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Development of Some Lacunary Interpolation by S. F. and Application

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The aim of this thesis was the development of the study of lacunary interpolation by spline functions and their applications by changed the boundary condition for quantic and sixtic spline functions, and the algorithm was used to find the new absolute error between the original function and the spline function, and also the error bounded between the derivatives of original function and the derivatives of spline functions. Firstly, the object of this work is to show that the change of the boundary conditions and the class of spline functions have effect on minimizing error bounds theoretically and practically, and for application, the )NEB( algorithm was used. Secondly, in this study, (0, 4) lacunary interpolation was generalized by quantic spline function to obtain, the existence, uniqueness, and error bounds for the generalized (0, 4) lacunary interpolation by quantic spline. Finally, the lacunary interpolation problem consisted of finding the sixth degree spline of deficiency four, interpolating the data given on the function value with first and fourth order in the interval [0,1]. Also, an extra initial condition was prescribed on the second derivative of the functions. ····· 10361100004

Mathematical Modelling of Dispersion of Atmospheric Aerosols

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The growth of population, indiscriminate establishment of industries, auto-mobiles etc., are some of the major causes for the atmospheric pollution, besides power shortage. There is a growing concern that pollution together with accelerated growth and development of nations may alter the climate due to the release of large amount of soot, carbon emission and other pollutants into the atmosphere in the form of ultra-fine dust particles which are suspended in the atmosphere called aerosols. They play an important role in the atmospheric processes favouring cloud formation due to large size aerosols and having adverse effects on health, depending on their size due to coagulation process. This book focuses on mathematical modelling of dispersion of aerosols in the presence/absence of electric field and first order chemical reaction using different dispersion models. The problems addressed here are representative of aerosol removal mechanisms. In order to keep the environmental problems mathematically tractable few simplifying assumptions have been made to the extent that they do not obscure the actual phenomena which was purportedly modelled in a restrictive yet representative sense. ····· 1036199981

Uncertainty in Vehicle Routing Problems

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The stochastic VRP differs from the VRP by the introduction of some element of variability within the system in question. A key difficulty in optimization under uncertainty is in dealing with an uncertainty space that is huge and frequently leads to a very large scale optimization models. Also many decisions, in real life problems are based on information which is both fuzzily imprecise and probabilistically uncertain. Therefore, it is necessary to develop routing and scheduling tools which could handle the uncertainty in every parameter. The main focus of this work is to investigate the variants of an uncertain VRP when general VRP solutions cause some violation when parameters are contaminated with perturbation. This work explores Genetic Algorithm with Fuzzy Logic, a rare but a promising combination, to discover some interesting results not only in single objective VRP but also in multi-objective stochastic VRP s.This book is an attempt to ignite interest in researcher in the field of hard combinatorial optimization problems by introducing new strategies in which a multi-objective stochastic VRP can be effectively handled to give reliable multiple solutions and set of routes. ····· 1036199778

On Ruled Surfaces in three-dimensional Minkowski Space

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In a Minkowski three dimensional space we define a semi-inner-product based on the so-called cosine-Minkowski function. We also construct an orthogonal 3D frame in Birkhoff sense, which is canonically adapted to ruled surfaces: beginning with the generator direction we complete this frame using the strictly convex and centrally symmetric unit ball B, which is described either by supporting function or vector representation. Based on the left-orthogonality defined by ball B, the striction curve of a ruled surface in a Minkowski 3-space can be declared in analogy to the Euclidean case. We define the new vector called Deformation vector which helps us to find the Frenet-Serret formulae of the ruled surface in the Minkowski three dimension spaces. In these formulae we insert the M-curvatures and M-Torsions with respect to the Minkowski frame. We also can define a covariant differentiation in a Minkowski 3-space, with this can declare geometric M-parallelity of the vector field of the generator of a skew ruled surface along its Minkowski striction curve. Using the second fundamental form the relation between Euclidean and Minkowski normal vectors is given. ····· 1036199776

