Authors:Angelo Monfroglio Pages: 1 - 18 Abstract: A recent result shows that a LP model with 0/1 values is of polynomial complexity. The paper reports a model for some important NP hard problems, such as the Propositional Satisfiability Problem, the Traveling Salesperson Problem, and the Minimal Set Covering Problem, by means of only two types of constraints: 'choice constraints'and 'exclusion constraints'. The article presents a linear 0/1 Simplex for solving the obtained integer program. This algorithm always finds a 0-1 integer solution that corresponds to a solution of the Constraint Satisfaction Problem and vice versa. The paper presents the results of experiments for solving a Conjunctive Normal Form hard cases by linear programming in polynomial time, confirming in practice the polynomial Acceleration of the Simplex SAT solver by means of intelligent pivot selection through neural networks is also decribed. There are several practical application of our approach: Agriculture production planning; Industry manifacturing and service; Engineering; Financial management; and, of course, transportation. PubDate: 2024-07-20 DOI: 10.9734/arjom/2024/v20i8813 Issue No:Vol. 20, No. 8 (2024)
Authors:Yohanna Tella, Anas Usman Pages: 19 - 32 Abstract: In this paper, we introduced some operations on multiset topological spaces to include union, intersection, arithmetic multiplication, Scalar multiplication and Raising to Arithmetic Power. Studies revealed that these operations are closed on the various classes of multiset topological spaces defined. PubDate: 2024-07-24 DOI: 10.9734/arjom/2024/v20i8814 Issue No:Vol. 20, No. 8 (2024)
Authors:Owunna Ikechukwu Bismarck, Okoh Ufuoma Pages: 33 - 57 Abstract: Moment of inertia, a fundamental concept in physics and engineering and a chief factor influencing the rotational motion of objects, is the quantitative measure of the rotational inertia of objects. It is the resistance that the objects exhibit to having their speed of rotation about an axis altered by the employment of a turning force. This paper presents a reevaluation of the moment of inertia. By exploring the arithmetic of zero and minus one factorial, we uncover the true essence of the particles involved in rotational motion. Our innovative approach reconciles intuition with mathematical precision, revealing the hidden structure underlying moment of inertia. This breakthrough enables a deeper understanding of physical systems, empowering researchers to tackle complex challenges with renewed confidence and creativity. Our work has far-reaching implications for novel applications and innovations in physics and engineering, illuminating the path for future discoveries. PubDate: 2024-07-26 DOI: 10.9734/arjom/2024/v20i8815 Issue No:Vol. 20, No. 8 (2024)
Authors:Grace Nkwese Mazoni, Clara Paluku Kasoki, Emilien Loranu Londjiringa, Camile Likotelo Binene Pages: 58 - 68 Abstract: This paper thoroughly examines the Hilbertian properties of the Sobolev space H1(\(\Omega\)). Based on the Lebesgue space L2(\(\Omega\)), H1(\(\Omega\)) is of particular importance in the analysis of functions with weak derivatives. The focus is on the Hilbertian structure of this space, which allows for the definition of a specific inner product and a rigorous verification of the associated completeness. These fundamental characteristics facilitate a detailed study of convergence, continuity, and orthogonality of functions in H1(\(\Omega\)), thereby enhancing its relevance for solving various complex mathematical problems. This paper aims to address gaps identified in the existing literature, where the explicit verification of these essential properties is sometimes omitted, thus compromising mathematical rigor and the applicability of results in various contexts. PubDate: 2024-07-26 DOI: 10.9734/arjom/2024/v20i8816 Issue No:Vol. 20, No. 8 (2024)
Authors:Takaaki Fujita Pages: 69 - 75 Abstract: The study of graph width parameters is highly significant in graph theory and combinatorics. Among these parameters, linear-width is particularly well-regarded and established. The concepts of Single Filter and Linear Obstacle pose challenges to achieving optimal linear-width in a connectivity system. In this concise paper, we present an alternative proof that establishes the cryptomorphism between Single Filter and Linear Obstacle. Although this proof may not be highly novel, we hope it will enhance the understanding of the intricate relationship between graph width parameters and ultrafilters. PubDate: 2024-07-27 DOI: 10.9734/arjom/2024/v20i8817 Issue No:Vol. 20, No. 8 (2024)
