Oscillatory Blood Flow in Bifurcating Capillaries | Chapter 12 | Theory and Applications of Mathematical Science Vol. 1

Oscillatory blood flow in bifurcating capillaries is examined. The governing nonlinear and coupled equations expressed in the form of the Boussinesq approximations are solved by the method of perturbation series expansions. Solutions for the concentration, temperature and velocity are obtained, and presented quantitatively using Malple 18 computational software. The results show that the rate of chemical reaction, Hartmann number (M²≤I.0), heat exchange parameter and Grashof number (Gr/Gc≤I.0) tend to increase the velocity of the flow. The increase in the velocity structure has some attendant implications. In fact, it tends to increase the rate of transport of oxygen and nutrient-rich blood to the tissues, and this in turn enhances the physiological well-being of man.

Author(s) Details

Dr. W. I. A. Okuyade
Department of Mathematics and Statistics, University of Port Harcourt, Port Harcourt, Nigeria.

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Differential Subordinations for Non-analytic Functions | Chapter 11 | Theory and Applications of Mathematical Science Vol. 1

In paper [1], Petru T. Mocanu has obtained suﬃcient conditions for a function in the classes C¹ (U), respectively C² (U) to be univalent and to map U onto a domain which is starlike (with respect to origin), respectively convex. Those conditions are similar to those in the analytic case. In paper [2], Petru T. Mocanu has obtained suﬃcient conditions of univalency for complex functions in the class C¹ which are also similar to those in the analytic case. Having those papers as inspiration, we have tried to introduce the notion of subordination for non-analytic functions of classes C¹ and C² following the classical theory of diﬀerential subordination for analytic functions introduced by S.S. Miller and P.T. Mocanu in papers [3] and [4] and developed in the book [5]. Let Ω be any set in the complex plane C, let p be a non-analytic function in the unit disc U, p ∈ C²(U) and let ψ(r, s, t; z) : C³×U → C. In article [6] we have considered the problem of determining properties of the function p, non-analytic in the unit disc U, such that p satisﬁes the diﬀerential subordination. ψ(p(z), Dp(z), D²p(z) − Dp(z); z) ⊂ Ω ⇒ p(U) ⊂ ∆. The present chapter is based on the results contained in paper [7], some parts of it have been removed and results obtained after the appearance of the paper have been added.

Author(s) Details

Georgia Irina Oros
Department of Mathematics and Computer Science, University of Oradea, Universitatii Street, No. 1, 410087 Oradea, Romania.

Gheorghe Oros
Department of Mathematics and Computer Science, University of Oradea, Universitatii Street, No. 1, 410087 Oradea, Romania.

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Homfly Polynomial of Knotted Trivalent Plane Graphs | Chapter 10 | Theory and Applications of Mathematical Science Vol. 1

We study the Homfly polynomial of periodic knotted trivalent plane graphs introduced in [1]. We show how periodicity of a knotted trivalent plane graphs is reflected in this polynomial. In particular, we derive congruences of periodic knotted trivalent plane graphs in terms of this polynomial invariant. These congruences yield criteria for periodicity of knotted trivalent plane graphs.

Author(s) Details

Ayman A. Aboufattoum
Department of Mathematics, Faculty of Science, Kuwait University, P.O.Box 5969, Safat-13060, Kuwait.

K. Qazaqzeh
Department of Mathematics, Faculty of Science, Kuwait University, P.O.Box 5969, Safat-13060,Kuwait.

E. A. Elsakhawy
Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt.

A. T. Diab
Department of Mathematics, Faculty of Science, Ain Shams University, Cairo 11566, Egypt.

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Computation of Partial Derivative of Matrix Determinant Arises in Multiparameter Eigenvalue Problems | Chapter 09 | Theory and Applications of Mathematical Science Vol. 1

This chapter considers an iterative scheme based on Newton’s method to find the solution of eigenvalues of Linear Multiparameter Matrix Eigenvalue Problems(LMEP). This chapter is also intended to review some iterative algorithms for computation of partial derivatives of matrix determinant involved in Newton’s Method. First algorithm is based on standard Jacobi formula and second one is based on LU-decomposition Method together with an algorithm to compute directly the entries of the matrices involved in decomposition. Finally, an implicit determinant method is used for the computation of the partial derivatives of matrix determinant. Although the algorithms can be used to find the approximate eigenvalues of LMEPs, but the numerical works are performed by considering three-parameter case for better convenience and to relax computational cost and time. Numerical example is presented to test the efficiency of each iterative algorithms. Errors in computed eigenvalues are also compared with exact eigenvalues evaluated by Δ-Method, adopted by Atkinson.

