Research ArticleOpen accessIn the keywordsNumber of Non-Unique Minors (of Various Orders) and Elements in the Calculation of General DeterminantsPatrick Marchisella, Gurudeo Anand TularamProblem statement: Many distinct properties of determinants have been studied and are known, yet a considerable number of properties still need further examination. This study investigates the number of minors (of various orders) and elements of a matrix A contained in the expansion of the general determinant of A, irrespective of the independence, principality and distinctness of such minors and … …Journal of Mathematics and Statistics, Vol. 8, Issue 3 · 13 Oct 2012 · 7,432 accessesView PDFCite
Research ArticleOpen accessIn the keywordsThe Importance of Numbers and the Need to Study Primes: The Prime QuestionsMatthew Curtis, Gurudeo A. TularamProblem statement: The study of prime numbers is important today as it was in ancient times. The level of interest in any form of mathematics of students in Australian high schools is decreasing and furthermore the level of interest in number theory is also less that it was before; prime numbers is not being considered as an area of interest … …Journal of Mathematics and Statistics, Vol. 7, Issue 4 · 14 Sep 2011 · 9,656 accessesView PDFCite
Research ArticleOpen accessIn the abstractIterative Feedforward Control for Bearing-Free Multibody SystemsNicola Y. Bailey, Christopher Lusty, Patrick S. KeoghAutomated machinery and robotics are commonly conventional multibody systems containing bearing components, which exhibit uncertain, discontinuous and complex tribological characteristics. These generate wear and fundamentally limit the precision of small scale motion due to the tribological effects being difficult to compensate for using model-based active control. However, they can be eliminated through the replacement of traditional bearing joints with flexure … …Journal of Mechatronics and Robotics, Vol. 5, Issue 1 · 6 Dec 2021 · 6,477 accessesView PDFCite
Research ArticleOpen accessIn the abstractConstructing Gibbs Measure in a Rigorous WayFarida Kachapova, Ilias KachapovEquilibrium statistical mechanics studies mathematical models for physical systems with many particles interacting with an external force and with one another. In this paper we describe an interaction model that generalizes several of these models in one model. An infinite model is constructed as the limiting case of finite interaction models, that is as a thermodynamic limit. The key point … …Journal of Mathematics and Statistics, Vol. 15, Issue 1 · 29 Oct 2019 · 6,591 accessesView PDFCite
Research ArticleOpen accessIn the abstractFormalizing Probability Concepts in a Type TheoryFarida KachapovaIn this paper we formalize some fundamental concepts of probability theory such as the axiomatic definition of probability space, random variables and their characteristics, in the Calculus of Inductive Constructions, which is a variant of type theory and the foundation for the proof assistant COQ. In a type theory every term and proposition should have a type, so in our … …Journal of Mathematics and Statistics, Vol. 14, Issue 1 · 12 Nov 2018 · 8,547 accessesView PDFCite
Research ArticleOpen accessIn the abstractDevelopment of Priority Oriented Scheduling Method to Increase the Reliability of Manufacturing SystemsSeyedehfarzaneh Nojabaei, Z. Leman, S. H. Tang, S. SulaimanScheduling occurs in every organization without considering the nature of its activities. In this regard, numerous scholars have attempted to schedule via divergent methods including classical scheduling, genetic algorithm, neural network and fuzzy logic and so on. Studies in manufacturing scheduling mostly deal with priority rules without any consideration of the system states. An appropriate scheduling leads to significant enhancement … …American Journal of Applied Sciences, Vol. 9, Issue 9 · 31 Jul 2012 · 7,015 accessesView PDFCite
Research ArticleOpen accessIn the abstractWhy College or University Students Hate Proofs in Mathematics?Mbaïtiga ZacharieProblem Statement: A proof is a notoriously difficult mathematical concept for students. Empirical studies have shown that students emerge from proof-oriented courses such as high-school geometry, introduction to proof, complex and abstract algebra unable to construct anything beyond very trivial proofs. Furthermore, most university students do not know what constitutes a proof and cannot determine whether a purported proof is … …Journal of Mathematics and Statistics, Vol. 5, Issue 1 · 31 Mar 2009 · 8,849 accessesView PDFCite
Research ArticleOpen accessIn the abstractSome Applications of Spanning Trees in Complete and Complete Bipartite GraphsS. N. DaoudProblem statement: The number of spanning trees τ(G) in graphs (networks) is an important invariant, it is also an important measure of reliability of a network. Approach: Using linear algebra and matrix analysis techniques to evaluate the associated determinants. Results: In this study we derive simple formulas for the number of spanning trees of complete graph Kn and complete bipartite … …American Journal of Applied Sciences, Vol. 9, Issue 4 · 15 Feb 2012 · 7,263 accessesView PDFCite
Research ArticleOpen accessIn the abstractNumber of Spanning Trees of Circulant Graphs C6n and their ApplicationsS. N. DaoudProblem statement: The number of spanning trees of a graph G is usually denoted by τ(G). A circulant graph with n vertices and k jumps is Cn (a1,…..,ak). Approach: In this study the number τ(G) of spanning trees of the circulant graphs C6n with some non-fixed jumps such as C6n (1, n), C6n (1, n, 2n), C6n (1, n, 3n), … …Journal of Mathematics and Statistics, Vol. 8, Issue 1 · 12 Dec 2011 · 7,626 accessesView PDFCite
Research ArticleOpen accessIn the abstractComplexity of Cocktail Party Graph and Crown GraphS. N. DaoudProblem statement: The number of spanning trees τ(G) in graphs (networks) was an important invariant. Approach: Using the properties of the Chebyshev polynomials of the second kind and the linear algebra techniques to evaluate the associated determinants. Results: The complexity, number of spanning trees, of the cocktail party graph on 2n vertices, given in detail in the text was proved. … …American Journal of Applied Sciences, Vol. 9, Issue 2 · 12 Dec 2011 · 7,868 accessesView PDFCite