A generalization of the regular function modulo n

Authors: Basem Alkhamaiseh

Source: Boletim da Sociedade Paranaense de Matemática, Vol 42 (2024)

Subject Terms: Renormalization, Study of properties and structures of commutative rings, Deformations and Structures of Hom-Lie Algebras, Generalization, Factorization Theory, Symbolic Computing in Algebraic Geometry and Cryptography, Evolutionary biology, Mathematical analysis, 01 natural sciences, Numerical Algebraic Geometry, QA1-939, FOS: Mathematics, Modulo, 0101 mathematics, Biology, Algebra over a field, Algebra and Number Theory, Arithmetic, 4. Education, Modulo operation, Pure mathematics, 16. Peace & justice, Algorithm, Computational Theory and Mathematics, Function (biology), Combinatorics, Physical Sciences, Computer Science, Idealization, Mathematics, Symbolic Computing

Access URL: https://doaj.org/article/c1c6e79afae34fa8879cfd3bad297496

Characterizing absolutely irreducible integer-valued polynomials over discrete valuation domains

Authors: Moritz Hiebler, Sarah Nakato, Roswitha Rissner

Source: Journal of Algebra. 633:696-721

Subject Terms: Study of properties and structures of commutative rings, Monomial Ideals and Algebraic Properties, Factorization Theory, Symbolic Computing in Algebraic Geometry and Cryptography, Commutative Algebra (math.AC), Polynomial, Mathematical analysis, 01 natural sciences, Discrete valuation ring, Residue field, Discrete valuation, Field (mathematics), Irreducible polynomial, FOS: Mathematics, Factorization, 0101 mathematics, 13A05, 11S05, 11R09, 13B25, 13F20, 11C08, Algebra and Number Theory, Pure mathematics, Irreducibility, Discrete mathematics, Mathematics - Commutative Algebra, Algorithm, Matrix polynomial, Computational Theory and Mathematics, Combinatorics, Physical Sciences, Computer Science, Kernel (algebra), Mathematics

Access URL: http://arxiv.org/abs/2211.15981

Connected domination in graphs and v-numbers of binomial edge ideals

Authors: Delio Jaramillo, Lisa Seccia

Source: Collectanea Mathematica. 75:771-793

Subject Terms: Algebraic number, Monomial Ideals and Algebraic Properties, Domination analysis, Symbolic Computing in Algebraic Geometry and Cryptography, 0102 computer and information sciences, Commutative Algebra (math.AC), 01 natural sciences, Mathematical analysis, Graph, Upper and lower bounds, Algebraic Geometry and Moduli Theory, FOS: Mathematics, Mathematics - Combinatorics, 0101 mathematics, Algebra and Number Theory, Statistics, Edge Ideals, Discrete mathematics, Mathematics - Commutative Algebra, Vertex (graph theory), Binomial (polynomial), Computational Theory and Mathematics, Combinatorics, Physical Sciences, Computer Science, Combinatorics (math.CO), Geometry and Topology, 05E40, 13P10, 13P25 (Primary), 05C69, 68M10 (Secondary), Mathematics

Access URL: http://arxiv.org/abs/2304.04898

Compact formula for skew-symmetric system of matrix equations

Authors: Abdur Rehman, Ivan Kyrchei

Source: Arabian Journal of Mathematics. 12:587-600

Subject Terms: Composite material, Convex Optimization, Matrix (chemical analysis), Moore–Penrose pseudoinverse, Geometry, Symbolic Computing in Algebraic Geometry and Cryptography, Skew, Hermitian matrix, 01 natural sciences, Field (mathematics), FOS: Mathematics, 0101 mathematics, Matrix Algorithms and Iterative Methods, Numerical Analysis, Algebra over a field, Chromatography, Numerical Optimization Techniques, 4. Education, Complex matrix, Pure mathematics, Applied mathematics, 16. Peace & justice, Computer science, Materials science, Algorithm, Chemistry, Computational Theory and Mathematics, Computer Science, Physical Sciences, Telecommunications, Inverse, Mathematics, Matrix Computations

Geometric aspects on Humbert-Edge curves of type 5, Kummer surfaces and hyperelliptic curves of genus 2

