On tractability of weighted integration over bounded and unbounded regions in

We prove that for the space of functions with mixed first derivatives bounded in norm, the weighted integration problem over bounded or unbounded regions is equivalent to the corresponding classical integration problem over the unit cube, provided that the integration domain and weight have product forms. This correspondence yields tractability of the general weighted integration problem.

     

On strong tractability of weighted multivariate integration

We prove that for every dimension and every number of points, there exists a point-set whose -weighted unanchored discrepancy is bounded from above by independently of provided that the sequence has for some (even arbitrarily large) . Here is a positive number that could be chosen arbitrarily close to zero and depends on but not on or . This result yields strong tractability of the corresponding integration problems including approximation of weighted integrals over unbounded domains such as . It also supplements the results that provide an upper bound of the form when .

     

Weighted allocation rules for standard fixed tree games

In this paper we consider standard fixed tree games, for which each vertex unequal to the root is inhabited by exactly one player. We present two weighted allocation rules, the weighted down-home allocation and the weighted neighbour-home allocation, both inspired by the painting story in Maschler et al. (1995) . We show, in a constructive way, that the core equals both the set of weighted down-home allocations and the set of weighted neighbour allocations. Since every weighted down-home allocation specifies a weighted Shapley value (Kalai and Samet (1988)) in a natural way, and vice versa, our results provide an alternative proof of the fact that the core of a standard fixed tree game equals the set of weighted Shapley values. The class of weighted neighbour allocations is a generalization of the nucleolus, in the sense that the latter is in this class as the special member where players have all equal weights.     

Weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces

In this paper, we give a new characterization for the boundedness of weighted differentiation composition operator from logarithmic Bloch spaces to Bloch‐type spaces and calculate its essential norm in terms of the n‐th power of induced analytic self‐map on the unit disk. From which a sufficient and necessary condition of compactness of this operator follows immediately.     

On the Hartogs-Bochner phenomenon for CR functions in

Let be a compact, connected, -smooth and globally minimal hypersurface in which divides the projective space into two connected parts and . We prove that there exists a side, or , such that every continuous CR function on extends holomorphically to this side. Our proof of this theorem is a simplification of a result originally due to F. Sarkis.

     

Complete rotation hypersurfaces with Hk constant in space forms

In this paper we classify all complete rotation hypersurfaces withH _k constant in ⁿ⁺¹ andH ⁿ⁺¹, is the normalizedk-th symmetric function of the principal curvatures. Partial results are also given forH ⁿ⁺¹.Partially supported by DGAPA-UNAM, México, CONACYT, México, under Project 1068P, and CNPp, Brazil.     

Some Theorems for Hypersurface of Randers Spaces

In this paper, we consider the hypersurfaces of Randers space with constant flag curvature. (1) Let (Mⁿ⁺¹, F) be a Randers-Minkowski space. If (Mⁿ, F) is a hypersurface of (Mⁿ⁺¹, F) with constant flag curvature K=1, then we can prove that M is Riemannian. (2) Let (Mⁿ⁺¹, F) be a Randers space with constant flag curvature. Assume (M, F) is a compact hypersurface of (Mⁿ⁺¹, F) with constant mean curvature|H|. Then a pinching theorem is established, which generalizes the result of[Proc. Amer. Math. Soc., 120, 1223-1229 (1994)] from the Riemannian case to the Randers space.     

Geometrical and Topological Properties of Real Polynomial Fibres

We establish a Gauss—Bonnet type formula for a smooth fibre of a nonproper real polynomial of ⁿ . For this we need to study topological properties of a generic hyperplane section of this fibre.     

Curves of positive solutions of boundary value problems on time-scales

Let TR be a time-scale, with a=infT, b=supT. We consider the nonlinear boundary value problem

(2)

(4)

u(a)=u(b)=0,