Bøger i Mathematics and Its Applicatio serien

Approach your problems from the right It isn't that they can't see the solution. end and begin with the answers. Then It is that they can't see the problem. one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Clad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Min­ kowsky lemma, coding theory and the structure of water meet one another in packing and covering theory: quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces.

1: General Aspects of Laryngeal Cancer.- 1. Introduction.- 1.1. Incidence.- 1.2. Predisposing factors.- 2. TNM staging.- 2.1. Introduction.- 2.2. Clinical classification.- 3. Diagnostic aspects.- 3.1. History.- 3.2. External examination.- 3.3. Laryngoscopy.- 4. Therapeutic options.- 4.1. Radiotherapeutic options.- 4.1.1. Technique.- 4.1.2. Prognostic factors of irradiation treatment.- 4.1.3. Complications due to radiation therapy.- 4.2. Surgical options.- 4.2.1. Laser therapy and microsurgical stripping.- 4.2.2. Laryngofissure and cordectomy.- 4.2.3. Vertical partial laryngectomy.- 4.2.4. Antero-frontal laryngectomy for excision of the anterior commissure.- 4.2.5. Supraglottic laryngectomy.- 4.2.6. (Wide-field) total laryngectomy.- 4.3. Chemotherapeutic options.- 5. Therapeutic management.- Tl- and T2-glottic carcinomas.- T1- and T2-subglottic carcinomas.- T2- and T2-supraglottic carcinomas.- T3- and T4-laryngeal cancer.- Nodal metastasis.- References.- 2: The Patterns of Growth And Spread of Laryngeal Cancer.- 1. Introduction.- 2. Spread of cancer in various regions.- 2.1. Cancer of the supraglottic region.- 2.2. Cancer of the glottic region.- 2.3. Cancer of the subglottic region.- 3. Cartilage invasion.- 4. Lymphatic spread.- 5. Vascular and perineural invasion.- References.- 3: The Radiological Examination of the Larynx.- 1. Introduction.- 2. Phonation manoeuvers.- 3. Frontal tomography.- 4. Contrast laryngography.- 5. Computed tomography.- 6. CT versus conventional radiological techniques.- 6.1. CT versus conventional tomography.- 6.2. CT versus contrast laryngography.- References.- 4: General Aspects of MR Imaging.- 1. Introduction.- 2. Technical principles.- 2.1. Properties of atomic nuclei.- 2.2. Resonance.- 2.3. Behaviour of a sample of nuclei.- 2.4. Proton density, tissue characteristics.- 2.5. Spin echo technique.- 3. The equipment.- 3.1. Magnet.- 3.2. Gradient system.- 3.3. Coils.- 3.4. Computer.- 4. Disadvantages of MR imaging.- 4.1. Claustrophobia.- 4.2. Contra-indications.- References.- 5: MR Imaging Techniques of the Larynx.- 1. Surface coils.- 1.1. Coil selection.- 2. Parameters.- 2.1. Pulse sequences.- 2.2. Slice thickness.- 2.3. Slice direction.- 2.4. Matrix size.- 2.5. Number of signal measurements.- 3. Artifacts.- 3.1. Motion artifacts.- 3.2. System artifacts.- 3.3. Chemical shift artifacts.- 3.4. Artifacts due to ferromagnetic implants.- 4. Performance of the laryngeal examination.- References.- 6: MR Imaging of the Normal Larynx.- 1. Introduction.- 2. MR imaging of laryngeal structures.- 2.1. Laryngeal skeleton.- 2.2. Laryngeal compartments.- 3. Landmarks.- 3.1. Hyoid bone.- 3.2. Aryepiglottic fold.- 3.3. False vocal cords.- 3.4. True vocal cords.- 3.5. Subglottic level.- References.- 7: MR Imaging of Laryngeal Cancer.- Abstract.- 1. Introduction.- 2. Materials and methods.- 3. Case reports.- Case 1.- Case 2.- Case 3.- Case 4.- Case 5.- Case 6.- Case 7.- 4. Discussion.- 5. Conclusions.- References.- 8: MR imaging of Normal and Cancerous Laryngeal Cartilages. Histopathological Correlation.- Abstract.- 1. Introduction.- 2. Materials and methods.- 3. Results.- 3.1. Epiglottic cartilage.- 3.2. Thyroid cartilage.- 3.3. Cricoid cartilage.- 3.4. Arytenoid cartilage.- 4. Discussion.- 5. Conclusions.- References.- 9: Dagnosis of Laryngeal Cartilage Invasion by Cancer. Comparison of CT and MR Imaging.- Abstract.- 1. Introduction.- 2. Materials and methods.- 2.1. Imaging techniques.- 2.2. Image interpretation.- 2.3. Pathological findings.- 3. Results.- 3.1. Epiglottic cartilage.- 3.2. Thyroid cartilage.- 3.3. Arytenoid cartilage.- 3.4. Cricoid cartilage.- 3.5. Group of patients for which no pathologic correlation was available.- 3.6. Movement artifacts.- 4. Discussion.- 4.1. Elastic cartilage: epiglottic cartilage.- 4.2. Hyaline cartilage: thyroid, cricoid and arytenoid cartilages.- 5. Summary.- References.- 10: MR Findings of Cartilage Invasion by Laryngeal Cancer. Value in Predicting Outcome of Radiation Therap...

