The second order nonlinear ordinary differential equation is executed as an auxiliary equation. For illustration, a new extension of so called (G’/G) method is considered to investigate the generalized Hirota-Satsuma coupled KdV equations for producing some new analytical solutions. The obtained solutions belong to hyperbolic functions, trigonometric functions and rational forms which show the wider applicability of this new extended method for handling other nonlinear evolution equations. The numerical results are also described in the figures.

Author(s) Details

Dr. Hasibun Naher Department of Mathematics and Natural Sciences, BRAC University, 66 Mohakhali, Dhaka 1212, Bangladesh.

This chapter is a tutorial exposition on how to translate concepts of voting systems to the Boolean domain, and consequently on how to use Boolean tools in the computation of a prominent index of voting powers, viz., the Banzhaf voting index. We discuss Boolean representations for yes-no voting systems, in general, and for weighted voting systems, in particular. Our main observation is that non-minimal winning coalitions are related to minimal ones via partial-order structures and also as particular subordinate loops that cover the all-1 cell in the Karnaugh map. We review the method of computing the total Banzhaf indices by the Conventional Karnaugh Map (CKM). Then we extend this method to handle larger problems via the Variable-Entered Karnaugh Map (VEKM). The map methods are demonstrated by two classical weighted voting systems.

Author(s) Details

Ali Muhammad Ali Rushdi Department of Electrical and Computer Engineering, Faculty of Engineering, King Abdulaziz University, P.O.Box 80204, Jeddah 21589, Saudi Arabia.

Omar Mohammed Ba-Rukab Department of Information Technology, Faculty of Computing and Information Technology, King Abdulaziz University, P.O.Box 344, Rabigh 21911, Saudi Arabia.

In this research, numerical solutions of continuous optimal control problems governed by linear damping evolution with delay and real coefficients are presented. The necessary conditions obtained from the knowledge of calculus of variation for optimal control problem constrained by delay differential equation is a linear two-point boundary value problem involving both delay and advance terms. Clearly, this coupling that exists between the state variable and the control variable is not amenable to analytical solution hence a direct numerical approach is adopted. We propose an augmented discretized continuous algorithm via quadratic programming, which is capable of handling optimal control problems constrained by delay differential equations. The discretization of the problem using trapezoidal rule (a one-step second order numerical scheme) and Crank-Nicholson with quadratic formulation amenable to quadratic programming technique for solution of the optimal control problems are considered. A control operator (penalized matrix), through the augmented Lagrangian method, is constructed. Important properties of the operator as regards sequential quadratic programming techniques for determining the optimal point are shown..

Author(s) Details

O. C. Akeremale Department of Mathematics, Federal University Lafia, P.M.B. 146, Lafia, Nasarawa State, Nigeria.

Dr. O. Olotu Department of Mathematical Sciences, Federal University of Technology, P.M.B. 704, Akure, Ondo State, Nigeria.

A. Olaiju Department of Mathematics and Statistics, Federal Polytechnics, Ilaro, P.M.B. 50, Ogun State, Nigeria.

In the present paper, using direct variational approach, and the monotone operator method, theexistence of nontrivial solutions for a quasilinear elliptic equation involving the p-Laplacian is obtained.

Author(s) Details

Mustafa Avci Department of Science, Grande Prairie Regional College, Grande Prairie, AB, Canada.

Aims:
NOAA’s (National Oceanic and Atmospheric Administration) – LEO environmental
satellites provide continuous coverage of Earth, supplying high-resolution
global meteorological, oceanic and space observation data. These satellites are
part of the international Search and Rescue Satellite Aided Tracking (SARSAT)
system. SARSAT is designed to provide distress alert and location data in order
to assist on search and rescue operation. SARSAT system detects and locates
distress beacons (406MHz) activated at distress location. System calculates the
distress event location using Doppler processing techniques. Each satellite
pass transmits information about distress location. Passes with too short
communication duration, are considered as missed passes. Communication duration
analysis, among SARSAT satellites and local user terminal (LUT) dedicated for
search and rescue services are provided. LUT implementation process and the
mask record are also given.

Study
Design:
Simulation.

Place and Duration of Study: NOAA Satellite Operations Facility, Suitland, MD, USA, October, 28 – December 24, 2009.

Methodology: Communication analysis, are based on the hypothetical terminal assumed to be implemented in Kosovo (LUTKOS). Four hypothetical beacons indicating random distress locations are considered. Satellite orbital altitude of 860 km, orbital time of 102 minutes and inclination of 98.7º. Communication duration is considered for period 1-30, October 2009. 57560 satellite passes were considered to conclude about missed passes.

