Results 11 to 20 of about 373,144 (279)

Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]

Adv Intell Discov
This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
europepmc   +2 more sources

Counting algebraic numbers in short intervals with rational points

Журнал Белорусского государственного университета: Математика, информатика, 2019
In 2012 it was proved that real algebraic numbers follow a non­uniform but regular distribution, where the respective definitions go back to H. Weyl (1916) and A. Baker and W. Schmidt (1970).
Vasily I. Bernik, Friedrich Götze, Nikolai I. Kalosha   +2 more
doaj   +1 more source

Convert between neutrosophic complex numbers forms [PDF]

Neutrosophic Sets and Systems, 2023
Complex numbers have been studied in previous papers, but the papers did not deal with the conversion from algebraic form of a neutrosophic complex number form to exponential or trigonometric form and vice versa, and this prompted us to search for a ...
Yaser Ahmad Alhasan, Iqbal Ahmed Musa, Suliman Sheen   +2 more
doaj   +1 more source

Multiplicative dependence of cubic algebraic numbers

Lietuvos Matematikos Rinkinys, 2017
We provide an infinite family of cubic algebraic integers α such that the set {α + x | x ∈ Z} is multiplicatively dependent.
Paulius Drungilas, Linas Klimavičius
doaj   +1 more source

An Introduction to The Split-Complex Symbolic 2-Plithogenic Numbers [PDF]

Neutrosophic Sets and Systems, 2023
The objective of this paper is to combine split-complex numbers with symbolic 2-plithogenic numbers in one algebraic structure called split-complex symbolic 2-plithogenic real numbers.
Rama Asad Nadweh, Oliver Von Shtawzen, Ahmad Khaldi   +2 more
doaj  

On Leonardo Pisano Hybrinomials

Mathematics, 2021
A generalization of complex, dual, and hyperbolic numbers has recently been defined as hybrid numbers. In this study, using the Leonardo Pisano numbers and hybrid numbers we investigate Leonardo Pisano polynomials and hybrinomials.
Ferhat Kürüz, Ali Dağdeviren, Paula Catarino   +2 more
doaj   +1 more source

On Complex Numbers in Higher Dimensions

Axioms, 2022
The geometric approach to generalized complex and three-dimensional hyper-complex numbers and more general algebraic structures being based upon a general vector space structure and a geometric multiplication rule which was only recently developed is ...
Wolf-Dieter Richter
doaj   +1 more source

Axiomatics for the external numbers of nonstandard analysis [PDF]

, 2017
Neutrices are additive subgroups of a nonstandard model of the real numbers. An external number is the algebraic sum of a nonstandard real number and a neutrix.
Berg, Imme van den, Dinis, Bruno
core   +2 more sources

Investigating Students’ Understanding of Complex Number and Its Relation to Algebraic Group Using and APOS Theory

Journal of Medives: Journal of Mathematics Education IKIP Veteran Semarang, 2023
This study focused on students’ inability to correctly use psychometric tests applied for complex numbers in the context of generating an Algebraic abelian group (closure, commutative, associatively, inverse, and identity).
Idowu Oluwaseun Longe, Aneshkumar Maharaj   +1 more
doaj   +1 more source

Virtual Betti numbers of real algebraic varieties [PDF]

, 2002
The weak factorization theorem for birational maps is used to prove that for all nonnegative i the ith mod 2 Betti number of compact nonsingular real algebraic varieties has a unique extension to a "virtual Betti number" beta_i defined for all real ...
McCrory, Clint, Parusinski, Adam
core   +3 more sources