Showing papers in "IOSR Journal of Mathematics in 2016"

Ricci Solitons on Para-Sasakian Manifolds

Abstract: The present paper aims at studying a Ricci solitons on para-Sasakian manifolds. We give the results on Ricci solitons in para-Sasakian manifold satisfying the conditions 0 = ) , ( R X S   , 0 = ) , ( P X R   and 0 = ) , ( H X R   ,where P , H are pseudo-projective and quasi-conharmonic curvature tensors, respectively. MSC(2000): 53C21; 53C44; 53C25.

Comparison of Fuzzy Multiplication Operation on Triangular Fuzzy Number

Abstract: The arithmetic operations on fuzzy number are basic content in fuzzy mathematics. But still the operations of fuzzy arithmetic operations are not established. There are some arithmetic operations for computing fuzzy number. Certain are analytical methods and further are approximation methods. In this paper we, compare the multiplication operation on triangular fuzzy number between cut method and standard approximation method and give example and graphical representation supporting each example.

On Consistency and Limitation of Independent t-test Kolmogorov Smirnov Test and Mann Whitney U test

Abstract: It is worth repeating that if data are approximately normally distributed then parametric tests (as in the modules on hypothesis testing) are more appropriate. However, there are situations in which assumptions for a parametric test are violated and a nonparametric test is more appropriate. This study was aimed to investigates the strength and Limitation of independent t-test, Mann Whitney U test and Kolmogorov Smirnov test procedures on independent samples from unrelated population, under situations where the basic assumptions of parametric are not met for different sample size. Testing hypothesis on equality of means require assumptions to be made about the format of the data to be employed. Sometimes the test may depend on the assumption that a sample comes from a distribution in a particular family; if there is a doubt, then a nonparametric tests like Mann Whitney U test or Kolmogorov Smirnov test is employed. Random samples were simulated from Normal, Uniform, Exponential, Beta and Gamma distributions. The three tests procedures were applied on the simulated data sets at various sample sizes (small and moderate) and their Type I error and power of the test were studied in both situations under study.

Application of Lie-Group Theory for solving CalogeroBogoyavlenskii- Schiff Equation

Abstract: This work deals with exact solutions of (2+1)-dimensional Calogero-Bogoyavlenskii-Schiff (CBS) equation. Solutions so obtained are derived by using similarity transformations method via Lie-group theory. Exploiting Lie-symmetries and using invariance property, the number of independent variables is reduced by one by using the method, which turns the CBS equation into a new ordinary differential equation. Thereafter, Author attained the explicit solution of the system under the restrictions imposed upon the functions and arbitrary constants involved in the infinitesimals which are derived by the STM. The importance of analytical solution increased since their physical analysis is described on the basis of graphical representation of profiles with the help of numerical simulations.

Study of Fuzzy Set Theory and Its Applications

Abstract: The purpose of this paper is to study fuzzy sets and their real applications. Also, we study some properties of fuzzy sets. As an application of fuzzy sets, we solve some test problems and their solutions are represented graphically using Mathematica.

The Use of Cooperative Learning With Number Head Together Model to Improve the Students’ Mathematics Subject

Abstract: This research was a class action that begins with the development of learning tools. The subjects were students of class V SD Inpres Mallengkeri Makassar in the academic year 2015/2016, the number of students 45, there were 22 male students and 23 female students. The research was conducted in two (2) cycles. Each cycle consists of four phases: planning (planning), action (action), observations (observation) and reflection (reflection). The results of this research were to increase student learning thoroughness of the first cycle to the second cycle. If the first cycle the number of pupils who achieve complete category amounted to 28 people or 68.3 per cent, then the second cycle of the entire student has managed to achieve complete category. It can be concluded that the application of learning models Number Head Together has a role in improving student learning outcomes

Triple diffusive convection in Oldroyd-B liquid

Abstract: A linear stability analysis is carried out for triple diffusive convection in Oldroyd-B liquid. The expressions of Rayleigh number for stationary and oscillatory convection has been obtained. The neutral curves for oscillatory mode for different values of stress relaxation parameter, strain retardation parameter, solute Rayleigh numbers, ratio of diffusivity of solutes and heat diffusivity and Prandtl number has been examined. It is found that the oscillatory triple diffusive convection sets in earlier in system with Oldroyd-B liquid as compared to Newtonian liquid system.

