Volume 53 , issue 1$-$2 ( 2001 ) | back |

The generalized cohomology theories, Brumfiel-Madsen formula and topological construction of BGG-type operators | 1--13 |

**Abstract**

In this work, we investigate the topological construction of $BGG$-type operators, giving details about complex orientable theories, Becker-Gottlieb transfer and a formula of Brumfiel-Madsen. We generalize the $BGG$ operators on the Morava $K$-theory and the others $\Bbb F_p$-generalized cohomology theories.

**Keywords:** Generalized cohomology theory, Bernstein-Gelfand-Gelfand operators.

**MSC:** 55R10, 55R12

Best $\lambda$-approximations for analytic functions of medium growth on the unit disc | 15--19 |

**Abstract**

In this paper we investigate the asymptotic relation between maximum moduli of a class of functions analytic on the unit disc and their partial sums, i.e.\ we formulate the problem of best $\lambda$-approximations. We also give an application of our results to Karamata's Tauberian Theorem for series.

**Keywords:** Best $\lambda$-approximation, Karamata's Tauberian theorem.

**MSC:** 30E10, 40E05

Some characterizations of the Lorentzian spherical timeline and null curves | 21--27 |

**Abstract**

In [5] and [6] the authors have characterized the Lorentzian spherical spacelike curves in the Minkowski $3$-space $E_1^3$. In this paper, we shall characterize the Lorentzian spherical timelike and null curves in the same space.

**Keywords:** Lorentzian 3-space, Lorentzian
sphere, causal character, curvature, torsion.

**MSC:** 53C50, 53C40

Estimation in uniform minification processes and their transformations | 29--35 |

**Abstract**

Unknown parameters of the uniform minification processes and their
transformations are estimated in this paper. Three different
methods of estimating are considered. The first one is supported
by the properties of the process (maximum or minimum of the
quotient of successive values of the sequence), the second one is
based on the probabilities $P\{X_n>X_{n-1}\}$ and
$P\{X_n

**Keywords:** Minification process, estimation, method of moments.

**MSC:** 62M10

Sufficient conditions for elliptic problem of optimal control in $R^n$ in Orlicz Sobolev spaces | 37--49 |

**Abstract**

This paper is concerned with the local minimization problem for a variety of non Frechet-differentiable G\^ateaux functional $J(f)\equiv\int_{\Omega}v(x,u,f)\,dx$ in the Orlicz-Sobolev space $(W^1_0L_M^*(\Omega),\|.\|_{M})$, where $u$ is the solution of the Dirichlet problem for a linear uniformly elliptic operator with nonhomogenous term $f$ and $\|.\|_{M}$ is the Orlicz norm associated with an N-function~$M$. We use a recent extension of Frechet-differentiability (approach of Taylor mappings see [2]), and we give various assumptions on $v$ to guarantee a critical point is a strict local minimum. Finally, we give an example of a control problem where classical Frechet differentiability cannot be used and their approach of Taylor mappings works.

**Keywords:** Minimization problem, G\^ateaux functional, Orlicz-Sobolev space,
uniformly elliptic operator, Frechet-differentiability, control problems.

**MSC:** 49K27

Multi point boundary value problems for second order differential inclusions | 51--58 |

**Abstract**

In this paper we investigate the existence of solutions on a compact interval to a multi-point boundary value problem for a class of second order differential inclusions. We shall rely on a fixed point theorem for condensing maps due to Martelli.

**Keywords:** Multi point boundary value problems,
differential inclusion, existence, fixed point.

**MSC:** 34A60, 34B10, 34B15