No abstract available

[en] It is shown that any self-dual cone in a real Hilbert space with finite dimensions is homogeneous if and only if it is facially homogeneous (according to the meaning given by Alain Connes). A spectral theory is developed in these cones, which is analogous to that of self-adjoint operators on a Hilbert space of finite dimension

[en] The mapping of a straight line in the particle-hole space onto the manifold of Slater determinants is found to induce a trajectory whose curvature is between 1 and √3. This curvature depends on the direction of the line, which renders the particle-hole space anisotropic. There are indications that collective motion induces a large curvature of the path

No abstract available

[en] It was discussed the possibility of introducing a multi-resolution in a Hilbert space which is not necessarily a space of functions. It was investigated which of the classical properties can be translated to this more general framework ant the way in which this can be done. It is commented on the procedure proposed by means of many examples

[en] It is shown that as a system which can be characterized by a finite-dimensional Hilbert space is observed more and more frequently, the probability that it will always be found in its initial state tends to one

[en] Lomonaco and Kauffman introduced knot mosaic system to give a definition of quantum knot system. This definition is intended to represent an actual physical quantum system. A knot (m, n)-mosaic is an m×n matrix of mosaic tiles which are T₀ through T₁₀ depicted, representing a knot or a link by adjoining properly that is called suitably connected. An interesting question in studying mosaic theory is how many knot (m, n)-mosaics are there. D_m,n denotes the total number of all knot (m, n)-mosaics. This counting is very important because the total number of knot mosaics is indeed the dimension of the Hilbert space of these quantum knot mosaics. In this paper, we find a table of the precise values of D_m,n for 4⩽m⩽n⩽6. Mainly we use a partition matrix argument which turns out to be remarkably efficient to count small knot mosaics. (paper)

[en] In this paper we study the existence of periodic solutions for second order Hamiltonian systems -u-bar + Au = ∇V(t,u) when V is T-periodic in t and singular in u. More precisely, we assume V(t,x) → +∞ as x → δΩ, for a given open and bounded set Ω is included in R^N. We prove the existence of at least one non trivial T-periodic solution by means of variational techniques. (author). 10 refs

No abstract available

[en] Let (x_n)_n≥0 be a non expansive sequence in a real Hilbert space H, (i.e. every i,j ≥ 0, parallel x_i+1 - x_j+1parallel≤parallel x_i - x_jparallel) and s_n = 1/n Σ_i=0^n-1 x_i. We prove the following results containing J.B. Baillon's ergodic theorems: 1) s_n converges weakly in H if and only if lim inf_n→+∞ parallel s_nparallel < +∞. 2) x_n converges weakly in H if and only if (x_n)_n≥0 is weakly asymptotically regular and lim inf_n→+∞ parallel x_n parallel < +∞. 3) If moreover: every i,j ≥ 0, parallel x_i+1 + x_j+1parallel ≤ parallel x_i + x_jparallel then s_n converges strongly in H. This is obtained as a consequence of a result of H. Brezis and F.E. Browder which we prove here by using Herglotz's theorem. 4) Under the same assumptions as in 3) the sequence (x_n)_n≥0 converges strongly in H if and only if (x_n)_n≥0 is asymptotically regular. (author). 33 refs