This is one of two volumes devoted to single and multistage systems in scheduling theory respectively. The main emphasis throughout is on the analysis of the computational complexity of scheduling problems. This volume is devoted to the problems of determining optimal schedules for systems consisting of either a single machine or several parallel machines. The most important statements and algorithms which relate to scheduling are described and discussed in detail. The book has an introduction followed by four chapters dealing with the elements of graph theory and the computational complexity of algorithms, polynomially solvable problems, priority-generating functions, and NP-Hard problems, respectively. Each chapter concludes with a comprehensive biobliography and review. The volume also includes an appendix devoted to approximation algorithms and extensive reference sections. For researchers and graduate students of management science and operations research interested in production planning and flexible manufacturing.

These are the proceedings of the international conference on "Nonlinear numerical methods and Rational approximation II" organised by Annie Cuyt at the University of Antwerp (Belgium), 05-11 September 1993. It was held for the third time in Antwerp at the conference center of UIA, after successful meetings in 1979 and 1987 and an almost yearly tradition since the early 70's. The following figures illustrate the growing number of participants and their geographical dissemination. In 1993 the Belgian scientific committee consisted of A. Bultheel (Leuven), A. Cuyt (Antwerp), J. Meinguet (Louvain-Ia-Neuve) and J.-P. Thiran (Namur). The conference focused on the use of rational functions in different fields of Numer­ ical Analysis. The invited speakers discussed "Orthogonal polynomials" (D. S. Lu­ binsky), "Rational interpolation" (M. Gutknecht), "Rational approximation" (E. B. Saff) , "Pade approximation" (A. Gonchar) and "Continued fractions" (W. B. Jones). In contributed talks multivariate and multidimensional problems, applications and implementations of each main topic were considered. To each of the five main topics a separate conference day was devoted and a separate proceedings chapter compiled accordingly. In this way the proceedings reflect the organisation of the talks at the conference. Nonlinear numerical methods and rational approximation may be a nar­ row field for the outside world, but it provides a vast playground for the chosen ones. It can fascinate specialists from Moscow to South-Africa, from Boulder in Colorado and from sunny Florida to Zurich in Switzerland.

Approach your problems from the right It isn't that they can't see the solution. It end and begin with the answers. Then is that they can't see the problem. one day, perhaps you will find the final question. G. K. Chesterton. The Scandal of Father Brown 'The Point of a Pin'. 'The Hermit Gad in Crane Feathers' in R. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. How­ ever, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the stI11fture of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisci­ plines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classifi~ation schemes.

Functional Analysis has become one of the main branches in Chinese mathematics. Many outstanding contributions and results have been achieved over the past sixty years. This authoritative collection is complementary to Western studies in this field, and seeks to summarise and introduce the historical progress of the development of Functional Analysis in China from the 1940s to the present. A broad range of topics is covered, such as nonlinear functional analysis, linear operator theory, theory of operator algebras, applications including the solvability of some partial differential equations, and special spaces that contain Banach spaces and topological vector spaces. Some of these papers have made a significant impact on the mathematical community worldwide. Audience: This volume will be of interest to mathematicians, physicists and engineers at postgraduate level.