Results: For Doppler processing at least four events are required. Duration of 250s is considered as the lower margin, providing at least four Doppler events. The highest events density was in between 300s to 700s, sufficient for distress location determination. Only 3% of total considered passes were below 250s. The ratio of missed passes over total passes for the whole ground segment results as 0.17%, or in average 0.021% per month.

Conclusion: Through LUTKOS simulation, it is confirmed communication reliability and proper functionality of LUTKOS with a single SARSAT satellite.

Author(s) Details

Dr. Shkelzen Cakaj Post and Telecommunication of Kosovo, Prishtina, Kosovo. Faculty of Electrical and Computing Engineering, University of Prishtina, Kosovo. Faculty of Information Technology, Polytechnic University of Tirana, Albania.

Diagnostic testing concerning categorical or dichotomized variables is ubiquitous in many fields including, in particular, the field of clinical or epidemiological testing. Typically, results are aggregated in two-by-two contingency-table format, from which a surprisingly huge number of indicators or measures are obtained. In this chapter, we study the eight most prominent such measures, using their medical context. Each of these measures is given as a conditional probability as well as a quotient of certain natural frequencies. Despite its fundamental theoretical importance, the conditional probability interpretation does not seem to be appealing to medical students and practitioners. This paper attempts a partial remedy of this situation by visually representing conditional probability formulas first in terms of two-variable Karnaugh maps and later in terms of simplified acyclic (Mason) Signal Flow Graph (SFGs), resembling those used in digital communications or DNA replication. These graphs can be used, among other things, as parallels to trinomial graphs that function as a generative model for the ternary problems of conditional probabilities, which were earlier envisioned by Pedro Huerta and coworkers. The arithmetic or algebraic reading or solving of a typical conditional-probability problem is facilitated and guided by embedding the problem on the SFG that parallels a trinomial graph. Potential extensions of this work include utilization of more powerful features of SFGs, interrelations with Bayesian Networks, and reformulation via Boolean-based probability methods.

Author(s) Details

Ali Muhammad Ali Rushdi Department of Electrical and Computer Engineering, King Abdulaziz University, P.O.Box 80204, Jeddah, 21589, Kingdom of Saudi Arabia.

Fayez Ahmad Talmees Department of Electrical and Computer Engineering, King Abdulaziz University, P.O.Box 80204, Jeddah, 21589, Kingdom of Saudi Arabia.

Aims:
Analytical modeling of the combined systems photovoltaic-thermoelectric (PV +
TEG). The advantage of these systems is double:

On the one hand, they allow to cool the
photovoltaic cells (PV), which avoids the loss of electrical efficiency
observed in the devices,

On the other hand, recover this lost
energy in the form of heat, and transform it into electrical energy thanks to
the thermoelectric modules operating in Seebeck mode.

Study
Design: Laboratory of Radiation Physics LPR,
FAST-UAC, 01 BP 526, Cotonou, Benin. Department of Physics (FAST) and Doctoral
Formation Materials Science (FDSM), University of Abomey-Calavi, Benin.

Methodology: We considered the temperature distribution in the semiconductor plate of the Thermoelectric Generator System (TEG). We resolved the thermal conductivity equation described by:

Where
a^2 is the thermal diffusivity, Q(x, y, z) is the heat flow going from
the PV to the TEG module which is dissipated through the latter; using
constants variation method. We assumed that the temperature along the y-axis is
considered uniform.

Results: The results obtained show that, the temperature distribution in the form of a traveling wave is maintained by external heating. This depends on both the hot and cold side temperature and the temperature span.

Conclusion: The heat flux available at the hot side of the TEG is assumed to be what remains of the absorbed radiation of the PV power production.

Author(s) Details

Géraud F. Hounkpatin Département de Physique (FAST) et Formation Doctorale Sciences des Matériaux (FDSM), Université d’Abomey-Calavi, Bénin. Laboratoire de Physique du Rayonnement LPR, FAST-UAC, 01 BP 526 Cotonou, Bénin.

Macaire Agbomahéna Laboratoire de Physique du Rayonnement LPR, FAST-UAC, 01 BP 526 Cotonou, Bénin. Laboratoire de Caractérisation Thermophysique des Matériaux et Appropriation Energétique (Labo CTMAE/EPAC/UAC), Abomey-Calavi, Bénin.

