DOCSLIB.ORG

Notices of the American Mathematical Society

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Calendar This Calendar lists all of the meetings which have been approved by the Council up to the date this issue of the cNotictiJ was sent to press. The summer and annual meetings are joint meetings of the Mathematical Association of America and the American Mathematical Society. The meeting dates which fall rather far in the future are subject to change; this is particularly true of meetings to which no numbers have yet been assigned. Abstracts should be submitted on special forms which are available in most departments of mathematics; forms can also be obtained by writing to the headquarters of the Society. Abstracts to be presented at the meeting in person must be received at the headquarters of the Society in Providence, Rhode Island, on or before the deadline for the meeting. Meeting Deadline for Abstracts* Number Date Place and News Items 731 January 22-26, 1976 San Antonio, Texas Nov, 5, 1975 (82nd Annual Meeting) 732 March 4-5, 1976 Tallahassee, Florida Jan. 8, 1976 733 March 15-20, 1976 Urbana, illinois Jan. 8, 1976 734 April 11-14, 1976 New York, New York Feb. 17, 1976 735 April 23-24, 1976 Reno, Nevada Feb. 17, 1976 736 June 18-19, 1976 Portland, Oregon April 27, 1976 737 August 24-28, 1976 Toronto, Canada June 15, 1976 (Both Summer Meeting) November 19-20, 1976 Columbia, South Carolina November 26-27, 1976 Albuquerque, New Mexico January 27-31, 1977 St. Louis, Missouri (83rd Annual Meeting) *Deadline for abstracts not presented at a meeting (by title) February 1976 issue: January 6 April 1976 issue: February 10 OTHER EVENTS February 24, 1976 Symposium on Some Mathematical Questions in Biology, Boston, Massachusetts March 15-18, 1976 Symposium on Probability, Urbana, lllinois Please alf"JX the peel-off label on these c/'(oticti) to correspondence with the Society concerning fiscal matters, changes of address, promotions, or when placing orders for hooks and journals. The c){olit:ri) of the American Mathematical Society is published by the American Mathematical Society, P. 0. Box 6248, Providence, Rhode Island 02940, in January, February, April, June, August, October, November, and December. Subscription prices for the 1975 volume (Volume 22) are list $14.00, member $7.00. Subscription prices for the 1976 volume (Volume 23) are list $19.00, member $9.50. The subscription price for members is included in the annual dues. Back issues of the cNotictiJ are available for a two year period only and cost $2.88 per issue list price, $2.16 per issue member price for Volume 21 (1974) and $3.65 per issue list price, $2.74 per issue member price for Volume 22. Orders for subscriptions or back issues must be accompanied by payment and should he sent to the Society at P. 0. Box 1571, Annex Station, Providence, Rhode Island 02901. Other corre­ spondence should he addressed to P. 0. Box 6248, Providence, Rhode Island 02940. Second class postage paid at Providence, Rhode Island, and additional mailing offices. Copyright© 1975 by the American Mathematical Society Printed in the United States of America OF THE AMERICAN MATHEMATICAL SOCIET'Y Everett Pitcher and Gordon L. Walker, Editors Hans Samelson, Associate