Contribution Study of M/M(a, b)/1 Queueing System with vacation Polices
The underlying assumption of queuing theory is that arrivals to the system are characterized by a probability distribution, the Poisson distribution, and service times by another known distribution, the exponential distribution. These assumptions enable analysts to devise easily solvable mathematical models, which may be used to evaluate system performance. Single Server Bulk service M / M (a, b) / 1 Queueing System, when solving the single server bulk service queueing models numerically, the results of system measures have been obtained effectively by using Matlab software.
Computational Methods with Probability
Numerical methods and probability are crucial for solving complex problems and understanding uncertain outcomes in various fields. Numerical methods provide tools for approximating solutions to problems that are difficult or impossible to solve analytically, while probability helps quantify and analyze randomness in real-world phenomena. Our purpose in writing this book was to provide a clear, accessible treatment of Mathematics for students studying graduate or post graduate courses in science and engineering. It focuses on the interpretation of mathematical results, especially in real world settings. In addition to end of section practice and homework sets, examples of each topic are explained step-by-step throughout the text and followed by a problem that is designed as extra practice for students. The objective is to learn what methods are available and more importantly, when they should be applied. Many examples are presented to clarify the use of the techniques and to demonstrate what conclusions can be made.
Functional Differential Systems
This book is a trail-blazer in robust formulations, investigations of computational feasibility and electronic implementations of mathematical results. It developed and used the core concept and computable expressions for determining matrices to establish necessary and sufficient conditions for Euclidean controllability of certain classes of functional differential systems. To actualize the applications of variation of constants formulas for initial and terminal function problems, as well as the characterization of controllability in terms of indices of control systems, this book pioneered the formulation and validation of the expressions and structures of solution and control index matrices for some classes of hereditary systems. To eliminate all computational and implementation constraints and achieve large-scale industrial applicability of the results, the book developed and provided software codes with a user guide for the implementation of results on the C++ platform. This has placed the generally neglected implementation aspect of mathematical results on the front burner, thus providing implementation paradigm shift.
Logic
This groundbreaking textbook presents a new approach to the study of logic by combining classical foundations with modern information-theoretic perspectives. Following a detailed introduction, it offers an information-theoretic formalization of logic. Subsequently, well-known but still unsolved problems, such as the P versus NP problem, are addressed using the provided tools. An optimization algorithm for the target requirements of logical problem-solving-regarding computability, expressiveness, and consistency-is presented, and finally, a few applications in other fields are showcased. The book offers students and researchers a comprehensive journey through the fundamental principles of logic while introducing innovative concepts at the intersection of logic, information theory, and computational complexity. Key features include: -Solid foundations in classical logic, including propositional and predicate logic, validity, and formal inference. -Novel integration of Shannon's information theory with traditional logical concepts. -Exploration of new approaches to axiomatization and formalization in light of G繹del's incompleteness results. -In-depth analysis of the P versus NP problem with information-theoretic and optimization approaches. -Clear explanations and examples suitable for beginners and beyond. -Applications in mathematics, computer science, and related fields.
Advances Statistic Inference Process Driven Fraction Process
One of the important problems in studying stochastic phenomena is to develop stochastic models and understand their implications behind the phenomenon. Long range dependence is an important stochastic phenomena and it needs study of special type of stochastic processes for modelling. My earlier book on Statistical Inference for Fractional Diffusion Processes (2010) dealt with several aspects for modelling by fractional Brownian motion. This book will contain my work on parametric and nonparametric inference for processes driven by fractional processes such as fractional Brownian motion, mixed fractional Brownian motion, sub-fractional Brownian motion, alpha-stable noise, fractional Levy process and Gaussian processes.
Numerical Linear Algebra with Applications
Numerical Linear Algebra with Applications: Using MATLAB and Octave, Second Edition provides practical knowledge on modern computational techniques for the numerical solution of linear algebra problems. The book offers a unified presentation of computation, basic algorithm analysis, and numerical methods to compute solutions. Useful to readers regardless of background, the text begins with six introductory courses to provide background for those who haven't taken applied or theoretical linear algebra. This approach offers a thorough explanation of the issues and methods for practical computing using MATLAB as the vehicle for computation. Appropriate for advanced undergraduate and early graduate courses on numerical linear algebra, this useful textbook explores numerous applications to engineering and science.
Projective Groups of Perspective Collineations in the Plane Treated Synthetically
A Treatise Of Geometry, Containing The First Six Books Of Euclid's Elements
Chaotic Maps, Fractals, and Rapid Fluctuations
This book was developed from lecture notes for an introductory graduate course and provides an essential introduction to chaotic maps in finite-dimensional spaces. Furthermore, the authors show how to apply this theory to infinite-dimensional systems corresponding to partial differential equations to study chaotic vibration of the wave equation subject to various types of nonlinear boundary conditions. The book provides background on chaos as a highly interesting nonlinear phenomenon and explains why it is one of the most important scientific findings of the past three decades. In addition, the book covers key topics including one-dimensional dynamical systems, bifurcations, general topological, symbolic dynamical systems, and fractals. The authors also show a class of infinite-dimensional nonlinear dynamical systems, which are reducible to interval maps, plus rapid fluctuations of chaotic maps. This second edition includes updated and expanded chapters as well as additional problems.
