Non-parametric Tuning of PID Controllers: A Modified Relay-Feedback-Test Approach

The relay feedback test (RFT) has become a popular and efficient in process identification and automatic controller tuning. Non-parametric Tuning of PID Controllers couples new modifications of classical RFT with application-specific optimal tuning rules to form a non-parametric method of test-and-tuning. Test and tuning are coordinated through a set of common parameters so that a PID controller can obtain the desired gain or phase margins in a system exactly, even with unknown process dynamics. The concept of process-specific optimal tuning rules in the nonparametric setup, with corresponding tuning rules for flow, level pressure, and temperature control loops is presented in the text. Common problems of tuning accuracy based on parametric and non-parametric approaches are addressed. In addition, the text treats the parametric approach to tuning based on the modified RFT approach and the exact model of oscillations in the system under test using the locus of a perturbedrelay system (LPRS) method. Industrial loop tuning for distributed control systems using modified RFT is also described. Many of the problems of tuning rules optimization and identification with modified RFT are accompanied by MATLAB (R) code, downloadable from http://extras.springer.com/978-1-4471-4464-9 to allow the reader to duplicate the results. Non-parametric Tuning of PID Controllers is written for readers with previous knowledge of linear control and will be of interest to academic control researchers and graduate students and to practitioners working in a variety of chemical- mechanical- and process-engineering-related industries.

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146.990000 USD

Food Analysis

This book provides information on the techniques needed to analyze foods in laboratory experiments. All topics covered include information on the basic principles, procedures, advantages, limitations, and applications. This book is ideal for undergraduate courses in food analysis and is also an invaluable reference to professionals in the food industry. General information is provided on regulations, standards, labeling, sampling and data handling as background for chapters on specific methods to determine the chemical composition and characteristics of foods. Large, expanded sections on spectroscopy and chromatography also are included. Other methods and instrumentation such as thermal analysis, ion-selective electrodes, enzymes, and immunoassays are covered from the perspective of their use in the analysis of foods. A website with related teaching materials is accessible to instructors who adopt the textbook.

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111.56 USD

Robust Control of Time-delay Systems

Recently, there have been significant developments in robust control of time-delay systems. This volume presents a systematic treatment of robust control for such systems in the frequency domain. The emphasis is on systems with a single input or output delay, although the delay-free part of the plant can be multi-input-multi-output, in which case the delays in different channels should be the same. The author covers the whole range of H-infinity control of time-delay systems: from controller parameterization implementation; from the Nehari problem to the four-block problem; from theoretical developments to practical issues. The major tools used are similarity transformation, the chain-scattering approach and J-spectral factorization. Self-contained, Robust Control of Time-delay Systems will interest control theorists and mathematicians working with time-delay systems. Its methodical approach will be of value to graduates studying general robust control theory or its applications in time-delay systems.

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167.990000 USD

Deterministic Global Optimization: Theory, Methods and Applications

The vast majority of important applications in science, engineering and applied science are characterized by the existence of multiple minima and maxima, as well as first, second and higher order saddle points. The area of Deterministic Global Optimization introduces theoretical, algorithmic and computational ad vances that (i) address the computation and characterization of global minima and maxima, (ii) determine valid lower and upper bounds on the global minima and maxima, and (iii) address the enclosure of all solutions of nonlinear con strained systems of equations. Global optimization applications are widespread in all disciplines and they range from atomistic or molecular level to process and product level representations. The primary goal of this book is three fold : first, to introduce the reader to the basics of deterministic global optimization; second, to present important theoretical and algorithmic advances for several classes of mathematical prob lems that include biconvex and bilinear; problems, signomial problems, general twice differentiable nonlinear problems, mixed integer nonlinear problems, and the enclosure of all solutions of nonlinear constrained systems of equations; and third, to tie the theory and methods together with a variety of important applications.

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524.990000 USD

Modern Aspects of Electrochemistry

Recognized experts present incisive analyses of both fundamental and applied problems in this continuation of a highly acclaimed series. Topics in Number 35 include: Impedance spectroscopy with specific applications to electrode processes involving hydrogen; Fundamentals and contemporary applications of electroless metal deposition; The development of computational electrochemistry and its application to electrochemical kinetics; Analysis of electrolyte solutions at high concentrations; Applications of the Born theory to solvent polarization by ions and its extensions to treatment of kinetics of ionic reactions. GBP/LISTGBP

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125.990000 USD

Microarrays: Preparation, Microfluidics, Detection Methods, and Biological Applications

Combinatorial chemistry is used to find materials that form sensor microarrays. This book discusses the fundamentals, and then proceeds to the many applications of microarrays, from measuring gene expression (DNA microarrays) to protein-protein interactions, peptide chemistry, carbodhydrate chemistry, electrochemical detection, and microfluidics.