Derivation of One-Sixth Hybrid Block Method for Solving General First Order Ordinary Differential Equations

Abstract: This paper focuses on the derivation of one-sixth hybrid block method for the general solution of first order initial values problems of ordinary differential equations. The new proposed method was derived by using the approach of collocation and interpolation of Chebyshev polynomials, approximate solution at some selected points to get a continuous linear multistep method, which was evaluated at some off-grid points to generate hybrid linear multistep methods. Basic properties of the proposed method wasexamined and the method found to be zero-stable, consistent and convergent. The efficiency of the method was tested on some numerical examples and in particular, on well-known SIR Model, Prothero-Robinson oscillatory problem and highly stiff oscillatory problem. On comparison, the new proposed method performed favourably when compare with the existing method proposed by other researchers in the area of Numerical Analysis.

A Tabu Search Approximation for finding the Shortest distance using Traveling Salesman Problem

Abstract: In this research, we present the basic concepts of Tabu search method for optimizing problem such as Traveling Salesman Problem (TSP). The main purpose of this work is to understand the symmetric TSP, solve this problem by using Tabu search method to find the shortest distance with small search space and computational needs and then using a computer program (using MATLAB software) to solve large scale Symmetric TSP. Finally, we find the shortest distance to visit 64 district headquarters of Bangladesh.

A Model to Optimize University Course Timetable Using Graph Coloring and Integer Linear Programming

Abstract: This paper presents the design and construction of a faculty course timetable. The system uses an Integer Linear Programming model which attempts to assign groups of course units to time periods where each group is a result of a graph coloring approach. Limited number of lecture halls, large number of subject combinations and growing number of student registration have made the problem very tight which results thousands of variables and constraints to the model. The quality of the solution depends on the location of the time period assigned to the set of course units. Hence the objective function is defined to optimize the allocation of time periods to course units. The model results a feasible solution which has reduced the maximum idle time of students to three hours and it can be implemented with the lecture halls currently available in the faculty of Applied Sciences, University of Sri Jayewardenepura. The model is flexible and allows to change the constraints depending on the faculty requirements and other factors and if necessary, construct alternative schedules.

A Modified Method for Solving Delay Differential Equations of Fractional Order

Abstract: In this paper, generalized Hat functions operational matricesare proposed and combined with the method of steps to solve linear and nonlinear delay differential equations of fractional order.We convert the delay differential equationsof fractional order to non-delay differential equationsof fractional orderon a given intervalby apply the method of steps, and then apply the operational matrices for generalized Hat function on the obtained non-delay differential equationsof fractional order to transform linear and nonlinear non-delay differential equationsof fractional order into a system of algebraic equations and then find the solution.Two illustrative examples will be presented to show the accuracy and efficiencyof the proposed method.

Parallelized methods for solving polynomial equations

Abstract: The current microprocessors are concentrating on the multiprocessor or multi - core system architecture. The parallel algorithms are recently focusing on multi - core system to take full utilization of multiple processors available in the system. The design of parallel algorithm and performance measurement is the major issue on today's multi - core environment. Numerical problems arise in almost every branch of science which requires fast solution. In this paper we have presented parallel algorithms for computing the solution of system of non - linear equations and approximate the simple zeros of polynomial equations. The experimental results reveal that the performances of parallel algorithms are better than sequential. We implemented the parallel algorithms using multithreading features of OpenMP.

Estimation of the Parameters of Compound Weibull Distribution

Abstract: This paper explores the potential of the Compound Weibull Distribution (CW) in theory and practice. Statistical lifetime distributions are commonly used in various fields for modeling data sets where the CW distribution is the most applicable. This distribution is presented with its properties and graphical representations. Some special cases and related distributions to the CW distribution are derived. Moments (M), maximum likelihood (ML) and Bayesian based on informative prior methods are used to estimate the unknown parameters of the distribution. Markov Chain Monte Carlo (MCMC) technique is used to compute the Bayesian estimates with different prior distributions based on squared and absolute error loss functions. The simulation is performed to investigate and compare between the estimators with different sizes and one set of the parameter's values. In the sense of the mean squared error (MSE), the results showed that case 1 of Bayesian method, with gamma prior distribution and under squared error loss function (B1sq) is the best estimation method. A real data set is used to compare between the Weibull and the CW distributions and the results showed that the CW distribution provides better fit than the Weibull distribution.