Editor CONTENTS MEETINGS Calendar of Meetings . • • . • • • • . • . • • . • . • • . • • • . • • . Inside Front Cover Program for the November Meeting in Blacksburg, Virginia • • . • . • . • • . • • . • . • • 332 Abstracts for the Meeting: A-719-A-734 Program for the November Meeting in Los Angeles, California • • • • • • • • . • • • • . • • 337 Abstracts for the Meeting: A-734-A-739 PRELllVIINARY ANNOUNCEMENTS OF MEETINGS • • • • • • • • • • • • • • • • • • • . • . • • • • • • 340 ORGANIZERS AND TOPICS OF SPECIAL SESSIONS • • • • • • • • • • • • • • • • . • • • • • • • • • • 354 INVITED SPEAKERS AT AMS MEETINGS • • • • • • • • • • • . • . • • • • • • • • • . • • • • • • • • • • 354 CASE STUDIES, Some Mathematicians with Nonacademic Employment • • • • . • • • • • . • • • • 355 1975 REPORT ON EMPLOYMENT DATA AND ACADEMIC MATHEMATICS • • . • • • • • . • . 357 NEWS ITEMS AND ANNOUNCEMENTS . • • • • • • • • • • • • • • • • • • • • • • • . • • • • • • . 353, 362 PUBLIC UNDERSTANDING OF MATHEMATICS • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • 363 CONVERSION OF TEACHING ASSISTANTSHIPS TO JUNIOR FACULTY POSITIONS • • • • • • 366 SPECIAL MEETINGS INFORMATION CENTER • • • • • • • . • • • • • • • . • • • • • • • . • • • • • • 367 VISITING MATHEMATICIANS, Supplementary List • • . • • . • • • • • • • • • • • • • • • • • • • • • • 369 PERSONAL ITEMS . • . • • • • • • • • • . • • • • • . • . • • • • • • • . • • • • • • • • • • • . • • • • • . 370 LETTERS TO THE EDITOR .•.••••••••••••••••••.••.•••••••••••• ·. • • • . • 371 NEW AMS PUBLICATIONS • • . • • • • • • • • • • • • . • • • • • • • • • • • • • • • • • • • • • . • • • • • • 372 QUERIES . • • • • • • . • • • • • • • • . • • • • • • . • • • • • . • • • • • • • • • • • • • • • . • . • • • • • • • • 374 ABSTRACTS . • • . • • • • • • • . • • . • • • • • • • . • • • • . • • • • • • • • • • • • • • • • • • • • • • A-703 SITUATIONS WANTED . • • . • • • • • . • . • • . • • • • . • • • • • • • • • • . • • . • • • • • • • • • • A-744 RESERVATION FORM • • • • • • • • . • • • • • • • • • • • • . • • • • • • • . • • . • • . • • . • • • • • • A-754 The Seven Hundred Twenty-Ninth Meeting Virginia Polytechnic Institute and State University Blacksburg, Virginia November 7-8, 1975 The seven hundred twenty-ninth meeting of ACCOMMODATIONS the American Mathematical Society will be held Reservations at the Virginia Polytechnic Institute and state Uni­ for lodging should have been made through versity in macksburg, Virginia, from noon Fri­ the Donaldson Brown Center for Continuing day, November 7, until noon Saturday, Novem­ Education, using the preregistration ber 8, 1975. and reservation form which was in the October By invitation of the Committee to Select issue of these cNotiaiJ, prior to the deadline of Hour Speakers for the Southeastern Sectional October 27. However, telephone reservations Meetings there will be three one-hour addresses. will be accepted after that date by calling the Professo~ Robert J. Daverman of the University department of mathematics at (703) 951-6536. of Tennessee will give a lecture at 1:00 p.m. DONALDSON BROWN Friday, entitled "Embeddings of (n - I)-spheres CENTER FOR CONTINU­ ING EDUCATION inn-space." Professor James D. Buckholtz of (703) 