Ion synthesis and laser annealing of Cu nanoparticles in Al2O3

Al₂O₃ samples with Cu nanoparticles, synthesised by ion implantation at 40 keV with a dose of 1×10¹⁷ ion/cm² and a current density from 2.5 to 12.5 μA/cm², were annealed using ten pulses from a KrF excimer laser with a single pulse fluence of 0.3 J/cm². The copper depth distribution, formation and modification of metal nanoparticles under the ion implantation and laser treatment were studied by Rutherford backscattering (RBS), energy dispersive X-ray (EDX) analysis, atomic force microscopy (AFM) and optical spectroscopy. It was found that laser annealing leads to a reduction in the nanoparticle size without diffusion of metal atoms into the bulk. The change in particle size and the possibility for oxidation of the copper particles are examined in the framework of Mie theory. Calculations presented show that under excimer laser treatment, Cu nanoparticles are more likely to be reduced in size than to undergo oxidation. Received: 19 April 2001 / Accepted: 7 November 2001 / Published online: 23 January 2002     

The existence of smooth densities for the prediction filtering and smoothing problems

The qualitative behavior of buckled states of two different models of elastic beams is studied. It is assumed that random imperfections affect the governing nonlinear equations. It is shown that near the first critical value of the buckling load the stochastic bifurcation is described asymptotically by an algebraic equation whose coeffficients are Gaussian random variables. The corresponding asymptotic expansion for the displacement is to lowest order a Gaussian stochastic process.Work supported by NSF Grant No. DCR81-14726.Work supported by NSF Grant No. DMS87-01895.     

Cohomological properties of the quantum shuffle product and application to the construction of quasi-Hopf algebras

For a commutative algebra the shuffle product is a morphism of complexes. We generalize this result to the quantum shuffle product, associated to a class of non-commutative algebras (for example all the Hopf algebras). As a first application we show that the Hochschild-Serre identity is the dual statement of our result. In particular, we extend this identity to Hopf algebras. Secondly, we clarify the construction of a class of quasi-Hopf algebras.     

The dual of a finitely generated multiplication module

This paper is based on the M. Sc. thesis written by the third author under the supervision of the first two authors. It was submitted to the University of Baghdad in 1986.     

A remark on Serrin’s Theorem

An approximation theorem for families of weakly coercive convex functions by means of countably many smooth families of convex functions is proved. As a consequence, the classical “three-fold” lower semicontinuity theorem for integral functionals of the Calculus of Variations by James Serrin is unified in one single statement.     

Asymptotic expansions in sequential estimation for the first-order random coefficient autoregressive model: Regenerative approach

Edgeworth expansions for the distribution of a sequential least squares estimator in the random coefficient autoregressive (RCA) model are derived. The regenerative approach to second-order asymptotic analysis of Markov-type statistical models is developed.     

Extended non-abelian gauge symmetries in the classical WZNW model

Higher spin extensions of the non-Abelian gauge symmetries for the classical WZNW model are considered. Both linear and nonlinear realizations of the extended affine Kac-Moody algebra are obtained. It is a characteristic property of the WZNW model that it admits a higher spin linear realization of the extended affine Kac-Moody algebra which is equivalent to the corresponding higher spin nonlinear realization of the same algebra. However, in both cases, the higher spin Noether currents do not span an invariant space with respect to their generating transformations. Here, the current space is extended to an invariant space which allows us to gauge the symmetry.Supported by Bulgarian Foundation on Fundamental Research under contract Ph-318/93-95.     

Asymptotic Behavior of Sobolev-Type Orthogonal Polynomials on a Rectifiable Jordan Curve or Arc

Our object of study is the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product <formula> \langle f, g \rangle = ∈t_{E} f(ξ) \overline{g(ξ)} ρ(ξ) |d ξ|+ f(Z) A g(Z)^H, </formula> where E is a rectifiable Jordan curve or arc in the complex plane f(Z) = (f(z_1), \ldots, f^{(l_1)}(z_1) , \ldots , f(z_m) , \ldots ,f^{(l_m)}(z_m)), A is an M \times M Hermitian matrix, M l ₁ + ⋅s + l _m + m , |d ξ| denotes the arc length measure, ρ is a nonnegative function on E , and z _i ∈Ω, i=1,2,\ldots,m , where Ω is the exterior region to E . July 23, 1999. Dates revised: September 11, 2000 and February 16, 2001. Date accepted: February 26, 2001.     

Multiderivations of Coxeter arrangements

Let V be an ℓ-dimensional Euclidean space. Let G⊂O(V) be a finite irreducible orthogonal reflection group. Let ? be the corresponding Coxeter arrangement. Let S be the algebra of polynomial functions on V. For H∈? choose α _H ∈V ^* such that H=ker(α _H ). For each nonnegative integer m, define the derivation module D ^(m) (?)={θ∈Der _S |θ(α _H )∈Sα ^m _H }. The module is known to be a free S-module of rank ℓ by K. Saito (1975) for m=1 and L. Solomon-H. Terao (1998) for m=2. The main result of this paper is that this is the case for all m. Moreover we explicitly construct a basis for D ^(m) (?). Their degrees are all equal to mh/2 (when m is even) or are equal to ((m−1)h/2)+m _i (1≤i≤ℓ) (when m is odd). Here m ₁≤···≤m _ℓ are the exponents of G and h=m _ℓ+1 is the Coxeter number. The construction heavily uses the primitive derivation D which plays a central role in the theory of flat generators by K. Saito (or equivalently the Frobenius manifold structure for the orbit space of G). Some new results concerning the primitive derivation D are obtained in the course of proof of the main result. Oblatum 27-XI-2001 & 4-XII-2001?Published online: 18 February 2002     

Properties of holomorphic Wiener functions —skeleton,contraction, and local Taylor expansion

Summary We show that each holomorphic Wiener function has a skeleton which is intrinsic from several viewpoints. In particular, we study the topological aspects of the skeletons by using the local Taylor expansion for holomorphic Wiener functions.Supported in part by the Grant-in-Aid for Science Research 03740120 Min. Education