Bibliometric Analysis of Research Publications of Al-Jouf University, Saudi Arabia during the Year 2006-2017

The study investigates the research contributions of Al-Jouf University, Saudi Arabia in terms of its publication output during 2006-2017 as reflected through Scopus database. The study, using Microsoft Excel, analyses the year-wise research productivity, its citation impact, national and international collaborations, top collaborating institutions, subject-wise distribution of papers, journals used for communication, most preferred journals for publication, most prolific authors, number of citations received, and top cited papers of the University during the period under study. The paper concluded that Al-Jouf University is growing and improving in terms of research publication output

Bayesian Analysis of Generalized Exponential Distribution

Bayesian estimators of unknown parameters of a two parameter generalized exponential distribution are obtained based on non-informative priors using different loss functions

Bayesian Analysis of Location-Scale Family of Distributions Using S-PLUS and R Software

The Normal and Laplace’s methods of approximation for posterior density based on the location-scale family of distributions in terms of the numerical and graphical simulation are examined using S-PLUS and R Software

Symmetric Duality in Mathematical Programming

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Some Aspects of Mathematical Programming in Statictics

The Almighty has created the Universe and things present in it with an order and proper positions and the creation looks unique and perfect. No one can even think much better or imagine to optimize these further. People inspired by these optimum results started thinking about usage of optimization techniques for solving their real life problems. The concept of constraint optimization came into being after World War II and its use spread vastly in all fields. However, in this process, still lots of efforts are needed to uncover the mysteries and unanswered questions, one of the questions always remains live that whether there can be a single method that can solve all types of nonlinear programming problems like Simplex Method solves linear programming problems. In the present thesis, we have tried to proceed in this direction and provided some contributions towards this area. The present thesis has been divided into five chapters, chapter wise summary is given below: Chapter-1 is an introductory one and provides genesis of the Mathematical Programming Problems and its use in Statistics. Relationship of mathematical programming with other statistical measures are also reviewed. Definitions and other pre-requisites are also presented in this chapter. The relevant literature on the topic has been surveyed. Chapter-2 deals with the two dimensional non-linear programming problems. We develop a method that can solve approximately all type of two dimensional nonlinear programming problems of certain class. The method has been illustrated with numerical examples. Chapter-3 is devoted to the study of n-dimensional non-linear programming problems of certain types. We provide a new method based on regression analysis and statistical distributions. The method can solve n-dimensional non-linear programming problems making use of regression analysis/co-efficient of determination. In chapter-4 we introduce a filtration method of mathematical programming. This method divides the constraints into active and non active and try to eliminate the less important constraints (non-active constraints) and solve the problem with only active constraints. This helps to find solution in less iterations and less in time while retaining optimality of the solution. The final chapter-5 deals with an interesting relationship between linear and nonlinear programming problems. Using this relationship, we can solve linear programming problems with the help of non-linear programming problems. This relationship also helps to find a better alternate solutions to the linear programming problems. In the end, a complete bibliography is provided

Duality in mathematical programming.

In this thesis entitled, “Duality in Mathematical Programming”, the emphasis is given on formulation and conceptualization of the concepts of second-order duality, second-order mixed duality, second-order symmetric duality in a variety of nondifferentiable nonlinear programming under suitable second-order convexity/second-order invexity and generalized second-order convexity / generalized second-order invexity. Throughout the thesis nondifferentiablity occurs due to square root function and support functions. A support function which is more general than square root of a positive definite quadratic form. This thesis also addresses second-order duality in variational problems under suitable second-order invexity/secondorder generalized invexity. The duality results obtained for the variational problems are shown to be a dynamic generalization for thesis of nonlinear programming problem.Digital copy of Thesis.University of Kashmir

Some Aspects Of Duality In Variational Problems And Optimal Control

This thesis is divided into six chapters. In the Ist chapter we present a brief survey of related work done in the area of multiobjective mathematical programming, optimal control and game theory. Chapter Two: In this chapter sufficient optimality criteria are derived for a control problem under generalized invexity. A Mond-Weir type dual to the control problem is proposed and various duality theorems are validated under generalized invexity assumptions on functionals appearing in the problems. It is pointed out that these results can be applied to the control problem with free boundary conditions and have linkage with results for nonlinear programming problems in the presence of inequality and equality constraints already established in the literature. Chapter Three: In this chapter a mixed type dual to the control problem in order to unify Wolfe and Mond-Weir type dual control problem is presented in various duality results are validated and the generalized invexity assumptions. It is pointed out that our results can be extended to the control problems with free boundary conditions. The duality results for nonlinear programming problems already existing in the literature are deduced as special cases of our results. Chapter Four: In this chapter two types of duals are considered for a class of variational problems involving higher order derivative. The duality results are derived without any use of optimality conditions. One set of results is based on Mond-Weir type dual that has the same objective functional as the primal problem but different constraints. The second set of results is based on a dual of an auxiliary primal with single objective function. Under various convexity and generalized convexity assumptions, duality relationships between primal and its various duals are established. Problems with natural boundary values are considered and the analogues of our results in nonlinear programming are also indicated. Chapter Five: In this chapter a certain constrained dynamic game is shown to be equivalent to a pair of symmetric dual variational problems which have more general formulation than those already existing in the literature. Various duality results are proved under convexity and generalized convexity assumptions on the appropriate functional. The dynamic game is also viewed as equivalent to a pair of dual variational problems without the condition of fixed points. It is also indicated that our equivalent formulation of a pair of symmetric dual variational problems as dynamic generalization of those already studied in the literature. Chapter Six: In this chapter a mixed type second-order dual to a variational problem is formulated as a unification of Wolfe and Mond-Weir type dual problems already treated in the literature and various duality results are validated under generalized second order invexity. Problems with natural boundary values are formulated and it also is pointed out that our duality results can be regarded as dynamic generalizations of those of (static) nonlinear programming. The subject matter of the present research thesis is fully published in the form of the following research papers written by the author: (1) Sufficiency and Duality In Control Problems with Generalized Invexity, Journal of Applied Analysis,Vol, 14 No. 1 (2008),pp.27-42. (2) Mixed Type Duality for Control Problems with Generalized Invexity, Journal of Applied Mathematics and Informatics,Vol. 26(2008), No.5-6 , pp. 819-837. (3) On Multiobjective Duality for Variational Problems, The Open Operational Research Journal,2012, 6, 1-8. (4) Constrained Dynamic Game and Symmetric Duality For Variational Problems, Journal of Mathematics and System Science 2(2012), 171-178. (5) Mixed Type Second – Order Dulaity For Variational Problems, Journal of Informatics and Mathematical Sciences , Vol5,No.1, pp.1-13,(2013)

