Theory and Practice of Mathematics and Computer Science Vol. 6

In this paper, we have considered a very general Holling type predator-prey system with selective harvesting and where both of the species follow logistic growth. The uniform boundedness of the system has been studied together with the conditions of existence. Also, we have obtained the criteria for local stability of various equilibrium points then considering suitable Lyapunov function, the global stability of the system has been discussed. After that using Pontryagin Maximal Principle, we have studied the optimal harvesting policy for the system. At the end, the problem has been illustrated through some numerical examples. Finally, we have discussed the problem with the help of a numerical example by using arbitrary feasible parametric values and using MATLAB, we observed from stability diagram (Fig. 1) and phase portrait (Fig. 2) that as the values of  decreases, the steady state value of Prey population increases. This is quite good result for ecological sustainability of species. Our model may be extended by incorporating time delay and stochasticity in the system.

The aim of this paper is to define a new class of functions namely a* homeomorphism and strongly a* homeomorphism and study their properties. Additionally, we relate and compare these functions with some other functions in topological spaces. 

In a recent communication in the scientific journal symmetry [1] we outlined the harmonic evolution of structural symmetry on the basis of three principles: atomic attraction, repulsion, and the limitations in 3D space. We described a simple bottom-up atomistic crystal growth model derived for equivalent atoms and a pair potential entailing a maximum number of equilibrium distances in the atoms local vicinity to obtain high symmetric structural motifs, among them the Platonic Solids, as well as a phase diagram summarizing stable regions of close-packed fcc and hcp, next to bcc symmetry. In dependence on the pair potentials short- and long-range characteristics the, by symmetry, rigid lattices relax isotropically within the potential well. The first few coordination shells with lattice-specific fixed distances not necessarily determine, which equilibrium symmetry prevails.
To highlight the applicability of the model to scientific cases of solid state physics, the present chapter recaptures the evolution of structural symmetry in crystals accompanied with the basic principles outlined above and underlying weights. This guides us to a holistic view of similarities to structural characteristics in other fields, such as music and art. An impulse is given by Goldschmidts
work on fundamental rational series in sciences reflecting the potential of mathematical series as fundamental tool for further quantitative insights.

The increased use of energy and the depletion of the fossil fuel reserves combined with the increase of the environmental pollution have encouraged the search for clean and pollution-free sources of energy. One of these is wind energy. The wind power industry has seen an unprecedented growth in last few years. The surge in orders for wind turbines has resulted in a producer’s market. This market imbalance, the relative immaturity of the wind industry, and rapid developments in data processing technology have created an opportunity to improve the performance of wind farms and change misconceptions surrounding their operations. This research offers a new paradigm for the wind power industry, data-driven modeling. Each wind Mast generates extensive data for many parameters, registered as frequently as every minute. As the predictive performance approach is novel to wind industry, it is essential to establish a viable research road map. This paper proposes a Statistical analysis and data-mining-based methodology for long term wind forecasting (ANN), which is suitable to deal with large real databases. The paper includes a case study based on a real database of  five years of wind speed data for a site and discusses results of wind power density was determined by using the Weibull and Rayleigh probability density functions. Wind speed predicted using wind speed data with Datamining methodology using intelligent technology as Artificial Neural Networks (ANN). MATLAB R2008a Neural Network Toolbox used for the training the ANN back propagation algorithm and a PROLOG program is designed to calculate the monthly and Annual mean wind speed. The Statistical  analysis of  wind speed prediction  shows that Weibull distribution is more suitable than Rayleigh distribution and by seeing the values of the k we can conclude that Higher values of k imply a sharper maximum in the frequency distribution curve and consequently a lower wind power density.

In this paper, we obtain an analytic solution to the initial valued problem of the Duffing oscillator with fractional order derivative. The Homotopy analysis method (HAM) was used to obtain the said analytic solution to the proposed initial valued problem. In order to achieve our goal, the problem was first converted to its augmented equivalent system of equations having the same order. The accuracy of the result obtained was demonstrated with an example and the solution illustrated graphical. For the excitation amplitude ? and the excitation frequency ?, it was observed that as they increase, the amplitude also increase. As the unit of time increases, it was observed that the system becomes more chaotic and this behaviour is not out of place.

For the three-body problem, we consider the Lagrange stability. To analyze the stability, along with integrals of energy and angular momentum, we use relations by the author from [1], which band together separately squared mutual distances between bodies (mass points) and squared mutual distances from bodies to the barycenter of the system. We prove the Lagrange stability theorem, which allows us to define more exactly the character of hyperbolic-elliptic and parabolic-elliptic final evolutions.

