The Discounted Limit Theorems

The large deviation theorems, exponential inequalities and a non-uniform estimate of the Berry–Esséen theorem in a discounted version are proved.Dedicated to Professor Vytautas Statulevičius on the occasion of his 75th birthday.     

Influence of oxidation time on semiconductive behaviour of thermally grown oxide films on AISI 304L

The oxide films formed on AISI 304L stainless steel at 300 °C in the oxidation time range between 2 and 4 h have been studied by photoelectrochemistry. Photocurrents were investigated as a function of the wavelength of the incident light and the electrode potential. The investigation allowed the determination of the semiconductive properties of the oxides. The oxide films showed n-type behaviour. A duplex structure of the oxide films has been suggested on the basis of the photocurrent spectra, with an internal oxide layer having an optical gap (E_g2 = 2.16-2.3 eV) depending on the applied potential and oxidation time, higher to that of the external oxide layer (E_g1 ≈ 1.9 eV). Significant variations in the amplitude of the photocurrent were detected as a function of the applied potential and the oxidation time.     

On the genericity of chaos

Let M be a compact manifold with dimM?2. We prove that some iteration of the generic homeomorphism on M is semiconjugated to the shift map and has infinite topological entropy (Theorem 1.1).     

A Note on Log-Convexity of q-Catalan Numbers

The q-Catalan numbers studied by Carlitz and Riordan are polynomials in q with nonnegative coefficients. They evaluate, at q = 1, to the Catalan numbers: 1, 1, 2, 5, 14,…, a log-convex sequence. We use a combinatorial interpretation of these polynomials to prove a q-log-convexity result. The sequence of q-Catalan numbers is not q-log-convex in the narrow sense used by other authors, so our work suggests a more flexible definition of q-log convex be adopted. Received January 2, 2007     

Coalgebraic representations of distributive lattices with operators

We present a framework for extending Stone's representation theorem for distributive lattices to representation theorems for distributive lattices with operators. We proceed by introducing the definition of algebraic theory of operators over distributive lattices. Each such theory induces a functor on the category of distributive lattices such that its algebras are exactly the distributive lattices with operators in the original theory. We characterize the topological counterpart of these algebras in terms of suitable coalgebras on spectral spaces. We work out some of these coalgebraic representations, including a new representation theorem for distributive lattices with monotone operators.     

Random Walks And The Colored Jones Function

It can be conjectured that the colored Jones function of a knot can be computed in terms of counting paths on the graph of a planar projection of a knot. On the combinatorial level, the colored Jones function can be replaced by its weight system. We give two curious formulas for the weight system of a colored Jones function: one in terms of the permanent of a matrix associated to a chord diagram, and another in terms of counting paths of intersecting chords. Electronic supplementary material to this article is available at and is accessible to authorized users. * S. G. was partially supported by an NSF and by an Israel-US BSF grant. † M. L. was partly supported by GAUK 158 grant and by the Project LN00A056 of the Czech Ministry of Education.     

Characterization of host-lattice emission and energy transfer in BaMgAl10O17:Eu

Host-lattice emission, energy transfer and degradation processes are characterized in undoped and Eu-doped BaMgAl₁₀O₁₇. Undoped BaMgAl₁₀O₁₇ exhibits a broad emission centered at 265 nm when excited at wavelengths shorter than 190 nm. This emission is assigned to exciton recombination at Ba-O groups in the cation layer of the lattice. The emission exhibits excellent overlap with the excitation band of Eu²⁺ in this host, providing a means of host-to-activator energy transfer in the doped phosphor. The exciton emission is relatively stable to thermal damage, but undergoes a peak shift and significant decrease in intensity after exposure to VUV radiation. Heating of VUV-damaged materials in air leads to some repair of the spectral properties.     

Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models

Parameters of Gaussian multivariate models are often estimated using the maximum likelihood approach. In spite of its merits, this methodology is not practical when the sample size is very large, as, for example, in the case of massive georeferenced data sets. In this paper, we study the asymptotic properties of the estimators that minimize three alternatives to the likelihood function, designed to increase the computational efficiency. This is achieved by applying the information sandwich technique to expansions of the pseudo-likelihood functions as quadratic forms of independent normal random variables. Theoretical calculations are given for a first-order autoregressive time series and then extended to a two-dimensional autoregressive process on a lattice. We compare the efficiency of the three estimators to that of the maximum likelihood estimator as well as among themselves, using numerical calculations of the theoretical results and simulations.     

Ihara zeta functions of digraphs

After defining and exploring some of the properties of Ihara zeta functions of digraphs, we improve upon Kotani and Sunada’s bounds on the poles of Ihara zeta functions of undirected graphs by considering digraphs whose adjacency matrices are directed edge matrices.     

Temperature‐modulated differential scanning calorimetry studies on the origin of double melting peaks in isothermally melt‐crystallized poly(L‐lactic acid)

In this work, the melting behaviors of nonisothermally and isothermally melt‐crystallized poly(L ‐lactic acid) (PLLA) from the melt were investigated with differential scanning calorimetry (DSC) and temperature‐modulated differential scanning calorimetry (TMDSC). The isothermal melt crystallizations of PLLA at a temperature in the range of 100–110 °C for 120 min or at 110 °C for a time in the range of 10–180 min appeared to exhibit double melting peaks in the DSC heating curves of 10 °C/min. TMDSC analysis revealed that the melting–recrystallization mechanism dominated the formation of the double melting peaks in PLLA samples following melt crystallizations at 110 °C for a shorter time (≤30 min) or at a lower temperature (100, 103, or 105 °C) for 120 min, whereas the double lamellar thickness model dominated the formation of the double melting peaks in those PLLA samples crystallized at a higher temperature (108 or 110 °C) for 120 min or at 110 °C for a longer time (≥45 min). © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 466–474, 2007