Abstract: Publication year: 2018Source: Applied Mathematics, Volume 8, Number 3I. M. Esuabana, U. A. AbasiekwereOne of the most recent mathematical concepts, the regularization methods for solving integral equations, has brought in yet another dimension into the existing problems and has helped to usher in a new body of knowledge for further consideration. Indeed, new inputs have placed other numerical methods for solving integral equations in the fastest lane, since a number of methods were analysed with respect to accuracy, convergence and stability properties. Most of the work was done on the assumptions that the kernel and the right-hand side are known without error and that the approximating equation can be exact, whereas, as is often the case, these may not be true. Consequently, the effect can be observed in the study of regularization methods for solving Volterra type integral equations of the first kind. Classical regularization methods tend to destroy the non-anticipatory (or causal) nature of the original Volterra problem because such methods typically rely on the computation of the Volterra adjoint operator. In this paper, we highlight the general concept of the regularization method of solution for Volterra integral equation of the first kind without destroying the Volterra structure.

Abstract: Publication year: 2018Source: Applied Mathematics, Volume 8, Number 2Ojo Ayodele Oluwaseun, Adebisi Sunday AdesinaThe benefits and worthy outputs of orderliness is enormous. When orderliness is imposed, services can be effectively and efficiently provided and distributed. In an atmosphere where orderliness is acquired, things work normally and the desired results and goals are realized. This notion, calls for what is well known as queue. Part of the aims and aspirations of many institutions of higher learning is to be a leading and world class institutions for high level of academic and moral excellence. All these are only attainable in an atmosphere where peace and harmony are well pronounced. To do this there is no doubt the need for orderliness and decorum. It is in view of this that this research is thus tailored towards using the concept of queuing in giving necessary and sufficient recommendation towards the fulfillment of the expectations.

Abstract: Publication year: 2018Source: Applied Mathematics, Volume 8, Number 2Min-Hai HuangA Dirichlet boundary-value problem for the modified Helmholtz equation in the quarter-plane was discussed. By using the Fokas transform method, the solution in the form of integral representation was given.

Abstract: Publication year: 2018Source: Applied Mathematics, Volume 8, Number 2Yanti Rini, Hajjah AlyaumaWe discuss a numerical solution of Nth-order fuzzy differential equations with initial value by third order Runge Kutta method based on combination of arithmatics, harmonics and geometrics means. Moreover, the convergence, stability and error analysis also discussed. The algorithm is illustrated by solving the Nth-order of fuzzy initial value problem. The numerical simulation show that the new method worked and give an accurate solution.

Abstract: Publication year: 2018Source: Applied Mathematics, Volume 8, Number 1Timothy Sands, Jae Jun Kim, Brij AgrawalThis manuscript reveals both the full experimental and methodical details of a most-recent patent that demonstrates a much-desired goal of rotational attitude control actuators, namely extremely high torque without mathematical singularity and accompanying loss of attitude control. The paper briefly reviews the most recent literature, and then gives theoretical development for implementing the methods described in the patent to compute a non-singular steering command to the actuators. The theoretical developments are followed by computer simulations used to verify the theoretical computation methodology, and then laboratory experiments are used for validation on a free-floating hardware simulator.

Abstract: Publication year: 2018Source: Applied Mathematics, Volume 8, Number 1Sencer TaneriBosons and Fermions are observable in nature while Quarks appear only in triplets for matter particles. We find a theoretical proof for this statement in this paper by investigating 2-dim model. The occupation numbers q are calculated by a power law dependence of occupation probability and utilizing Hausdorff dimension for the infinitely small mesh in the phase space. The occupation number for Quarks are manipulated and found to be equal to approximately three as they are Parafermions.

Abstract: Publication year: 2018Source: Applied Mathematics, Volume 8, Number 1S. I. HamidovWe consider the two-sector model of the economic dynamics. The problem of the distribution of labor between sectors is considered under the condition that the total consumption is maximized. As a production function is taken a function with constant elasticity of the substitution (CES). Potential opportunity of the sectors is analyzed.

Abstract: Publication year: 2017Source: Applied Mathematics, Volume 7, Number 4Ohochuku N. StephenThis article brings together the various current procedures used to construct the tangents (common or equal) to the two circles in a two circle system, radical points/axis and homothetic points that are essential to these constructions with the aim of showing the important contributions of the radii of the circles in these operations. Two new methods one for constructing external homothetic point and the other for a pair of special radical points using combinations of the radii are also added as update. All the methods listed show that the radii of the two circles combined in different ways can be used to determine respectively the external homothetic point and the radical points/axis which are essential in the construction of tangents in two circle systems.

Abstract: Publication year: 2017Source: Applied Mathematics, Volume 7, Number 3Salah H. Abid, Russul K. AbdulrazakIn this paper, we introduce a new family of continuous distributions based on [0,1] truncated Fréchet distribution. [0,1] truncated Fréchet Generalized Gamma distribution is discussed as special cases. The cumulative distribution function, the rth moment, the mean, the variance, the skewness, the kurtosis, the mode, the median, the characteristic function, the reliability function and the hazard rate function are obtained for the distributions under consideration. It is well known that an item fails when a stress to which it is subjected exceeds the corresponding strength. In this sense, strength can be viewed as "resistance to failure". Good design practice is such that the strength is always greater than the expected stress. The safety factor can be defined in terms of strength and stress as strength/ stress. So, the [0,1] TFGG strength-stress model with different parameters will be derived here. The Shannon entropy and Relative entropy will be derived also.

Abstract: Publication year: 2017Source: Applied Mathematics, Volume 7, Number 3Ohochuku N. StephenThe inherent properties of a regular polygon, viz equal sides and equal base angles, have been used with each side subtending the same angle (that is equal to the external angle) at the centre of the polygon to develop a method currently in use for the construction of any regular polygon. This paper reports of the use of the equal sides, equal base angles and equal angles (each of which is equal to half the external angle) subtended by the sides at the corner to generate new methods for the construction of a regular polygon. The harnessing of equal diagonals with the equal sides and equal exterior angle yielded another method of regular polygon construction and this is also presented here. These novel methods are less demanding, clear and straight forward compared to any existing methods requiring direct construction of base or external angle as a pre-requisite as in these new methods.