On Sp-open sets, Sp-continuity & Sp-compactness in Topological spaces

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In this thesis we introduce a new types of semi-open sets called Sp-open sets which is semi-open set and it is a union of preclosed sets. By this set we define a new type of continuity called Sp-continuity and also almost and weakly Sp-continuity are defined. At final we introduce new concept of semi-compactness called Sp-compact spaces. ····· 1036199682

Lie-group analysis of Newtonian/non-Newtonian fluids flow

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In this book, group methods are presented for finding the similarity solutions for some systems of partial differential equations, which govern the problems of convective flow in the boundary layer of Newtonian and non-Newtonian fluid. We will use three methods for finding the similarity representations (i) Scaling transformations, (ii) Infinitesimal Lie group analysis and (iii) Suitable similarity transformations. Lie groups, and hence their infinitesimal generators, can be naturally extended or `prolonged` to act on the space of independent variables, dependent variables and derivatives of the dependent variables up to any finite order. As a consequence, the seemingly intractable nonlinear conditions of group invariance of a given system of differential equations reduce to linear homogeneous equations determining the infinitesimal generators of the group. Since these determining equations form an over determined system of linear homogeneous partial differential equations. If a system of partial differential equations is invariant under a Lie group of point transformations, one can find, constructively, special solutions, called similarity solutions or invariant solutions. ····· 1036199657

On Fuzzy Differential Games

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The notion of the game is decision under uncertainty involving two or more intelligent opponents ,in which each opponent aspires to optimize his own decision at the expense of the other opponents .An opponent is referred to as a player The theory of games was born by Von Neumann`s in 1928 and in 1944 Von Neumann and Morgenstern introduced the concept of control for each player in the game and how the player seeks his control to minimize his own scalar cost criterion subject to specified constraints. The theory of fuzzy set is developed for solving problems in which their information`s are uncertain. Most of real life problems are considered as large scale ,solving these problems are appropriate decomposition techniques. ····· 1036199617

Estimate Survival Function for Brain Cancer Disease

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The subject of reliability and survival is one of the most important subjects and statistical procedure in current time which is interested in many fields, especially in medical, industrial and engineering fields. The Weibull distribution is one of the most popular failure time dealing with various data because its flexibility. In this research deriving and finding the survival probability function, hazard probability function and failure (death) probability function for three parameters weibull distribution of brain cancer in complete data to satisfying that estimating all parameters (shape, scale and location) using three classical methods (MLE method, ME method and OLS method)to find the survival function. Depending on sample from real data which describe the duration of survivor for patients who suffer from the brain cancer based on diagnosis of disease or the enter of patients in a hospital for period 1/1/2009 until 31/12/2009.Calculating and estimating survival, hazard and failure (death) functions from calculating and estimating the three parameters in Weibull distribution by using three classical previous mention methods. ····· 1036199388

Solution of Fuzzy Linear and Non-linear Equations

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Fuzzy sets are sets whose elements have degrees of membership. Fuzzy set theory was formalized by Professor Lotfi Zadeh at the University of California in 1965 as an extension of the classical notion of set. In classical set theory, the membership of elements in a set is assessed in binary terms according to a bivalent condition an element either belongs or does not belong to the set. Fuzzy sets generalize classical sets are special cases of the membership functions of fuzzy sets, if the latter only take values 0 or 1. Classical bivalent sets are in fuzzy set theory usually called crisp sets. On the other hand fuzzy set is more specified than crisp set. It can take a decision between membership grade 0 to 1, i.e. unit interval [0, 1]. This book attempts to fill the needs of the algorithms of Newton s method, Fixed-Point Iteration method and Bisection method which are used to solve fuzzy non-linear equations for the linear fuzzy real number. The procedures to obtain solutions of different types of fuzzy linear equations have also been discussed. The book has been outlined into four chapters. ····· 1036199358

