"Presents a theory of difference and functional equations with continuous argument based on a generalization of the Riemann integral introduced by N.E. Norlund, allowing differentation with respect to the independent variable and permitting greater flexibility in constructing solutions and approximations. Discusses linear transformations that state conditions for convergence of Newton series and Norlund sums!"

A Useful Guide to the Interrelated Areas of Differential Equations, Difference Equations, and Queueing Models Difference and Differential Equations with Applications in Queueing Theory presents the unique connections between the methods and applications of differential equations, difference equations, and Markovian queues. Featuring a comprehensive collection of topics that are used in stochastic processes, particularly in queueing theory, the book thoroughly discusses the relationship to systems of linear differential difference equations. The book demonstrates the applicability that queueing theory has in a variety of fields including telecommunications, traffic engineering, computing, and the design of factories, shops, offices, and hospitals. Along with the needed prerequisite fundamentals in probability, statistics, and Laplace transform, Difference and Differential Equations with Applications in Queueing Theory provides: A discussion on splitting, delayed-service, and delayed feedback for single-server, multiple-server, parallel, and series queue models Applications in queue models whose solutions require differential difference equations and generating function methods Exercises at the end of each chapter along with select answers The book is an excellent resource for researchers and practitioners in applied mathematics, operations research, engineering, and industrial engineering, as well as a useful text for upper-undergraduate and graduate-level courses in applied mathematics, differential and difference equations, queueing theory, probability, and stochastic processes.

This text introduces a classification of equations and systems not solved with respect to the higher-order derivative, and studies boundary-value problems for these classes of equations. It includes mathematical results from S.L. Sobolev's study on the small oscillations of a rotating fluid.

This peerless reference/text unfurls a unified and systematic study of the two types of mathematical models of dynamic processes-stochastic and deterministic-as placed in the context of systems of stochastic differential equations. Using the tools of variational comparison, generalized variation of constants, and probability distribution as its met

"A treatise on finite difference ineuqalities that have important applications to theories of various classes of finite difference and sum-difference equations, including several linear and nonlinear finite difference inequalities appearing for the first time in book form."

This edited volume gathers selected, peer-reviewed contributions presented at the fourth International Conference on Differential & Difference Equations Applications (ICDDEA), which was held in Lisbon, Portugal, in July 2019. First organized in 2011, the ICDDEA conferences bring together mathematicians from various countries in order to promote cooperation in the field, with a particular focus on applications. The book includes studies on boundary value problems; Markov models; time scales; non-linear difference equations; multi-scale modeling; and myriad applications.

With the development of the scanning tunneling microscope, nanoscience became an important discipline. Single atoms could be manipulated in a controlled manner, and it became possible to change matter at its 'ultimate' level; it is the level on which the properties of matter emerge. This possibility enables to construct and to produce devices, materials, etc. with very small sizes and completely new properties. That opens up new perspectives for technology and is in particular relevant in connection with nano-engineering.Nanosystems are unimaginably small and very fast. No doubt, this is an important characteristic. But there is another feature, possibly more relevant, in connection with nanoscience and nanotechnology. The essential point here is that we work at the 'ultimate level'. This is the smallest level at which the properties of our world emerge, at which functional matter can exist. In particular, at this level biological individuality comes into existence. This situation can be expressed in absolute terms: This is not only the strongest material ever made, this is the strongest material it will ever be possible to make (D Ratner and M Ratner, Nanotechnology and Homeland Security). This is a very general statement. All aspects of matter are concerned here. Through the variation of the composition various forms of matter emerge with different items.Nanosystems are usually small, but they offer nevertheless the possibility to vary the structure of atomic (molecular) ensembles, creating a diversity of new material-specific properties. A large variety of experimental possibilities come into play and flexible theoretical tools are needed at the basic level. This is reflected in the different disciplines: In nanoscience and nanotechnology we have various directions: Materials science, functional nanomaterials, nanoparticles, food chemistry, medicine with brain research, quantum and molecular computing, bioinformatics, magnetic nanostructures, nano-optics, nano-electronics, etc.The properties of matter, which are involved within these nanodisciplines, are ultimate in character, i.e., their characteristic properties come into existence at this level. The book is organized in this respect.

With the development of the scanning tunneling microscope, nanoscience became an important discipline. Single atoms could be manipulated in a controlled manner, and it became possible to change matter at its 'ultimate' level; it is the level on which the properties of matter emerge. This possibility enables to construct and to produce devices, materials, etc. with very small sizes and completely new properties. That opens up new perspectives for technology and is in particular relevant in connection with nano-engineering.Nanosystems are unimaginably small and very fast. No doubt, this is an important characteristic. But there is another feature, possibly more relevant, in connection with nanoscience and nanotechnology. The essential point here is that we work at the 'ultimate level'. This is the smallest level at which the properties of our world emerge, at which functional matter can exist. In particular, at this level biological individuality comes into existence. This situation can be expressed in absolute terms: This is not only the strongest material ever made, this is the strongest material it will ever be possible to make (D Ratner and M Ratner, Nanotechnology and Homeland Security). This is a very general statement. All aspects of matter are concerned here. Through the variation of the composition various forms of matter emerge with different items.Nanosystems are usually small, but they offer nevertheless the possibility to vary the structure of atomic (molecular) ensembles, creating a diversity of new material-specific properties. A large variety of experimental possibilities come into play and flexible theoretical tools are needed at the basic level. This is reflected in the different disciplines: In nanoscience and nanotechnology we have various directions: Materials science, functional nanomaterials, nanoparticles, food chemistry, medicine with brain research, quantum and molecular computing, bioinformatics, magnetic nanostructures, nano-optics, nano-electronics, etc.The properties of matter, which are involved within these nanodisciplines, are ultimate in character, i.e., their characteristic properties come into existence at this level. The book is organized in this respect.

The methods of functional analysis have helped solve diverse real-world problems in optimization, modeling, analysis, numerical approximation, and computer simulation. Applied Functional Analysis presents functional analysis results surfacing repeatedly in scientific and technological applications and presides over the most current analytical and n

"Combines the theoretical and practical aspects of linear and integer programming. Provides practical case studies and techniques, including rounding-off, column-generation, game theory, multiobjective optimization, and goal programming, as well as real-world solutions to the transportation and transshipment problem, project scheduling, and decentralization."