APAV - Academy of Sciences, Letters, Arts and Technology (E-Journals)
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From Archimedes and the oxen problem to Pell's equation
Full text linkAs part of the laboratory activities designed for the students of the second year of the Mathematical High School by the research group in Mathematics Education of the Department of Mathematics of the University of Salerno, the theme “From Archimedes and the oxen problem to Pell’s equation” has been designed. The course has not yet been delivered to students and in this paper the didactic path to be developed in the classroom will be described. The students initially will retrace the various solution approaches proposed over the centuries. Subsequently, with a heuristic approach, they will tackle the resolution of the proposed problem by exploiting properties related to the theory of numbers. With the help of some schedules, provided by the teachers-tutors, they will conjecture and argue by answering questions aimed at stimulating didactic reflection. This workshop path involves processes such as exploring and conjecturing through the articulation of different ways of working (individual and in groups), manual and digital
Existence and Uniqueness of Solutions for System of Nonlinear Fractional Reaction Diffusion Equations
Full text linkIn this paper, to develop monotone method for non-linear system of Riemann-Liouville (R-L) reaction-diffusion equations with initial and boundary conditions. The monotone method yields monotone sequences which converges uniformly and monotonically to minimal and maximal solutions.To investigate the existence and uniqueness of solutions by monotone method for R-L reaction-diffusion equations with initial and boundary conditions
A Nonlinear Generalizations of Dynamic Inequalities on Time Scales
Full text linkConsidering the distinctive generalization of the Gronwall-Bellman inequality, in this paper we innovates new dynamical inequalities on time scale. These inequalities will be acted a profound tools for studying qualitative properties such as uniqueness, existence, stability and asymptotic behavior of solutions of dynamic equations on time scale
The modified divisor graph of commutative ring
No full textLet be a finite commutative ring with unity. We have introduced a divisor graph of the ring, denoted by . It is an undirected simple graph with a vertex set , and two distinct vertices and in are adjacent if and only if there exists such that or . Clearly, and unit elements are adjacent to all elements of the ring. Thus, we adopt the idea of Anderson and Livingston and remove the zero and unit vertices from the vertex set. A new graph is called the modified divisor graph, noted by symbol .In this study, we have focused on the structural properties of . Moreover, we have determined the diameter, girth, clique number, vertex connectivity, and edge connectivity of for every natural number . The purpose of studying this graph is to find relationships between the ring theoretic properties of and the graph theoretic properties of
Positivist and Interpretivist Ideas of Anol Bhattacherjee on The Methods of Data Collection: A Textual Critique
Full text linkIn the literature, the distinction between positivism and interpretivism based on ontological assumptions is somehow clear. Problems in dividing them based on epistemological assumptions continue to exist and appear in several works; for instance, Bhattacherjee’s book (2012) introduced the concept of research design and categorization of methods of data collection based on positivist and interpretivist epistemological assumptions. While acknowledging Bhattacherjee's contribution, nonetheless, the paper argues that since both the quantitative and qualitative research approaches share a few epistemological assumptions, strictly categorizing them into positivism and interpretivism raises some confusion. Consequently, impacting communication among researchers and the implementation of the research projects. Therefore, the paper describes Bhattacherjee's contributions and limitations in understanding the dichotomy existing between positivist and interpretivist methods of data collection. The paper's suggestions aim to resolve such confusion and restore research approaches and their methods of data collection to their original philosophical positions. Thus minimizing the existing confusion on research methodology in the current literature
Partial sharing of small functions with exact difference
Full text linkWe have proven certain uniqueness results related owing to the partial sharing of small functions of with difference polynomials of the form , where are small functions of . As a consequence of this, we have deduced the conditions under which, is identically equal to its exact difference operator
On the Regularity of the Entropy Solution of the Fractional-Semigeostrophic Equation Using Ultrafilters
Full text linkThis paper explores the regularity properties of the entropy solution to the fractional semigeostrophic (FSG) equation, leveraging the advanced mathematical framework of ultrafilters. The FSG equation, which extends the classical semigeostrophic model by incorporating fractional derivatives, is critical in modeling geophysical fluid dynamics with more accuracy, particularly in scenarios involving anomalous diffusion. Traditional methods to study entropy solutions often face limitations due to the complex nature of fractional derivatives and the nonlinearity inherent in the FSG equation. By employing ultrafilters, a powerful tool in non-standard analysis, we overcome these challenges and provide new insights into the regularity of entropy solutions. Our results demonstrate that the use of ultrafilters not only simplifies the analysis but also enhances the understanding of the smoothness and stability of the entropy solutions. This work lays the groundwork for future studies on fractional partial differential equations in geophysical contexts, potentially leading to more accurate predictive models in meteorology and oceanography
(⊙, ∨)-Derivations on EMV-algebras and EBL-algebras
Full text linkIn the paper, we will study (∘, ∨)-derivations on EMV-algebras and EBL-algebras. Firstly, we define the notions of (∘, ∨)-derivations on EMV-algebras and EBL-algebras, and we also introduce some classes of (∘, ∨)-derivations on EMV-algebras and EBL-algebras, such as principal (∘, ∨)-derivations and isotone (∘, ∨)-derivations. In addition, we construct some lattice structures of (∘, ∨)-derivations on EMV-algebras and give a classification of EBL-algebras with (∘, ∨)-derivations
Using the three-way matrix for AHP-group decision-making
Full text linkThe Analytic Hierarchy Process (AHP) is one of the most well-known and used multi-criteria methods in the field of decision problems. In many situations, the decision is not up to a single person but involves multiple decision-makers with different preferences with respect to the various elements of the problem. Applying a traditional AHP with certain preference aggregation mechanisms, the procedure is very burdened by the many pairwise comparison matrices due to the number of decision-makers. The aim of this paper is to summarize the problem of representing the different preferences between the criteria and the alternatives, for the various decision makers using the three-way data matrix. This matrix allows us to examine, in a contemporary and global manner, the preferences of several decision-makers in the decision-making context. Three-way principal component models can be used to treat the three-way matrix, particularly for the derivation of AHP priorities
Best proximity point for weak cyclic Kannan type contraction map and cyclic Chatterjea type contraction map
Full text linkIn this paper, we introduce an innovative category of contractions termed "cyclic Chatterjea type contraction" and "weak cyclic Kannan type contraction." Subsequently, we establish a theorem for determining the best proximity point in a uniformly convex Banach space, specifically focusing on weak cyclic Kannan type contractions. Furthermore, we extend our investigation to include cyclic Chatterjea type contractions in uniformly convex Banach spaces. To support our findings, we present illustrative examples