Two approaches to compute GL(3) automorphic forms

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Ce Bian and Andrew Booker exhibited the first example of a third degree transcendental L-function at the American Institute of Mathematics (AIM). These L-functions encode deep underlying connections between many different areas of mathematics. While the result was announced the news caused excitement at the workshop attended by 25 of the world`s leading analytic number theorists. `This breakthrough opens a door to the study of higher degree L-functions,` said Dennis Hejhal, Professor of Mathematics at the University of Minnesota and Uppsala University. `It`s a big advance` added Harold Stark of the University of California, San Diego, who, 30 years ago was the first to accurately calculate second degree transcendental L-functions. `I thought we were years away from doing this. The geometry of what you have to do and the scale of the computation are orders of magnitude harder.` Dorian Goldfeld, Professor of Mathematics at Columbia University summarized the excitement, saying ``This discovery is analogous to finding planets in remote solar systems. We know they are out there, but the problem is to detect them and determine what they look like. It gives us a glimpse of new worlds` ····· 1036199207

Tropical Geometry

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The main topic of this book is the tropical semiring. Tropical geometry is a relatively new, but rapidly growing field in mathematics. The tropical semiring first appeared in computer sciences, but has deep relations with many fields of mathematics. These include algebraic geometry, mirror symmetry, complex analysis, combinatorics, logic, computer algebra and statistical models. In this book the main topic is the relation between tropical geometry and Voronoi diagrams. The author starts by discussing tropical addition and multiplication and what the graphs of polynomials, defined using this type of addition and multiplication, look like. Next, she discusses the notion of a tropical amoeba and how Voronoi diagrams relate to this notion. She will also consider power diagrams, a type of generalization of the Voronoi diagram, and look at their relation to tropical amoebas. She will show that every tropical polynomial defines a power diagram and, even better, also a Voronoi diagram. Lastly the author also approaches tropical geometry from the view of algebraic geometry. She will show how the spine of an amoeba in algebraic geometry relates to the tropical amoeba. ····· 1036199200

World Mixed Series in Bi-Topological Spaces : Using Mathematics

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Each topic is treated in systematic logical and lucid manner. The Scope and depth of coverage of each topic are strictly according to the world wide fuzzy topological space syllabus.Concepts are introduced in a sequential way with detailed explanations. Dr. Sadanand N. Patil is a working as Assistant Professor and H.O.D in the D/o. Mathematics, KLS s, VDRIT, HALIYAL. Karnataka, INDIA. Affiliated to VTU, BELGAUM. Since last 5 yrs he is teaching to UG & PG students of engineering stream. He has obtained M.Sc. (Mathematics) in the year 2002, PGDCA, in the year 2003 and He has obtained Ph.D. in Mathematics in the year 2009. Under the K U, Dharwad. The title of the thesis is SOME RECENT ADVANCE TOPICS IN TOPOLOGY, (FUZZY TOPOLOGICAL SPACES). Presently he is guiding to 6 candidates for Ph.D. in the field of FUZZY LOGIC Using FUZZY TOPOLOGICAL SPACES. As young scientist (DST) presented 2 papers in International Conference On Mathematics And Statistics Held At Kuala-Lampur, Malayasia (3 -5, November 2010). As senior scientist (DST) presented 2 papers in World Science Congress (LONDON) Is An IAENG , London, UK (July 6 - 9, 2011.) He Presented 5 Papers International Conference in Abroad, Presented 42 Papers In Various National and International Conferences and also Published 40 Papers In Various International Reputed Journals. ····· 1036199096

Trkal Flows and the Emergence of Metastable Streamline-Vortex Tubes

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Behavior of incompressible fluids at large values of the Reynolds number is usually considered as essentially turbulent and close to chaotic with high entropy. Nevertheless, low entropy coherent large scale structures are observed in geophysical and atmospheric phenomena, characterized by the alignment of the velocity and vorticity vectors. In his treatise on `Trkal Flows and the Emergence of Metastable Streamline-Vortex Tubes` Dr. Alexander Libin proposes a mathematical model for this phenomena,based on the asymptotic analysis at large values of the Reynolds number of the long wavelength perturbations of the Trkal solutions for 3-D Navier-Stokes equation.At the background, a dual pair of decaying Beltrami flows couples into a long-living triplet with a flow in the orthogonal direction to the dual pair plane.The plain flow is confined by a large invariant domain of a size characterized by the square root of the Reynolds number,just as the characteristic time period for the large scale plain flow stability.At these times the orthogonal flow is governed by intrinsically unstable equation,which might be considered as the manifestation of the hydrodynamic instability. ····· 1036198976