951-8322 (Conference the University of Kentucky will lecture on "strong Headquarters) Single convergence and polynomial expansions of ana­ $10.00 plus tax lytic function" at 4:30 p.m. Friday, and Profes­ Twin $16.00 plus tax sor William Jaco of Rice University will speak on ECONO-TRAVEL "Three-manifold groups: A survey" at 9:00a.m. MOTOR HOTEL Saturday, All of the invited addresses will be Route 460, Route 643 held in the auditorium of the Donaldson Brown (703) 951-4242 Center for Continuing Education. 1 Bed 1 person $ 9. 90 1 Bed 2 persons $12.90 SPECIAL SESSIONS 2 Beds 2/3/4 persons $15.90 In addition to the regular sessions for con­ (all include telephone services) tributed papers, there wiil be three special ses­ sions •. Professor John Burns of Virginia Poly­ HOLIDAY INN Route 460 technic Institute and state University has orga­ South nized a special session on Differential Equations (703) 951-1330 and Control Theory; the speakers will include 1 Bed 1 person $15. 00 1 Bed Richard Datko, Kenneth W. Neves, George Red­ 2 persons $21. 00 dien James Reneke, Curtis Travis, and Glenn 2 Beds 2 persons $24. 00 (each Webb. Professor Richard E. Hodel of Duke Uni­ additional person $3. 50) versity has organized a special session on Point Set Theory (more specifically, Generalized Met­ IMPERIAL MOTOR LODGE South Main Street rizable Spaces); the speakers will be D. K. Burke, (703) P. W. Harley ill/R. M, stephenson, W.K.Lind­ 552-4011 2 Beds in every gren, David J, Lutzer, Peter J, Nyikos, G. M. room Reed, Frank G. Slaughter, Jr., E. K, vanDou­ 1 person $ 9.95 wen, Michael L. Wage, and J. M. Worrell, Jr. 2 persons $13.59 A special session on Binary Relations has been 3 persons $15.59 arranged by Professor Eugene M. Norris of the University of South Carolina; the speakers will LAKE TERRACE MOTEL be D. I, Adu, S. Y. Bang/R. T. Yeh, Alexander South Main Street (Route 460 Business) R. Bednarek/Stanislaw M. Ulam, Kim K. -H. But­ (703) 552-5132 ler/B. Schwarz, Temple H. Fay, Richard J. 2 Beds in every room Greechie, Kenneth D. Magill, Jr., and Richard 1 person $ 8. 00-$ 9. 00 D. Mauldin, 2 persons $12. 00-$14. 00 (each additional person $2.00 plus tax) REGISTRATION MARRIOTT The registration desk, which will be located INN Prices in the lobby of the Donaldson Brown Continuing Fork Road (Route 685) (702) 552-7001 Education Center, will be open from 10:00 a.m. 2 Beds to 1:00 p.m., and from 3:30p.m. to 5:00p.m. in every room Single on Friday, November 7, 1975. The registration $17.00 Double fee will be $3. 75, of which $1 will go to the So­ $24.00 ciety, ($1. 00 higher if on pool side) 332 RED LION INN TRAVEL Prices Fork Road and Route 460 Bypass Blacksburg is on U.S.Route 460 about (703) 552-7770 eight miles from Route I-81. Those traveling by 1 Bed 1 person $13. 75 automobile on I-81 should take Exit 37. The Blacks­ 2 Beds 2 persons $21. 50 burg Limousine Service from the Woodrum Air­ ($3. 00 each additional person) port in Roanoke to Blacks burg, is available at $6 per person one way, or $11 per person round trip. UNIVERSITY MOTEL (Individuals desiring this service should contact Route 460 South and 3900 South Main Street, the macksburg
Recommended publications
  • Part III 3-Manifolds Lecture Notes C Sarah Rasmussen, 2019