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178.490000 USD

Mathematical Models in Population Biology and Epidemiology

The goal of this book is to search for a balance between simple and analyzable models and unsolvable models which are capable of addressing important questions on population biology. Part I focusses on single species simple models including those which have been used to predict the growth of human and animal population in the past. Single population models are, in some sense, the building blocks of more realistic models -- the subject of Part II. Their role is fundamental to the study of ecological and demographic processes including the role of population structure and spatial heterogeneity -- the subject of Part III. This book, which will include both examples and exercises, is of use to practitioners, graduate students, and scientists working in the field.

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94.450000 USD

Light-Associated Reactions of Synthetic Polymers

This book combines theoretical explanations of the reactions of light and polymeric materials with development of light responsive polymeric materials for various practical applications. Photo associated reactions and light responsive materials have great potential to improve existing industrial processes, including capturing solar energy. This book presents a range of reactions and materials with some of the most exciting current and future applications.

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https://magrudy.com/book/light-associated-reactions-of-synthetic-polymers-9780387318035/

167.990000 USD

Radioanalytical Chemistry

This work is a comprehensive and much-needed tool for the teaching and practice of radioanalytical chemistry. It encompasses a concise theoretical background, laboratory work, and data interpretation. It also contains chapters on the most current and visible applications of radioanalytical techniques. Its emphasis on the practical aspects on laboratory setup and operation make it a valuable tool for training professionals and students alike.

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89.240000 USD

Enzyme Biocatalysis: Principles and Applications

This book was written with the purpose of providing a sound basis for the design of enzymatic reactions based on kinetic principles, but also to give an updated vision of the potentials and limitations of biocatalysis, especially with respect to recent app- cations in processes of organic synthesis. The ?rst ?ve chapters are structured in the form of a textbook, going from the basic principles of enzyme structure and fu- tion to reactor design for homogeneous systems with soluble enzymes and hete- geneous systems with immobilized enzymes. The last chapter of the book is divided into six sections that represent illustrative case studies of biocatalytic processes of industrial relevance or potential, written by experts in the respective ?elds. We sincerely hope that this book will represent an element in the toolbox of gr- uate students in applied biology and chemical and biochemical engineering and also of undergraduate students with formal training in organic chemistry, biochemistry, thermodynamics and chemical reaction kinetics. Beyond that, the book pretends also to illustrate the potential of biocatalytic processes with case studies in the ?eld of organic synthesis, which we hope will be of interest for the academia and prof- sionals involved in R&D&I. If some of our young readers are encouraged to engage or persevere in their work in biocatalysis this will certainly be our more precious reward.

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262.490000 USD

Heterogeneous Enantioselective Hydrogenation: Theory and Practice

Heterogeneous Enantioselective Hydrogenation: Theory and Practice reviews the development of enantioselective hydrogenation reaction catalysts. It looks at the first relatively ineffective catalysts right through to modern highly effective enantioselective catalytic systems, comparable in their efficiency to chiral metal complexes and enzymatic systems. The book begins with a summary of the first work on heterogeneous metal catalysts, which showed only the principal possibilities of enantioselective reactions. It then elaborates on metal catalysts which have enantioselectivities close to 100%. Finally, the practical utilization of chiral catalytic systems in processes of hydrogenation is described. The alpha- and beta-hydroxy carboxylic acid esters produced are precursors for manufacturing many synthones used for medicines as well as for monomers used for biodegradable polyesters, both of which have important practical applications. The volume summarizes more than 800 scientific papers in the field of enantioselective catalytic hydrogenation reactions, mainly those using heterogeneous metal catalysts. It provides detailed explanations of special techniques for the preparation of effective dissymmetric catalysts which provide highly efficient catalytic systems.

