We show that the wave map equation in R is in general illposed in the critical space Ḣ1/2, and the Besov space Ḃ 1/2,1 2 . The problem is attributed to the bad behaviour of the one-dimensional bilinear expression D(fDg) in these spaces.

In this paper we establish some endpoint estimates for bilinear pseudodifferential operators with symbol in the class BS1,1m, involving space of functions local bounded mean oscillation bmo(Rn). As a consequence also obtain an estimate Kato-Ponce type.

We state an approximate controllability result for the bilinear Schrödinger equation in the case in which the uncontrolled Hamiltonian has discrete non-resonant spectrum. This result applies both to bounded or unbounded domains and to the case in which the control potential is bounded or unbounded. In addition we get some controllability properties for the density matrix. Finally we show, by me...

This paper deals with the robust filtering problem for uncertain bilinear stochastic discrete-time systems with estimation error variance constraints. The uncertainties are allowed to be norm-bounded and enter into both the state and measurement matrices. We focus on the design of linear filters, such that for all admissible parameter uncertainties, the error state of the bilinear stochastic sy...

The way services offered by cloud computing gets its unprecedented and undisputed popularity, so security concerns. Among them the storage as service model (SaaS) is of forefront these SaaS liberates individuals enterprises from management IT infrastructure data centers to concentrate on their core business. Because untrusted out-of-premise architecture users are reluctant outsource personal im...

One of the leading problems of algebraic complexity theory is matrix multiplication. The näıve multiplication of two n× n matrices uses n multiplications. In 1969 Strassen [19] presented an explicit algorithm for multiplying 2 × 2 matrices using seven multiplications. In the opposite direction, Hopcroft and Kerr [11] and Winograd [20] proved independently that there is no algorithm for multiply...

The multilinear pseudo-differential operators with symbols in the Hörmander class S0,0 are considered. A complete identification of cases where those define bounded between local Hardy spaces is given. Some results for boundedness Wiener amalgam also These extensions and improvements known bilinear case.

We propose a new computational complexity assumption from bilinear map, based on which we construct Verifier-Local Revocation group signatures with shorter lengths than previous ones.