The Local Cultural Values In The Interaction Of Matematics Learning At School

Abstract: Abstrac: This research is an interdisciplinary study that aims to examine the cultural values of Bugisi Makassar which is involved in the interaction of the mathematics learning. This research was done at one of the schools in the city of Makassar by recording anecdotal for observing and analyzing the interactions that occur between teachers and students and also between students and students. The important recording is observing the cultural values of Bugisi Makassar that is involved in the interaction process. The result of this research shows that the dual concepts of the culture of bugis Makassar are siri' and pacce that is involved in the interaction of mathematics learning process between the interaction of teacher and students and also between students and students. This research also shows that in the interaction between teacher and students, the teacher always gives a motivation to students so they can get a good achievement. It is the realization of the siri' cultural value, as well as the students, are competing and trying to do their projects as well. Another result that related with the value of pacce is reflected in the teacher effort to help the students who have a difficulties and also a problem with their academic. So, the cultural values of siri and pacce as the main concept in the culture of Bugis Makassar I. Background The teaching and learning activities require a positive interaction between teacher and students, and also the students and student. The interaction is not only about how the teacher convey the material to students, but interaction requires students" understanding of humanely. Cobb, Wood, & Yackel (1991) states that mathematics classroom can be viewed as a social context in understanding of mathematics which a way of construction and negotiation. Thus, Atweh, Bleicher & Cooper (1998) reveals that the mathematics classroom is a place of teacher and students to build the interactive social environment, with the main goal of enhancing the teaching process. The other side of students who are studying in schools, they also has own character from their surroundings as the socialization process, including socio-cultural factors. The mathematics learning in schools is expected to establish the logical reasoning and attitude of students, and also to extend the supplies of students to implement the mathematics in their daily life. Soedjadi (1999) stated that teaching mathematics in every level of schools is basically referred for two main purposes, which are the formal purpose and the material purpose. The formal purpose of mathematics is relating of structuring the logical reasoning and the attitude of students, whereas the material purpose of mathematics is relating to the uses of mathematics, in the field of mathematics itself or in another field. Sagala (2003) suggests two learning characteristics, namely: (1) in the learning process involves the maximum of students" mental processes, not only demanding students to listen and take notes, but it requires the activity of students in the process of thinking, (2) in the learning process, builds a communicative atmosphere by giving a lot of discussions which is directed to improve and enhance students" thinking ability, that can help students to acquire the knowledge of their own construction. While in the relation to the study of mathematics, Nickson (1992) suggested that learning of mathematics is an effort to help students to construct the concepts or principles of mathematics on their own through a process of internalization, so the concept or principle was rebuilt. The process of construct the mathematical concepts or principles cannot be separated from the process of mathematical thinking which is a cognitive activity, while on the other side of human cognitive activities can only take place within the social and cultural environment. According to Vygotsky, all high-level cognitive work in humans has its origins in the social interactions of every individual in a specific cultural context (Bruming et al, 1995). Whereas on every teaching and learning activities required interaction, the interaction between students and another student, student interaction with the teacher and also student interaction with other learning tools. The exposure above illustrates that the activity of learning mathematics cannot be discharged by the cultural background of students in the interactions of mathematics learning, and thus required an effort to assess the socio-cultural background of students in the interactions of teaching and learning activities based on local cultural background.

On The Fuzzy Implicative Ideal of a BH-Algebra

Abstract: In this paper, we study a fuzzy implicative ideal of a BH-algebra. We give some properties of this fuzzy ideal and link it with other types of fuzzy ideals and fuzzy subset of a BH-algebra.

