Description
This volume is a collection of surveys of research problems in
topology and its applications. The topics covered include general
topology, set-theoretic topology, continuum theory, topological
algebra, dynamical systems, computational topology and functional
analysis.
Audience
Senior researchers in active centres, junior researchers and
mathematicians.
Contents
Part 1. General Topology
1. Selected ordered space problems (H. Bennett and D. Lutzer) 2.
Problems on star-covering properties (M. Bonanzinga and M.
Matveev) 3. Function space topologies (D.N. Georgiou, S.D.
Iliadis and F. Mynard) 4. Spaces and mappings: special networks (C.
Liu and Y. Tanaka) 5. Extension problems of real-valued
continuous functions (H. Ohta and K. Yamazaki) 6. LE(k)-spaces (O.
Okunev) 7. Problems on (ir) resolvability (O. Pavlov) 8.
Topological games and Ramsey theory (M. Scheepers) 9. Selection
principles and special sets of reals (B. Tsaban)
Part 2. Set-theoretic Topology
10. Introduction: Twenty problems in set-theoretic topology (M.
Hrusak and J.T. Moore) 11. Thin-tall spaces and cardinal
sequences (J. Bagaria) 12. Sequential order (A. Dow) 13. On D-spaces
(T. Eisworth) 14. The fourth head of BN (I. Farah) 15. Are
stratifiable spaces M1? (G. Gruenhage) 16. Perfect compacta and
basis problems in topology (G. Gruenhage and J.T. Moore) 17.
Selection problems for hyperspaces (V. Gutev and T. Nogura) 18.
Efimov's problem (K.P. Hart) 19. Completely separable MAD
families (M. Hrusak and P. Simon) 20. Good, splendid and Jakovlev
(I. Juhasz and W.A.R. Weiss) 21. Homogeneous compacta (J. van
Mill) 22. Compact spaces with hereditarily normal squares (J.T.
Moore) 23. The metrization problem for Frechet groups (J.T. Moore
and S. Todorcevic) 24. Cech-Stone remainders of discrete spaces (P.J.
Nyikos) 25. First countable, countably compact, noncompact spaces
(P.J. Nyikos) 26. Linearly Lindelof problems (E. Pearl) 27. Small
Dowker spaces (P.J. Szeptycki) 28. Reflection of topological
properties to N1 (F.D. Tall) 29. The Scarborough-Stone problem (J.E.
Vaughan)
Part 3. Continuum Theory
30. Questions in and out of context (D.P. Bellamy) 31. An update
on the elusive fixed-point property (C.L. Hagopian) 32.
Hyperspaces of continua (A. Ilanes) 33. Inverse limits and
dynamical systems (W.T. Ingram) 34. Indecomposable continua (W.
Lewis) 35. Open problems on dendroids (V. Martinez-de-la-Vega and
J.M. Martinez-Montejano) 36. ?-Homogeneous continua (S.B. Nadler,
Jr.) 37. Thirty open problems in the theory of homogeneous
continua (J.R. Prajs)
Part 4. Topological Algebra
38. Problems about the uniform structures of topological groups (A.
Bouziad and J-P. Troallic) 39. On some special classes of
continuous maps (M.M. Clementino and D. Hofmann) 40. Dense
subgroups of compact groups (W.W. Comfort) 41. Selected topics
from the structure theory of topological groups (D. Dikranjan and
D. Shakhmatov) 42. Recent results and open questions relating Chu
duality and Bohr compactifications of locally compact groups (J.
Galindo, S. Hernandez and T-S. Wu) 43. Topological transformation
groups: selected topics (M. Megrelishvili) 44. Forty-plus
annotated questions about large topological groups (V. Pestov)
Part 5. Dynamical Systems
45. Minimal flows (W.F. Basener, K. Parwani and T. Wiandt) 46.
The dynamics of tiling spaces (A. Clark) 47. Open problems in
complex dynamics and "complex" topology (R.L. Devaney)
48. The topology and dynamics of flows (M.C. Sullivan)
Part 6. Computer Science
49. Computational topology (D. Blackmore and T.J. Peters)
Part 7. Functional Analysis
50. Non-smooth analysis, optimisation theory and Banach space
theory (J.M. Borwein and W.B. Moors) 51. Topological structures
of ordinary differential equations (V.V. Filippov) 52. The
interplay between compact spaces and the Banach spaces of their
continuous functions (P. Koszmider) 53. Tightness and t-equivalence
(O. Okunev) 54. Topological problems in nonlinear and functional
analysis (B. Ricceri) 55. Twenty questions on metacompactness in
function spaces (V.V. Tkachuk)
Part 8. Dimension Theory
56. Open problems in infinite-dimensional topology (T. Banakh, R.
Cauty and M. Zarichnyi) 57. Classical dimension theory (V.A.
Chatyrko) 58. Questions on weakly infinite-dimensional spaces (V.V.