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262.490000 USD

PEM Fuel Cells with Bio-Ethanol Processor Systems: A Multidisciplinary Study of Modelling, Simulation, Fault Diagnosis and Advanced Control

An apparently appropriate control scheme for PEM fuel cells may actually lead to an inoperable plant when it is connected to other unit operations in a process with recycle streams and energy integration. PEM Fuel Cells with Bio-Ethanol Processor Systems presents a control system design that provides basic regulation of the hydrogen production process with PEM fuel cells. It then goes on to construct a fault diagnosis system to improve plant safety above this control structure. PEM Fuel Cells with Bio-Ethanol Processor Systems is divided into two parts: the first covers fuel cells and the second discusses plants for hydrogen production from bio-ethanol to feed PEM fuel cells. Both parts give detailed analyses of modeling, simulation, advanced control, and fault diagnosis. They give an extensive, in-depth discussion of the problems that can occur in fuel cell systems and propose a way to control these systems through advanced control algorithms. A significant part of the book is also given over to computer-aided engineering software tools that can be used to evaluate the dynamic performance of the overall plant. PEM Fuel Cells with Bio-Ethanol Processor Systems is intended for use by researchers and advanced students on chemical, electrical-electronic and mechanical engineering courses in which dynamics and control are incorporated with the traditional steady-state coverage of flowsheet synthesis, engineering economics and optimization.

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209.990000 USD

Thermal Solid Waste Utilisation in Regular and Industrial Facilities

Proceedings of the International Workshop, Thermal Solid Waste Utilization in Regular and Industrial Facilities, held in Kazimierz Dolny, Poland, November 28-30, 1999. In recent years, industrial and urban growth has resulted in growing volumes of nondegradable wastes, and this volume focuses on the technologies related to recycling and material reuse which are now being favoured over land disposal. There is an overview on waste utilisation in industrial facilities, particularly cement kilns, from an ecological as well as technological aspect, and some innovative solutions of pyrolitic and plasma reactors, used for hazardous wastes combustion.

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115.490000 USD

Combustion Chemistry

Detailed study of the rates and mechanisms of combustion reactions has not been in the mainstream of combustion research until the recent recognition that further progress in optimizing burner performance and reducing pollutant emission can only be done with fundamental understanding of combustion chemistry. This has become apparent at a time when our understanding of the chemistry, at least of small-molecule combustion, and our ability to model combustion processes on large computers have developed to the point that real confidence can be placed in the results. This book is an introduction for outsiders or beginners as well as a reference work for people already active in the field. Because the spectrum of combustion scientists ranges from chemists with little computing experience to engineers who have had only one college chemistry course, everything needed to bring all kinds of beginners up to the level of current practice in detailed combustion modeling is included. It was a temptation to include critical discussions of modeling results and computer programs that would enable outsiders to start quickly into problem solving. We elected not to do either, because we feel that the former are better put into the primary research literature and that people who are going to do combustion modeling should either write their own programs or collaborate with experts. The only exception to this is in the thermochemical area, where programs have been included to do routine fitting operations. For reference purposes there are tables of thermochemical, transport-property, and rate coefficient data.

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104.990000 USD

Landmarks in Organo-Transition Metal Chemistry: A Personal View

Since the discovery of ferrocene and the sandwich-type complexes, the development of organometallic chemistry took its course like an avalanche and became one of the scientific success stories of the second half of the twentieth century. Based on this development, the traditional boundaries between inorganic and organic chemistry gradually disappeared and a rebirth of the nowadays highly important field of homogeneous catalysis occurred. It is fair to say that despite the fact that the key discovery, which sparked it all off, was made more than 50 years ago, organometallic chemistry remains a young and lively discipline.

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https://magrudy.com/book/landmarks-in-organo-transition-metal-chemistry-9780387098470/

188.990000 USD

Computer-aided Nonlinear Control System Design: Using Describing Function Models

A systematic computer-aided approach provides a versatile setting for the control engineer to overcome the complications of controller design for highly nonlinear systems. Computer-aided Nonlinear Control System Design provides such an approach based on the use of describing functions. The text deals with a large class of nonlinear systems without restrictions on the system order, the number of inputs and/or outputs or the number, type or arrangement of nonlinear terms. The strongly software-oriented methods detailed facilitate fulfillment of tight performance requirements and help the designer to think in purely nonlinear terms, avoiding the expedient of linearization which can impose substantial and unrealistic model limitations and drive up the cost of the final product. Design procedures are presented in a step-by-step algorithmic format each step being a functional unit with outputs that drive the other steps. This procedure may be easily implemented on a digital computer with example problems from mechatronic and aerospace design being used to demonstrate the techniques discussed. The author's commercial MATLAB (R)-based environment, available separately from insert URL here, can be used to create simulations showing the results of using the computer-aided control system design ideas characterized in the text. Academic researchers and graduate students studying nonlinear control systems and control engineers dealing with nonlinear plant, particularly mechatronic or aerospace systems will find Computer-aided Nonlinear Control System Design to be of great practical assistance adding to their toolbox of techniques for dealing with system nonlinearities. A basic knowledge of calculus, nonlinear analysis and software engineering will enable the reader to get the best from this book.

