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Mathematical methods for engineers and scientists 1 : Complex analysis, determinants and matrices
Pedagogical insights gained through 30 years of teaching applied mathematics led the author to write this set of student oriented books. Topics such as complex analysis, matrix theory, vector and tensor analysis, Fourier analysis, integral transforms, ordinary and partial differential equations are presented in a discursive style that is readable and easy to follow.
Mathematical Foundation of Geodesy : Selected Papers of Torben Krarup
This volume contains selected papers by Torben Krarup, one of the most important geodesists of the 20th century. His writings are mathematically well founded and scientifically relevant. In this impressive collection of papers he demonstrates his rare innovative ability to present significant topics and concepts. Modern students of geodesy can learn a lot from his selection of mathematical tools for solving actual problems. The collection contains the famous booklet "A Contribution to the Mathematical Foundation of Physical Geodesy" from 1969, the unpublished "Molodenskij letters" from 1973, the final version of "Integrated Geodesy" from 1978, "Foundation of a Theory of Elasticity for Geodetic Networks" from 1974, as well as numerous trend setting papers on the theory of adjustment.
Manufacturing Systems Control Design : A Matrix-based Approach
The matrix-based approach presented here is a solution to the real-time application of control in discrete event systems and flexible manufacturing systems (FMS), and offers a sound practical basis for the design of controllers for manufacturing systems.
Magnetic Functions Beyond the Spin-Hamiltonian
Using the spin-Hamiltonian formalism the magnetic parameters are introduced through the components of the Lambda-tensor involving only the matrix elements of the angular momentum operator. The energy levels for a variety of spins are generated and the modeling of the magnetization, the magnetic susceptibility and the heat capacity is done. Theoretical formulae necessary in performing the energy level calculations for a multi-term system are prepared with the help of the irreducible tensor operator approach. The goal of the programming lies in the fact that the entire relevant matrix elements (electron repulsion, crystal field, spin-orbit interaction, orbital-Zeeman, and spin-Zeeman operators) are evaluated in the basis set of free-atom terms. The modeling of the zero-field splitting is done at three levels of sophistication. The spin-Hamiltonian formalism offers simple formulae for the magnetic parameters by evaluating the matrix elements of the angular momentum operator in the basis set of the crystal-field terms. The magnetic functions for dn complexes are modeled for a wide range of the crystal-field strengths.
Linear Systems
Linear systems theory plays a broad and fundamental role in electrical, mechanical, chemical and aerospace engineering, communications, and signal processing. A thorough introduction to systems theory with emphasis on control is presented in this self-contained textbook. The book examines the fundamental properties that govern the behavior of systems by developing their mathematical descriptions. Linear time-invariant, time-varying, continuous-time, and discrete-time systems are covered. Rigorous development of classic and contemporary topics in linear systems, as well as extensive coverage of stability and polynomial matrix/fractional representation, provide the necessary foundation for further study of systems and control.
Linear Models and Generalizations : Least Squares and Alternatives
Gives an up-to-date account of the theory and applications of linear models. The book can be used as a text for courses in statistics at the graduate level and as an accompanying text for courses in other areas. Some of the highlights in this book are as follows. A relatively extensive chapter on matrix theory (Appendix A) provides the necessary tools for proving theorems discussed in the text and offers a selection of classical and modern algebraic results that are useful in research work in econometrics, engineering, and optimization theory. The matrix theory of the last ten years has produced a series of fundamental results aboutthe de?niteness ofmatrices,especially forthe di?erences ofmatrices, which enable superiority comparisons of two biased estimates to be made for the ?rst time. We have attempted to provide a uni?ed theory of inference from linear models with minimal assumptions
Light scattering by systems of particles : Null-field method with discrete sources : Theory and programs
Light Scattering by Systems of Particles comprehensively develops the theory of the null-field method, while covering almost all aspects and current applications. The "Null-field Method with Discrete Sources" is an extension of the Null-field Method (also called T-Matrix Method) to compute light scattering by arbitrarily shaped dielectric particles. This book incorporates FORTRAN programs and exemplary simulation results that demonstrate all aspects of the latest developments of the method. Worked examples of the application of the FORTRAN programs show readers how to adapt or modify the programs for their specific application.
Lie Algebras and Applications
This book, designed for advanced graduate students and post-graduate researchers, provides an introduction to Lie algebras and some of their applications to the spectroscopy of molecules, atoms, nuclei and hadrons. In the first part, a concise exposition is given of the basic concepts of Lie algebras, their representations and their invariants. The second part contains a description of how Lie algebras are used in practice in the treatment of bosonic and fermionic systems. Physical applications considered include rotations and vibrations of molecules (vibron model), collective modes in nuclei (interacting boson model), the atomic shell model, the nuclear shell model, and the quark model of hadrons. One of the key concepts in the application of Lie algebraic methods in physics, that of spectrum generating algebras and their associated dynamic symmetries, is also discussed. The book contains many examples that help to elucidate the abstract algebraic definitions. It provides a summary of many formulas of practical interest, such as the eigenvalues of Casimir operators and the dimensions of the representations of all classical Lie algebras.
Laplacian Eigenvectors of Graphs : Perron-Frobenius and Faber-Krahn Type Theorems
Eigenvectors of graph Laplacians have not, to date, been the subject of expository articles and thus they may seem a surprising topic for a book. The authors propose two motivations for this new LNM volume: (1) There are fascinating subtle differences between the properties of solutions of Schrödinger equations on manifolds on the one hand, and their discrete analogs on graphs. (2) "Geometric" properties of (cost) functions defined on the vertex sets of graphs are of practical interest for heuristic optimization algorithms. The observation that the cost functions of quite a few of the well-studied combinatorial optimization problems are eigenvectors of associated graph Laplacians has prompted the investigation of such eigenvectors.