Authors:Wakwabubi N. Christine, Samuel B. Apima, Bonface Kwach Pages: 76 - 91 Abstract: Rotavirus is the most common cause of severe diarrheal disease in young children globally attributing approximately 527,000 deaths of children under five each year. A Rotavirus vaccine was developed in 1998, however, it takes time for vaccine induced immunity to take place. The aim of the study was develop and analyze a mathematical model on rotavirus infection which incorporated a time delay on effectiveness of vaccination with treatment. The developed model was shown to be positively invariant and bounded.Conditions for stability of the equilibrium points is obtained and it is also shown that a bigger time delay would make the population not to be predictable. The findings of this study is useful to the government, ministry of Health stakeholders and policy developers and further provides baseline information for studies of this nature. PubDate: 2024-07-30 DOI: 10.9734/arjom/2024/v20i8818 Issue No:Vol. 20, No. 8 (2024)
Authors:Samuel B. Apima, Jacinta M. Mutwiwa, Isaac K. Barasa Pages: 92 - 101 Abstract: In this study, the effects of a double dose vaccination are examined using the Covid-19 mathematical model. In addition to obtaining the basic reproduction number and analyzing the model's stability, the sensitivity analysis was also performed. The results obtained demonstrates that the model's solutions always converge to the endemic equilibrium point whenever reproduction number is greater than 1, irrespective of the initial solution. Sensitivity analysis demonstrated that the average number of encounters between infected/exposed individuals per unit time increases whenever the reproduction number R0 increases. Numerical analysis demonstrated that vaccination reduces the number of infected people compared to when no vaccination is administered. PubDate: 2024-08-03 DOI: 10.9734/arjom/2024/v20i8819 Issue No:Vol. 20, No. 8 (2024)
Authors:Ritu Yadav, Anil Kumar Sharma, Pujari Thakur Singh Pages: 102 - 118 Abstract: This article presents a report on a creation stock model that the point is to foster an ideal creation and stock procedure that boosts the general benefit while thinking about the impact of expansion on the decaying things over the long haul. The exponential demand rate is thought to accurately reflect real-world demand fluctuations over time. The model gives a manager’s realistic representation of the production and inventory system by considering these aspects, allowing them to make informed decisions. To enhance the creation and stock strategy, a numerical structure is created, consolidating different expense parts, for example, holding cost, arrangement cost, creation cost, and lack cost. The goal is to find the ideal creation amount and reorder point that limit the all-out cost and expand the general benefit. The proposed model's analytical results show a complex connection between the optimal production quantity, reorder point, and other relevant parameters. According to the findings, production inventory models must consider both the exponential demand rate and the inflation rate of deteriorating goods. The proposed model offers a pragmatic methodology for upgrading the creation and stock choices, at last improving the productivity and functional effectiveness of organizations managing crumbling things within the sight of expansion. This paper has followed an analytical approach to diminish the entire inventory cost. Finally, a sensitivity analysis was performed to study the effect of changes of different parameters of the model on the optimal policy. Moreover, in order to approve the determined models, we have clarified mathematical models and examined affectability. PubDate: 2024-08-03 DOI: 10.9734/arjom/2024/v20i8820 Issue No:Vol. 20, No. 8 (2024)
Authors:Henry Otoo, Lewis Brew, Benjamin Dadzie-Mensah Pages: 119 - 141 Abstract: Aims: Yellow fever is a severe and often fatal viral illness caused by the yellow fever virus Despite being largely overlooked, yellow fever continues to silently claim lives in many parts of the world. The study focuses on the epidemiological modelling of yellow fever dynamics between a host (human) and vector (mosquito) populations The human population was divided into five main compartments: Susceptible, Exposed, Infected, Isolated, and Recovered. The vector population was also divided into two compartments: Susceptible and Infected. Nonlinear differential equations describing these compartments were formulated. Stability analysis and numerical simulations were then performed based on the formulated equations. From the stability analysis, it was observed that the disease-free equilibrium is both locally and globally asymptotically stable. Similarly, the endemic equilibrium was found to be locally and globally asymptotically stable. The simulation also revealed a direct correlation between the transmission rate and disease spread. PubDate: 2024-08-06 DOI: 10.9734/arjom/2024/v20i8821 Issue No:Vol. 20, No. 8 (2024)
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