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136.490000 USD

Stabilization of Nonlinear Systems Using Receding-horizon Control Schemes: A Parametrized Approach for Fast Systems

While conceptually elegant, the generic formulations of nonlinear model predictive control are not ready to use for the stabilization of relatively fast systems. This book presents a successful approach to this problem based on a co-operation between structural considerations and on-line optimization. It also provides research showing how generic predictive control schemes can be extended from slow process-based systems to a variety of fast systems.

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178.490000 USD

The Inorganic Chemistry of Materials: How to Make Things out of Elements

P.J. van der Put offers students an original introduction to materials chemistry that integrates the full range of inorganic chemistry. Technologists who need specific chemical facts to manipulate matter will also find this work invaluable as an easy-to-use reference. The text includes practical subjects of immediate use for materials such as bonding, morphogenesis, and design that more orthodox materials science volumes often leave out.

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188.990000 USD

Drying of Polymeric and Solid Materials: Modelling and Industrial Applications

Drying of Polymeric and Solid Materials shows for the first time how the process of drying can be enhanced by combining mathematical and numerical models with experiments. The main advantages of this method are a significant saving of time and money. Numerical modelling can predict the kinetics of drying and the profiles of liquid concentration through the solid. This helps in the selection of optimal operational conditions. The simulation of the process is also crucial in the assessment of diffusity and the rate of evaporation.

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125.990000 USD

Hydrogen Production from Nuclear Energy

With the resurgence of nuclear power around the world, and the increasingly important role of hydrogen as a clean energy carrier, the utilization of nuclear energy for large-scale hydrogen production will have a key role in a sustainable energy future. Co-generation of both electricity and hydrogen from nuclear plants will become increasingly attractive. It enables load leveling together with renewable energy and storage of electricity in the form of hydrogen, when electricity prices and demand are lowest at off-peak hours of nuclear plants, such as overnight. Hydrogen Production from Nuclear Energy provides an overview of the latest developments and methods of nuclear based hydrogen production, including electrolysis and thermochemical cycles. Particular focus is given to thermochemical water splitting by the copper-chlorine and sulphur-based cycles. Cycle configurations, equipment design, modeling and implementation issues are presented and discussed. The book provides the reader with an overview of the key enabling technologies towards the design and industrialization of hydrogen plants that are co-located and linked with nuclear plants in the future. The book includes illustrations of technology developments, tables that summarize key features and results, overviews of recent advances and new methods of nuclear hydrogen production. The latest results from leading authorities in the fields will be presented, including efficiencies, costs, equipment design, and modeling.

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https://magrudy.com/book/hydrogen-production-from-nuclear-energy-9781447149378/

209.990000 USD

Innovations in Green Chemistry and Green Engineering: Selected Entries from the Encyclopedia of Sustainability Science and Technology

Processes that meet the objectives of green chemistry and chemical engineering minimize waste and energy use, and eliminate toxic by-products. Given the ubiquitous nature of products from chemical processes in our lives, green chemistry and chemical engineering are vital components of any sustainable future. Gathering together ten peer-reviewed articles from the Encyclopedia of Sustainability Science and Technology, Innovations in Green Chemistry and Green Engineering provides a comprehensive introduction to the state-of-the-art in this key area of sustainability research. Worldwide experts present the latest developments on topics ranging from organic batteries and green catalytic transformations to green nanoscience and nanotoxicology. An essential, one-stop reference for professionals in research and industry, this book also fills the need for an authoritative course text in environmental and green chemistry and chemical engineering at the upper-division undergraduate and graduate levels.

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104.990000 USD

Optimal Sampled-Data Control Systems

Among the many techniques for designing linear multivariable analogue controllers, the two most popular optimal ones are H2 and H-infinity optimization. The fact that most new industrial controllers are digital provides strong motivation for adapting or extending these techniques to digital control systems. This book, now available as a corrected reprint, attempts to do so. Part I presents two indirect methods of sampled-data controller design: These approaches include approximations to a real problem, which involves an analogue plant, continuous-time performance specifications, and a sampled-data controller. Part II proposes a direct attack in the continuous-time domain, where sampled-data systems are time-varying. The findings are presented in forms that can readily be programmed in, e.g., MATLAB.

