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26078 results in Abstract analysis

Page 912 of 1304

  • REGULAR-NILPOTENT GROUPS OF AUTOMORPHISMS

  • REZA ZOMORRODIAN
  • Journal:
    Glasgow Mathematical Journal / Volume 45 / Issue 1 / January 2003
    Published online by Cambridge University Press:
    01 May 2003, pp. 1-5
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  • Using the definition of regular p-group given by M. Hall [1], a new class of finite groups called regular-nilpotent has been defined. The action of these groups as automorphisms of compact Riemann surfaces has been investigated. It is proved that a necessary and sufficient condition for a Fuchsian group to cover a regular-nilpotent group is that its orbit genus be zero and its periods satisfy the least common multiple condition, first defined by Harvey [2] and Maclachlan [4].

  • COMPARISON BETWEEN USUAL AND VECTOR TIME DERIVATIVES

  • ÓSCAR LÓPEZ-POUSO
  • Journal:
    Glasgow Mathematical Journal / Volume 45 / Issue 1 / January 2003
    Published online by Cambridge University Press:
    01 May 2003, pp. 167-172
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  • We prove two comparison theorems between the time derivative of a real function $u(x, t)$ such that $u(\cdot,t)$ belongs to L$^1 (\Omega)$ for all $t$, and the time derivative of the vector function $\skew2\hat{u}(t) = u(\cdot, t)$.

  • HYPERKÄHLER STRUCTURES WITH TORSION ON NILPOTENT LIE GROUPS

  • BIRTE FEIX, HENRIK PEDERSEN
  • Journal:
    Glasgow Mathematical Journal / Volume 45 / Issue 1 / January 2003
    Published online by Cambridge University Press:
    01 May 2003, pp. 189-198
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  • Using the classification by Dotti and Fino [3] we show the existence of an HKT metric on a neighbourhood of the centre of any 8-dimensional nilpotent Lie group $G$ with invariant hypercomplex structure. This metric exists globally if the hypercomplex structure is abelian, and in these cases we construct an HKT structure on a neighbourhood of the zero section of the cotangent bundle $T^{*}G$ extending the HKT metric on $G$.

  • GORENSTEIN PROPERTY OF HOPF GRADED ALGEBRAS

  • Q.-S. WU, J. J. ZHANG
  • Journal:
    Glasgow Mathematical Journal / Volume 45 / Issue 1 / January 2003
    Published online by Cambridge University Press:
    01 May 2003, pp. 111-115
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  • Let $A$ be a locally finite, N-graded, noetherian algebra with a balanced dualizing complex. If $A$ is a Hopf algebra, then $A$ has finite injective dimension.

  • RIEMANN–LEBESGUE PROPERTIES OF BANACH SPACES ASSOCIATED WITH SUBSETS OF COUNTABLE DISCRETE ABELIAN GROUPS

  • PATRICK N. DOWLING, NARCISSE RANDRIANANTOANINA
  • Journal:
    Glasgow Mathematical Journal / Volume 45 / Issue 1 / January 2003
    Published online by Cambridge University Press:
    01 May 2003, pp. 159-166
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  • For a subset $\Lambda$ of the dual group of a compact metrizable abelian group, we introduce the type I-, II-, and III-$\Lambda$-Riemann–Lebesgue property of a Banach space. As an application we use these properties to characterize Rajchman sets.

  • PROPERTIES OF SUBGROUPS OF SOLVABLE GROUPS THAT IMPLY THEY ARE NORMALLY EMBEDDED

  • ARNOLD FELDMAN
  • Journal:
    Glasgow Mathematical Journal / Volume 45 / Issue 1 / January 2003
    Published online by Cambridge University Press:
    01 May 2003, pp. 45-52
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  • Recently, Ballester-Bolinches [1 and 2], Pedraza-Aguilera [2] and Perez-Ramos [2] have studied circumstances under which certain injectors and projectors, which are always pronormal, must be normally embedded. In this note we give a scheme for describing a minimal counterexample to a conjecture of the form: a subnormally embedded subgroup with properties $\alpha_1$, $\alpha_2,{\ldots\,},\alpha_{n}$ is normally embedded, where $\alpha_1$, $\alpha_2,{\ldots\,},\alpha_{n}$ satisfy certain conditions. We then show contradictions in certain cases involving finite solvable groups.

  • Preface

  • Mark J. Ablowitz, University of Colorado, Boulder, Athanassios S. Fokas, Imperial College of Science, Technology and Medicine, London
  • Book:
    Complex Variables
    Published online:
    05 September 2012
    Print publication:
    28 April 2003, pp xi-xii

  • Summary

    The study of complex variables is beautiful from a purely mathematical point of view and provides a powerful tool for solving a wide array of problems arising in applications. It is perhaps surprising that to explain real phenomena, mathematicians, scientists, and engineers often resort to the “complex plane.” In fact, using complex variables one can solve many problems that are either very difficult or virtually impossible to solve by other means. The text provides a broad treatment of both the fundamentals and the applications of this subject.

    This text can be used in an introductory one-or two-semester undergraduate course. Alternatively, it can be used in a beginning graduate level course and as a reference. Indeed, Part I provides an introduction to the study of complex variables. It also contains a number of applications, which include evaluation of integrals, methods of solution to certain ordinary and partial differential equations, and the study of ideal fluid flow. In addition, Part I develops a suitable foundation for the more advanced material in Part II. Part II contains the study of conformal mappings, asymptotic evaluation of integrals, the so-called Riemann–Hilbert and DBAR problems, and many of their applications. In fact, applications are discussed throughout the book. Our point of view is that students are motivated and enjoy learning the material when they can relate it to applications.

  • Part I - Fundamentals and Techniques of Complex Function Theory

  • Mark J. Ablowitz, University of Colorado, Boulder, Athanassios S. Fokas, Imperial College of Science, Technology and Medicine, London
  • Book:
    Complex Variables
    Published online:
    05 September 2012
    Print publication:
    28 April 2003, pp 1-2

  • Summary

    The first portion of this text aims to introduce the reader to the basic notions and methods in complex analysis. The standard properties of real numbers and the calculus of real variables are assumed. When necessary, a rigorous axiomatic development will be sacrificed in place of a logical development based upon suitable assumptions. This will allow us to concentrate more on examples and applications that our experience has demonstrated to be useful for the student first introduced to the subject. However, the important theorems are stated and proved.

Page 912 of 1304