Projective Groups of Perspective Collineations in the Plane Treated Synthetically
![An Introduction To Arithmetic. [with] Key](https://cdn.kingstone.com.tw/english/images/product/6487/9781024686487m.webp?Q=9ba4c "An Introduction To Arithmetic. [with] Key")
The Struggles of BSE-Math Student-Parent in the Online Learning Approach
![An Introduction To Arithmetic. [with] Key](https://cdn.kingstone.com.tw/english/images/product/2083/9781024682083m.webp?Q=ebb1f "An Introduction To Arithmetic. [with] Key")
Recent Trends in AI Enabled Technologies
This book constitutes the refereed proceedings of the Second International Conference on Recent Trends in AI Enabled Technologies, ThinkAI 2024, which took place in Hyderabad, India, during December 27-28, 2024. The 18 full papers in this book were carefully reviewed and selected from 75 submissions. These papers focus on topics of AI enabled technologies, including machine learning, soft computing, and deep learning algorithms.
The Magic Theorem
The Magic Theorem: a Greatly-Expanded, Much-Abridged Edition of The Symmetries of Things presents a wonder- fully unique re-imagining of the classic book, The Symmetries of Things. Begun as a standard second edition by the original author team, it changed in scope following the passing of John Conway. This version of the book fulfills the original vision for the project: an elementary introduction to the orbifold signature notation and the theory behind it.The Magic Theorem features all the material contained in Part I of The Symmetries of Things, now redesigned and even more lavishly illustrated, along with new and engaging material suitable for a novice audience. This new book includes hands-on symmetry activities for the home or classroom and an online repository of teaching materials.
A Graduate Course in Probability
This book grew out of the notes for a one-semester basic graduate course in probability. As the title suggests, it is meant to be an introduction to probability and could serve as textbook for a year long text for a basic graduate course. It assumes some familiarity with measure theory and integration so in this book we emphasize only those aspects of measure theory that have special probabilistic uses.The book covers the topics that are part of the culture of an aspiring probabilist and it is guided by the author's personal belief that probability was and is a theory driven by examples. The examples form the main attraction of this subject. For this reason, a large book is devoted to an eclectic collection of examples, from classical to modern, from mainstream to "exotic". The text is complemented by nearly 200 exercises, quite a few nontrivial, but all meant to enhance comprehension and enlarge the reader's horizons.While teaching probability both at undergraduate and graduate level the author discovered the revealing power of simulations. For this reason, the book contains a veiled invitation to the reader to familiarize with the programing language R. In the appendix, there are a few of the most frequently used operations and the text is sprinkled with (less than optimal) R codes. Nowadays one can do on a laptop simulations and computations we could only dream as an undergraduate in the past. This is a book written by a probability outsider. That brings along a bit of freshness together with certain "naiveties".
Noncommutative Measures and LP and Orlicz Spaces, with Applications to Quantum Physics
The theory of noncommutative Haagerup ��sup��/sup and Orlicz spaces is an important tool in both Quantum Harmonic Analysis and Mathematical Physics. Indeed, noncommutativity is arguably the raison-d'礙tre of the Heisenberg approach to quantum mechanics. Just as classical analysis formed the foundation for classical mechanics, a mature response to the challenges posed by quantum mechanics (from the Heisenberg perspective) similarly needs to be built on a well-developed foundation of noncommutative analysis. In the passage from the classical to the quantum setting, functions get replaced with (possibly noncommuting) operators. Von Neumann himself realised early on that some sort of noncommutative integral calculus tailored to this setting is therefore needed to meet this challenge. This book seeks to help address this need. The noncommutative Orlicz spaces presented here help in dealing with observable quantities and entropy. Goldstein and Labuschagne provide a detailed account of the current theories in a way that is useful and accessible to a wide range of readers, from graduate students to advanced users. Beginning with some foundational examples intended to build intuition for the theory to follow, including the theory of noncommutative decreasing arrangements, as developed by Fack and Kosaki, and of Orlicz spaces for general von Neumann algebras. The authors then present the theory of the more accessible tracial case, followed by that of the more demanding general (type III) case. The final part of the book is devoted to advanced theory and applications.
Existence of Positive Solutions
The study of the existence of positive solutions of operator equations in ordered Banach spaces, in which algebra, geometry and analysis are combined, has received much attention in the past few decades, but still in the present time.It is related to the existence of positive solutions of operator equations that have been raised in application, such as buckling of mechanical structures, design of suspension bridges, steady-state temperature distribution, chemical reactions, interaction between predators and prey, and management of natural resources.This problem can be reduced to the existence of an equation in an ordered Banach space.In this book we consider the existence of solutions of some types of equations in ordered Banach spaces.First, the existence and nonexistence of solutions of equations with differentiable concave-convex operators are discussed depending on the parameters.Next, based on the concept of partial incomplete compactness measure, we consider the existence of fixed points of monotone operators satisfying weak compactness conditions.Finally, we apply the bifurcation theory to consider the set of positive solutions of the boundary value problem.
The Magic Theorem
The Magic Theorem: a Greatly-Expanded, Much-Abridged Edition of The Symmetries of Things presents a wonder- fully unique re-imagining of the classic book, The Symmetries of Things. Begun as a standard second edition by the original author team, it changed in scope following the passing of John Conway. This version of the book fulfills the original vision for the project: an elementary introduction to the orbifold signature notation and the theory behind it.The Magic Theorem features all the material contained in Part I of The Symmetries of Things, now redesigned and even more lavishly illustrated, along with new and engaging material suitable for a novice audience. This new book includes hands-on symmetry activities for the home or classroom and an online repository of teaching materials.
Algebra; an Elementary Text-book for the Higher Classes of Secondary Schools and for Colleges
On Condition Numbers and the Distance to the Nearest Ill-posed Problem