When P indistinguishable balls are randomly distributed among L distinguishable boxes, and considering the dense system P >> L, our natural intuition tells us that the box with the average number of balls P/L has the highest probability and that none of boxes are empty; however in reality, the probability of the empty box is always the highest. This fact is with contradistinction to sparse system  P << L (i.e. energy distribution in gas) in which the average value has the highest probability. Here we show that when we postulate the requirement that all possible configurations of balls in the boxes have equal probabilities, a realistic "long tail" distribution is obtained. This formalism, when applied for sparse systems, converges to distributions in which the average is preferred. We calculate some of the distributions resulted from this postulate and obtain most of the known distributions in nature, namely: Zipf’s law, Benford’s law, particles energy distributions, and more.  Further generalization of this novel approach yields not only much better predictions for elections, polls,  market share distribution among competing companies, and so forth, but also a compelling probabilistic explanation for Planck's famous empirical finding that the energy of a photon is hv. This paper unifies everyday probability calculations done by surveyors, gamblers and economists with the calculations done by physicists, therefore enabling the applications of the methodology of statistical physics in economics and the life sciences.  

The problem of scheduling and allocation of resources, both space and time, has generated a lot of issues and has become of great concerns in daily human activities. The choice of best or appropriate computational algorithms for solving this problem has been the subject of several seminars and conferences organized to discuss the allocation of resources in different fields. The problem of resource scheduling deals with various criteria that are involved in the allocation of resources and associated variation on how the resources are to be allocated. The scheduling of an allocation of resources requires proper management of resources and time for various users to avoid clashes in timing of events. This paper presents a conceptual framework for solving resource allocation scheduling problems using timetabling as a representative scheduling problem requiring proper management of resources and time for various users to avoid clashes in timing of events. The work identifies the constraints involved in algorithms that have been used to solve several timetabling problem like airplane roster, lecture schedules, etc. The paper attempts to identify a good framework for the use of fuzzy algorithm implementation that will be of great value to those resolving timetabling oriented problems. The needed future works include implementation of these framework concepts for the grouping of resources when there are no venue capacities to handle such resources. A web implementation of the framework is highly desirable and also the development of other constraint-based scheduling activities like examination timetable could be incorporated into it.

We will discuss the concept of a split anti-fuzzy dominating set (SAFD) in the anti fuzzy graph ( ) and investigate the relationship of  ( )(split anti fuzzy domination number) with other known parameters of The anti-fuzzy graph. Some bounds and interesting results for this parameter are obtained. The split anti-fuzzy domination on some standard anti-fuzzy graph has been discussed with some suitable graphs.

It is important to fit count data with suitable model(s), models such as Poisson Regression, Quassi Poisson, Negative Binomial, to mention but a few have been adopted by researchers to fit zero truncated count data in the past. In recent times, dedicated models for fitting zero truncated count data have been developed, and they are considered sufficient. This study proposed Bayesian multi-level Poisson and Bayesian multi-level Geometric model, Bayesian Monte Carlo Markov Chain Generalized linear Mixed Models (MCMCglmms) of zero truncated Poisson and MCMCglmms Poisson regression model to fit health count data that is truncated at zero. Data of visits to visit to the doctor of patients under National Health Insurance Scheme in Nigeria was obtained and used to fit the models. Suitable model selection criteria were used to determine preferred models for fitting zero truncated data. Results obtained showed that Bayesian multi-level Poisson outperformed Bayesian multi-level Poisson Geometric model; also MCMCglmms of zero truncated Poisson outperformed MCMCglmms Poisson.

In the recent time cloud computing has come forwarded as one of the most admired computing model in knowledge domain that concerns about the distributed information systems to support the whole world as a cloud community. Distributed, virtualization and service-oriented nature have given ascendancy to cloud computing to distinguish from its core descendants like grid computing, geographical information systems, and distributed system. Although cloud computing dominants the e-society, but it is still in under research, progress. The architecture of cloud’s taxonomy and its services are very significant issues for cloudifications because every day some new advancements and developments are adjoined under its umbrella. The proposed taxonomy captures in a forthright way the concepts of cloud computing, and is therefore very appropriate for understanding cloud computing for cloudification. Having a clear taxonomy enables us to clearly identify the category our problem falls in. In this paper we proposed an extended and granular classification of taxonomy for cloud computing and specified services that is a detailed ontology of cloud, which will be helpful for researchers and stakeholders in better understanding, developing, and implementing cloud technology and services to their lives.

In this chapter, we use the idealization procedure for finite rings to construct a class of local quasi-3 prime Near-Rings N with a Jordan ideal J(N ) and admitting a Frobenius derivation. The structural characterization of N ; J(N ) and commutation of N via the Frobenius derivations have been explicitly determined. This work has also been extended to an investigation of the symmetries of the graphs ?(N ) of the classes of near-rings N studied. Indeed some structures and orders of the automorphism groups of ?(N ) have been determined.