    Part III 3-Manifolds Lecture Notes C Sarah Rasmussen, 2019

    Part III 3-manifolds Lecture Notes c Sarah Rasmussen, 2019 Contents Lecture 0 (not lectured): Preliminaries2 Lecture 1: Why not ≥ 5?9 Lecture 2: Why 3-manifolds? + Intro to Knots and Embeddings 13 Lecture 3: Link Diagrams and Alexander Polynomial Skein Relations 17 Lecture 4: Handle Decompositions from Morse critical points 20 Lecture 5: Handles as Cells; Handle-bodies and Heegard splittings 24 Lecture 6: Handle-bodies and Heegaard Diagrams 28 Lecture 7: Fundamental group presentations from handles and Heegaard Diagrams 36 Lecture 8: Alexander Polynomials from Fundamental Groups 39 Lecture 9: Fox Calculus 43 Lecture 10: Dehn presentations and Kauffman states 48 Lecture 11: Mapping tori and Mapping Class Groups 54 Lecture 12: Nielsen-Thurston Classification for Mapping class groups 58 Lecture 13: Dehn filling 61 Lecture 14: Dehn Surgery 64 Lecture 15: 3-manifolds from Dehn Surgery 68 Lecture 16: Seifert fibered spaces 69 Lecture 17: Hyperbolic 3-manifolds and Mostow Rigidity 70 Lecture 18: Dehn's Lemma and Essential/Incompressible Surfaces 71 Lecture 19: Sphere Decompositions and Knot Connected Sum 74 Lecture 20: JSJ Decomposition, Geometrization, Splice Maps, and Satellites 78 Lecture 21: Turaev torsion and Alexander polynomial of unions 81 Lecture 22: Foliations 84 Lecture 23: The Thurston Norm 88 Lecture 24: Taut foliations on Seifert fibered spaces 89 References 92 1 2 Lecture 0 (not lectured): Preliminaries 0. Notation and conventions. Notation. @X { (the manifold given by) the boundary of X, for X a manifold with boundary. th @iX { the i connected component of @X. ν(X) { a tubular (or collared) neighborhood of X in Y , for an embedding X ⊂ Y .
  • HE WANG Abstract. a Mini-Course on Rational Homotopy Theory

    HE WANG Abstract. a Mini-Course on Rational Homotopy Theory

    RATIONAL HOMOTOPY THEORY HE WANG Abstract. A mini-course on rational homotopy theory. Contents 1. Introduction 2 2. Elementary homotopy theory 3 3. Spectral sequences 8 4. Postnikov towers and rational homotopy theory 16 5. Commutative differential graded algebras 21 6. Minimal models 25 7. Fundamental groups 34 References 36 2010 Mathematics Subject Classification. Primary 55P62 . 1 2 HE WANG 1. Introduction One of the goals of topology is to classify the topological spaces up to some equiva- lence relations, e.g., homeomorphic equivalence and homotopy equivalence (for algebraic topology). In algebraic topology, most of the time we will restrict to spaces which are homotopy equivalent to CW complexes. We have learned several algebraic invariants such as fundamental groups, homology groups, cohomology groups and cohomology rings. Using these algebraic invariants, we can seperate two non-homotopy equivalent spaces. Another powerful algebraic invariants are the higher homotopy groups. Whitehead the- orem shows that the functor of homotopy theory are power enough to determine when two CW complex are homotopy equivalent. A rational coefficient version of the homotopy theory has its own techniques and advan- tages: 1. fruitful algebraic structures. 2. easy to calculate. RATIONAL HOMOTOPY THEORY 3 2. Elementary homotopy theory 2.1. Higher homotopy groups. Let X be a connected CW-complex with a base point x0. Recall that the fundamental group π1(X; x0) = [(I;@I); (X; x0)] is the set of homotopy classes of maps from pair (I;@I) to (X; x0) with the product defined by composition of paths. Similarly, for each n ≥ 2, the higher homotopy group n n πn(X; x0) = [(I ;@I ); (X; x0)] n n is the set of homotopy classes of maps from pair (I ;@I ) to (X; x0) with the product defined by composition.
  • On the Similarity Transformation Between a Matirx and Its Transpose

