Preface Prologue: The Exponential Function Chapter 1: Abstract Integration Set-theoretic notations and terminology The concept of measurability Simple functions Elementary properties of measures Arithmetic in [0, ] Integration of positive functions Integration of complex functions The role played by sets of measure zero Exercises Chapter 2: Positive Borel Measures Vector spaces Topological preliminaries The Riesz representation theorem Regularity properties of Borel measures Lebesgue measure Continuity properties of measurable functions Exercises Chapter 3: Lp-Spaces Convex functions and inequalities The Lp-spaces Approximation by continuous functions Exercises Chapter 4: Elementary Hilbert Space Theory Inner products and linear functionals Orthonormal sets Trigonometric series Exercises Chapter 5: Examples of Banach Space Techniques Banach spaces Consequences of Baire's theorem Fourier series of continuous functions Fourier coefficients of L1-functions The Hahn-Banach theorem An abstract approach to the Poisson integral Exercises Chapter 6: Complex Measures Total variation Absolute continuity Consequences of the Radon-Nikodym theorem Bounded linear functionals on Lp The Riesz representation theorem Exercises Chapter 7: Differentiation Derivatives of measures The fundamental theorem of Calculus Differentiable transformations Exercises Chapter 8: Integration on Product Spaces Measurability on cartesian products Product measures The Fubini theorem Completion of product measures Convolutions Distribution functions Exercises Chapter 9: Fourier Transforms Formal properties The inversion theorem The Plancherel theorem The Banach algebra L1 Exercises Chapter 10: Elementary Properties of Holomorphic Functions Complex differentiation Integration over paths The local Cauchy theorem The power series representation The open mapping theorem The global Cauchy theorem The calculus of residues Exercises Chapter 11: Harmonic Functions The Cauchy-Riemann equations The Poisson integral The mean value property Boundary behavior of Poisson integrals Representation theorems Exercises Chapter 12: The Maximum Modulus Principle Introduction The Schwarz lemma The Phragmen-Lindelof method An interpolation theorem A converse of the maximum modulus theorem Exercises Chapter 13: Approximation by Rational Functions Preparation Runge's theorem The Mittag-Leffler theorem Simply connected regions Exercises Chapter 14: Conformal Mapping Preservation of angles Linear fractional transformations Normal families The Riemann mapping theorem The class L Continuity at the boundary Conformal mapping of an annulus Exercises Chapter 15: Zeros of Holomorphic Functions Infinite Products The Weierstrass factorization theorem An interpolation problem Jensen's formula Blaschke products The Muntz-Szas theorem Exercises Chapter 16: Analytic Continuation Regular points and singular points Continuation along curves The monodromy theorem Construction of a modular function The Picard theorem Exercises Chapter 17: Hp-Spaces Subharmonic functions The spaces Hp and N The theorem of F. and M. Riesz Factorization theorems The shift operator Conjugate functions Exercises Chapter 18: Elementary Theory of Banach Algebras Introduction The invertible elements Ideals and homomorphisms Applications Exercises Chapter 19: Holomorphic Fourier Transforms Introduction Two theorems of Paley and Wiener Quasi-analytic classes The Denjoy-Carleman theorem Exercises Chapter 20: Uniform Approximation by Polynomials Introduction Some lemmas Mergelyan's theorem Exercises Appendix: Hausdorff's Maximality Theorem Notes and Comments Bibliography List of Special Symbols Index

Real and Complex Analysis. By W. Rudin. Pp. 412. 84s. 1966. (McGraw-Hill, New York.)

Machine Learning Approaches to Manufacturing

Artificial intelligence has been claimed to yield revolutionary advances in manufacturing. While most of the survey papers about artificial intelligence in manufacturing have been focused on knowledge-based expert systems, fewer attentions have been paid to neural networks. However, neural networks are able to learn, adapt to changes, and can mimic human thought processes with little human interventions. They could be of great help for the present computer-integrated manufacturing and the future intelligent manufacturing systems. This paper presents a state-of-the-art survey of neural network applications in manufacturing. The objective of this paper is to update information about the applications of neural networks in manufacturing, which will provide some guidelines and references for the research and implementation.

Applications of neural networks in manufacturing: a state-of-the-art survey

New approaches and techniques are continuously and rapidly introduced and adopted in today's manufacturing environment. Recently, there has been an explosion of interest in applying artificial neural networks to manufacturing. Artificial neural networks have several advantages that are desired in manufacturing practice, including learning and adapting ability, parallel distributed computation, robustness, etc. There is an expectation that neural network techniques can lead to the realization of truly intelligent manufacturing systems. This paper introduces the basic concepts of neural networks and reviews the current application of neural networks in manufacturing. The problems with neural networks are also identified and some possible solutions are suggested. The aim of the authors is to provide useful guidelines and references for the research and implementation of artificial neural networks in the field of manufacturing. >

Artificial neural networks in manufacturing: concepts, applications, and perspectives

In a dynamic manufacturing environment, manufacturing cell configurations based on current part mix and production process may need to be revised once the part mix or the production process has changed. However, machine and equipment moving costs make frequent reconfiguration uneconomical and sometimes impossible. Designing a sustainable cellular manufacturing system in a dynamic environment is studied in this paper. An integer programming model is developed to minimize material handling and machine costs as well as cell reconfiguration cost for a planning horizon of multiple time periods. Solving this integer programming problem is NP-complete. A decomposition approach is developed so that the decomposed subproblems can be solved with less computational effort. Dynamic programming is then employed to find a solution of the original problem. Numerical examples are presented to illustrate the model and the solution technique developed in this paper.

A mathematical programming model for system reconfiguration in a dynamic cellular manufacturing environment

The crux problem of group technology (GT) is the identification of part families requiring similar manufacturing processes and the rearrangement of machines to minimize the number of parts that visit more than one machine cell. This paper presents an improved method for part family formation, machine cell identification, bottleneck machine detection and the natural cluster generation using a self-organizing neural network. In addition, the generalization ability of the neural network makes it possible to assign the new parts to the existing machine cells without repeating the entire computational process. A computer program is developed to illustrate the effectiveness of this heuristic method by comparing it with the optimal technique for large-scale problems.

A self-organizing neural network approach for the design of cellular manufacturing systems

A three-phase network-flow-based procedure is developed for minimizing intercellular part moves in machine-part grouping problems. The unique feature of this methodology is its consideration of several variations related to the number of cells, the number of machines in each cell, and the part family size. The first phase computes a functional relationship between machines on the basis of either a machine-part matrix or actual operation sequences for the parts being considered. The final purpose of this phase is a network modeling of the problem. The second phase partitions the network according to mutually exclusive sets of nodes that represent manufacturing cells. A 0-1 integer programming model and a 0-1 quadratic programming model are discussed and network-flow-based solution procedures are developed. Finally, the third phase identifies the part families. A 0-1 integer programming model is formulated and the solution of this model is again performed through a network approach that allows the identific...

Network flow procedures for the analysis of cellular manufacturing systems

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A self-organizing neural network approach for the design of cellular manufacturing systems

Network flow procedures for the analysis of cellular manufacturing systems