linear isometries between linear block-codes to linear isometries of the ambient space. This paper explores the applicability of this theorem to rank-metric codes, providing examples and results.
JOURNAL OF SYMBOLIC COMPUTATION
(2024)
Article
Mathematics, Applied
Isaac Moselle
Summary: We demonstrate the homological stability for the family of Iwahori-Hecke algebras of type Bn, where homology is recognized by the relevant Tor group. This family of algebras is linked to the Coxeter groups of type Bn, which are groups of signed permutations. This result extends Hepworth's findings for Iwahori-Hecke algebras of type An.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Computer Science, Theory & Methods
Julia Lindberg, Jose Israel Rodriguez
Summary: In this paper, we investigate the Shor relaxation of quadratic programs by fixing a feasible set and examining the space of objective functions for which the Shor relaxation is exact. We establish conditions for the invariance of this region under the choice of generators defining the feasible set and describe its characteristics when the feasible set is invariant under the action of a subgroup of the general linear group. Furthermore, we apply these findings to quadratic binary programs and present an algorithm that generates candidate solutions based on an explicit description of objective functions where the Shor relaxation is exact.
JOURNAL OF SYMBOLIC COMPUTATION
(2024)
Article
Mathematics, Applied
Dmitri Pavlov
Summary: We prove that categories enriched in the Thomason model structure have a model structure that is Quillen equivalent to the Bergner model structure on simplicial categories, providing a new model for (infinity, 1)-categories. In addition, we construct model structures on modules and monoids in the Thomason model structure and prove that any model structure on the category of small categories that has the same weak equivalences as the Thomason model structure is not a cartesian model structure.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Markus Thuresson
Summary: Hereditary algebras are quasi-hereditary and exhibit certain regularity properties with respect to adapted partial orders. This article investigates the Ext-algebra of standard modules over path algebras of linear quivers and provides necessary and sufficient conditions for regular exact Borel subalgebras. The findings have implications for the understanding of linear quivers with arbitrary orientations.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
Edward L. Green, Sibylle Schroll
Summary: This paper studies the ideal C in the path algebra KQ, proving that KQ/C is always finite dimensional with finite global dimension, and it is Morita equivalent to an incidence algebra.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Computer Science, Theory & Methods
Martin Helmer, Elias Tsigaridas
Summary: We propose a probabilistic algorithm to test if a homogeneous polynomial ideal I defining a scheme X in Pn is radical. This algorithm utilizes Segre classes and other geometric notions from intersection theory and is applicable for certain classes of ideals. The algorithm terminates successfully with singly exponential complexity in n except in cases where all isolated primary components of X are reduced and there are no embedded root components outside of the singular locus of Xred = V(I), in which case it is unable to decide radically.
JOURNAL OF SYMBOLIC COMPUTATION
(2024)
Article
Mathematics, Applied
Adeel A. Khan
Summary: This paper constructs a cdh-local motivic homotopy category SHcdh(S) over an arbitrary base scheme S, and shows that there is a canonical equivalence SHcdh(S) similar to or equal to SH(S).
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Automation & Control Systems
Yihao Xu, Alexandre Seuret, Kun Liu, Senchun Chai
Summary: The recent literature on event-triggered control has shown the potential of dynamic periodic event-triggered control. The benefit of considering periodic event-triggered control is to avoid the Zeno phenomenon. This paper proposes a generic framework to emulate aperiodic dynamic event-triggered control law and relaxes the constraint on the periodicity of the allowable sampling instants.
NONLINEAR ANALYSIS-HYBRID SYSTEMS
(2024)
Article
Mathematics, Applied
Cordian Riener, Robin Schabert
Summary: This article focuses on the geometry of a class of hyperbolic polynomial families determined by linear conditions on the coefficients. These polynomials have all their roots on the real line. The set of hyperbolic polynomials is stratified according to the multiplicities of the real zeros, and this stratification also applies to the hyperbolic slices. The study shows that the local extreme points of hyperbolic slices correspond to hyperbolic polynomials with at most k distinct roots, and that the convex hull of such a family is generally a polyhedron. The article also explores the implications of these results for symmetric real varieties and symmetric semi-algebraic sets, particularly in terms of sparse representations and sampling.
JOURNAL OF PURE AND APPLIED ALGEBRA
(2024)
Article
Mathematics, Applied
He-Xia Ni, Li-Yuan Wang
Summary: In this paper, we investigate q-congruences on double basic hypergeometric sums and confirm several conjectures proposed by Zhi-Wei Sun using the 'creative microscoping' method and summation and transformation formulas for basic hypergeometric series.
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
(2024)
