On Uniformly Convex and Uniformly Kadec-Klee Renomings

We give a new construction of uniformly convex norms with a power type modulus on super-reflexive spaces based on the notion of dentability index. Furthermore, we prove that if the Szlenk index of a Banach space is less than or equal to ω (first infinite ordinal) then there is an equivalent weak* lower semicontinuous positively homogeneous functional on X* satisfying the uniform Kadec-Klee Property for the weak*-topology (UKK*). Then we solve the UKK or UKK* renorming problems for Lp(X) spaces and C(K) spaces for K scattered compact space.

On some Optimal (n,t,1,2) and (n,t,1,3) Super Imposed Codes

Partially supported by the Technical University of Gabrovo under Grant C-801/2008

Decomposition of Banach Space into a Direct Sum of Separable and Reflexive Subspaces and Borel Maps

* This paper was supported in part by the Bulgarian Ministry of Education, Science and Technologies under contract MM-506/95.

A Super-Dimension Approach in ROLAP Environments

Often the designer of ROLAP applications follows up with the question “can I create a little joiner table with just the two dimension keys and then connect that table to the fact table?” In a classic dimensional model there are two options - (a) both dimensions are modeled independently or (b) two dimensions are combined into a super-dimension with a single key. The second approach is not widely used in ROLAP environments but it is an important sparsity handling method in MOLAP systems. In ROLAP this design technique can also bring storage and performance benefits, although the model becomes more complicated. The dependency between dimensions is a key factor that the designers have to consider when choosing between the two options. In this paper we present the results of our storage and performance experiments over a real life data cubes in reference to these design approaches. Some conclusions are drawn.

Sub- and Super-solutions of a Nonlinear PDE, and Application to a Semilinear SPDE

2010 Mathematics Subject Classification: 35R60, 60H15, 74H35.