Knowledge Processing with Interval and Soft Computing
In particular, these chapters cover computing techniques for interval linear systems of equations, interval matrix singular-value decomposition, interval function approximation, and decision making with statistical and graph-based data processing. To enable these applications, the book presents a standards-based object-oriented interval computing environment in C++.
IUTAM Symposium on Multiscale Modelling of Damage and Fracture Processes in Composite Materials ; Proceedings of the IUTAM Symposium held in Kazimierz Dolny, Poland, 23-27 May 2005
This volume constitutes the Proceedings of the IUTAM Symposium. The main aim of the Symposium was to discuss the basic principles of damage growth and fracture processes in different types of composites: ceramic, polymer and metal matrix composites, cement and bituminous composites and wood. Nowadays, it is widely recognized that important macroscopic properties like the macroscopic stiffness and strength, are governed by processes that occur at one to several scales below the level of observation starting from nanoscale.
Composite materials : sustainable and eco-friendly materials and application
Covers innovations in the field of composite materials with a specific focus on eco-friendly and environmentally sustainable systems. All composite fields are explored, including polymer, metal, and ceramic matrix composites with an emphasis on sourcing raw materials in a sustainable way as well as the development of composite materials for environmental sustainability.
Completeness theory for propositional logics
Completeness is one of the most important notions in logic and the foundations of mathematics. Many variants of the notion have been de?ned in literature. We shallconcentrateonthesevariants,andaspects,of completenesswhicharede?ned in propositional logic. Completeness means the possibility of getting all correct and reliable sc- mata of inference by use of logical methods. The word ‘all’, seemingly neutral, is here a crucial point of distinction. Assuming the de?nition as given by E. Post we get, say, a global notion of completeness in which the reliability refers only to syntactic means of logic and outside the correct schemata of inference there are only inconsistent ones. It is impossible, however, to leave aside local aspects of the notion when we want to make it relative to some given or invented notion of truth. Completeness understood in this sense is the adequacy of logic in relation to some semantics, and the change of the logic is accompanied by the change of its semantics.
Cell-secreted vesicles : Methods and protocols
Pesents hands-on technological protocols used to target an array of cell-secreted extracellular vesicles (EVs) in a variety of biological systems. Beginning with methods for EV purification and analysis, the book continues with sections on the study of EV functions as well as specific systems and models allowing for the study of EVs of different origin. Written for the highly successful Methods in Molecular Biology series, chapters include introductions to their respective topics, lists of the necessary materials and reagents, step-by-step and readily reproducible laboratory protocols, and tips on troubleshooting and avoiding known pitfalls.
Cell Separation : Fundamentals, Analytical and Preparative Methods
This special volume on cell separations discusses fundamental and applied aspects of the analytical and preparative cell-separation technologies. The aim is to enlighten the reader with the new developments in cell-separation technologies and at the same time provide sufficient knowledge with other existing and more commonly used techniques. The volume is comprised of contributions from subject experts from both academia and industry, focuses on the research and commercial aspects of cell-separation technology, and provides readers with broader choice. Unlike protein separation, the major challenge in cell separation has been the recovery of the cells in viable form after they are bound to the separation matrix, as cells bind more strongly through multipoint attachment. This is an important focus of the present work and one we believe will provide new insight to researchers in this field
Cell Adhesion and Cytoskeletal Molecules in Metastasis
In this volume, the expression of specific adhesion molecules within human cancer tissues are highlighted. The expression signatures from published DNA microarray and immunohistochemistry studies are detailed. The concept that the alteration of specific adhesion molecules influence the cancer migration ability and cancer damage responses is detailed in this volume; both features are essential for the survival of an invading tumor cell. Defining the minimal adhesion receptors preserved on cancer cells during tumor progression will define the metastatic adhesion signature. Understanding the metastatic adhesion signature will reveal vulnerabilities that could be exploited for the prevention and/or eradication of the invading cancer cell.
Bone disorders
• Bone is the specialized type of connective tissue that has extracellular matrix containing calcium salts. • As bone is a connective tissue, it consists of cells and matrix. • Mineralized extracellular matrix provides hardness to bones. • Bone is a living tissue that shows dynamic structural changes in response to physical stress and hormonal changes. • In addition to support and protection of vital organs, bones act as a storehouse for calcium and phosphates. • Bone also performs hematopoietic function (production of blood cells).
Biocompatible nanocomposites : From synthesis to applications
Presents a focused overview of biocompatible nanocomposites, emphasizing recent advancements in material design, synthesis techniques, and their expanding applications in biomedicine. It spans key areas such as regenerative medicine, drug delivery, cancer therapy, biosensing, diagnostic imaging, and vaccine delivery —illustrating how these materials are transforming modern healthcare. The book reviews widely used biomaterials including polycaprolactone, bioactive ceramics, and polymer-based hybrids, discussing their roles in cardiovascular, orthopedic, dental, maxillofacial, and ophthalmic applications.
Basic Algebra
Basic Algebra and Advanced Algebra systematically develop concepts and tools in algebra that are vital to every mathematician, whether pure or applied, aspiring or established. Together, the two books give the reader a global view of algebra and its role in mathematics as a whole.Basic Algebra presents the subject matter in a forward-looking way that takes into account its historical development. It is suitable as a text in a two-semester advanced undergraduate or first-year graduate sequence in algebra, possibly supplemented by some material from Advanced Algebra at the graduate level. It requires of the reader only familiarity with matrix algebra, an understanding of the geometry and reduction of linear equations, and an acquaintance with proofs.
Basal Implantology
Helps oral implantologists to understand the principles that underlie the use of basal implants as a means to provide simple solutions to complex and highly demanding clinical situations without the need for prior bone grafting.