Authors: Abel Castorena, Juan Bosco Frías-Medina

Source: Glasgow Mathematical Journal. 65:612-624

Subject Terms: Geometry, Symbolic Computing in Algebraic Geometry and Cryptography, Diagonal, Moduli space, 01 natural sciences, Mathematics - Algebraic Geometry, Isomorphism (crystallography), Hyperelliptic curve, Engineering, Algebraic Geometry and Moduli Theory, Tropical Geometry, FOS: Mathematics, 0101 mathematics, Biology, Algebraic Geometry (math.AG), Mathematical Physics, Symmetric Spaces, Crystallography, Genus, Ecology, Crystal structure, Pure mathematics, Botany, Symplectic Geometry, Chemistry, Aerospace engineering, 14H45, 14H37, 14H10, Computational Theory and Mathematics, Combinatorics, FOS: Biological sciences, Physical Sciences, Computer Science, Proofs of Langlands Conjectures for GL(n), Geometry and Topology, Intersection (aeronautics), Type (biology), Mathematics

Access URL: http://arxiv.org/abs/2106.00813

On power integral bases of certain pure number fields defined by $x^{84}-m$

Authors: Lhoussain El Fadil, Mohamed Faris

Source: Revista de la Unión Matemática Argentina. :197-211

Subject Terms: Computational Theory and Mathematics, Algebraic Geometry and Moduli Theory, Bifurcations in Planar Polynomial Systems, Physics, Physical Sciences, Computer Science, FOS: Mathematics, Nilpotent Singularity, Thermodynamics, Symbolic Computing in Algebraic Geometry and Cryptography, Geometry and Topology, Power (physics), Mathematics

Complete Bell Polynomials and Recurrence Relations for Arithmetic Functions

Authors: R. Sivaraman, J. D. Bulnes, José Luis López Bonilla

Source: European Journal of Theoretical and Applied Sciences. 1:167-170

Subject Terms: Relation (database), Difference polynomials, Orthogonal polynomials, Combinatorial Mathematics and Algebraic Combinatorics, Symbolic Computing in Algebraic Geometry and Cryptography, 01 natural sciences, Database, Fuzzy Logic and Residuated Lattices, FOS: Mathematics, Discrete Mathematics and Combinatorics, 0101 mathematics, Bell polynomials, Algebra over a field, Arithmetic, Polynomial Systems, Pure mathematics, Recurrence relation, Discrete mathematics, Computer science, Programming language, Computational Theory and Mathematics, Combinatorics, Physical Sciences, Computer Science, Integer (computer science), Mathematics

The Impact of Compilation Flags and Choosing Single- or Double-Precision Variables in Linear Systems Solvers

Authors: Rafaela C. Brum, Maria Clícia Stelling de Castro, Cristiane Oliveira de Faria

Source: Trends in Computational and Applied Mathematics. 24:319-335

Subject Terms: Convex Optimization, Compiler, Symbolic Computing in Algebraic Geometry and Cryptography, Quantum mechanics, 01 natural sciences, 0103 physical sciences, FOS: Mathematics, Biology, Eigenvalues and eigenvectors, Numerical Analysis, Decomposition, Nonlinear Programming, Numerical Optimization Techniques, Ecology, Physics, Orthogonalization, Computer science, Programming language, Algorithm, Computational Theory and Mathematics, FOS: Biological sciences, Computer Science, Physical Sciences, Derivative-Free Optimization, Gaussian, Gaussian elimination, Cholesky decomposition, Mathematics, Symbolic Computing, Sum of Squares Techniques

Iterated and mixed discriminants

Authors: Alicia Dickenstein, Sandra Di Rocco, Ralph Morrison

Source: CONICET Digital (CONICET)
Consejo Nacional de Investigaciones Científicas y Técnicas