    On the Similarity Transformation Between a Matirx and Its Transpose

    Pacific Journal of Mathematics ON THE SIMILARITY TRANSFORMATION BETWEEN A MATIRX AND ITS TRANSPOSE OLGA TAUSSKY AND HANS ZASSENHAUS Vol. 9, No. 3 July 1959 ON THE SIMILARITY TRANSFORMATION BETWEEN A MATRIX AND ITS TRANSPOSE OLGA TAUSSKY AND HANS ZASSENHAUS It was observed by one of the authors that a matrix transforming a companion matrix into its transpose is symmetric. The following two questions arise: I. Does there exist for every square matrix with coefficients in a field a non-singular symmetric matrix transforming it into its transpose ? II. Under which conditions is every matrix transforming a square matrix into its transpose symmetric? The answer is provided by THEOREM 1. For every n x n matrix A — (aik) with coefficients in a field F there is a non-singular symmetric matrix transforming A into its transpose Aτ'. THEOREM 2. Every non-singular matrix transforming A into its transpose is symmetric if and only if the minimal polynomial of A is equal to its characteristic polynomial i.e. if A is similar to a com- panion matrix. Proof. Let T = (ti1c) be a solution matrix of the system Σ(A) of the linear homogeneous equations. (1) TA-ATT=O ( 2 ) T - Tτ = 0 . The system Σ(A) is equivalent to the system (3) TA-ATTT = 0 ( 4 ) T - Tτ = 0 which states that Γand TA are symmetric. This system involves n2 — n equations and hence is of rank n2 — n at most. Thus there are at least n linearly independent solutions of Σ(A).1 On the other hand it is well known that there is a non-singular matrix To satisfying - A* , Received December 18, 1958.
  • An Embedding Theorem for Proper N-Types

    An Embedding Theorem for Proper N-Types

    View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by Elsevier - Publisher Connector Topology and its Applications 48 (1992) 215-233 215 North-Holland An embedding theorem for proper n-types Luis Javier Hernandez Deparfamento de Matem&icar, Unicersidad de Zaragoza, 50009 Zaragoza, Spain Timothy Porter School of Mathematics, Uniuersity College of North Wales, Bangor, Gwynedd LL57 I UT, UK Received 2 August 1991 Abwact Hermindez, L.J. and T. Porter, An embedding theorem for proper n-types, Topology and its Applications 48 (1993) 215-233. This paper is centred around an embedding theorem for the proper n-homotopy category at infinity of a-compact simplicial complexes into the n-homotopy category of prospaces. There is a corresponding global version. This enables one to prove proper analogues of various classical results of Whitehead on n-types, .I,,-complexes, etc. Keywords: n-type, proper n-type, Edwards-Hastings embedding AMS (MOS) Subj. Class: SSPlS, 55 P99 Introduction In his address to the 1950 Proceedings of the International Congress of Mathematicians, Whitehead described the program on which he has been working for some years [31]. He mentioned in particular the realization problem: that of deciding if a given set of homomorphisms defined on homotopy groups of complexes, K and K’, have a geometric realization, K + K’. His attempt to study this problem involved examining algebraic structures, containing more information than the homotopy groups, so that homomorphisms that preserved the extra structure would be realizable. In particular he divided up the problem of finding such models into simpler steps involving n-types as introduced earlier by Fox [13, 141 and gave algebraic models for 2-types in a paper with MacLane [24].
  • The Stability Problem in Shape, and a Whitehead Theorem

    The Stability Problem in Shape, and a Whitehead Theorem

    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 214, 1975 THE STABILITYPROBLEM IN SHAPE,AND A WHITEHEAD THEOREMIN PRO-HOMOTOPY BY DAVID A. EDWARDSAND ROSS GEOGHEGAN(l) ABSTRACT. Theorem 3.1 is a Whitehead theorem in pro-homotopy for finite-dimensional pro-complexes. This is used to obtain necessary and sufficient algebraic conditions for a finite-dimensional tower of complexes to be pro-homot- opy equivalent to a complex (§4) and for a finite-dimensional compact metric space to be pointed shape equivalent to an absolute neighborhood retract (§ 5). 1. Introduction. The theory of shape was introduced by Borsuk [2] for compact metric spaces (compacta) and was extended in a natural way by Fox [13] to all metric spaces. Shape theory agrees with homotopy theory on metric absolute neighborhood retracts (ANR's) and there is ample evidence that as a way of doing algebraic topology on "bad" spaces, shape theory is "better" than homot- opy theory. There is, of course, both shape theory and pointed shape theory. Borsuk [5] has shown that the distinction is important. What we call the stability prob- lem (unpointed or pointed version) is loosely expressed by the question: when is a "bad" space shape equivalent to a "good" space? Specifically, for compacta, this takes two forms: Problem A. Give necessary and sufficient conditions for a compactum Z to have the Fox shape of an ANR. Problem B. Give necessary and sufficient conditions for a compactum Z to have the Borsuk shape of a compact polyhedron. We lay the ground rules as follows. The conditions in Problems A and B should be intrinsic.
  • A Local to Global Argument on Low Dimensional Manifolds

