DSpace Collection: Volume 28 Number 1
http://hdl.handle.net/10525/462
Serdica Mathematical Journal Volume 28, Number 1, 2002The Collection's search engineSearch the Channelsearch
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Multibody System Mechanics: Modelling, Stability, Control, and Robustness by V. A. Konoplev and A. Cheremensky
http://hdl.handle.net/10525/490
Title: Multibody System Mechanics: Modelling, Stability, Control, and Robustness by V. A. Konoplev and A. Cheremensky<br/><br/>Authors: Konoplev, V.; Cheremensky, A.<br/><br/>Abstract: The Union of Bulgarian Mathematicians starts a new series of publica-tions: Mathematics and Its Applications. The first issue of the series is “Multi-body System Mechanics: Modelling, Stability, Control and Robustness”. The authors are well known mathematicians with various published booksand articles. Professor Vladimir Konoplev works in the Institute of Problems ofMechanical Engineering, Russian Academy of Sciences (St. Petersburg, Russia),while Professor Alexander Cheremensky works in the Institute of Mechanics,Bulgarian Academy of Sciences (Sofia, Bulgaria). The book contains results of the development of a new computer-aidedmathematical formalism of the multibody system mechanics which may be easilyimplemented by the use of computer algebra tools for symbolic computations andof standard software for numerical ones.<br/><br/>Description: BOOK REVIEWSMultibody System Mechanics: Modelling, Stability, Control, and Ro-bustness, by V. A. Konoplev and A. Cheremensky, Mathematics and its Appli-cations Vol. 1, Union of Bulgarian Mathematicians, Sofia, 2001, XXII + 288 pp.,$ 65.00, ISBN 954-8880-09-01On Parabolic Subgroups and Hecke Algebras of some Fractal Groups
http://hdl.handle.net/10525/489
Title: On Parabolic Subgroups and Hecke Algebras of some Fractal Groups<br/><br/>Authors: Bartholdi, Laurent; Grigorchuk, Rostislav<br/><br/>Abstract: We study the subgroup structure, Hecke algebras, quasi-regularrepresentations, and asymptotic properties of some fractal groups of branchtype. We introduce parabolic subgroups, show that they are weakly maximal,and that the corresponding quasi-regular representations are irreducible.These (infinite-dimensional) representations are approximated by finite-dimensional quasi-regular representations. The Hecke algebras associated tothese parabolic subgroups are commutative, so the decomposition in irreducible components of the finite quasi-regular representations is given bythe double cosets of the parabolic subgroup. Since our results derive fromconsiderations on finite-index subgroups, they also hold for the profinitecompletions G of the groups G. The representations involved have interesting spectral properties investigated in [6]. This paper serves as a group-theoretic counterpart to thestudies in the mentioned paper. We study more carefully a few examples of fractal groups, and in doingso exhibit the first example of a torsion-free branch just-infinite group. We also produce a new example of branch just-infinite group of intermediate growth, and provide for it an L-type presentation by generators andrelators.<br/><br/>Description: * The authors thank the “Swiss National Science Foundation” for its support.Porosity and Variational Principles
http://hdl.handle.net/10525/488
Title: Porosity and Variational Principles<br/><br/>Authors: Marchini, Elsa<br/><br/>Abstract: We prove that in some classes of optimization problems, likelower semicontinuous functions which are bounded from below, lower semi-continuous or continuous functions which are bounded below by a coercivefunction and quasi-convex continuous functions with the topology of theuniform convergence, the complement of the set of well-posed problems isσ-porous. These results are obtained as realization of a theorem extendinga variational principle of Ioffe-Zaslavski.Compactness in the First Baire Class and Baire-1 Operators
http://hdl.handle.net/10525/487
Title: Compactness in the First Baire Class and Baire-1 Operators<br/><br/>Authors: Mercourakis, S.; Stamati, E.<br/><br/>Abstract: For a polish space M and a Banach space E let B1 (M, E)be the space of first Baire class functions from M to E, endowed with thepointwise weak topology. We study the compact subsets of B1 (M, E) andshow that the fundamental results proved by Rosenthal, Bourgain, Fremlin,Talagrand and Godefroy, in case E = R, also hold true in the generalcase. For instance: a subset of B1 (M, E) is compact iff it is sequentially(resp. countably) compact, the convex hull of a compact bounded subset ofB1 (M, E) is relatively compact, etc. We also show that our class includesGulko compact.In the second part of the paper we examine under which conditions abounded linear operator T : X ∗ → Y so that T |BX ∗ : (BX ∗ , w∗ ) → Y is aBaire-1 function, is a pointwise limit of a sequence (Tn ) of operators withT |BX ∗ : (BX ∗ , w∗ ) → (Y, · ) continuous for all n ∈ N. Our results in thiscase are connected with classical results of Choquet, Odell and Rosenthal.