The central limit theorem and the problem of equivalence of ensembles

In this paper we show that the local limit theorem is a consequence of the integral central limit theorem in the case of a Gibbs random field _t ,tZ corresponding to a finite range potential.We apply this theorem to show that the equivalence between Gibbs and canonical ensemble is a consequence of the integral central limit theorem and of very weak conditions on decrease of correlations.Research supported by a C.N.R.-Ak. Nauk. U.R.S.S. fellowship     

Time evolution of infinite classical systems with singular,long range,two body interactions

Existence of dynamics for infinitely many hard-spheres inv dimensions is proven in a set of full equilibrium measure.Singular unbounded perturbations are considered with pair potentials diverging as (x – a)^–, >2 anda is the hard-core diameter. Long range forces are allowed with potentials decreasing at infinity asx , <v. The result corrects and generalizes a proof given in a previous paper by the same authors.Research partially supported by a CNR fellowship Posit. 204530.Research partially supported by a CNR fellowship.     

Some existence and regularity results for abstract non-autonomous parabolic equations

We study existence, uniqueness and regularity of the strict, classical and strong solutions $\text{u? C(¦0, T ¦,E)}$ of the non-autonomous evolution equation $\text{u′(t) ? A(t)u(t)=?(t)}$, with the initial datum u(0) = x, in a Banach space E, under the classical Kato-Tanabe assumptions. The domains of the operators A(t) are not needed to be dense in E. We prove necessary and sufficient conditions for existence and Hölder regularity of the solution and its derivative.     

Atom-surface elastic scattering with additive potential

An additive corrugated potential with linear repulsion and long range attractive well is proposed for atom-surface scattering. The computational procedure yielding the scattering probabilities (essentially linear algebra) proves to be much simpler than with other potentials. For a given shape of the corrugation function and for high values of the steepness parameter one obtains results close to those of the hard corrugated wall model, while an important enhancement of the specular intensity appears, in particular at large angles of incidence, when the steepness parameter is small.     

On the Critical Capacity of the Hopfield Model

We estimate the critical capacity of the zero-temperature Hopfield model by using a novel and rigorous method. The probability of having a stable fixed point is one when α≤ 0.113 for a large number of neurons. This result is an advance on all rigorous results in the literature and the relationship between the capacity α and retrieval errors obtained here for small α coincides with replica calculation results. Received: 1 December 1999 / Accepted: 21 July 2000     

Maximal space regularity for abstract linear non-autonomous parabolic equations

The linear non-autonomous evolution equation $\text{u′(t) ? A(t) u(t) = ?(t), t ∈ [0, T]}$, with the initial datum u(0) = x, in the space C([0, T], E), where E is a Banach space and {A(t)} is a family of infinitesimal generators of bounded analytic semigroups is considered; the domains D(A(t)) are supposed constant in t and possibly not dense in E. Maximal regularity of the strict and classical solutions, i.e., regularity of u′ and A(·)u(·) with values in the interpolation spaces D_A(0)(θ, ∞) and D_A(0)(θ) between D(A(0)) and E, is studied. A characterization of such spaces in a concrete case is also given.     

Regio-selective deprotection of peracetylated sugars via lipase hydrolysis

Purified lipases (via interfacial activation on hydrophobic supports) from different microbial extracts have been evaluated in the regio-selective hydrolysis of peracetylated sugars (peracetylated glucose, ribose and sucrose). Among the enzymes tested, lipases from Candida rugosa (CRL) and from Pseudomonas fluorescens (PFL) exhibited the best properties in these reactions.Then, we have prepared two different immobilized lipase preparations obtained by interfacial activation on hydrophobic supports or by covalent attachment on glutaraldehyde agarose. Interfacially activated lipases exhibited a higher activity than covalently attached enzymes (even by a 100-fold factor), giving the higher yields of mono deacetylated sugars (in some instances by more than a threefold factor) in short reaction times. In the hydrolysis of 1,2,3,5-tetra-O-acetyl-β-d-ribofuranose catalyzed by PFL adsorbed on octyl agarosa, hydrolyzed mainly the 3 position (30% of yield) while the CRL gave the hydrolysis only in position 5 (about 50% of yield).Depending on the enzyme immobilized preparation, we have been able also to obtain selective hydrolysis of 1,2,3,4,6-penta-O-acetyl-α/β-d-glucopyranose obtaining a free hydroxyl group in position 1, 4 or 6. Moreover, selective hydrolysis in the 4′ position of peracetylated sucrose was achieved when the hydrolysis is performed with CRL immobilized on octyl-agarose (yield was 77%).     

A simple and flexible atom-surface potential with easy-to-handle vibrational spectrum

A highly flexible empirical potential V_p(z) suitable to describe the main features of the laterally averaged atom-surface interaction is presented and an accurate expression for the vibrational spectrum of the atom in V_p(z) is given. This establishes a simple method of inversion of the atom-surface vibrational spectra particularly suitable for levels located in the deepest 9/10 of the potential well. The present method is complementary to the one introduced by Le Roy [5].