We consider harmonic maps into pseudo-Riemannian manifolds. We show the removability of isolated singularities for continuous maps, i.e. that any continuous map from an open subset of R into a pseudoRiemannian manifold which is two times continuously differentiable and harmonic everywhere outside an isolated point is actually smooth harmonic everywhere. Introduction Given n ∈ N and two nonnegat...

Abstract. We give a new proof of regularity of biharmonic maps from four-dimensional domains into spheres, showing first that the biharmonic map system is equivalent to a set of bilinear identities in divergence form. The method of reverse Hölder inequalities is used next to prove continuity of solutions and higher integrability of their second order derivatives. As a byproduct, we also prove t...

We define Lie 3-algebras and prove that these are in 1-to-1 correspondence with the 3-term Lie infinity algebras whose bilinear and trilinear maps vanish in degree (1, 1) and in total degree 1, respectively. Further, we give an answer to a question of [Roy07] pertaining to the use of the nerve and normalization functors in the study of the relationship between categorified algebras and truncate...

Let R be a commutative ring. Unless indicated otherwise, all modules are R-modules and all tensor products are taken over R, so we abbreviate ⊗R to ⊗. A bilinear function out of M1 × M2 turns into a linear function out of the tensor product M1 ⊗ M2. In a similar way, a multilinear function out of M1 × · · · ×Mk turns into a linear function out of the k-fold tensor product M1 ⊗ · · · ⊗Mk. We wil...

Structure-preserving cryptography is a world where messages, signatures, ciphertexts and public keys are entirely made of elements of a group over which a bilinear map is efficiently computable. While structure-preserving signatures have received much attention the last 6 years, structure-preserving encryption schemes have undergone slower development. In particular, the best known structure-pr...

Given three Banach spaces X, Y and Z and a bounded bilinear map B : X×Y → Z, a sequence x = (xn)n ⊆ X is called B-absolutely summable if ∑∞ n=1 ‖B(xn, y)‖Z < ∞ for any y ∈ Y . Connections of this space with `weak(X) are presented. A sequence x = (xn)n ⊆ X is called B-unconditionally summable if ∑∞ n=1 |〈B(xn, y), z∗〉| < ∞ Preprint submitted to Elsevier 21 December 2007 for any y ∈ Y and z∗ ∈ Z∗...

We propose a new group signature scheme which is secure if we assume the Decision Diffie-Hellman assumption, the q-Strong Diffie-Hellman assumption, and the existence of random oracles. The proposed scheme is the most efficient among the all previous group signature schemes in signature length and in computational complexity. This paper is the full version of the extended abstract appeared in A...

We consider the iterative resolution scheme for the Navier-Stokes equation, and focus on the second iterate, more precisely on the map from the initial data to the second iterate at a given time t. We investigate boundedness properties of this bilinear operator. This new approach yields very interesting results: a new perspective on Koch-Tataru solutions; a first step towards weak strong unique...

We consider the problem of simultaneously estimating surface texture map and the pseudo illumination, which is the combined effect of illumination and surface BRDF, given the object geometry and its calibrated images taken from multiple viewpoints. We derive the bilinear reflection equation that relates the texture albedos and the pseudo illumination to the surface reflectance. The reflection e...

Digital multisignatures improve security of digital signatures and reduce fraud by collusion. In this paper we first present a new secure signature scheme which is based on a variant of Strong Diffie-Hellman Assumption, called SDH2 assumption. Then, we extend this signature for a new multisignature scheme without interaction between users. Our proposed schemes which work in groups equipped with...