We established some regularity criteria for the Navier-Stokes equations in a bounded domain concerning the quotients of p=(1+ juj ) and rp=(1+ juj ) for some suitable : The results extend and generalize some previous ones given by Y. Zhou in the paper [Math. Ann. 328 (2004) 173-192 ]. Mathematics Subject Classi…cation (2000): 35B45, 35B65, 76D05

We introduce weighted automata over in…nite words with Muller acceptance condition and we show that their behaviors coincide with the semantics of weighted restricted MSO-sentences. Furthermore, we establish an equivalence property of weighted Muller and weighted Büchi automata over certain semirings. Keywords: Weighted logics, Weighted Muller automata, In…nitary formal power series, Weighted B...

Non-linear martingale problems in the McKean-Vlasov sense for superprocesses are studied. The stochastic calculus on historical trees is used in order to show that there is a unique solution of the non-linear martingale problems under Lipschitz conditions on the coe cients. Mathematics Subject Classi cation (1991): 60G57, 60K35, 60J80.

We explain in this note how to adapt the proofs in our previous work [5] An approximation result for special functions with bounded deformation (to appear in J. Math. Pures Appl., 2004), to dimension higher than two. Mathematics Subject Classi cation (2000): 26A45, 49Q20, 74B05, 74R10.

Characterizations of fuzzy ideals of a pseudo-BCH-algebra are established. Conditions for a fuzzy set to be a fuzzy ideal are given. The homomorphic properties of fuzzy ideals are provided. Finally, characterizations of Noetherian pseudo-BCH-algebras and Artinian pseudoBCH-algebras via fuzzy ideals are obtained. Mathematics Subject Classi…cation: 03G25, 06F35.

A new proof of the existence of the standard closed model structure for the category of simplicial presheaves on an arbitrary Grothendieck site is given. This proof uses the principle of Boolean localization. 1991 Mathematics Subject Classi cation: Primary 55U10, secondary 18F20, 55U35.

We study iteration and recursion operators in the denotational semantics of typed λ-calculi derived from the multiset relational model of linear logic. Although these operators are de ned as xpoints of typed functionals, we prove them nitary in the sense of Ehrhard's niteness spaces. 1991 Mathematics Subject Classi cation. 03B70, 03D65, 68Q55.

We give an alternative proof of the Hasse principle for principal homogeneous spaces de ned over elds of virtual cohomological dimension at most one which is based on a special decomposition of elements in Chevalley groups. 1991 Mathematics Subject Classi cation: Primary 20G10; Secondary 11E72, 12D15.

In this article we apply a method for encrypting messages based on the properties of the quasigroups According to the analysis given in the article the method is extremely secure Beside that the plain text and its cipher text are of the same length and the encoding is of stream nature guarantying a very fast implementation AMS Mathematics Subject Classi cation A P N

We survey recent results about game-theoretic characterizations of computational complexity classes. We also show how these results are used to prove that certain natural optimization functions are as hard to approximate closely as they are to compute exactly. 1991 Mathematics Subject Classi cation: 68Q15