Fixed Point Theorems in Topological Spaces with Application to Fratal

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The problems associated in the present research work which are taken care of are related to the study of fixed point theorems in semi Hausdorff space, uniform space and Banach space along with studying the applications of fixed point theorem in economics and analyzing the theory of fractals and application of fixed point theory. In this work, the introductory part of fractal theory, the important applications of fractal in image compression and a model of fixed point theorem in dynamical system is taken into consideration keeping in view its application in various areas like planetary motion, stock market prices, meteorological data etc. Also theorem of maximal elements in Banach space and existence of maximal elements and equilibrium for pair of maps in ····· 1036198928

A generalization of Lie theory

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The notion of generalized group was introduced by Professor Molaei. After that he introduced top spaces as a generalization of Lie groups in 2004. A top space is a generalized group and a smooth manifold that its multiplication and inverse maps are smooth. In this book we give a review of recent works on top spaces with finite number of identities and a kind of top spaces with infinte number of identities (right top spaces). ····· 1036198832

Statistical Analysis of Diffusion Tensor Imaging

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This thesis tackles three major challenges in diffusion tensor imaging analysis with statistical methodologies. We firstly develop a novel Bayesian multi-tensor model with reparameterisation for capturing water diffusion at voxels with one or more distinct fibre orientations. A mixture Markov chain Monte Carlo (MCMC) algorithm is then developed to study the uncertainty of fibre orientations. Secondly, we apply non-Euclidean statistics to define the sample mean of diffusion tensor data which are employed for tensor field processing. In particular, Procrustes analysis, a powerful statistical shape analysis tool, is compared with the Log-Euclidean, Riemannian, Cholesky and power Euclidean approaches. A new anisotropy measure, Procrustes anisotropy, is defined. We finally use directional statistics to design uniformly distributed diffusion gradient direction schemes with different numbers of directions. All methods are illustrated through synthetic examples as well as white matter tractography of a healthy human brain. ····· 1036198790

Branes, Tachyons and String Theory

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In this publication we start by reviewing the motivational history, progress and major theoretical achievements of String Theory. Throughout we pay particular attention to the concept of Tachyons, particles which travel faster than light, and Branes, physical surfaces on which open strings can end. Next, we proceed to investigate specific aspects of Tachyon condensation mechanisms as a route to remove such unphysical particles, in particular extending the known results to the case of multiple coincident Branes. We further introduce the reader to the Geometrical Tachyon interpretation in which the Tachyon is understood as an extra radial direction in space. In this setup we also proceed to determine how this duality behaves in the presence of multiple Branes. Overall this book will take the reader through important examples of open questions in String theory and provides an excellent starting point to familiarise oneself with the less geometrical aspects of the mathematical machinery required by the standard String Theorist. ····· 1036198713

Graceful labelings of Tp-related trees

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Paper Publications of the Author : Kaladevi,V. Graceful Labeling of Supersubdivision of F-Tree and Pn+-Tree , Bulletin of Pure and Applied Mathematics, 2010. Kaladevi,V. Harmonius Colour of Supersubdivision of Star Graphs , Bulletin of Pure and Applied Mathematics, 2010. Kaladevi,V. and Backialakshmi,P. Maximum Distance Matrix of Super Subdivision of Star Graph , Antarctica Journal of Mathematics, Volume 8 (2011). Kaladevi,V. and Backialakshmi,P. Detour Distance Polynomial of Double Star Graph and Cartesian Product of P2 and Cn , Antarctica Journal of Mathematics, Volume 8 (2011). Kaladevi,V. and Kavitha,G. Edge-Odd Graceful Labelings Of Some Special Trees , Antarctica Journal of Mathematics, 2011. ····· 1036198707

