相关论文: Smarandache Sequences: Explorations and Discoverie…
We use the Maple system to check the investigations of S. S. Gupta regarding the Smarandache consecutive and the reversed Smarandache sequences of triangular numbers [Smarandache Notions Journal, Vol. 14, 2004, pp. 366-368]. Furthermore, we…
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 a proper subset one understands a set included in A,…
A Smarandache multi-space is a union of $n$ different spaces equipped with some different structures for an integer $n\geq 2$, which can be both used for discrete or connected spaces, particularly for geometries and spacetimes in…
We describe the computer algebra software package SpectralSequences for the computer algebra system Macaulay2. This package implements many data types, objects and algorithms which pertain to, among other things, filtered complexes,…
We report on experience with an investigation of the analytic structure of the solution of certain algebraic complex equations. In particular the behavior of their series expansions around the origin is discussed. The investigation imposes…
The present work has been designed for students in secondary school and their teachers in mathematics. We will show how with the help of our knowledge of number systems we can solve problems from other fields of mathematics for example in…
Generally the study of algebraic deals with the concepts like groups, semigroups, groupoids, loops, rings, near-rings, semirings and vector spaces. The study of bialgebraic structures deals with the study of bistructures like bigroups,…
In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.
In this book, we introduce the notion of Smarandache special definite algebraic structures. We can also call them equivalently as Smarandache definite special algebraic structures. These new structures are defined as those strong algebraic…
As dynamic and control systems become more complex, relying purely on numerical computations for systems analysis and design might become extremely expensive or totally infeasible. Computer algebra can act as an enabler for analysis and…
Computer algebra systems are a great help for mathematical research but sometimes unexpected errors in the software can also badly affect it. As an example, we show how we have detected an error of Mathematica computing determinants of…
What is Sequence Algebra? This is a question that any teacher or student of mathematics or computer science can engage with. Sequences are in Calculus, Combinatorics, Statistics and Computation. They are foundational, a step up from number…
I describe a method for computer algebra that helps with laborious calculations typically encountered in theoretical microhydrodynamics. The program mimics how humans calculate by matching patterns and making replacements according to the…
Collatz Conjecture sequences increase and decrease in seemingly random fashion. By identifying and analyzing the forms of numbers, we discover that Collatz sequences are governed by very specific, well-defined rules, which we call cascades.
We study convergence almost everywhere of sequences of Schr\"odinger means. We also replace sequences by uncountable sets.
This work connects two mathematical fields - computational complexity and interval linear algebra. It introduces the basic topics of interval linear algebra - regularity and singularity, full column rank, solving a linear system, deciding…
Over 300 sequences and many unsolved problems and conjectures related to them are presented herein together with theorems corollaries, formulae, examples, mathematical criteria, etc. (about integer sequences, numbers, quotients, residues,…
In this survey I should like to introduce some concepts of algebraic geometry and try to demonstrate the fruitful interaction between algebraic geometry and computer algebra and, more generally, between mathematics and computer science. One…
These lectures given to graduate students in theoretical particle physics, provide an introduction to the ``inner workings'' of computer algebra systems. Computer algebra has become an indispensable tool for precision calculations in…
We initiate the study of cortex algebras (commutative Banach algebras with extendable multiplicative-linear functionals) and the spectral permanence property. In addition, we analyze some particular examples in this context and present open…