Subject Terms: ALGEBRAIC VARIETIES, Artificial intelligence, DISCRIMINANTS, Computational Mechanics, ITERATED DISCRIMINANT, Geometry, Symbolic Computing in Algebraic Geometry and Cryptography, Quadric, Mathematical analysis, 01 natural sciences, Mathematics - Algebraic Geometry, Engineering, POLYNOMIAL SYSTEMS, Codimension, FOS: Mathematics, 0101 mathematics, MIXED DISCRIMINANT, Isogeometric Analysis in Computational Engineering, Algebraic Geometry (math.AG), Tangent, Multivariate Polynomials, Pure mathematics, SEGRE-VERONESE VARIETIES, Computer science, Computational Theory and Mathematics, Combinatorics, Computer Science, Physical Sciences, Tangent space, DUAL VARIETY, Iterated function, Mathematics, Discriminant

File Description: application/pdf

Access URL: http://arxiv.org/abs/2101.11571
http://hdl.handle.net/11336/226860

A semigroup defining the Gröbner degeneration of a toric ideal

Authors: Casillas, Hernán de Alba, Duarte, Daniel, Antuna, Raúl Vargas

Source: Semigroup Forum. 106:569-588

Subject Terms: Algebraic number, Monomial Ideals and Algebraic Properties, Computational Mechanics, Semigroup, Symbolic Computing in Algebraic Geometry and Cryptography, Epistemology, Commutative Algebra (math.AC), Mathematical analysis, Engineering, Betti number, FOS: Mathematics, Mathematics - Combinatorics, Isogeometric Analysis in Computational Engineering, Ideal (ethics), Algebra over a field, Algebra and Number Theory, Toric Algebra, Pure mathematics, Discrete mathematics, Mathematics - Commutative Algebra, FOS: Philosophy, ethics and religion, Philosophy, Computational Theory and Mathematics, Physical Sciences, Computer Science, Combinatorics (math.CO), Uniqueness, Mathematics

Access URL: http://arxiv.org/abs/2201.04220

Nash blowups of toric varieties in prime characteristic

Authors: Daniel Duarte, Jack Jeffries, Luis Núñez-Betancourt

Source: Collectanea Mathematica. 75:629-637

Subject Terms: Prime characteristic, Combinatorial Topology, Nash blowup, Monomial Ideals and Algebraic Properties, Resolution of singularities, Variety (cybernetics), Symbolic Computing in Algebraic Geometry and Cryptography, 01 natural sciences, Mathematical analysis, Mathematics - Algebraic Geometry, Algebraic Geometry and Moduli Theory, Prime (order theory), FOS: Mathematics, 0101 mathematics, Algebraic Geometry (math.AG), Jacobian matrix and determinant, Algebra and Number Theory, Toric variety, Applied Mathematics, Statistics, Pure mathematics, Toric varieties, Gravitational singularity, Applied mathematics, Dimension (graph theory), Computational Theory and Mathematics, Combinatorics, Physical Sciences, Computer Science, Geometry and Topology, Mathematics

File Description: application/pdf

Access URL: http://arxiv.org/abs/2208.05599

A Primal-Dual Interior-Point Algorithm Based on a Kernel Function with a New Barrier Term

Authors: Safa Guerdouh, Wided Chikouche, İmene Touil

Source: Statistics, Optimization & Information Computing. 11:773-784

Subject Terms: Economics, Symbolic Computing in Algebraic Geometry and Cryptography, Evolutionary biology, Mathematical analysis, Quantum mechanics, Term (time), Upper and lower bounds, Interior-Point Methods, Eigenvalue Problems, FOS: Mathematics, Interior point method, Biology, Economic growth, Matrix Algorithms and Iterative Methods, Numerical Analysis, Numerical Optimization Techniques, Physics, 4. Education, Exponential function, Discrete mathematics, 16. Peace & justice, Algorithm, Computational Theory and Mathematics, Combinatorics, Function (biology), Physical Sciences, Computer Science, Derivative-Free Optimization, Convergence (economics), Kernel (algebra), Iterative Methods, Mathematics, Matrix Computations

The effective monoids of some blow-ups of Hirzebruch surfaces

Authors: Gloria Andablo-Reyes, Brenda Leticia De La Rosa-Navarro, Mustapha Lahyane