Basile B. Kounouhéwa Département de Physique (FAST) et Formation Doctorale Sciences des Matériaux (FDSM), Université d’Abomey-Calavi, Bénin. Laboratoire de Physique du Rayonnement LPR, FAST-UAC, 01 BP 526 Cotonou, Bénin. Centre Béninois de la Recherche Scientifique et Technique (CBRST), 03 BP 1665 Cotonou, Bénin.

Vianou I. Madogni Département de Physique (FAST) et Formation Doctorale Sciences des Matériaux (FDSM), Université d’Abomey-Calavi, Bénin. Laboratoire de Physique du Rayonnement LPR, FAST-UAC, 01 BP 526 Cotonou, Bénin.

Antoine Vianou Laboratoire de Caractérisation Thermophysique des Matériaux et Appropriation Energétique (Labo CTMAE/EPAC/UAC), Abomey-Calavi, Bénin.

Cossi N. Awanou Département de Physique (FAST) et Formation Doctorale Sciences des Matériaux (FDSM), Université d’Abomey-Calavi, Bénin. Laboratoire de Physique du Rayonnement LPR, FAST-UAC, 01 BP 526 Cotonou, Bénin.

Relations between different magnitudes in a triangle, such as the radius of the circumcircle of the triangle, the radius of the incircle of the triangle, the radii of the excircles the triangle (which are tangent to one side from the outside and the continuations of the two other sides), as well as their relations with the side lengths the triangle and certain segments in the triangle, are a fascinating subject. We present a proven scheme of 15 relations between the sides of a triangle, the radii of incircles and excircles of the triangle, the area and half the perimeter of the triangle, which serve as signs of a right-angled triangle, together with the 16^{th} relation which is the Pythagorean Theorem. The relations are investigated dynamically using the computerized software.

Author(s) Details

Prof. Moshe Stupel “Gordon” and “Shaanan”-Academic College, Haifa, Israel and “Shaanan”-Academic College, Haifa, Israel.

Dr. Avi Sigler “Shaanan”-Academic College, Haifa, Israel.

In this paper, we define a new generalized difference sequence space l(p, θ, ∆^{m}, s) involving lacunarysequence where p = (p_{r}) is a bounded sequence of positive real numbers with p_{r} >1 for all r ∈ N and s ≥ 0. Then, we examine the uniform Opial property, k-NUC property and Banach-Saksproperty of type p for this space.

Author(s) Details

Sushomita Mohanta Department of Mathematics, Utkal University, Vani-Vihar, Bhubaneswar-751004, India.

In this chapter are compared four heuristic functions with high efficiency for an optimum solving of 8-puzzle. The analysis is realized among Chebyshev distance, Hamming distance and Manhattan distance using A* search algorithm implemented in Java. The two heuristic functions defined using Chebyshev distance are more informed than Hamming and Manhattan heuristics. This chapter also presents necessary stages in object oriented development of an interactive software dedicated to simulate the A* search algorithm for 8-puzzle. The modelling of software is achieved through specific UML diagrams representing phases of analysis, design and implementation, the system thus being described in a clear and practical manner. In order to confirm that second Chebyshev heuristic is more efficient was used space complexity performance criteria. The space complexity was measured by number of generated nodes from search tree, by number of expanded nodes and by effective branching factor. From experimental results obtained by using second Chebyshev heuristic, improvements were observed regarding space complexity of A* algorithm versus Hamming, Manhattan and first Chebyshev heuristics. Analysing the results presented in graphics, it can be asserted that number of steps made for obtaining the solution is the same for similar configurations, determining the optimal solutions for all four examined heuristics. But, investigating generated nodes number in the search tree associated with the A* algorithm using second Chebyshev heuristic, it can be observed that this number is strictly less than number obtain by using other three heuristics. Calculating approximately effective branching factor for all four heuristics, there were obtained values illustrated in figures. The values of b* appropriate to function h_{C2} are more appropriate to value 1 than values of b* appropriate to functions h_{M}, h_{H}, and h_{C1}, so the A* algorithm using h_{C2} heuristic drives to an optimal solution in a way that appears to be linear. According to these experimental values, results the superiority of second Chebyshev heuristic from Manhattan, Hamming and first Chebyshev heuristics. In this case we can say that h_{C2} heuristic dominates h_{M}, h_{H}, and h_{C1} heuristics, from space complexity point of view.

Author(s) Details

Anca-Elena Iordan Department of Electrical Engineering and Industrial Informatics, Engineering Faculty of Hunedoara, Polytechnic University Timisoara, Romania.