Related papers: Smarandache Sequences: Explorations and Discoverie…
We examine the convergence properties of sequences of nonnegative real numbers that satisfy a particular class of recursive inequalities, from the perspective of proof theory and computability theory. We first establish a number of results…
Pairs of numerically computed trajectories of a chaotic system may coalesce because of finite arithmetic precision. We analyse an example of this phenomenon, showing that it occurs surprisingly frequently. We argue that our model belongs to…
These course notes are about computing modular forms and some of their arithmetic properties. Their aim is to explain and prove the modular symbols algorithm in as elementary and as explicit terms as possible, and to enable the devoted…
We study compositions whose parts are colored by subsequences of the Fibonacci numbers. We give explicit bijections between Fibonacci colored compositions and several combinatorial objects, including certain restricted ternary and…
We develop a random model for relation algebras. We prove some preliminary results and pose questions that lay out a new direction of research.
A combinatorial methods are used to investigate some properties of certain generalized Stirling numbers, including explicit formula and recurrence relations. Furthermore, an expression of these numbers with symmetric function is deduced.
Motivated by some recent developments in abstract theories of quadratic forms, we start to develop in this work an expansion of Linear Algebra to multivalued structures (a multialgebraic structure is essentially an algebraic structure but…
This paper investigates the behaviour of one of the most famous Smarandache's sequence given by A061076 on oeis. In particular we first study the behaviour of two sequences (A061077, A061078) strictly connected with the main Smarandache's…
A dual approach to defining the triangle sequence (a type of multidimensional continued fraction algorithm, initially developed in NT/9906016) for a pair of real numbers is presented, providing a new, clean geometric interpretation of the…
One emerging application of machine learning methods is the inference of galaxy cluster masses. In this note, machine learning is used to directly combine five simulated multiwavelength measurements in order to find cluster masses. This is…
In this paper, we define an ordering relation for a set of complex numbers, and research the properties and theorems of the ordering, solve some simple complex inequalities with the ordering.
The algebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief economic…
Sheaf cohomology or, more generally, higher direct images of coherent sheaves along proper morphisms are central to modern algebraic geometry. However, the computation of these objects is a non-trivial and expensive task which easily…
Mathematical information is essential for technical work, but its creation, interpretation, and search are challenging. To help address these challenges, researchers have developed multimodal search engines and mathematical question…
Algebraic statistics uses tools from algebra (especially from multilinear algebra, commutative algebra and computational algebra), geometry and combinatorics to provide insight into knotty problems in mathematical statistics. In this survey…
Generally, in any human field, a Smarandache Structure on a set A means a weak structure W on A such that there exists a proper subset B which is embedded with a stronger structure S. By proper subset one understands a set included in A,…
The Python package ComCH is a lightweight specialized computer algebra system that provides models for well known objects, the surjection and Barratt-Eccles operads, parameterizing the product structure of algebras that are commutative in a…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
Number sequences defined by a linear recursion relation are studied by means of generating functions. Indices of the terms in the recursion relation have arbitrary differenses. In addition to formulas for the nth term an algorithm is…
In this note, we propose a simple-looking but broad conjecture about star-algebras over the field of real numbers. The conjecture enables many matrix decompositions to be represented by star-algebras and star-ideals. This paper is written…