Mathematics with Technology in Teaching

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Studies have shown that the use of computer technologies enhance the learning of students. The integration of ICT is seen as a priority by governments and schools both in Australia and overseas but despite the resultant provision of infrastructure and professional development, little appears to be happening in secondary school classrooms. Mathematics education in public secondary schools in New South Wales, Australia and around the world has been experiencing a wave of reforms directed toward the integration of technology in mathematics courses. This book modeled mathematics teachers use and non use of technology in teaching using variables such as: beliefs of mathematics teachers about teaching and learning of mathematics with or without technology, barriers to computer use and professional development undertaken by teachers with technology. It also contains a comprehensive discussion of learning theories that are useful in teaching mathematics with technology. The prospective and experienced mathematics teachers interviewed shared their teaching experiences when to use and not use technology. ····· 1036198696

Stochastic Differential Equations Driven by Levy Processes

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Stochastic differential equations driven by Levy processes are used as mathematical models for random dynamic phenomena in applications arising from fields such as finance and insurance, to capture continuous and discontinuous uncertainty. For many applications, a stochastic differential equation does not have a closed-form solution and the weak Euler approximation is applied. In such numerical treatment of stochastic differential equations, it is of theoretical and practical importance to estimate the rate of convergence of the discrete time approximation. In this book, it is systematically investigated the dependence of the rate of convergence on the regularity of the coefficients and driving processes. The model under consideration is of a more general form than existing ones, and hence is applicable to a broader range of processes, from the widely-studied diffusions and stochastic differential equations driven by spherically-symmetric stable processes to stochastic differential equations driven by more general Levy processes. These processes can be found in a variety of fields, including physics, engineering, economics, and finance. ····· 1036198652

Numerical Solution of NBV Problem for Elliptic Differential Equations

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Bitsadze-Samarskii nonlocal boundary value problem for elliptic differential equation in a Hilbert space H with the self-adjoint positive definite operators A is considered. The well-posedness of this problem in Hölder spaces with a weight is established. The coercivity inequalities for the solutions of the nonlocal boundary value problem for elliptic equation are obtained. The second and fourth orders of accuracy difference schemes for the approximate solutions of this nonlocal boundary value problem are presented. The stability estimates, coercivity and almost coercivity inequalities for the solution of these difference schemes are established. The well-posedness of these difference schemes in Hölder spaces with a weight is proved. The Matlab implementation of these difference schemes for elliptic equation is presented. The theoretical statements for the solution of these difference schemes are supported by the results of numerical examples. ····· 1036198493

Some Existence and Uniqueness Results for Difference Equations

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In this book some existence and uniqueness results for difference first order initial value problems and second order difference boundary value problems are obtained. For this Banach contraction principle, Schauder s fixed point theorem and Tychnoff s fixed point theorem are used. Moreover some comparison theorems are obtained using lower and upper solutions as well as maximal and minimal solution of such difference equations. ····· 1036198420

Cosmological Dynamical Systems

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Over the last century, the investigations in Gravitation and Cosmology have attracted the attention of thousand of human minds. Apart this boom in popularity, the homework task for cosmologists is to try to give an answer to the reasons why the present Universe has the properties that are observed. In spite of having a well-established theoretical framework like the Einstein`s gravity theory (GR), which is valid in an amplest rank of energies and that has responded satisfactorily to numerous empirical verifications, are numerous unanswered intriguing questions. Is the dark energy the cause of the acceleration of the expansion What is its equation of state nowadays Why the energy densities of matter and dark energy of the same order of magnitude nowadays Will be the acceleration of the expansion an indication that the action of Einstein-Hilbert must be modified Can be reached the isotropic degree of the universe that is observed today, independently of the initial degree of anisotropy In this book are studied, from the perspective of the dynamical systems, several Universe models that try to give answers to some of these questions. ····· 1036198409

Numerical Techniques for Solving the Transportation Problems

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In this study, we discussed the functionality of transportation problem and regular simplex method then compared their run-time and optimized values with non-linear method called the Lagrange multiplier method. Lagrange multiplier is an algorithm that uses different mechanisms to choose the best optimal solutions. This method based on transforming the linear structure transportation problem into the nonlinear structure and solved it directly, by the techniques.We concluded that the computational results with a Lagrange method are better, easier and shorter than those with a specialized simplex method for large problems. ····· 1036198330

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