The Word Biblical Commentary delivers the best in biblical scholarship, from the leading scholars of our day who share a commitment to Scripture as divine revelation. This series emphasizes a thorough analysis of textual, linguistic, structural, and theological evidence. The result is judicious and balanced insight into the meanings of the text in the framework of biblical theology. These widely acclaimed commentaries serve as exceptional resources for the professional theologian and instructor, the seminary or university student, the working minister, and everyone concerned with building theological understanding from a solid base of biblical scholarship. Overview of Commentary Organization Introduction-covers issues pertaining to the whole book, including context, date, authorship, composition, interpretive issues, purpose, and theology. Each section of the commentary includes: Pericope Bibliography-a helpful resource containing the most important works that pertain to each particular pericope. Translation-the author's own translation of the biblical text, reflecting the end result of exegesis and attending to Hebrew and Greek idiomatic usage of words, phrases, and tenses, yet in reasonably good English. Notes-the author's notes to the translation that address any textual variants, grammatical forms, syntactical constructions, basic meanings of words, and problems of translation. Form/Structure/Setting-a discussion of redaction, genre, sources, and tradition as they concern the origin of the pericope, its canonical form, and its relation to the biblical and extra-biblical contexts in order to illuminate the structure and character of the pericope. Rhetorical or compositional features important to understanding the passage are also introduced here. Comment-verse-by-verse interpretation of the text and dialogue with other interpreters, engaging with current opinion and scholarly research. Explanation-brings together all the results of the discussion in previous sections to expose the meaning and intention of the text at several levels: (1) within the context of the book itself; (2) its meaning in the OT or NT; (3) its place in the entire canon; (4) theological relevance to broader OT or NT issues. General Bibliography-occurring at the end of each volume, this extensive bibliography contains all sources used anywhere in the commentary.

Based on the results of over 10 years of research and development by the authors, this book presents a broad cross section of dynamic programming (DP) techniques applied to the optimization of dynamical systems. The main goal of the research effort was to develop a robust path planning/trajectory optimization tool that did not require an initial guess. The goal was partially met with a combination of DP and homotopy algorithms. DP algorithms are presented here with a theoretical development, and their successful application to variety of practical engineering problems is emphasized. Applied Dynamic Programming for Optimization of Dynamical Systems presents applications of DP algorithms that are easily adapted to the reader's own interests and problems. The book is organized in such a way that it is possible for readers to use DP algorithms before thoroughly comprehending the full theoretical development. A general architecture is introduced for DP algorithms emphasizing the solution to nonlinear problems. DP algorithm development is introduced gradually with illustrative examples that surround linear systems applications. Many examples and explicit design steps applied to case studies illustrate the ideas and principles behind DP algorithms. DP algorithms potentially address a wide class of applications composed of many different physical systems described by dynamical equations of motion that require optimized trajectories for effective maneuverability. The DP algorithms determine control inputs and corresponding state histories of dynamic systems for a specified time while minimizing a performance index. Constraints may be applied to the final states of the dynamic system or to the states and control inputs during the transient portion of the manoeuvre.

The battle between dark and light rages and the world is on the cusp of a tipping point. Will an age of darkness befall mankind or will the light prevail? David and Aurora have seen visions of each other their entire lives but never met, until now. Aurora a fearsome warrior and David a simple farmer are thrust into the heart of the battle. An ancient prophecy foretells of their final showdown with the Dark One. Will their faith be strong enough for them to prevail? Join them as they embark on their journey to the lair of the beast knowing they may never return.

Clearly illustrated guide to build a balanced kinetic sculpture, of birch plywood and stainless steel, that glides around slowly with the motion of ambient air in a room. . Clear instructions and material selection guide . Traceable full scale templates with matchlines . Examples of steaming and bending plywood . Illustrations of forming steel rod and balancing tips . Great project for individuals or parent & child teams . Educational, challenging, inspiring and fun to build "This is a wonderful parent & child project or just to make it for yourself or as a gift. The hands-on experience of making the sculpture and understanding the physics in balancing it just right is rewarding in itself. Another reward is the finished product: A gliding conversation piece taking flight on the air."

