Serdica Mathematical Journal

Volume 37, Number 2, 2011

C O N T E N T S

• Bedratyuk, L. Weitzenböck derivations and classical invariant theory, II: The symbolic method (pp. 87−106)
• Barraa, M. Generalized derivations and norm equality in normed ideals (pp. 107−112)
• Mejjaoli, H. Dunkl-Schrödinger equations with and without quadratic potentials (pp. 113−142)
• Arbit, A. V. The Lindelöf number greater than continuum is u-invariant (pp. 143−162)
• Kurdachenko, L. A., I. Ya. Subbotin. On groups whose contranormal subgroups are normally complemented (pp. 163−172)

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  A B S T R A C T S

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  WEITZENBÖCK DERIVATIONS AND CLASSICAL INVARIANT THEORY, II: THE SYMBOLIC METHOD
  Leonid Bedratyuk leonid.uk@gmail.com

  2000 Mathematics Subject Classification: 13N15, 13A50, 13F20.
  Key words: Classical invariant theory, Symbolic method, Locally nilpotent derivations.

  An analogue of the symbolic method of classical invariant theory for a representation and manipulation of the elements of the kernel of Weitzenböck derivations is developed.

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  GENERALIZED DERIVATIONS AND NORM EQUALITY IN NORMED IDEALS
  Mohamed Barraa barraa@hotmail.com

  2000 Mathematics Subject Classification: 47A10, 47A12, 47A30, 47B10, 47B20, 47B37, 47B47, 47D50.
  Key words: Generalized derivation, norm, norm ideal, S-universasl operator, numerical range, spectrum, quasi-nilpotent operator, hyponormal operator.

  We compare the norm of a generalized derivation on a Hilbert space with the norm of its restrictions to Schatten norm ideals.

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  DUNKL-SCHRÖDINGER EQUATIONS WITH AND WITHOUT QUADRATIC POTENTIALS
  Hatem Mejjaoli hmejjaoli@kfu.edu.sa, hatem.mejjaoli@ipest.rnu.tn

  2000 Mathematics Subject Classification: Primary 42A38. Secondary 42B10.
  Key words: Nonlinear Dunkl-Schrödinger equation, Strichartz estimate, local and global well-posedness, blow up, scattering, wave operators.

  The purpose of this paper is to study the dispersive properties of the solutions of the Dunkl-Schrödinger equation and their perturbations with potential. Furthermore, we consider a few applications of these results to the corresponding nonlinear Cauchy problems.

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  THE LINDELÖF NUMBER GREATER THAN CONTINUUM IS u-INVARIANT
  A. V. Arbit arbit@mail.tsu.ru

  2000 Mathematics Subject Classification: 54C35, 54D20, 54C60.
  Key words: Function spaces, u-equivalence, u-invariant, Lindelöf number, set-valued mappings.

  Two Tychonoff spaces X and Y are said to be l-equivalent (u-equivalent) if C_p(X) and C_p(Y) are linearly (uniformly) homeomorphic. N. V. Velichko proved that countable Lindelöf number is preserved by the relation of l-equivalence. A. Bouziad strengthened this result and proved that any Lindelöf number is preserved by the relation of l-equivalence. In this paper it has been proved that the Lindelöf number greater than continuum is preserved by the relation of u-equivalence.

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  ON GROUPS WHOSE CONTRANORMAL SUBGROUPS ARE NORMALLY COMPLEMENTED
  L. A. Kurdachenko lkurdachenko@hotmail.com,
  I. Ya. Subbotin isubboti@nu.edu

  2000 Mathematics Subject Classification: 20F16, 20E15.
  Key words: Contranormal subgroups, abnormal subgroups, complemented subgroups, normally complemented subgroups.

  Groups in which every contranormal subgroup is normally complemented has been considered. The description of such groups G with the condition Max-n and such groups having an abelian nilpotent residual satisfying Min-G have been obtained.

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