Optimalisering

This book introduces the advances in synchromodal logistics and provides a framework to classify various optimisation problems in this field. It explores the application of this framework to solve a broad range of problems, such as problems with and without a central decision-maker, problems with and without full information, deterministic problems, problems coping with uncertainty, optimisation of a full network design problem. It covers theoretical constructs, such as discrete optimisation, robust optimisation, optimisation under uncertainty, multi-objective optimisation and agent based equilibrium models. Moreover, practical elaborated use cases are presented to deepen understanding. The book gives both researchers and practitioners a good overview of the field of synchromodal optimisation problems and offers the reader practical methods for modelling and problem-solving.

This book features contributions from the GTM 2020 International Meeting on Game Theory held virtually from St. Petersburg, Russia, including presentations by plenary speakers. The topics cover a wide range of game-theoretic models and include both theory and applications, including applications to management.

Written by leading scholars from various disciplines, this book presents current research on topics such as public choice, game theory, and political economy. It features contributions on fundamental, methodological, and empirical issues around the concepts of power and responsibility that strive to bridge the gap between different disciplinary approaches. The contributions fall into roughly four sub-disciplines: voting and voting power, public economics and politics, economics and philosophy, as well as labor economics.On the occasion of his 75th birthday, this book is written in honor of Manfred J. Holler, an economist by training and profession whose work as a guiding light has helped advance our understanding of the interdisciplinary connections of concepts of power and responsibility. He has written many articles and books on game theory, and worked extensively on questions of labor economics, politics, and philosophy.

This book is a rigorous but practical presentation of the techniques of uncertainty quantification, with applications in R and Python. This volume includes mathematical arguments at the level necessary to make the presentation rigorous and the assumptions clearly established, while maintaining a focus on practical applications of uncertainty quantification methods. Practical aspects of applied probability are also discussed, making the content accessible to students. The introduction of R and Python allows the reader to solve more complex problems involving a more significant number of variables. Users will be able to use examples laid out in the text to solve medium-sized problems. The list of topics covered in this volume includes linear and nonlinear programming, Lagrange multipliers (for sensitivity), multi-objective optimization, game theory, as well as linear algebraic equations, and probability and statistics. Blending theoretical rigor and practical applications, this volume will be of interest to professionals, researchers, graduate and undergraduate students interested in the use of uncertainty quantification techniques within the framework of operations research and mathematical programming, for applications in management and planning.

This book uses logic, philosophy, and whimsical storytelling to investigate the magic of succeeding by believing. In particular, we look at the "supposed" secret to success: if you believe you will succeed, then you will succeed. What happens when you adopt this belief? The logical consequences may be surprising. For example, under certain conditions, this supposed secret becomes a logical, self-fulfilling prophecy.Through a progression of 15 chapters, we follow a narrative-going deeper and deeper into the rabbit hole of the supposed secret. Most chapters include a short story to illustrate a logical concept relating to the supposed secret, and most chapters also include a rigorous analysis to satisfy the skeptics. My fundamental thesis is that "magicians" (those who believe in the supposed secret) are logically empowered by the supposed secret to success-even according to skeptical logic.Just a draft. Peer review appreciated.

A problem in graph theory that has received increased attention during the past 50 years concerns studying methods of distinguishing the vertices of a connected graph from one another.There are many ¿elds of mathematics now in the mathematics curriculum that overlap into graph theory. Large areas of set theory, pure combinatorics, algebra, geometry and especially topology consider problems of graph theory. However, since graph theory now makes its appearance in so many ¿elds and especially since a large amount of graph theory could be developed and presented at the high school or undergraduate level, it would seem to merit more than just a passing glance in the curriculum. First, however, a great e¿ort is needed to introduce graphs as a logical abstract mathematical system. A sequential rigorous development with preciseness of de¿nitions and süciently complete to reveal its basic nature and applications is needed.

Mathematics acts an important role in many aspects of fields. Graph theory, which will be applied in structural models, is an important area of mathematics. This structural arrangement of various things or techniques leads to new creations and improvements to the current order to enhance these areas. Graph theory is that part of Discrete Mathematics that has a large amount of application in real-life situations like facility locational problems, science and technology, and communication networks. Graph Theory is a great place to learn about methodologies in discrete mathematics, and the results have applications in a variety of fields including computing, social science, and natural data analysis. In both pure and applied mathematics, the last 50 years have seen a barrage of effort in graph theory. A graph is a set of nodes connected by links. A graph is a set of points with lines connecting them. The vertices and edges of a graph are also known as points and lines, respectively. The vertex set is denoted as ¿¿¿¿(¿¿¿¿), and the edge set is denoted as ¿¿¿¿(¿¿¿¿). Every branch of mathematics requires some kind of product concept to allow the combination or breakdown of its fundamental structures. The graph product is a relatively new concept in graph theory that is growing fast. Human genetics, a dynamic location problem, and networks are just a few examples of where graph products are used. Products are frequently seen as a convenient language for describing structures, but they are increasingly being used in more significant ways.

The Standard Model is a remarkably successful theory. It is a quantum theory describing the electromagnetic, weak and the strong interactions in nature. Its biggest shortcoming lies in its inability to describe gravity in the quantum regime. Furthermore, the con-stituents of dark matter and their interactions remain poorly understood, making it clear that there is much physics beyond Standard Model. String theory has the promise to pro-vide a quantum theory of gravity unifying all forces of nature [1-4]. It is a theory of interacting strings and other extended objects like D-branes. Its spectrum always con-tains a massless spin-2 state whose low energy interactions are as in general relativity. String perturbation theory is known to be ultraviolet ¿nite. At present, the most promis-ing direction to connect string theory with nature is by compactifying ten dimensional string theories on six dimensional Calabi-Yau manifolds. Much progress has taken place in this direction, and this remains an active area of research. Furthermore, the techniques of perturbative quantum ¿eld theory fail in the case of strong interactions (QCD) at low energies. However, a close cousin of QCD, i.e. N = 4 supersymmetric Yang-Mills theory in four dimensions at strong coupling can be understood via its string theory dual due to a mathematical correspondence [5, 6]. This has given hope that string theory can shed light on strong dynamics.

This thesis titled "Study of Some Dark Energy and String Models in Certain Alternative Theories of Gravitation" consists of eight chapters and deals with the investigation of some spatially homogeneous and anisotropic cosmological models in the frame work of Brans-Dicke (1961) and Saez-Ballester (1986) scalar-tensor theories, Barber's (1982) second self-creation theory and f(R, T ) modi¿ed theory of gravity (Harko et al. 2011), which are viable alternatives to Einstein's theory of gravitation.The main aim of cosmology is to construct mathematical models of the universe and compare these models with the present day universe as observed by astronomers. A full picture should comprise both an inventory of the present matter content (including its spatial distribution) and an understanding of the dynamics governing past and future evolution of the universe as a whole. Technological advances have brought an increasing ability to gather enormous quantities of data to further our understanding.

This open access book serves as a compact source of information on sine cosine algorithm (SCA) and a foundation for developing and advancing SCA and its applications. SCA is an easy, user-friendly, and strong candidate in the field of metaheuristics algorithms. Despite being a relatively new metaheuristic algorithm, it has achieved widespread acceptance among researchers due to its easy implementation and robust optimization capabilities. Its effectiveness and advantages have been demonstrated in various applications ranging from machine learning, engineering design, and wireless sensor network to environmental modeling. The book provides a comprehensive account of the SCA, including details of the underlying ideas, the modified versions, various applications, and a working MATLAB code for the basic SCA.