Author(s) Details

Niranjan Bora
Department of Mathematics, Dibrugarh University Institute of Engineering and Technology (DUIET), Dibrugarh, 786004, Assam, India.

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Energy Integration to Ensure Effective Generation Supply and Distribution in Ghana Corporation Perspective | Chapter 08 | Theory and Applications of Mathematical Science Vol. 1

Aims: The objectives of the research are to examine the awareness and efficiency of the renewable energy law in Ghana; determine the main source for energy generated by the VRA, GRIDCO, and ECG; determine the distribution gap and find out how effectively these corporations are making use of the other resources to generate electric energy in Ghana.

Study Design: Purposive Sampling technique study design.

Place and Duration of Study: Volta River Authority, Ghana Grid Company, Electricity Company of Ghana, Ghana, between April 2016 and August 2016.

Methodology: We included sampled employees from the Volta River Authority, Ghana Grid Company, Electricity Company of Ghana. A total of 300 employees of the three organizations were selected for the research. The study employed a purposive sampling technique in selecting the employees from the three organizations.

Results: Data collected was analyzed using appropriate descriptive and inferential statistics. Results revealed that all employees are aware of the Renewable Energy Law Act 832 and that it is defined as energy obtained from non-depleting sources such as “Wind energy”, “Solar energy”, “Bio-energy”, “Geothermal energy”, and “Ocean energy”. Also, this study has established that, “hydro power sources”, “thermal energy sources”; and “renewable energy sources” are the main sources of energy generated by the Volta River Authority and also the type of renewable energy currently generated by the Volta River Authority is the solar energy.

Furthermore, the study has been able to establish that the Volta River Authority currently produce between 2100 to 2499 megawatts of electricity but however, there is a distribution gap or shortfall of about 900 to 1299 megawatts of electricity. Finally, findings from the study revealed that other corporations generate about 900 to 1299 megawatts of electricity.

Conclusion: “High-Cost” and “Lack of trust in the technology” are the factors that will prevent the adoption of renewable energy sources. Also, “Lack of budget funding” and “Unavailability of Gas/Crude oil to power plants” are the barriers to improving energy efficiency. It was however recommended that, the government should endeavor to initiate informative programs aimed at promoting renewable energy and provide capital subsidies and make investments through specialized agencies created for the promotion of renewable energy development and for installation of renewable energy.

Author(s) Details

Mr. Francois Mahama
Department of Mathematics and Statistics, Ho Technical University, Ghana.

Carlos Ankora
Department of Computer Science, Ho Technical University, Ghana.

Noble Kuadey
Department of Computer Science, Ho Technical University, Ghana.

Lily Bensah
Department of Computer Science, Ho Technical University, Ghana.

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Ensemble of Soft Computing Techniques for Inline Intrusion Detection System | Chapter 07 | Theory and Applications of Mathematical Science Vol. 1

An intrusion detection system automates the supervising activities in a computer network and computer system. It is used to analyses activities in network or computer. Basically, intrusion detection system is used to identify abuse or incomplete threats of abuse of computer security policies. It detects intruders, malicious actions, malicious code, and unwanted communications over the Internet. Despite the advancements and substantial research efforts, the general intrusion detection system gives high false positive rate, low classification accuracy and slow speed. For overcoming these limitations, many researchers are trying to design and implement intrusion detection systems that are easy to use and easy to install. There are many methods and techniques of intrusion detection system. Soft computing techniques are gradually being used for intrusion detection system. In this chapter, we present the ensemble approach of different soft computing techniques for designing and implementing inline intrusion detection system. In this work, three base classifiers are implemented using different artificial neural networks. Initially, Neuro-fuzzy neural network, Multilayer Perceptron and Radial Basis Function neural network have been constructed. These three networks have been combined using voting methods of machine learning. Three base classifiers are separately trained and evaluated in term of classification accuracy, false positive rate, false negative rate, sensitivity, specificity and precision. The voting combination ensemble method of machine learning has used to combine these three trained models. The performance ensemble classifier is evaluated and compared with the performances of base classifiers. In our study, we found that final ensemble classifier using Neuro-fuzzy, Multilayer Perceptron and Radial Basis Function neural network is superior to the individual base classifier in detection of intruder in network. The performance of ensemble classifier is measured in terms of classification accuracy and sensitivity. It is also found that ensemble based classifier for intrusion detection system has reasonable classification accuracy, the best sensitivity and false negative rate with very low false positive rate on test data set. The experimental results show that the base classifiers take very less time to build models and the proposed ensemble classifier for intrusion detection system takes very less time to test data set. These advantages can help to deploy the intrusion detection system to easily capture and detect online packets.

