Relative entropy tuples,relative u.p.e. and c.p.e. extensions

Relative entropy tuples both in topological and measure-theoretical settings, relative uniformly positive entropy (rel.-u.p.e.) and relative completely positive entropy (rel.-c.p.e.) are studied. It is shown that a relative topological Pinsker factor can be deduced by the smallest closed invariant equivalence relation containing the set of relative entropy pairs. A relative disjointness theorem involving relative topological entropy is proved. Moreover, it is shown that the product of finite rel.-c.p.e. extensions is also rel.-c.p.e.. The first author is partially supported by NCET, NNSF of China (no. 10401031) and CNRS-K.C.Wong Fellowship. The second author is supported by the national key project for basic science (973). The third author is supported by NNSF of China (no. 10401031).     

Optimization of the Relaxation Parameter for S.S.O.R. and A.D.I. Preconditioning

We present and compare several approaches for the optimization of the relaxation parameter both for A.D.I. and S.S.O.R. basic iteration and preconditioning conjugate gradient method. For each kind of preconditioning a detailed link between estimates of the spectral radius of the iteration matrix and of the condition number resulting from preconditioning is proposed. It allows to choose the best approach in order to obtain the optimal relaxation parameter and the corresponding optimal estimates either of the spectral radius of the iteration matrix and of the resulting condition mumber of the S.S.O.R. and A.D.I. preconditioning.     

Evaluations of Parameters for the Optimization of S.S.O.R. and A.D.I. Preconditioning

The main goal of this paper is to give two ways to estimate the needed parameters in order to obtain the condition number of S.S.O.R. preconditioned matrices, namely, the algebraic matricial formulation of convexity Riesz theorem and the tridiagonal Fourier analysis. The improvement with respect to Axelsson's approach is explicitly given. Estimations of the condition number in the case of A.D.I. preconditioning is also considered.     

O.R.C.S. 1981 Results

Journal of the Operational Research Society -     

The Isolated D. R. E. Degrees are Dense in the R. E. Degrees

In the present paper we prove that the isolated differences of r. e. degrees are dense in the r. e. degrees. Mathematics Subject Classification: 03D25.     

Two-point b.v.p. for multivalued equations with weakly regular r.h.s.

A two-point boundary value problem associated to a semilinear multivalued evolution equation is investigated, in reflexive and separable Banach spaces. To this aim, an original method is proposed based on the use of weak topologies and on a suitable continuation principle in Fréchet spaces. Lyapunov-like functions are introduced, for proving the required transversality condition. The linear part can also depend on the state variable x and the discussion comprises the cases of a nonlinearity with sublinear growth in x or of a noncompact valued one. Some applications are given, to the study of periodic and Floquet boundary value problems of partial integro-differential equations and inclusions appearing in dispersal population models. Comparisons are included, with recent related achievements.     

Selectively c.c.c. spaces

We present a study about a natural way of defining a selective version of the c.c.c. property. This definition and some related properties were already considered under different names in other works, such as Daniels et al. (1994) [9], Scheepers (2000) [12]. Here we will present some of its relations with other selective properties and we present some examples that show the differences among the properties considered. We also study the behavior of these properties when the products are considered.     

Flavones ofPajanelia multijuga P.DC. andLigustrum neilgherense var. obovata C.B.Cl.

From the hexane and methanol extracts of the bark ofPajanelia multijuga P.DC., oroxylin A and chrysin have been isolated. Methanol extract of the leaves ofLigustrum neilgherense var. obovata C.B.Cl. afforded d-mannitol and kaempferitrin. Structures of these compounds have been confirmed by shifts of the methoxyl groups on addition of benzene and Eu(dpm)₃ induced shifts in the NMR.