Modalities for an Allegorical Conceptual Data Model by Bartosz Zieliński, Paweł Maślanka, Ścibor Sobieski

“…Mathematically, our work demonstrates how to enrich with modal operators and to give a many world semantics to an abstract algebraic logic framework. We also give some examples of applications of the modal extension.…”
Get full text

Polite Combination of Algebraic Datatypes by Sheng, Ying, Zohar, Yoni, Ringeissen, Christophe, Lange, Jane, Fontaine, Pascal, Barrett, Clark

“…Abstract Algebraic datatypes, and among them lists and trees, have attracted a lot of interest in automated reasoning and Satisfiability Modulo Theories (SMT). …”
Get full text

18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics, Fall 2005 by Johnson, Steven G., 1973-

“…Emphasis is placed on abstract algebraic approaches rather than detailed solutions of partial differential equations, the latter being done by computers.…”
Get full text

Classification of Robinson-Trautman and Kundt geometries with Large D limit by Pınar Kirezli

“…Abstract Algebraic classification of higher dimensional, shear-free, twist-free, expanding (or non-expanding) spacetime is studied with the limit of D → ∞. …”
Get full text

Integrating the Case Studies Pedagogy and the Anthropological Theory of Didactics to Enhance the Teaching and Learning of Algebra in Undergraduate STEM Education by José Luis Díaz

“…This article emphasizes the power of real-world scenarios and active pedagogy, a student-centered approach that makes abstract algebraic ideas tangible. The Anthropological Theory of Didactics (ATD) is spotlighted as a perspective that treats mathematical knowledge as a cultural artifact, embedding mathematics concepts deeply within cultural and historical contexts. …”
Get full text

Concrete–Representational–Abstract (CRA) Instructional Approach in an Algebra I Inclusion Class: Knowledge Retention Versus Students’ Perception by Sherri K. Prosser, Stephen F. Bismarck

“…Implications include increased use of manipulatives to teach abstract algebraic topics to support students’ conceptual understanding and destigmatizing the use of manipulatives in secondary mathematics classrooms.…”
Get full text

Kinematic Hopf algebra for amplitudes from higher-derivative operators by Gang Chen, Laurentiu Rodina, Congkao Wen

“…In particular, the kinematic algebraic structure is unaltered and the derivative corrections only arise when mapping the abstract algebraic generators to physical BCJ numerators. …”
Get full text

Spectral resolutions in effect algebras by Anna Jenčová, Sylvia Pulmannová

“…Effect algebras were introduced as an abstract algebraic model for Hilbert space effects representing quantum mechanical measurements. …”
Get full text

Irreducible representations of some finite groups and galois stability of integral representations by Yahya, Zainab

“…A representation makes an abstract algebraic object more concrete by describing its elements by matrices and the algebraic operations in terms of matrix addition and matrix multiplication. …”
Get full text

On degenerations and invariants of low-dimensional complex nilpotent Leibniz algebra by Mohamed, Nurul Shazwani, Said Husain, Sharifah Kartini, Yunos, Faridah

“…Throughout the paper we are dealing with mathematical background with abstract algebraic structures. The present paper is devoted to the degenerations of low-dimensional nilpotent Leibniz algebras over the field of complex numbers. …”
Get full text

Comparison Between Algebraic Cryptanalysis on DES and NTRU by Fadila Paradise, Kiki Ariyanti Sugeng

“…Abstract Algebraic cryptanalysis is a cryptanalysis method that aims to exploit the algebraic structure of an encryption algorithm to obtain the secret key. …”
Get full text

Fusion action systems by Matthew J.K. Gelvin. by Gelvin, Matthew J. K. (Matthew Justin Karcher)

Get full text

Identical relations in simple groups by Oates, S

“…Birkhoff, contained in his paper "On the Structure of Abstract Algebras", Proc. Cam. Phil. Soc. 31 (1935) 433-454, we have that there is a one-one correspondence between varieties of groups and closed sets of identical relations.…”

On degenerations and invariants of low-dimensional complex nilpotent Leibniz algebras by Mohamed, Nurul Shazwani, Said Husain, Sharifah Kartini, Yunos, Faridah

“…Throughout the paper we are dealing with mathematical background with abstract algebraic structures. The present paper is devoted to the degenerations of low-dimensional nilpotent Leibniz algebras over the field of complex numbers. …”
Get full text