Abstract. To deal with the divergence-free constraint in a double curl problem: curlμ−1curlu = f and div εu = 0 in Ω, where μ and ε represent the physical properties of the materials occupying Ω, we develop a δ-regularization method: curlμcurluδ + δεuδ = f to completely ignore the divergence-free constraint div εu = 0. It is shown that uδ converges to u in H(curl ; Ω) norm as δ → 0. The edge fi...

We consider the problem of solving packing/covering LPs online, when the columns of the constraint matrix are presented in random order. This problem has received much attention: the main open question is to figure out how large the right-hand sides of the LPs have to be (compared to the entries on the left-hand side of the constraint) to get (1 + ε)-approximations online? It is known that the ...

This article is devoted to obtain the Γ-limit, as ε tends to zero, of the family of functionals u 7→ ∫ Ω f ( x, x ε , . . . , x ε ,∇u(x) ) dx, where f = f(x, y, . . . , yn, z) is periodic in y, . . . , yn, convex in z and satisfies a very weak regularity assumption with respect to x, y, . . . , yn. We approach the problem using the multiscale Young measures.

We consider the semilinear equation ε(−∆)u+ V (x)u− u = 0, u > 0, u ∈ H(R ) where 0 < s < 1, 1 < p < N+2s N−2s , V (x) is a sufficiently smooth potential with infR V (x) > 0, and ε > 0 is a small number. Letting wλ be the radial ground state of (−∆)wλ +λwλ−w λ = 0 in H 2s(RN ), we build solutions of the form uε(x) ∼ k ∑ i=1 wλi ((x− ξ ε i )/ε), where λi = V (ξ ε i ) and the ξ ε i approach suita...

The Johnson-Lindenstrauss lemma is one of the corner stone results in dimensionality reduction. It says that given N , for any set of N vectors X ⊂ Rn, there exists a mapping f : X → Rm such that f(X) preserves all pairwise distances between vectors in X to within (1 ± ε) if m = O(ε lgN). Much effort has gone into developing fast embedding algorithms, with the Fast JohnsonLindenstrauss transfor...