    A Local to Global Argument on Low Dimensional Manifolds

    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 373, Number 2, February 2020, Pages 1307–1342 https://doi.org/10.1090/tran/7970 Article electronically published on November 1, 2019 A LOCAL TO GLOBAL ARGUMENT ON LOW DIMENSIONAL MANIFOLDS SAM NARIMAN Abstract. ForanorientedmanifoldM whose dimension is less than 4, we use the contractibility of certain complexes associated to its submanifolds to cut M into simpler pieces in order to do local to global arguments. In par- ticular, in these dimensions, we give a different proof of a deep theorem of Thurston in foliation theory that says the natural map between classifying spaces BHomeoδ(M) → BHomeo(M) induces a homology isomorphism where Homeoδ(M) denotes the group of homeomorphisms of M made discrete. Our proof shows that in low dimensions, Thurston’s theorem can be proved without using foliation theory. Finally, we show that this technique gives a new per- spective on the homotopy type of homeomorphism groups in low dimensions. In particular, we give a different proof of Hacher’s theorem that the homeomor- phism groups of Haken 3-manifolds with boundary are homotopically discrete without using his disjunction techniques. 1. Introduction Often, in h-principle type theorems (e.g. Smale-Hirsch theory), it is easy to check that the statement holds for the open disks (local data) and then one wishes to glue them together to prove that the statement holds for closed compact manifolds (global statement). But there are cases where one has a local statement for a closed disk relative to the boundary. To use such local data to great effect, instead of covering the manifold by open disks, we use certain “resolutions” associated to submanifolds (see Section 2) to cut the manifold into closed disks.
  • Historical Notes on Loop Theory

    Historical Notes on Loop Theory

    Comment.Math.Univ.Carolin. 41,2 (2000)359–370 359 Historical notes on loop theory Hala Orlik Pflugfelder Abstract. This paper deals with the origins and early history of loop theory, summarizing the period from the 1920s through the 1960s. Keywords: quasigroup theory, loop theory, history Classification: Primary 01A60; Secondary 20N05 This paper is an attempt to map, to fit together not only in a geographical and a chronological sense but also conceptually, the various areas where loop theory originated and through which it moved during the early part of its 70 years of history. 70 years is not very much compared to, say, over 300 years of differential calculus. But it is precisely because loop theory is a relatively young subject that it is often misinterpreted. Therefore, it is extremely important for us to acknowledge its distinctive origins. To give an example, when somebody asks, “What is a loop?”, the simplest way to explain is to say, “it is a group without associativity”. This is true, but it is not the whole truth. It is essential to emphasize that loop theory is not just a generalization of group theory but a discipline of its own, originating from and still moving within four basic research areas — algebra, geometry, topology, and combinatorics. Looking back on the first 50 years of loop history, one can see that every decade initiated a new and important phase in its development. These distinct periods can be summarized as follows: I. 1920s the first glimmerings of non-associativity II. 1930s the defining period (Germany) III. 1940s-60s building the basic algebraic frame and new approaches to projective geometry (United States) IV.
  • 1 Whitehead's Theorem

