On the spectral properties of Witten-Laplacians, their range projections and Brascamp-Lieb's inequality

A study is made of a recent integral identity of B. Helffer and J. Sjöstrand, which for a not yet fully determined class of probability measures yields a formula for the covariance of two functions (of a stochastic variable); in comparison with the Brascamp-Lieb inequality, this formula is a more flexible and in some contexts stronger means for the analysis of correlation asymptotics in statistical mechanics. Using a fine version of the Closed Range Theorem, the identity's validity is shown to be equivalent to some explicitly given spectral properties of Witten-Laplacians on Euclidean space, and the formula is moreover deduced from the obtained abstract expression for the range projection. As a corollary, a generalised version of Brascamp-Lieb's inequality is obtained. For a certain class of measures occuring in statistical mechanics, explicit criteria for the Witten-Laplacians are found from the Persson-Agmon formula, from compactness of embeddings and from the Weyl calculus, which give results for closed range, strict positivity, essential self-adjointness and domain characterisations.Supported by TMR grant FMRX-CT960001 of the European Commision, PDE and QM at Université de Paris-Sud, France; partly by the Danish Natural Sciences Research Council, grant 9700987.     

On Two Theorems about Symplectic Reflection Algebras

We give a new proof and an improvement of two Theorems of J. Alev, M.A. Farinati, T. Lambre and A.L. Solotar [1] : the first one about Hochschild cohomology spaces of some twisted bimodules of the Weyl Algebra W, and the second one about Hochschild cohomology spaces of the smash product G * W (G a finite subgroup of SP (2n)) and, as a consequence, we then give a new proof of a Theorem of P. Etingof and V. Ginzburg (Invent Math 147:243–348, 2002), which shows that the Symplectic Reflection Algebras are deformations of G * W (and, in fact, all possible ones). Dedicated to my friend J.-C. Cortet.     

Femtosecond laser-induced ZnSe nanowires on the surface of a ZnSe wafer in water

We present a simple route for ZnSe nanowire growth in the ablation crater on a ZnSe crystal surface. The crystal wafer, which was horizontally dipped in pure water, was irradiated by femtosecond laser pulses. No furnace, vacuum chamber or any metal catalyst were used in this experiment. The size of the nanowires is about 1-3 μm long and 50-150 nm in diameter. The growth rate is 1-3 μm/s, which is much higher than that achieved with molecular-beam epitaxy and chemical vapor deposition methods. Our discovery reveals a rapid and simple way to grow nanowires on designed micro-patterns, which may have potential applications in microscopic optoelectronics.     

The First Order Asymptotics of the Extreme Eigenvectors of Certain Hermitian Toeplitz Matrices

The paper is concerned with Hermitian Toeplitz matrices generated by a class of unbounded symbols that emerge in several applications. The main result gives the third order asymptotics of the extreme eigenvalues and the first order asymptotics of the extreme eigenvectors of the matrices as their dimension increases to infinity. This work was partially supported by CONACYT projects 60160 and 80504, Mexico.     

A double arity hierarchy theorem for transitive closure logic

In this paper we prove that thek-ary fragment of transitive closure logic is not contained in the extension of the (k–1)-ary fragment of partial fixed point logic by all (2k–1)-ary generalized quantifiers. As a consequence, the arity hierarchies of all the familiar forms of fixed point logic are strict simultaneously with respect to the arity of the induction predicates and the arity of generalized quantifiers.Although it is known that our theorem cannot be extended to the sublogic deterministic transitive closure logic, we show that an extension is possible when we close this logic under congruence.Supported by a grant from the University of Helsinki. This research was initiated while he was a Junior Researcher at the Academy of FinlandThis article was processed by the author using the LATEX style filepljourlm from Springer-Verlag.     

Spread of a catalytic branching random walk on a multidimensional lattice

For a supercritical catalytic branching random walk on ${\mathbb{Z}}^d$, $d\in \mathbb{N}$, with an arbitrary finite catalysts set we study the spread of particles population as time grows to infinity. It is shown that in the result of the proper normalization of the particles positions in the limit there are a.s. no particles outside the closed convex surface in ${\mathbb{R}}^d$ which we call the propagation front and, under condition of infinite number of visits of the catalysts set, a.s. there exist particles on the propagation front. We also demonstrate that the propagation front is asymptotically densely populated and derive its alternative representation.     

