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Notes on Number Theory

Mathematics
This paper presents a set of survey-style notes linking core themes of pure algebra with central topics in algebraic and analytic number theory. We begin with finite extensions of Q and describe algebraic number fields through their realization as finite-
Miroslav Stoenchev, Slavi Georgiev, Venelin Todorov   +2 more
doaj   +1 more source

New restricted and extended soft set operations: restricted gamma and extended gamma operations [PDF]

Big Data and Computing Visions
Soft set theory has been well-known as an innovative approach to managing uncertainty-related problems and modelling uncertainty since Molodtsov introduced it in 1999. It has been applied in a variety of contexts, both theoretical and practical. The core
Aslıhan Sezgin, Fitnat Aybek
doaj   +1 more source

New Algebraic Groups Produced By Graphical Passwords Based On Colorings And Labellings

MATEC Web of Conferences, 2017
Safety of plain text passwords has been questioned in current researching information passwords. Graphical passwords are another way for alternative text-based passwords and to improve the user account security.
Sun Hui, Zhang Xiaohui, Zhao Meimei, Yao Bing   +3 more
doaj   +1 more source

Split Quaternionic Representations of Horadam Sequences and Their Binet, Generating Function, and Cassini-Type Identities

Journal of Mathematics
This study establishes a novel algebraic connection between Horadam numbers and the split quaternion algebra. To this end, two fundamental constructs are introduced: the Fibonacci Sq,r-split quaternions and the Horadam sq,r-split quaternions, which ...
İskender Öztürk, Hasan Çakır
doaj   +1 more source

Exploring Gröbner bases for practical problem-solving applications [PDF]

Computational Algorithms and Numerical Dimensions
Gröbner bases serve as a crucial theoretical cornerstone in contemporary (polynomial) ring theory. The development of Gröbner basis theory originated from efforts to address theoretical issues related to ideals in polynomial rings and to solve systems of
Hamed Farahani
doaj   +1 more source

Cyclotomic Classes in a Product of Finite Abelian Groups and Applications

Journal of Mathematics
Cyclotomic classes of finite abelian groups have been extensively investigated for many decades, largely because of their nice algebraic structure and the breadth of their theoretical and practical applications.
Somphong Jitman
doaj   +1 more source

Enumeration of rooted 3-connected bipartite planar maps

Comptes Rendus. Mathématique
We provide the first solution to the problem of counting rooted 3-connected bipartite planar maps. Our starting point is the enumeration of bicoloured planar maps according to the number of edges and monochromatic edges, following Bernardi and Bousquet ...
Noy, Marc, Requilé, Clément, Rué, Juanjo   +2 more
doaj   +1 more source

x-y duality in topological recursion for exponential variables via quantum dilogarithm

SciPost Physics
For a given spectral curve, the theory of topological recursion generates two different families $\omega_{g,n}$ and $\omega_{g,n}^\vee$ of multi-differentials, which are for algebraic spectral curves related via the universal $x-y$ duality formula.
Alexander Hock
doaj   +1 more source

Algebraic structures of Vassiliev invariants for knot families

Nuclear Physics B
We explore algebraic relations on Vassiliev knot invariants related with correlators in the 3-dimensional Chern–Simons theory. Vassiliev invariants form infinite-dimensional algebra.
E. Lanina, A. Sleptsov
doaj   +1 more source

Theory of Algebraic Numbers

The American Mathematical Monthly, 2006
D. J. Lewis, Harry Pollard
openaire   +3 more sources