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International Journal of Engineering, Mathematical and Physical Sciences

ISSN: 2517-9934

Total 5 content found

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Extended Arithmetic Precision in Meshfree Calculations

Year: 2020 Volume: 14 Issue: 9 101 - 106 Pages

Abstract: Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Matching on Bipartite Graphs with Applications to School Course Registration Systems

Year: 2020 Volume: 14 Issue: 9 93 - 100 Pages

Abstract: Nowadays, most universities use the course enrollment system considering students’ registration orders. However, the students’ preference level to certain courses is also one important factor to consider. In this research, the possibility of applying a preference-first system has been discussed and analyzed compared to the order-first system. A bipartite graph is applied to resemble the relationship between students and courses they tend to register. With the graph set up, we apply Ford-Fulkerson (F.F.) Algorithm to maximize parings between two sets of nodes, in our case, students and courses. Two models are proposed in this paper: the one considered students’ order first, and the one considered students’ preference first. By comparing and contrasting the two models, we highlight the usability of models which potentially leads to better designs for school course registration systems.

Pure and Mixed Nash Equilibria Domain of a Discrete Game Model with Dichotomous Strategy Space

Year: 2020 Volume: 14 Issue: 9 86 - 92 Pages

Abstract: We present a discrete game theoretical model with homogeneous individuals who make simultaneous decisions. In this model the strategy space of all individuals is a discrete and dichotomous set which consists of two strategies. We fully characterize the coherent, split and mixed strategies that form Nash equilibria and we determine the corresponding Nash domains for all individuals. We find all strategic thresholds in which individuals can change their mind if small perturbations in the parameters of the model occurs.

Validity of Universe Structure Conception as Nested Vortexes

Year: 2020 Volume: 14 Issue: 9 76 - 85 Pages

Abstract: This paper introduces the Nested Vortexes conception of the universe structure and interprets all the physical phenomena according this conception. The paper first reviews recent physics theories, either in microscopic scale or macroscopic scale, to collect evidence that the space is not empty. But, these theories describe the property of the space medium without determining its structure. Determining the structure of space medium is essential to understand the mechanism that leads to its properties. Without determining the space medium structure, many phenomena; such as electric and magnetic fields, gravity, or wave-particle duality remain uninterpreted. Thus, this paper introduces a conception about the structure of the universe. It assumes that the universe is a medium of ultra-tiny homogeneous particles which are still undiscovered. Like any medium with certain movements, possibly because of a great asymmetric explosion, vortexes have occurred. A vortex condenses the ultra-tiny particles in its center forming a bigger particle, the bigger particles, in turn, could be trapped in a bigger vortex and condense in its center forming a much bigger particle and so on. This conception describes galaxies, stars, protons as particles at different levels. Existing of the particle’s vortexes make the consistency of the speed of light postulate is not true. This conception shows that the vortex motion dynamic agrees with the motion of all the universe particles at any level. An experiment has been carried out to detect the orbiting effect of aggregated vortexes of aligned atoms of a permanent magnet. Based on the described particle’s structure, the gravity force of a particle and attraction between particles as well as charge, electric and magnetic fields and quantum mechanics characteristics are interpreted. All augmented physics phenomena are solved.