Span 80 effect on the solvent extraction for heavy oil recovery

In this study, we used the Span 80 to enhance solvent extraction process, and we explored the mechanism. The results indicated different solvents would obtain different oil recovery, and toluene showed the optimal oil recovery, and the n-heptane showed the lowest oil recovery. The complex solvents could improve oil recovery. Toluene could make the heavy oil show the lowest viscosity (89.6 Pa.S), and n-heptane make the heavy oil show the highest viscosity (176.3 Pa.S). Complex solvents could decrease the heavy oil viscosities. The higher C/H was, the higher heavy oil recovery was, and when the asphaltene and resins content increase, the C/H would increase. The C/H showed the highest value (9.09, by toluene) and the lowest value (8.15). In this study, Span 80 could increase heavy oil C/H ratio, decrease heavy oil viscosity. Span 80 could make the sands surface more hydrophilic, and then the solvent loss would decrease. The oil recovery was high after 10 times recycle use.     

Robust exponential attractors for a phase-field system with memory

H.G. Rotstein et al. proposed a nonconserved phase-field system characterized by the presence of memory terms both in the heat conduction and in the order parameter dynamics. These hereditary effects are represented by time convolution integrals whose relaxation kernels k and h are nonnegative, smooth and decreasing. Rescaling k and h properly, we obtain a system of coupled partial integrodifferential equations depending on two relaxation times ɛ and σ. When ɛ and σ tend to 0, the formal limiting system is the well-known nonconserved phase-field model proposed by G. Caginalp. Assuming the exponential decay of the relaxation kernels, the rescaled system, endowed with homogeneous Neumann boundary conditions, generates a dissipative strongly continuous semigroup S_{ɛ, σ}(t) on a suitable phase space, which accounts for the past histories of the temperature as well as of the order parameter. Our main result consists in proving the existence of a family of exponential attractors for S_{ɛ, σ}(t), with ɛ, σ ∈ [0, 1], whose symmetric Hausdorff distance from tends to 0 in an explicitly controlled way.     

Structure and Photoelectric Characteristics of Functional Polymers and of Compositions Based on Them

The electronic processes in disordered organic solids were analyzed, classified, and summarized. They include the photogeneration of charge pairs, electron transport, geminal and bimolecular recombination, and the capture of charge carriers in local electronic states. General criteria were formulated for the targeted search for and the creation of new prospective polymers and their compositions with organic pigments and related compounds having specific photoelectric characteristics for electrographic and holographic media, photoelectric converters, and electroluminescent and photorefractive devices.     

Physicochemical Studies on an All-Purpose Pesticide Spray Adjuvant-(APSA-80)

APSA-80, an useful pesticide spray adjuvant is a mixture of 2-[2-(4-nonylphenoxy) ethoxy] ethanol, 1-butanol and tall oil fatty acids. It is strongly surface active and can decrease the surface tension of water to ～20 mNm^?1 at its critical micelle concentration (CMC) of 0.006 g%. APSA-80 itself and its binary mixtures, (APSA-80 + water) and (APSA-80 + isopropylmyristate [IPM]) and ternary mixtures (APSA-80 + water +IPM) can undergo a number of physical changes with rise in temperature; the main changes are in color, turbidity and phases. The ternary mixtures of APSA-80/water/IPM with changing compositions can form mono-, bi-, and triphasic solutions as well as gels and viscous solutions. The gel and viscous phases show characteristic rheological properties of both shear thinning and thickening types. They also show permeation of hydrophilic and oleophilic dyes through them. SEM and optical microscopic measurements have shown interesting surface morphologies of the gels and their vertical projections in three-dimensional pictorial mode. Salts like LiCl, NaCl, KCl, CsCl, MgSO₄, and Al₂(SO₄)₃ can have both minor and major effects on the gel consistencies. The alkanols like ethanol, propanol, and isopropanol are also mild to fairly large gel influencing co solvents. The antibacterial properties of APSA-80 have been studied with two Gram positive bacteria and a yeast; the activities found were moderate.