Serdica Mathematical Journal

Volume 36, Number 2, 2010

C O N T E N T S

• Bedratyuk, L. Weitzenböck derivations and classical invariant theory: I. Poincaré series (pp. 99-120)
• Anastassiou, G. A. O. Duman. Fractional trigonometric Korovkin theory in statistical sense (pp. 121-136)
• Khan, M. A., S. Uddin, K. Singh. Totally umbilical pseudo-slant submanifolds of a nearly cosymplectic manifold (pp. 137-148)
• Gasparis, I., M. K. Papadiamantis, D. Z. Zisimopoulou. More l_r saturated L^∞ spaces (pp. 149-170)
• Fιndιk, Ş Normal and normally outer automorphisms of free metabelian nilpotent Lie algebras (pp. 171-210)

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  A B S T R A C T S

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  WEITZENBÖCK DERIVATIONS AND CLASSICAL INVARIANT THEORY: I. POINCARÉ SERIES
  Leonid Bedratyuk leonid.uk@gmail.com

  2000 Mathematics Subject Classification: 13N15, 13A50, 16W25.
  Key words: classical invariant theory, covariants, binary forms, derivations, Poincaré series.

  By using classical invariant theory approach, formulas for computation of the Poincaré series of the kernel of linear locally nilpotent derivations are found.

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  FRACTIONAL TRIGONOMETRIC KOROVKIN THEORY IN STATISTICAL SENSE
  George A. Anastassiou ganastss@memphis.edu,
  Oktay Duman oduman@etu.edu.tr

  2000 Mathematics Subject Classification: 41A25, 41A36.
  Key words: The trigonometric Korovkin theorem, statistical convergence, fractional calculus, Caputo fractional derivatives.

  In the present paper, we improve the classical trigonometric Korovkin theory by using the concept of statistical convergence from the summability theory and also by considering the fractional derivatives of functions. We also show that our new results are more applicable than the classical ones.

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  TOTALLY UMBILICAL PSEUDO-SLANT SUBMANIFOLDS OF A NEARLY COSYMPLECTIC MANIFOLD
  M. A. Khan meraj79@gmail.com,
  Siraj Uddin siraj.ch@gmail.com,
  Khushwant Singh khushwantchahil@gmail.com

  2000 Mathematics Subject Classification: 53C40, 53B25.
  Key words: Slant submanifold, pseudo-slant submanifold, totally umbilical, nearly cosymplectic.

  In the present note we study totally umbilical pseudo-slant submanifolds of a nearly cosymplectic manifold. We have obtained a classification theorem for totally umbilical pseudo-slant submanifolds of a nearly cosymplectic manifold.

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  MORE l_r SATURATED L^∞ SPACES
  I. Gasparis ioagaspa@math.auth.gr,
  M. K. Papadiamantis mpapadiamantis@yahoo.gr,
  D. Z. Zisimopoulou dzisimopoulou@hotmail.com

  2000 Mathematics Subject Classification: 05D10, 46B03.
  Key words: Banach theory, l_r saturated, L^Ґ spaces.

  Given r ∈(1, ∞), we construct a new L^∞ separable Banach space which is l_r saturated.

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  NORMAL AND NORMALLY OUTER AUTOMORPHISMS OF FREE METABELIAN NILPOTENT LIE ALGEBRAS
  Şehmus Fιndιk sfindik@cu.edu.tr

  2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.
  Key words: free Lie algebras, free metabelian nilpotent Lie algebras, inner automorphisms, normal automorphisms.

  Let L_m,c be the free m-generated metabelian nilpotent of class c Lie algebra over a field of characteristic 0. An automorphism φ of L_m,c is called normal if φ(I) = I for every ideal I of the algebra L_m,c. Such automorphisms form a normal subgroup N(L_m,c) of Aut (L_m,c) containing the group of inner automorphisms. We describe the group of normal automorphisms of L_m,c and the quotient group of Aut (L_m,c) modulo N(L_m,c).

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