We extend the study [1] devoted to the dynamic response of a structure made of two linearly elastic bodies connected by a thin soft adhesive layer made of a Kelvin Voigt type nonlinear viscoelastic material to the case of a Generalized Standard Material with a positive definite quadratic density of free energy. A concise formulation in terms of an evolution equation in a Hilbert space of possib...

Let C denote the category of Hilbert modules which are similar to contractive Hilbert modules. It is proved that if H0, H ∈ C and if H1 is similar to an isometric Hilbert module, then the sequence 0 → H0 → H → H1 → 0 splits. Thus the isometric Hilbert modules are projective in C. It follows that ExtC (K, H) = 0, whenever n > 1, for H, K ∈ C. In addition, it is proved that (Hilbert modules simil...

begin{abstract} in this paper, we introduce an iterative method for amenable semigroup of non expansive mappings and infinite family of non expansive mappings in the frame work of hilbert spaces. we prove the strong convergence of the proposed iterative algorithm to the unique solution of a variational inequality, which is the optimality condition for a minimization problem. the results present...

we derive whole series of new integral inequalities of the hardy-type, with non-conjugate exponents. first, we prove and discuss two equivalent general inequa-li-ties of such type, as well as their corresponding reverse inequalities. general results are then applied to special hardy-type kernel and power weights. also, some estimates of weight functions and constant factors are obtained. ...

We introduce an explicit definition for ’hidden correlations’ on individual entities in a compound system: when one individual entity is measured, this induces a well-defined transition of the ’proper state’ of the other individual entities. We prove that every compound quantum system described in the tensor product of a finite number of Hilbert spaces can be uniquely represented as a collectio...

| We consider the problem of synthesizing feasible signals in a Hilbert space in the presence of inconsistent convex constraints, some of which must imperatively be satissed. This problem is formalized as that of minimizing a convex objective measuring the amount of violation of the soft constraints over the intersection of the sets associated with the hard ones. The resulting convex optimizati...