We consider the regularity of Leray-Hopf solutions to Navier-Stokes equations on critical case u ∈ L 2 w (0, T ; L ∞ (R 3)). By a new embedding inequality in Lorentz space we proved that if u L 2 w (0,T ;L ∞ (R 3)) is small then the Leray-Hopf solutions are regular. Particularly, an open problem proposed in [7] was solved.

We show that the transfer matrix of the A (1) N−1 open spin chain with diagonal boundary fields has the symmetry Uq (SU(l)) × Uq (SU(N − l)) × U(1), as well as a “duality” symmetry which maps l ↔ N − l. We exploit these symmetries to compute exact boundary S matrices in the regime with q real.

a necessary and sufficient condition in terms of lower cut sets are given for the insertion of a $gamma-$continuous function between two comparable real-valued functions.

open-celled foams are capable to allow the passage of fluids through their structure, because of interconnections between the open cells or bubbles and therefore these structures can be used as a membrane and filter. in thiswork, we have studied the production of polystyrene open-celled microcellular foam by using co2 as blowing agent. to achieve such structures, it is necessary to control the ...

Let f : U → Spec (K) be a smooth open curve over a field K ⊃ k, where k is an algebraically closed field of characteristic 0. Let ∇ : L → L ⊗ Ω1U/k be a (possibly irregular) absolute, integrable connection on a line bundle L. A formula is given for the determinant of de Rham cohomology with its Gauß-Manin connection ( detRf∗(L ⊗ Ω1U/K), det∇GM )

We introduce an abstract concept for decomposing spaces with respect to a substructuring of a bounded domain. In this setting we define weakly conforming finite element approximations of quadratic minimization problems. Within a saddle point approach the reduction to symmetric positive Schur complement systems on the skeleton is analyzed. Applications include weakly conforming variants of least...