Source: Arabian Journal of Mathematics. 12:601-612

Subject Terms: Algebra and Number Theory, Monomial Ideals and Algebraic Properties, 4. Education, Motivic Cohomology, Geometry, Symbolic Computing in Algebraic Geometry and Cryptography, Computer science, Algorithm, Computational Theory and Mathematics, Algebraic Geometry and Moduli Theory, Physical Sciences, Computer Science, FOS: Mathematics, Geometry and Topology, Surface (topology), Mathematics

Public key exchange protocols based on tropical lower circulant and anti circulant matrices

Authors: B. Amutha, R. Perumal

Source: AIMS Mathematics, Vol 8, Iss 7, Pp 17307-17334 (2023)

Subject Terms: Alternative medicine, Semiring, lower-$ s $-circulant matrix, Circulant matrix, Encryption, Symbolic Computing in Algebraic Geometry and Cryptography, Mathematical analysis, Upper and lower bounds, anti-$ s $-$ p $-circulant matrix, key exchange protocol, tropical semiring, Artificial Intelligence, Computer security, tropical cryptography, QA1-939, FOS: Mathematics, Pathology, Key exchange, Key (lock), Cryptography and Error-Correcting Codes, Pairing-based Cryptography, Computer network, Advanced Cryptographic Schemes and Protocols, Discrete mathematics, Public-key cryptography, Computer science, Computational Theory and Mathematics, Combinatorics, Computer Science, Physical Sciences, Protocol (science), Medicine, Mathematics

Access URL: https://doaj.org/article/583a49316a9d4930acefe676e7b9afa7

Solving singular equations of length eight over torsion-free groups

Authors: Mairaj Bibi, Saqib Ali, Muhammad Shoaib Arif, Kamaleldin Abodayeh

Source: AIMS Mathematics, Vol 8, Iss 3, Pp 6407-6431 (2023)

Subject Terms: relative presentation, Bifurcations in Planar Polynomial Systems, star graph, Symbolic Computing in Algebraic Geometry and Cryptography, weight test, 01 natural sciences, Torsion (gastropod), torsion free group, Computational Theory and Mathematics, Mathematical physics, Physical Sciences, Computer Science, 0103 physical sciences, QA1-939, FOS: Mathematics, Abelian Integrals, Medicine, Geometry and Topology, Anatomy, 0101 mathematics, Mathematics, Foundations of Geometric Mathematics

Access URL: https://doaj.org/article/7cd599ac058a42f28876943fee07af73

The 'Elliptic' matrices and a new kind of cryptography

Authors: Zakariae Cheddour, Abdelhakim Chillali, Ali Mouhib

Source: Boletim da Sociedade Paranaense de Matemática, Vol 41 (2022)

Subject Terms: FOS: Computer and information sciences, Encryption, Symbolic Computing in Algebraic Geometry and Cryptography, Artificial Intelligence, Computer security, Prime (order theory), Elliptic curve, QA1-939, FOS: Mathematics, Cryptography and Error-Correcting Codes, Algebra over a field, 4. Education, Pure mathematics, Finite field, Discrete mathematics, Public-key cryptography, Computer science, Elliptic curve cryptography, Algorithm, Computational Theory and Mathematics, Combinatorics, Applications of Elliptic Curve Cryptography in Security, Computer Science, Physical Sciences, Cryptography, Mathematics, Block (permutation group theory), Information Systems

Access URL: https://doaj.org/article/0969b32389e84a198136ccded49d0244

Univariate rational sums of squares

Authors: Teresa Krick, Bernard Mourrain, Ágnes Szántó

Contributors: Mourrain, Bernard

Source: Revista de la Unión Matemática Argentina. :215-237

Subject Terms: Sum of Squares, Computational Mechanics, Symbolic Computing in Algebraic Geometry and Cryptography, 0102 computer and information sciences, Polynomial, Mathematical analysis, 01 natural sciences, Mathematics - Algebraic Geometry, Engineering, Prime (order theory), Univariate, FOS: Mathematics, Modulo, Positive polynomials, Convex cone, 0101 mathematics, Floating-Point Arithmetic in Scientific Computation, Isogeometric Analysis in Computational Engineering, Algebraic Geometry (math.AG), Exact computation, Arithmetic, Multivariate Polynomials, Zero (linguistics), Statistics, [MATH.MATH-AG] Mathematics [math]/Algebraic Geometry [math.AG], Rational function, Pure mathematics, Linguistics, Discrete mathematics, Multivariate statistics, FOS: Philosophy, ethics and religion, Semi-Definite Matrix, Certificate, Philosophy, Real roots, Computational Theory and Mathematics, Explained sum of squares, Combinatorics, Computer Science, Physical Sciences, FOS: Languages and literature, Mathematics