Degree Based Topological Indices of n-Butane Isomers

Abstract: Let G be a molecular graph. A graph G=(V(G),E(G) ) consists of the vertex set V(G) and the edge set E(G) such that each edge e in E is assigned an unordered pair of vertices (u, v), called the end vertices of e. The skeleton of an organic molecule (usually, of a hydrocarbon) represents simple graph. Thus the vertices of molecular graph represent the carbon atoms, and edges the carbon-carbon bonds. In molecular graph we have many topological indices. In this paper, we are computing some topological indices values of butane isomers.

Total Semi - µ Strong (Weak) Domination in Intuitionistic Fuzzy Graph

Abstract: In the initial stage we proposed the concept of Total Strong (Weak) domination in Fuzzy graph. It deal with the real time application that helps a individual person in crossing a road traffic signal. We will be giving a single value for vertices and edges. Enhancing the same concept, the Total Strong (Weak) domination in Intuitionistic Fuzzy graph was proposed. Here we will be giving a double value for the vertices and edges. Now in this paper, we demonstrate the concept of Total Semi- µ Strong (Weak) domination in Intuitionistic Fuzzy Graph. Theoretically Semi- µ Strong intuitionistic fuzzy graphs took minimum value between the two edges. Also we have proved some equivalent theorems and examples. Index Terms: Intuitionistic Fuzzy graph, Strong (Weak) intuitionistic fuzzy graph, Total Strong (Weak) IFG, Total Semi - µ Strong (Weak) Domination in IFG, Fuzzy domination number. MSC2016 codes - 05C72, 05C69, 03E72, 03F55

Run-up Flow of Oldroyd-B Fluid through a Parallel plate channel

Abstract: In this paper, we consider the unsteady hydrodynamic flow of an incompressible Oldroyd-B fluid in a parallel plate channel, initially induced by a constant pressure gradient. The pressure gradient is suddenly withdrawn and the upper plate moves with a uniform velocity while the lower plate continues to be at rest. The arising flow is referred to as run up flow. The unsteady governing equations are solved as initial value problem using Laplace transform technique. The expressions for velocity, shear stresses on both plates and discharge are obtained. The behaviour of the velocity, shear stresses and mass flux has been discussed in detail with respect to variations in different governing flow parameters and is presented through graphs.

Pre-Service Teachers’ Didactic Conceptual Structures in the Absolute and Quadratic Inequalities

Abstract: This paper examined the didactic conceptual structures of preservice teachers in the absolute and quadratic inequalities to deduce mistakes and errors. Quasi-experimental and mixed exploratory sequential designs were adopted on the participants who worked in 37 groups of 10 members in the Department of Basic Education, University of Education, Winneba in Ghana. The data collection instruments consisted of 15 openended items on the basic ideas of the absolute and quadratic inequalities to identify the didactic content knowledge in solving the problems. The thematic analysis of the conceptual structures as well as the marked scores revealed the errors and mistakes in the inner structures, inner relations, representations, and verticalhorizontal relations preservice teachers had confronted in solving problems in absolute and quadratic inequalities. The implications of these would impact negatively on the teaching and learning of mathematics curriculum, and inappropriately applied in a variety of daily lives.

Mathematical Modeling on Two Phase Hepatic Systolic Blood Flow through arteries due to Hepatitis A

Abstract: The study of mathematical model of two phase blood flow in artery presented here. P.N. Pandey and V. Upadhyay have considered the blood flow has two phased, one of which is that of red blood cells and other is plasma. They have also applied the non-Newtonian power law model in bio fluid mechanical set-up. We have collected a clinical data in the case of Hepatitis A. The overall presentation is in tensorial form and solution technique adapted is analytical as well as numerical. The role of Hematocrit is explicit in the determination of blood pressure in case of Hepatitis A infection. The graphical presentation for particular parametric value is much closer to the clinical observation.

