let $a$ be an abelian topological group and $b$ a trivial topological $a$-module. in this paper we define the second bilinear cohomology with a trivial coefficient. we show that every abelian group can be embedded in a central extension of abelian groups with bilinear cocycle. also we show that in the category of locally compact abelian groups a central extension with a continuous section can b...

This paper is devoted to the semilocal convergence, using centered hypotheses, of a third order Newton-type method in a Banach space setting. The method is free of bilinear operators and then interesting for the solution of systems of equations. Without imposing any type of Fréchet differentiability on the operator, a variant using divided differences is also analyzed. A variant of the method u...

We consider the composition of random i.i.d. aane maps of a Hilbert space to itself. We show convergence of the n'th composition in the Wasserstein metric via a contraction argument. The contraction condition involves the operator norm of the expectation of a bilinear form. This is contrasted with the usual contraction condition of a negative Lyapunov exponent. Our condition is stronger but eas...

We consider the multilinear pseudo-differential operators with symbols in a generalized $S_{0,0}$-type class and prove boundedness of from $(L^2, \ell^{q_1}) \times \cdots (L^2, \ell^{q_{N}})$ to \ell^{r})$, where \ell^{q})$ denotes $L^2$-based amalgam space. This extends previous result by same authors, which treated bilinear gave $L^2 L^2$ \ell^{1})$ boundedness.

The unitary operator for the free-evolution part is defined as Û0(−∞, t) ≡ T exp{−(i/~) ∫ t −∞ dt Ĥdet(t)} with T being the time-ordering, and, for the interaction part, we have defined ÛI(−∞, t) ≡ T exp{−(i/~) ∫ t −∞ dt ′Ĥ int (t ′)}. For the measurement to be linear, Ĥdet only involves linear or quadratic functions of canonical coordinates, among which their commutators are classical numbers,...

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 present a rigorous derivation of the Ericksen-Leslie equation starting from the Doi-Onsager equation. As in the fluid dynamic limit of the Boltzmann equation, we first make the Hilbert expansion for the solution of the Doi-Onsager equation. The existence of the Hilbert expansion is connected to an open question whether the energy of the EricksenLeslie equation is dissipated. We show that the...

An operator formalism for bosonic system on arbitrary algebraic curves is introduced. The classical degrees of freedom are identi ed and their commutation relations are postulated. The explicit realization of the algebra formed by the elds is given in the Hilbert space equipped with a bilinear form. The construction is based on the "gaussian" representation for system on the complex sphere [Alv...

Gelfand and Dikii gave a bosonic formal variational calculus in [5, 6] and Xu gave a fermionic formal variational calculus in [13]. Combining the bosonic theory of Gelfand-Dikii and the fermionic theory, Xu gave in [14] a formal variational calculus of super-variables. Fermionic Novikov algebras are related to the Hamiltonian super-operator in terms of this theory. A fermionic Novikov algebra i...