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https://magrudy.com/book/optimal-sampled-data-control-systems-9781447130390/

146.990000 USD

Surface Phenomena and Latexes in Waterborne Coatings and Printing Technology

THE CURRENT STATE OF THE ART of waterborne polymers, paints, coatings, inks and printing processes is presented in this volume. This is the third volume in the series on waterborne coating and printing technology. It documents several invited papers and the proceedings of the International Symposium on Surface Phenomena and Latexes in Waterborne Coatings and printing Technology sponsored by the Fine Particle Society (FPS). The FPS meeting was held in Las Vegas, Nevada, July 13-17, 1992. The volume deals with various basic and applied aspects of research on waterborne coating!printing technology. Major topics discussed involve waterborne polymers and polymer blends, pigment grinding, millbases, paint formulation, and characterization of coating films. This edition includes sixteen selected papers related to recent developments in waterborne technology. These papers are divided in three broad categories: (1) Waterborne Polymers and pigment Dispersions, (2) Latex Film, Wetting Phenomena and Printing Gloss, (3) Surfactants and Polymers in Aqueous Coating!printing Systems. This volume includes discussions of various waterborne polymers in coating!printing systems. The editors hope that this volume will serve its intended objective of reflecting the current understanding of formulation and process problems related to waterborne coatings, paints and inks. In addition, it will be a valuable reference source for both novices as well as experts in the field of waterborne technology. It will also help the readers to understand underlying surface phenomena and will enhance the reader's potential for solving critical formulation, evaluation and process problems.

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167.990000 USD

Electrochemical Engineering and Energy

This volume contains the papers presented at the Third European Symposium on electrochemical engineering Electrochemical Engineering and Energy , held on March 23- 25, 1994 in Nancy, France. This meeting was organised by the Laboratoire des Sciences du Genie Chimique, CNRS, and the Centre de Perfectionnement des Industries Chimiques, in conjunction with the Groupe Fran~ais de Genie des Procectes, the Society of Chemical Industry, Dechema, and the European Federation of Chemical Engineeling. The organisers would like to thank the members of the Scientific Committee for the careful selection and refereeing of the papers. We are grateful to all contributors for the thorough preparation of their manuscripts. Thanks are due to the International Society of Electrochemistry, District Urbain de Nancy, Region Lorraine, Electticite de France, Institut National Poly technique de Lorraine, and CNRS for their support. The meeting was devoted to the role of electrochemical engineeting and its relationship to the general issue of energy. The twenty-four papers contained here represent new research results and the potential technological developments in a variety of impOltant and relevant areas of the field. The remaining three papers are expert reviews in areas of current technological concern where electrochemical engineering can clearly be seen to have major relevance to energy policy and environmental protection.

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https://magrudy.com/book/electrochemical-engineering-and-energy-9781461360704/

83.990000 USD

Transport Analysis

It has been my experience in teaching graduate and undergraduate courses that if the students are conversant with the pertinent mathematical proce- dures, and can think mathematically, there is almost no limit to their comprehension. Most courses that are considered difficult by students are either poorly taught or require a degree of mathematical sophistication that the students do not possess. In Transport Analysis, I have culled some basic momentum transport (fluid flow) and mass transport phenomena and explicitly revealed the derivation of the governing equations. There is no mystery, no omitted steps or it can be shown phrases that are usually the bane of the student. There are chapters that review basic calculus, vector and matrix concepts, Laplace transform operations, and finite difference calculus. Ordinary dif- ferential and partial differential equations are derived and solved. This book is intended for undergraduates and graduate students in engineering, chemistry, physics, and even biology and medicine. It is also intended for my non-engineering colleagues with whom I have collaborated during our cooperative research in the life sciences. If they knew what is contained in Transport Analysis, they probably wouldn't need me. v Acknowledgments To Barbara and Michael, who helped keep me alert, happy, and ful- filled. To Barbara, who deserves belated thanks for doing the drawings in Everyday Science. To Anne Hagedorn, thanks for doing some of the typing. To Gerry DenterIein, thanks for keeping tabs on the drawings.