The Improved Ant Colony Optimization for the Multi-Dominated QoE Evaluation Point Selection Problem

Abstract: Quality of Experience (QoE) evaluation, compared with Quality of Service (QoS), can better reflect the quality of the network by considering the end-user's experience. Based on the number of users and the difference of user's behavior, the operators need to selectsome candidate test points which can perfectly represent all the users, and use the selected test points to simulate the user's behavior in the network. Due to users' different behavior, every candidate test point dominates different users' different behavior, which is described by corresponding dominated matrixes. In this article we present the multi-dominated QoE evaluation point selection problem and establish a 0-1 integer linear programming model. Because this problem is NPhard,weadopt an improved ant colony optimization algorithm to solve it. And three methods of heuristic information description are proposed in the improved ACO. In order to demonstrate the effectiveness of the proposed method,some instance with 500 user points are generated and the performance of improved ACOs with three heuristic functions are given. Simulation results show thatthe quality of solution provided by the improved ACO has improved by 3.5% and 10% respectively compared with ACO and greedy algorithm when all the users are dominate. What’s more, the average convergence speed of improved ACOs has increased by 88%, among them H1-IMACO reaches 94% and the average elapsed (running) time is significantly reduced by 57.6%. Keywords: QoE evaluation, multi-dominated point selection, 0-1 integer linear programming, the improved Ant Colony Optimization, heuristic information I. Introduction As the Internet constantly deeply influences people's lives, people don’t focus on how to access network resources any more, but how to get better network resources. As a result, the satisfaction degree of the user’s experience is the greatest concern for the current network service providers. People used to improve the network’s performance and the overall utilization through improving bandwidth, latency, jitter and packet loss, which may affect the network’s quality of service (QoS) in network transport. However, these studies are all about the network infrastructure and they cannot fulfill the real user’s experience. QoE evaluation from the perspective of the user brings in the quality of the user’s experience to describe the performance of the network, that is to hope users evaluate their own experience evaluation every time. [1,2] For example, there are a lot of domestic video sites such as sohu, iQIYI, youku and so on. Assume the user will assign a value to his every experience according to his own satisfaction degree after browsing a video website. It is easy to know that different users have different satisfaction with the same video site, and the same user satisfactions of different video sites are also different. However, not every user will comment on his experience and also a user will not comment his every experience. To get the quality of network accurately we want to simulate uses’ behavior and give the evaluation. But It needs not only plenty of manpower and material, but also enormous and continuous financial support upon this procedure. So we need to find a way to select part of the test points not only instead of all the users as many as possible but comprehensively considering all the different user behaviors. Give a network only with the candidate test nodes (like workstation, server, network equipment) and user nodes (like terminal users). If a candidate node can monitor or serve some user nodes, we call the candidate node can dominate those user nodes. Here every user has kinds of behavior. Under different user behavior the same candidate node dominates different subset of user nodes. This article is to select some candidate nodes as less as possible that can dominate all the user nodes under every user behavior. It is easy to find that when there is only one user behavior, this problem can be described as a set-covering problem (SCP). So this paper tries to design an algorithm solving this problem from algorithms using in SCP. As we all know, the classical SCP has been proved to be a NP-hard problem, which cannot be solved in polynomial time. [3] Although no exact algorithms are for more complex or larger SCP, at present most researches use approximate heuristic algorithms to optimize it and get better results, and one of them is the ant colony optimization. Ant Colony Optimization (ACO) is a kind of evolutionary algorithms based on swarm intelligence. It pays