Provides a comprehensive and in-depth treatment of one of the most important control problems: the nonlinear output regulation problem. Contains up-to-date research results and algorithms and tools for approaching and solving the output regulation problem and other related problems, such as robust stabilization of nonlinear systems. The author also offers personal insights about solving the output regulation problem. Output regulation is a general mathematical formulation of many control problems encountered in daily life including cruise control of automobiles, landing and takeoff of aircraft, manipulation of robot arms, orbiting of satellites, and speed regulation of motors. Nonlinear Output Regulation provides a self-contained treatment starting with an introduction to the linear output regulation problem and a review of the fundamental nonlinear control theory. The author's presentation strikes a balance between the theoretical foundation of the problem and the practical applications of the theory. The book is accompanied by many examples, including practical case studies with numerical simulations based on MATLAB /SIMULINK. In addition to the time-tested results on the output regulation problem obtained over the past two decades by the author and other leading researchers in this field, the book highlights a newly developed general framework that converts the robust output regulation problem for a given nonlinear system into a robust stabilization problem for an augmented system. This general framework is based on the construction of nonlinear internal models and offers greater flexibility to incorporate recent new stabilization techniques, thus setting the stage for systematically tackling robust output regulation with global stability. This general framework has been successfully applied to solve the output regulation problem with global stability for several classes of important nonlinear problems.

Linear matrix inequalities (LMIs) have recently emerged as useful tools for solving a number of control problems. This book provides an up-to-date account of the LMI method and covers topics such as recent LMI algorithms, analysis and synthesis issues, nonconvex problems, and applications. It also emphasizes applications of the method to areas other than control. The basic idea of the LMI method in control is to approximate a given control problem via an optimization problem with linear objective and so-called LMI constraints. The LMI method leads to an efficient numerical solution and is particularly suited to problems with uncertain data and multiple (possibly conflicting) specifications. Since the early 1990s, with the development of interior-point methods for solving LMI problems, the LMI approach has gained increased interest. One advantage of this technique is its ability to treat large classes of control problems via efficient numerical tools. This approach is widely applicable, not only in control but also in other areas where uncertainty arises. LMI techniques provide a common language for many engineering problems. Notions now popular in control, such as uncertainty and robustness, are being used in other areas through the use of LMIs. This technique is particularly attractive for industrial applications. It is well suited for the development of CAD tools that help engineers solve analysis and synthesis problems.

H-Infinity control originated from an effort to codify classical control methods, where one shapes frequency response functions to meet certain objectives. H-Infinity control underwent tremendous development in the 1980s and made considerable strides toward systematizing classical control. This book addresses the next major issue of how this extends to nonlinear systems. At the core of nonlinear control theory lie two partial differential equations (PDEs). One is a first-order evolution equation called the information state equation, which constitutes the dynamics of the controller. One can view this equation as a nonlinear dynamical system. Much of this volume is concerned with basic properties of this system, such as the nature of trajectories, stability, and, most important, how it leads to a general solution of the nonlinear H-Infinity control problem. The second PDE actually builds on a classical type of partial differential inequality (PDI) called a Bellman-Isaacs inequality. While the information state PDE determines the dynamics of the controller, the PDI determines the output of the controller. The authors explore the system theoretic significance of the PDI and present its gross structure. These equations are only a few years old and their study is an expanding area of research. This book also emphasizes the theory effecting computer solvability of the information state equation, which at the outset looks numerically intractable, but which surprisingly is in many cases tractable. For example, the theory shows that careful initialization has a major influence on computer solvability. The authors keep the book self-contained by using the appendices to help explain certain prerequisite material. The reader should have a basic knowledge of control theory, real analysis and differential equations, nonlinear operator theory, and nonlinear PDEs.

The efficiency and reliability of manufactured products depend on, among other things, geometrical aspects; it is therefore not surprising that optimal shape design problems have attracted the interest of applied mathematicians and engineers. This self-contained, elementary introduction to the mathematical and computational aspects of sizing and shape optimization enables readers to gain a firm understanding of the theoretical and practical aspects so they may confidently enter this field. In contrast to existing texts on structural optimization, Introduction to Shape Optimization: Theory, Approximation, and Computation treats sizing and shape optimization in a comprehensive way, covering everything from mathematical theory (existence analysis, discretizations, and convergence analysis for discretized problems) through computational aspects (sensitivity analysis, numerical minimization methods) to industrial applications. Some of the applications included are contact stress minimization for elasto-plastic bodies, multidisciplinary optimization of an airfoil, and shape optimization of a dividing tube. By presenting sizing and shape optimization in an abstract way, the authors are able to use a unified approach in the mathematical analysis for a large class of optimization problems in various fields of physics.