Author(s) Details

D. P. Gaikwad
Department of Computer Engineering, All India Shri Shivaji Memorial Society’s College of Engineering, Pune, India.

Dr. R. C. Thool
Department of Computer Engineering, All India Shri Shivaji Memorial Society’s College of Engineering, Pune, India.

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Determinant of Matrix by Order Condensation | Chapter 06 | Theory and Applications of Mathematical Science Vol. 1

A simple and direct process is derived to compute the determinant of any square matrix of high order. The approach involves successive applying the matrix order condensation algorithm. A computer program listing in MATLAB is included and examples for finding the determinant of a given 7×7 matrix are given here for illustration.

Author(s) Details

Dr. Feng Cheng Chang
Allwave Corporation, Torrance, California, USA.

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Convex Programming Based on Hahn-Banach Theorem | Chapter 05 | Theory and Applications of Mathematical Science Vol. 1

The main objective of this chapter is to present the separation theorems, important consequences of Hahn-Theorem theorem. Therefore, we begin with an overview on convex sets and convex functionals. Then go on with the Hahn-Banach theorem and separation theorems. Follow these results specification: first for normed spaces and then for a subclass of these spaces, the Hilbert spaces. In this last case plays a key role the Riesz representation theorem. Separation theorems are key results in convex programming. Then the chapter ends with the outline of applications of these results in convex programming, Kuhn-Tucker theorem, and in minimax theorem, two important tools in operations research, management and economics, for instance.

Author(s) Details

Manuel Alberto M. Ferreira
ISTAR-IUL – Information Sciences, Technologies and Architecture Research Center (ISTA), Portugal.

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Fuzzy Model, Neural Network and Empirical Model for the Estimation of Global Solar Radiation for Port-Harcourt, Nigeria | Chapter 04 | Theory and Applications of Mathematical Science Vol. 1

The invaluable role of the estimation of global solar radiation in solar engineering systems provides very useful direction for various solar applications. This paper employs the Adaptive Neuro Fuzzy Inference System (ANFIS), Artificial Neural Network (ANN) and regressive technique for the prediction of global solar radiation(GSR) on horizontal surface using temperature swing and relative humidity as input parameters covering years 1981 to 2005. The performance of the models was tested using statistical indicators such as mean bias error (MBE), root mean square error (RMSE) and correlation coefficient (CC). The results with ANFIS and ANN method provide a relatively better prediction with ANFIS the more preferable.

Author(s) Details

Olumide Olufemi Akinnawo
Department of Physical and Earth Sciences, Crawford University, Igbesa, Ogun State, Nigeria.

Oluwaseun Caleb Adebayo
Department of Physics, Federal University of Technology, P.M.B. 704, Akure, Ondo State, Nigeria.

Abel Giwa Usifo
Department of Physical and Earth Sciences, Crawford University, Igbesa, Ogun State, Nigeria.

Abiodun Kazeem Ogundele
Southwestern University of Nigeria, Okun-Owa, Sagamu-Benin Expressway, Ijebu-Ode, Ogun State, Nigeria.

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Automatic Task Splitting for Uniprocessor Systems Scheduled with Non-Preemptive EDF | Chapter 03 | Theory and Applications of Mathematical Science Vol. 1

Although preemptive scheduling dominates non-preemptive scheduling from a schedulability perspective, the latter will often be chosen by developers of real-time systems with resource constraints due to the inherently lower system overheads, easier code implementation and timing analysis. This paper is concerned with the uniprocessor scheduling of periodic and sporadic tasks with arbitrary relative deadlines in real-time systems using the non-preemptive version of the Earliest Deadline First (npEDF) algorithm. Although npEDF is known to be optimal among the non-preemptive work-conserving schedulers, it can still be restrictive in the sense that there exists uniprocessor-feasible task sets (with arbitrarily low CPU utilization) that are not schedulable with npEDF. For such task sets, system developers are forced to either consider the use of an alternate scheduling strategy or refactor the task software in some beneficial way. One such beneficial way is to apply a concept known as ‘task splitting’. However to date, little guidance has been available to assist developers with the latter process, and it is often performed on an ad-hoc basis. This paper will propose the application of a fast and efficient task splitting technique to assist developers with this software refactoring process, which can thus be used to maximize the achievable CPU utilization whilst retaining the benefits of non-preemption. Examples and experimental results are given to illustrate the performance of the algorithm. For random but representative task sets, the results also indicate that in the average case only a relatively small number of tasks require the application of task splitting to become schedulable under npEDF.

Author(s) Details

Michael Short
School of Computing, Engineering and Digital Technologies, Teesside University, Middlesbrough, UK.

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