    1 Whitehead's Theorem

    1 Whitehead's theorem. Statement: If f : X ! Y is a map of CW complexes inducing isomorphisms on all homotopy groups, then f is a homotopy equivalence. Moreover, if f is the inclusion of a subcomplex X in Y , then there is a deformation retract of Y onto X. For future reference, we make the following definition: Definition: f : X ! Y is a Weak Homotopy Equivalence (WHE) if it induces isomor- phisms on all homotopy groups πn. Notice that a homotopy equivalence is a weak homotopy equivalence. Using the definition of Weak Homotopic Equivalence, we paraphrase the statement of Whitehead's theorem as: If f : X ! Y is a weak homotopy equivalences on CW complexes then f is a homotopy equivalence. In order to prove Whitehead's theorem, we will first recall the homotopy extension prop- erty and state and prove the Compression lemma. Homotopy Extension Property (HEP): Given a pair (X; A) and maps F0 : X ! Y , a homotopy ft : A ! Y such that f0 = F0jA, we say that (X; A) has (HEP) if there is a homotopy Ft : X ! Y extending ft and F0. In other words, (X; A) has homotopy extension property if any map X × f0g [ A × I ! Y extends to a map X × I ! Y . 1 Question: Does the pair ([0; 1]; f g ) have the homotopic extension property? n n2N (Answer: No.) Compression Lemma: If (X; A) is a CW pair and (Y; B) is a pair with B 6= ; so that for each n for which XnA has n-cells, πn(Y; B; b0) = 0 for all b0 2 B, then any map 0 0 f :(X; A) ! (Y; B) is homotopic to f : X ! B fixing A.
  • ABSTRACT XUE, XIANGZHONG. Electronic

    ABSTRACT XUE, XIANGZHONG. Electronic

    ABSTRACT XUE, XIANGZHONG. Electronic System Optimization Design via GP-Based Surrogate Modeling. (Under the direction of Dr. Paul D. Franzon.) For an electronic system with a given circuit topology, the designer’s goal is usually to automatically size the device and components to achieve globally optimal performance while at the same satisfying the predefined specifications. This goal is motivated by a human desire for optimality and perfection. This research project improves upon current optimization strategies. Many types of convex programs and convex fitting techniques are introduced and compared, and the evolution of Geometric Program (GP)-based optimization approaches is investigated through a literature review. By these means, it is shown that a monomial-based GP can achieve optimal performance and accuracy only for long-channel devices, and that a piecewise linear (PWL)-based GP works well only for short-channel, narrow devices without many data fitted. Based on known GP optimizer and convex PWL fitting techniques, an innovative surrogate modeling and optimization algorithm is proposed to further improve performance accuracy iteratively for a wide transistor with a short channel. The new surrogate strategy, which comprises a fine model and a coarse model, can automatically size the device to create a reusable system model for designing electronic systems and noticeably improving prediction accuracy, particularly when compared to the pure, GP-based optimization method. To verify the effectiveness and viability of the proposed surrogate strategy, a widely used two-stage optimization design is employed, entailing an operational amplifier (op-amp) and LC-tuned oscillator. In addition, an involved analysis and simulation demonstrate that the optimal results of both coarse and fine models in the proposed surrogate strategy may gradually converge to each other iteratively while achieving over 10% improvement in performance accuracy compared to the previous, PWL-based GP algorithm.
  • Microfilms International 300 N /EE B ROAD

    Microfilms International 300 N /EE B ROAD

    INFORMATION TO USERS This was produced from a copy of a document sent to us for microfilming. While the most advanced technological means to photograph and reproduce this document have been used, the quality is heavily dependent upon the quality of the material submitted. The following explanation of techniques is provided to help you understand markings or notations which may appear on this reproduction. 1.The sign or “target” for pages apparently lacking from the document photographed is “Missing Page(s)” . If it was possible to obtain the missing page(s) or section, they are spliced into the film along with adjacent pages. This may have necessitated cutting through an image and duplicating adjacent pages to assure you of complete continuity. 2. When an image on the film is obliterated with a round black mark it is an indication that the film inspector noticed either blurred copy because of movement during exposure, or duplicate copy. Unless we meant to delete copyrighted materials that should not have been filmed, you will find a good image of the page in the adjacent frame. 3. When a map, drawing or chart, etc., is part of the material being photo­ graphed the photographer has followed a definite method in “sectioning” the material. It is customary to begin filming at the upper left hand comer of a large sheet and to continue from left to right in equal sections with small overlaps. If necessary, sectioning is continued again—beginning below the first row and continuing on until complete. 4. For any illustrations that cannot be reproduced satisfactorily by xerography, photographic prints can be purchased at additional cost and tipped into your xerographic copy.
  • Save Pdf (0.27