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https://magrudy.com/book/transport-analysis-9781461580874/

114.450000 USD

Digital Control Systems: Design, Identification and Implementation

The extraordinary development of digital computers (microprocessors, microcontrollers) and their extensive use in control systems in all fields of applications has brought about important changes in the design of control systems. Their performance and their low cost make them suitable for use in control systems of various kinds which demand far better capabilities and performances than those provided by analog controllers. However, in order really to take advantage of the capabilities of microprocessors, it is not enough to reproduce the behavior of analog (PID) controllers. One needs to implement specific and high-performance model based control techniques developed for computer-controlled systems (techniques that have been extensively tested in practice). In this context identification of a plant dynamic model from data is a fundamental step in the design of the control system. The book takes into account the fact that the association of books with software and on-line material is radically changing the teaching methods of the control discipline. Despite its interactive character, computer-aided control design software requires the understanding of a number of concepts in order to be used efficiently. The use of software for illustrating the various concepts and algorithms helps understanding and rapidly gives a feeling of the various phenomena.

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https://magrudy.com/book/digital-control-systems-design-identification-and-implementation-9781849965514/

115.490000 USD

Catalytic Carbonylation Reactions

In this book, leading experts from academia and industry offer a comprehensive presentation and discussion of the major reaction types of carbon monoxide. The authors highlight important carbonylation reactions such as hydroformylation, alkoxy-carbonylations, co/olefin-copolymerization, Pauson-Khand reactions and others. They illustrate applications in organic synthesis and give industrial examples. This volume is designed to provide graduate students and researchers with essential information on the use of carbon monoxide in organic synthesis.

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https://magrudy.com/book/catalytic-carbonylation-reactions-9783540330028/

367.490000 USD

Fuzzy Model Identification for Control

This book presents new approaches to constructing fuzzy models for model-based control. Simulated examples and real-world applications from chemical and process engineering illustrate the main methods and techniques. Supporting MATLAB and Simulink files create a computational platform for exploration of the concepts and algorithms.

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https://magrudy.com/book/fuzzy-model-identification-for-control-9781461265795/

136.490000 USD

Microscale Heat Transfer - Fundamentals and Applications: Proceedings of the NATO Advanced Study Institute on Microscale Heat Transfer - Fundamentals and Applications in Biological and Microelectromechanical Systems, Cesme-Izmir, Turkey, 18-30 July, 2004

This volume contains an archival record of the NATO Advanced Institute on Microscale Heat Transfer - Fundamental and Applications in Biological and Microelectromechanical Systems held in Cesme - Izmir, Turkey, July 18-30, 2004. The ASIs are intended to be high-level teaching activity in scientific and technical areas of current concern. In this volume, the reader may find interesting chapters and various Microscale Heat Transfer Fundamental and Applications. The growing use of electronics, in both military and civilian applications has led to the widespread recognition for need of thermal packaging and management. The use of higher densities and frequencies in microelectronic circuits for computers are increasing day by day. They require effective cooling due to heat generated that is to be dissipated from a relatively low surface area. Hence, the development of efficient cooling techniques for integrated circuit chips is one of the important contemporary applications of Microscale Heat Transfer which has received much attention for cooling of high power electronics and applications in biomechanical and aerospace industries. Microelectromechanical systems are subject of increasing active research in a widening field of discipline. These topics and others are the main themeof this Institute.

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219.450000 USD

Fluid Dynamics of Viscoelastic Liquids

This book is about two special topics in rheological fluid mechanics: the elasticity of liquids and asymptotic theories of constitutive models. The major emphasis of the book is on the mathematical and physical consequences of the elasticity of liquids; seventeen of twenty chapters are devoted to this. Constitutive models which are instantaneously elastic can lead to some hyperbolicity in the dynamics of flow, waves of vorticity into rest (known as shear waves), to shock waves of vorticity or velocity, to steady flows of transonic type or to short wave instabilities which lead to ill-posed problems. Other kinds of models, with small Newtonian viscosities, give rise to perturbed instantaneous elasticity, associated with smoothing of discontinuities as in gas dynamics. There is no doubt that liquids will respond like elastic solids to impulses which are very rapid compared to the time it takes for the molecular order associated with short range forces in the liquid, to relax. After this, all liquids look viscous with signals propagating by diffusion rather than by waves. For small molecules this time of relaxation is estimated as lQ-13 to 10-10 seconds depending on the fluids. Waves associated with such liquids move with speeds of 1 QS cm/s, or even faster. For engineering applications the instantaneous elasticity of these fluids is of little interest; the practical dynamics is governed by diffusion, *say, by the Navier-Stokes equations. On the other hand, there are other liquids which are known to have much longer times of relaxation.

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https://magrudy.com/book/fluid-dynamics-of-viscoelastic-liquids-9781461287858/

125.990000 USD