Fedorchuk) 59. Some problems in the dimension theory of compacta
(B.A. Pasynkov)
Part 9. Invited Papers
60. Problems from the Lviv topological seminar (T. Banakh, B.
Bokalo, I. Guran, T. Radul and M. Zarichnyi) 61. Problems from
the Bizerte-Sfax-Tunis Seminar (O. Echi, H. Marzougui and E.
Salhi) 62. Cantor set problems (D.J. Garity and D. Repovs) 63.
Problems from the Galway Topology Colloquium (C. Good, A. Marsh,
A. McCluskey and B. McMaster) 64. The lattice of quasi-uniformities
(E.P. de Jager amd H-P.A. Kunzi) 65. Topology in North Bay: some
problems in continuum theory, dimension theory and selections (A.
Karasev, M. Tuncali and V. Valov) 66. Moscow questions on
topological algebra (K.L. Kozlov, E.A. Reznichenko and O.V.
Sipacheva) 67. Some problems from George Mason University (J.
Kulesza, R. Levy and M. Matveev) 68. Some problems on generalized
metrizable spaces (S. Lin) 69. Problems from the Madrid
Department of Geometry and Topology (J.M.R. Sanjurjo) 70.
Cardinal sequences and universal spaces (L. Soukup)
List of contributors Index
Hardbound, publication date: MAR-2007
ISBN-13: 978-0-444-52208-5
ISBN-10: 0-444-52208-5
Included in series
Mathematics in Science and Engineering,vol 212
Description
In this book, we study theoretical and practical aspects of
computing methods for mathematical modelling of nonlinear systems.
A number of computing techniques are considered, such as methods
of operator approximation with any given accuracy; operator
interpolation techniques including a non-Lagrange interpolation;
methods of system representation subject to constraints
associated with concepts of causality, memory and stationarity;
methods of system representation with an accuracy that is the
best within a given class of models; methods of covariance matrix
estimation; methods for low-rank matrix approximations; hybrid
methods based on a combination of iterative procedures and best
operator approximation; and methods for information compression
and filtering under condition that a filter model should satisfy
restrictions associated with causality and different types of
memory. As a result, the book represents a blend of new methods
in general computational analysis, and specific, but also
generic, techniques for study of systems theory ant its
particular branches, such as optimal filtering and information
compression.
Audience
This book is intended for: Applied mathematicians and Electrical
engineers And: Statisticians
Contents
Preface Contents 1 Overview I Methods of Operator Approximation
in System Modelling near Operator Approximation with Preassigned
Accuracy 2.1 Introduction 2.2 Generic formulation of the problem
2.3 Operator approximation in space C([0; 1]): 2.4 Operator
approximation in Banach spaces by polynomial operators 2.5
Approximation on compact sets in topological vector spaces 2.6
Approximation on noncompact sets in Hilbert spaces 2.7 Special
results for maps into Banach spaces 2.8 Concluding remarks 3
Interpolation of Nonlinear Operators 65 3.1 Introduction 3.2
Lagrange interpolation in Banach spaces 3.3 Weak interpolation of
nonlinear operators 3.4 Some related results 3.5 Concluding
remarks 4 Realistic Operators and their Approximation 4.1
Introduction 4.2 Formalization of concepts related to description
of real-world objects 4.3 Approximation of R!continuous operators
4.4 Concluding remarks 5 Methods of Best Approximation for
Nonlinear Operators 5.1 Introduction 5.2 Best Approximation of
nonlinear operators in Banach spaces: Deterministic case 5.3
Estimation of mean and covariance matrix for random vectors 5.4
Best Hadamard-quadratic approximation 5.5 Best polynomial
approximation 5.6 Best causal approximation 5.7 Best hybrid
approximations 5.8 Concluding remarks II Optimal Estimation of
Random Vectors 6 Computational Methods for Optimal Filtering of
Stochastic Signals 6.1 Introduction 6.2 Optimal linear Filtering
in Finite dimensional vector spaces 6.3 Optimal linear Filtering
in Hilbert spaces 6.4 Optimal causal linear Filtering with
piecewise constant memory 6.5 Optimal causal polynomial Filtering
with arbitrarily variable memory 6.6 Optimal nonlinear Filtering
with no memory constraint 6.7 Concluding remarks 7 Computational
Methods for Optimal Compression and Reconstruction of Random Data
7.1 Introduction 7.2 Standard Principal Component Analysis and
Karhunen-Loeeve transform (PCA{KLT) 7.3 Rank-constrained matrix
approximations 7.4 Generic PCA{KLT 7.5 Optimal hybrid transform
based on Hadamard-quadratic approximation 7.6 Optimal transform
formed by a combination of nonlinear operators 7.7 Optimal
generalized hybrid transform 7.8 Concluding remarks Bibliography
Index
Hardbound, 284 pages, publication date: MAR-2007
ISBN-13: 978-0-444-53044-8
ISBN-10: 0-444-53044-4
Included in series
Mathematics in Science and Engineering,vol 211
Description
There is an ever increasing need for modelling complex processes
reliably. Computational modelling techniques, such as CFD and MD
may be used as tools to study specific systems, but their
emergence has not decreased the need for generic, analytical
process models. Multiphase and multicomponent systems, and high-intensity
processes displaying a highly complex behaviour are becoming
omnipresent in the processing industry.