Some contributions to optimality criteria and duality in Multiobjective mathematical programming.

This thesis entitled, “some contributions to optimality criteria and duality in multiobjective mathematical programming”, offers an extensive study on optimality, duality and mixed duality in a variety of multiobjective mathematical programming that includes nondifferentiable nonlinear programming, variational problems containing square roots of a certain quadratic forms and support functions which are prominent nondifferentiable convex functions. This thesis also deals with optimality, duality and mixed duality for differentiable and nondifferentiable variational problems involving higher order derivatives, and presents a close relationship between the results of continuous programming problems through the problems with natural boundary conditions between results of their counter parts in nonlinear programming. Finally it formulates a pair of mixed symmetric and self dual differentiable variational problems and gives the validation of various duality results under appropriate invexity and generalized invexity hypotheses. These results are further extended to a nondifferentiable case that involves support functions.Digital copy of Thesis.University of Kashmir

On some contributions to size-biased probability distributions.

Statistical distributions and models are used in many applied areas such as economics, engineering, social, health and biological sciences. In this era of inexpensive and faster personnel computers, practitioners of statistics and scientists in various disciplines have no difficulty in fitting a probability model to describe the distributions of a real-life data set. Traditional enviromentric theory and practice have been occupied with randomization and replication. But in environmental and ecological work, observations also fall in the non-experimental, non-replicated and non-random catogries.The problems of model specification and data interpretation then acquire special importance and great concern. The theory of weighted distributions provides a unifying approach for these problems. Weighted distributions take into account the method of ascertainment, by adjusting the probabilities of actual occurrence of events to arrive at a specification of the probabilities of those events as observed and recorded. Failure to make such adjustments can lead to incorrect conclusions. The weighted distributions arise when the observations generated from a stochastic process are not given equal chance of being recorded; instead they are recorded according to some weight function. When the weight function depends on the lengths of the units of interest, the resulting distribution is called length biased. More generally, when the sampling mechanism selects units with probability proportional to some measure of the unit size, resulting distribution is called size-biased. Size-biased distributions are a special case of the more general form known as weighted distributions. These distributions arise in practice when observations from a sample are recorded with unequal probability. In Bayesian Statistics, the posterior distribution summarizes the current state of knowledge about all the uncertain quantities including unobservable parameters. In this thesis, the efforts have been made to study the areas.Digital copy of Ph.D thesisUniverity of Kashmir

Effect of Plant Growth Hormones on Shoot and Root Regeneration in Rose under In Vitro Conditions

Background: Rose is a commercially important shrub. This research aimed to observe the influence of different plant growth hormones on development of shoots and roots of Rosa Indica L. in tissue culture.Methods: Various concentrations of N6-Benzylaminopurine (BAP), 1-Naphthaleneacetic acid (NAA), Indole-3-acetic acid (IAA), and Indole-3-butyric acid (IBA) were used in the study. The different concentrations of BAP (2.00, 3.00, and 4.00 mg l-1) and IAA (2.00 and 3.00 mg l-1) were tested for shoot induction. While varying concentrations of IAA and IBA were analyzed for root proliferation.Results: The results of the study indicated that the fastest shoot initiation (17.77 days), the highest number of shoots bottle-1 (3.55), the maximum shoot length (4.72 cm), and the utmost number of leaves bottle-1 (53.67) were observed on MS media containing 3.00 mg l-1 BAP, 3.00 mg l-1 IAA, and 30 g l-1 sugar, while the highest number of shoots bottle-1 were produced under MS + 2.00 mg l-1 BAP + 3.00 mg l-1 IAA + 30 g l-1 sugar. Regarding root induction, the maximum number of roots (4.67) and root length (2.60 cm) were observed under half strength MS media supplemented with 30 g l-1 sugar.Conclusion: The study suggested that MS media containing 3.00 mg l-1 BAP and IAA could be used for tissue culturing rose plants. For root induction, half-strength MS media, along with sugar, could be used. The study gives an insight into potential media compositions for the propagation of rose. The suggested media can have promising uses in commercial multiplication of this important plant.Keywords: Rose; Tissue culture; Micropropagation; MS media; Shoot developmen