attention to the cooperation of ant individuals and use the mechanism of feedback pheromones quickly and efficiently to search the optimal The Improved Ant Colony Optimization for the Multi-Dominated QoE Evaluation Point Selection DOI: 10.9790/5728-1205048694 www.iosrjournals.org 87 | Page solution. [4,5,6] Ant colony algorithm has successfully applied many complicated combinatorial optimization problems. [7] And its excellent optimization ability provides a new train of thought when solving SCP. Most variants of ACO have fresh perspectives from the influence of defining the heuristic information [8,9], the new transition rule when selecting the next point [10] and other new ideas of designing feasible solutions [11,12]. Those are also the aspects we consider to design an improved ACO to solve the point selection problem under many user behaviors. What’s more, the setting of parameters in ACO is also an important matter [13,14], and documents [15,16,17] give some strategies when tuning them. The classical SCP is for one certain coverage condition, but this article proposes to combine many coverage condition together based on users’ different behaviors, what’s more, for different user behavior the candidate node has different coverage. To synthetically consider these behaviors and select as less as possible candidate points this article expand from the following steps. Firstly, a network topology is given with the candidate test points and user points. If the candidate test point can dominate a user point, there is an edge between them. And under different user behavior there is a dominated matrix. This article puts forward the multi-dominated QoE evaluation point selection problem, called Multi-Dominated Point Selection Problem (MDPSP). Then from aspects of the heuristic information, the new transition rule and adaptive mechanisms this article design an improved ACO to solve MDPSP, which improved the ACO’s shortcoming of slow speed of convergence and easily getting local optimum solution. Finally, utilize an instance generated by MATLAB to test the performance of the improved ACO and compared with the solution of ACO and greedy algorithm it achieves good results.The rest of the paper is organized as follows. In section 2we give the mathematicaldescription of the multi-dominant QoE evaluation point selection problem and establish 0-1 integer linear programming. In section 3 we give the outline of the improved ACO when using in MDPSP. Section 4 represents three heuristic function that is important for the ant’s selection strategy. In section 5we firstly set the optimal combinations of parameters for improved ACOs with three heuristic functions. Secondly using them solve the multi-dominant point selection problem and analyze the performance of improved ACOscompared with greedy algorithm and traditional ACO. Section 6 concludes the article. II. Problem Description and mathematical model In a network exist workstation, server, network equipment and terminal users. And one workstation, sever or network equipment can monitor or server terminal users in a certain distance and in this case the operator can simulate some users’ different behavior on it to give the evaluation. The final goal is to select parts of them as less as possible and to synthetically consider all the user behaviors that sometimes have different importance for operators. This article gives a network topology with two kinds of points -candidate test points (like workstation, server, network equipment), denoted as Y = yj , j ∈ J = 1,2, ... , m and user points (terminal users), denoted as X = xi , i ∈ I = 1,2, ... n and candidate test point can connect with user points. If a candidate test point yj can connect some user points xi1 , xi2 , ... , xih ⊆ X, we say yj dominates xi1 , xi2 , ... , xih and there is an edge between yj and xih 0 , h0 ∈ 1,2, ... , h . The set of users’ different behavior is U = {1, 2, ... , l} and for one behavior t there is a dominate matrixDu = dij u , u ∈ U, i ∈ I, j ∈ J, where dij u = 1, ifxicanbedominnatedbyyj 0, ot𝑕erwise . To better understand this model Fig.1 is given for l = 2. And there are seven user points and two candidate test points. At this time, we get D1 = 1 0 1 0 1 0 0 1 0 1 0 1 0 1 , D2 = 1 0 1 1 0 1 1 0 1 0 0 1 0 1 . Fig.1 A simple example The problem aims to select some yj as less as possible, which can dominate X under every dominate matrix, so this article represents the Multi-Dominated QoE evaluation Point Selection Problem, short for MDPSP. It can be formally formulated as a 0-1 integer linear program: Minimize yj m j =1 (1) Subject to dij u yj m j =1 ≥ 1, ∀i ∈ I , ∀u ∈ U (2) yj ∈ 0,1 , ∀j ∈ J (3) User point