This book discusses an elegant, but little-known technique for
formulating process models in process technology: stochastic
process modelling. The technique is based on computing the
probability distribution for a single particle's position in the
process vessel, and/or the particle's properties, as a function
of time, rather than - as is traditionally done - basing the
model on the formulation and solution of differential
conservation equations.
Using this technique can greatly simplify the formulation of a
model, and even make modelling possible for processes so complex
that the traditional method is impracticable.
Stochastic modelling has sporadically been used in various
branches of process technology under various names and guises.
This book gives, as the first, an overview of this work, and
shows how these techniques are similar in nature, and make use of
the same basic mathematical tools and techniques.
The book also demonstrates how stochastic modelling may be
implemented by describing example cases, and shows how a
stochastic model may be formulated for a case, which cannot be
described by formulating and solving differential balance
equations.
Key Features:
- Introduction to stochastic process modelling as an alternative
modelling technique
- Shows how stochastic modelling may be succesful where the
traditional technique fails
- Overview of stochastic modelling in process technology in the
research literature
- Illustration of the principle by a wide range of practical
examples
- In-depth and self-contained discussions
- Points the way to both mathematical and technological research
in a new, rewarding field
Audience
Researchers in the processing industry. Also suitable for
researchers and graduate students in universities, mathematics,
physics and engineering departments.
Hardbound, publication date: JUL-2007
ISBN-13: 978-0-444-52026-5
ISBN-10: 0-444-52026-0
Included in series
Handbook of the History of Logic,vol 4
Description
It is widely accepted that the 19th century had little of value
to add to the development of logic, except in Germany toward the
end of the century in the revolutionary work of Frege. Logicians
who have some historical command of their subject will know this
to be an overstatement, and will rightly cite the contributions
of the English logicians DeMorgan and Boole. But by and large the
details of these contributions have been lost on even those who
acknowledge their existence. It is true that J.S. Mill's A System
of Logic was widely read in its day, and was used as a textbook
at Oxford and Cambridge until nicely into the 20th century. Yet
the received opinion, for which Frege is largely responsible, is
that Mill's writings on logic are of little importance. It is
also acknowledged that the British idealists, notably Bradley,
wrote books and articles on what they purported to be questions
of logic; but since idealism has been virtually abandoned in the
past 100 years, idealist logic has not had much of an innings in
the mainstream of logical theory. Lewis Carroll is better known
for his Alice books than for his little puzzle in Mind about
inference and implication. Few are aware that he was a
mathematician of some distinction, and the author of a well-regarded
book on logic, which many decades later was the subject of a
dismissive review by Quine. Other names are recognizable in other
contexts. Coleridge was a poet. Whatley was a divine and a writer
of hymns. Hamilton was a hapless rival of Mill. Whewell was a
philosopher of science. Venn invented some diagrams. Jevons
mathematized economics. In fact, they were all logicians. Other
names leave no echo ? MacColl, for example ? and others echo
falsely ? for example, the Benthem who was both a logician and
not Jeremy. The present volume of the Handbook of the History of
Logic is designed to repair these misconceptions and lacunae. The
authors of its chapters have dome a masterly job of establishing
19th century Britain as a substantial force in logic, developing
new ideas, some of which would be overtaken by, and other that
would anticipate, the century's later capitulation to the
mathematization of logic. British Logic in the Nineteenth Century
is an indispensable research tool for anyone interested in the
development of logic, including researchers, graduate and senior
undergraduate students in logic, history of logic, mathematics,
history of mathematics, computer science, AI, linguistics,
cognitive science, argumentation theory, and the history of ideas.
Audience
The Handbook is aimed at researchers and historians in all areas
of logic, including computer scientists and artificial
intelligence theorists, theorists of legal reasoning and
cognitive psychologists.
Table of Contents:
1. "Bentham's Logic" by Charissa Varma and Gordon
McOuat 2. "Coleridge's Logic" by Timothy Milnes 3.
"Whately's Logic" by James Van Evra 4. "Hamilton's
Logic" by Ralph Jessop 5. "Whewell's Logic" by
Laura Snyder 6. "Mill's Logic" by Fred Wilson 7. "DeMorgan's
Logic" by Michael Hobards & Joan Richards 8. "Boole's
Logic" by Dale Jacquette 9. "French Logique and British
Logic: On the Origins of Augustus deMorgan early Logical
Enquiries 1805-1835" by Maria Panteki 10. "Lewis
Carroll's Logic" by Amirouche Moktefi 11. "Venn's Logic"
by James Van Evra 12. "Jevons' Logic" by Bert
Mosselmans and Ard Van Moer 13. "MacColl's Logic" by
Shahid Rahman 14. "The Idealists" by David Sullivan
Hardbound, publication date: NOV-2007
ISBN-13: 978-0-444-51610-7
ISBN-10: 0-444-51610-7