    Save Pdf (0.27

    The other two groups deal with a variety of plane situa­ tions: measures of approximation of a convex set by another convex set of some given class (symmetric sets, sets of con­ stant width etc*)» extremal properties of triangles inscribed in and circumscribed about convex sets, properties of curves of constant width, and so on. Although the general level and workmanship are inferior to those of the author1 s Cambridge Tract on convexity, the present collection contains some interesting and important things and will be of interest to the specialist, Z« A* Melzak, McGill University Fallacies in Mathematics» by E.A. Maxwell, Cambridge University Press, Macmillan Company of Canada L»td. $2*75, In this book the author, a Fellow of Queen1 s College, Cambridge, is acquainting his readers (College and High School teachers as well as interested pupils) in an often amusing and always interesting way with the fallacies a mathematician is apt to meet in the fields of elementary geometry, algebra and trigonometry and calculus* He distinguishes between mistakes (not discussed in the book), howlers and fallacies in the proper sense like this gem: 1= <JT = J(-l){-l) = V-l J-l = i.i = -1. The first 10 serious chapters presenting a choice selection of fallacies in each of the fields with subsequent detailed discussion are followed by a chapter on miscellaneous howlers, e.g., the following. Solve (x+3)(2-x) = 4* Answer: Either x -I- 3 = 4 „ a • x = 1 or 2 - x = 4 / , x = «2, correct» The book is most instructive for any mathematics teacher, Hans Zassenhaus, California Institute of Technology Some Aspects of Analysis and- Probability, by Irving Kaplansky, Marshall Hall Jre , Edwin Hewitt and Robert Fortet* Surveys in Applied Mathematics IV.
  • Mathematicalsciences News

    Mathematicalsciences News

    mathematical sciences news 2015 contents 2015 Letter from Department 03 Head, Tom Bohman Math News Shorts 04 Faculty Notes 06 Editor-in-Chief Tom Bohman Writer Feature 08 Amy Pavlak Laird Alumnus and Nobel Laureate Contributing Writers Bill Hrusa John Nash Wins Abel Prize David Kinderlehrer Dejan Slep ´cev Photography Democracy 2.1 16 Carnegie Mellon University photographers Ken Andreyo and Tim Kaulen Graphic Design Carnegie Mellon University Marketing & Communications Po-Shen Loh Receives 20 NSF CAREER Award Carnegie Mellon University Department of Mathematical Sciences Wean Hall 6113 Pittsburgh, PA 15213 Boris Bukh Wins Sloan 22 math.cmu.edu Research Fellowship Carnegie Mellon University does not discriminate in admission, employment, or administration of its programs or activities on the basis of race, color, national origin, sex, handicap or disability, age, sexual orientation, gender identity, religion, Undergraduate creed, ancestry, belief, veteran status or genetic 24 information. Furthermore, Carnegie Mellon University does not discriminate and is required Research not to discriminate in violation of federal, state or local laws or executive orders. Inquiries concerning the application of and compliance with this statement should be directed to the Vice President for Campus Affairs, Carnegie Mellon University, 5000 Forbes Avenue, Class of 2015 Pittsburgh, PA 15213, telephone 412-268-2056. 26 Obtain general information about Carnegie Mellon University by calling 412-268-2000. Produced for the Department of Mathematical Sciences by the Marketing & Communications, November, 2015, 16-177. ©2015 Carnegie Mellon University, All rights reserved. No part of this publication may be reproduced in any form without written permission from Carnegie Mellon Unversity’s Department of Mathematical Sciences.