On Jordan Higher Bi­Derivations On Prime Gamma Rings

Abstract: n this study , we define the concepts of a higher bi­derivation , Jordan higher bi­derivation and Jordan triple higher bi­derivation on Г­rings and show that a Jordan higher bi­derivation on 2­torsion free prime Г­ring is a higher bi­derivation .

Comparison between Logistic and Calibration Linear Regression

Abstract: This paper hosts a comparison between logistic regression model and calibration linear model . Both models were applied on random sample of 120 people , 100 are infected with blood cancer and 20 are fit . And we have 3 independent variables , age , pcv , mch . When applying both models we discovered that the values of standard errors in calibration regression model are less than the value of standard errors in logistic regression model , meaning that calibration regression method was better . Some other results were reached , like when applying logistic all variables mentioned above have significant influence on cancer infection , we also found that pcv variable is the most influential in cancer infection , followed by the rest age and msh. Keyword: Linear model, classical estimator, calibration model,vce(robust) ,efficiency, Blood cancers.

Modeling Medical Oxygen Demand Using Box-Jenkins Methodology Applied Study on Soba University Hospital

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Time Evolution of Various Cosmological Parameters and Their Inter-Dependence in the Framework of Brans-Dicke Theory

Abstract: A theoretical model, regarding the time dependence of several cosmological parameters, has been constructed in the framework of generalized Brans-Dicke theory, using its field equations for spatially flat FRW metric. An empirical expression of the scalar field parameter, written in terms of the scale factor, has been substituted into the field equations to obtain expressions of Brans-Dicke dimensionless parameter (ω) and the density of matter (ρ), in terms of several relevant cosmological parameters. The dark energy, which is regarded as responsible for the accelerated expansion of the universe, is assumed to have generated from matter. On the basis of a model of matter to dark energy conversion, an expression of the density of dark energy has been derived. Using these relations of matter and dark energy density, expressions regarding the proportions of matter and dark energy have been formulated. To study the time dependence of all these quantities, an empirical time dependent expression of scale factor has been incorporated into their expressions. This scale factor expression has been so chosen that, the deceleration parameter derived from it, changes sign from positive to negative, as time goes on, implying the widely accepted change of phase from deceleration to acceleration, in cosmic expansion. Time dependence of gravitational constant and various other parameters and their interdependence have been depicted graphically.

Dynamics of the Shift Transformation on the GMLSm

Abstract: The topological Markov chain A  on the Golden Mean Lookalike Shift of order m [GMLSm] is a very typical topological discrete system possessing rich dynamical properties. In this paper we establish some results in connection with the chaotic properties of this Markov chain. In particular, we prove that it is Devaney chaotic (DevC), Auslander-Yorke chaotic and generically  -chaotic. Further, it has been shown that A  has chaotic as well as modified weakly chaotic dependence on initial conditions. Moreover, the zeta function for this Markov chain has been derived.

A Class of Fourth Order Approximate Solutions of Stationary Exterior Fields of Einstein-Maxwell Equations

Abstract: A class of approximate solutions of stationary exterior fields of Einstein-Maxwell (EM) equations are obtained by expanding the metric in powers of a certain parameter and solving explicitly the first few orders in terms of four harmonic functions. Previously these approximate solutions in closed form were found upto third order. In the present paper we obtain new fourth order equations and find their approximate solutions for the particular choice of the harmonic functions. The harmonic functions are so chosen that all the approximate solutions obtained are asymptotically flat. Here some relations obtained are claimed to be a 'laboratory' with which future attempts at exact solutions in terms of harmonic functions may be tested.

Viscous Dissipation Effects on Radiative MHD Boundary Layer Flow of Nano fluid Past a Wedge through Porous Medium with Chemical Reaction

Abstract: Magnetohydrodynamics (MHD) boundary layer flow past a wedge through porous medium with the influence of thermal radiation, heat source, viscous dissipation and chemical reaction has been analyzed in the present study. The governing nonlinear boundary layer equations for momentum, thermal energy and concentration are transformed to a system of nonlinear ordinary coupled differential equations by using suitable similarity transformation. The transmuted model is shown to be controlled by a number of thermo- physical parameters, viz. the magnetic parameter, heat generation parameter, Permeability parameter, Porosity parameter, Mass and Thermal convective parameters, Prandtl number, Lewis number, Brownian motion parameter, thermophoresis parameter, chemical reaction parameter and pressure gradient parameter. Numerical elucidations are obtained with the legendary Nactsheim-Swigert shooting technique together with Runge-Kutta six order iteration schemes.

A Bivariate Mathematical Model by Using Gonadotropin Releasing Hormone agonist (GnRHa) for the Prevention of Chemotherapy- Induced Ovarian Failure in Patients

Abstract: The problem of generating bivariate life distributions from univariate once is drawing the attention of the reliability analyst. Amongst those approaches, the characterization approach and the modeling approach are very appealing. In fact characterization approach is of interest to both theoreticians and applied workers. Here we have used a bivariate distribution for application by extending the univariate distribution through characterization approach. In our application we have considered cancer patients with chemotherapy treatment and taking GnRHa, FSH, and Estradiol as women stress effects. .