File Description: application/pdf

Access URL: http://arxiv.org/abs/2112.00490
https://hal.science/hal-03442193v2/document
https://doi.org/10.33044/revuma.2904
https://hal.science/hal-03442193v2

A novel geometric method based on conformal geometric algebra applied to the resection problem in two and three dimensions

Authors: Jorge Rafael Montesó Ventura, Fernando Martínez, Francisco Manzano‐Agugliaro, Aleš Návrat, Jaroslav Hrdina, Ahmad H. Eid, Francisco Manzano-Agugliaro

Source: Journal of Geodesy. 98

Subject Terms: Deformations and Structures of Hom-Lie Algebras, Snellius-Pothenot, Geometry, Symbolic Computing in Algebraic Geometry and Cryptography, Triangulation, 01 natural sciences, Geometric algebra, Numerical Algebraic Geometry, Tropical Geometry, 0103 physical sciences, FOS: Mathematics, 0105 earth and related environmental sciences, Algebra over a field, Algebra and Number Theory, Applied Mathematics, Pure mathematics, Resection problem, Geometric Algebra, Quaternionic Analysis and Applications, Computational Theory and Mathematics, Physical Sciences, Computer Science, Algebra representation, Conformal map, Universal geometric algebra, Mathematics, Conformal geometric algebra

File Description: text; application/pdf

Access URL: http://hdl.handle.net/11012/249518

Équation de Pell–Abel et applications

Authors: Gendron, Quentin

Source: Comptes Rendus. Mathématique, Vol 360, Iss G9, Pp 975-992 (2022)

Subject Terms: Economics, Hyperelliptic curve cryptography, Encryption, Symbolic Computing in Algebraic Geometry and Cryptography, Mathematical analysis, 01 natural sciences, Hyperelliptic curve, Algebraic Geometry and Moduli Theory, QA1-939, FOS: Mathematics, Modulo, 0101 mathematics, Degree (music), Biology, Order (exchange), Algebraic Varieties, Algebra over a field, Genus, Bifurcations in Planar Polynomial Systems, Physics, Zero (linguistics), Pure mathematics, Botany, Linguistics, Fixed point, Acoustics, Discrete mathematics, Public-key cryptography, Computer science, FOS: Philosophy, ethics and religion, Elliptic curve cryptography, Philosophy, Operating system, Computational Theory and Mathematics, Combinatorics, Physical Sciences, Computer Science, FOS: Languages and literature, Geometry and Topology, Mathematics, Finance

Access URL: https://doaj.org/article/57d13653937c4008b1bc455d82b90bcd

The constant solution method for solving large scale differential Sylvester matrix equations with time invariant coefficients

Authors: Abderrahman Bouhamidi, Lakhdar Elbouyahyaoui, Mohammed Heyouni

Source: Numerical Algorithms. 96:449-488

Subject Terms: Composite material, Sylvester's law of inertia, Matrix (chemical analysis), Symmetric matrix, Symbolic Computing in Algebraic Geometry and Cryptography, Mathematical analysis, Quantum mechanics, Polynomial, Differential equation, Numerical Integration Methods for Differential Equations, FOS: Mathematics, Differential algebraic equation, Linear differential equation, Matrix Algorithms and Iterative Methods, Eigenvalues and eigenvectors, Numerical Analysis, Exact differential equation, Physics, 4. Education, Sylvester matrix, Matrix exponential, Applied mathematics, Materials science, Sylvester equation, Matrix polynomial, Computational Theory and Mathematics, Matrix differential equation, Computer Science, Physical Sciences, Polynomial matrix, Time-Stepping Schemes, Universal differential equation, Mathematics, Ordinary differential equation