Square-free integers as ideal norms

Elaborating on Katzel＇s result, Zhai obtained a sharp short interval result for the number of ways of expressing a square-free integer as sums of two squares. In this note we view Zhai＇s decom- position as one by degree 1 prime ideals in the Gaussian field and extend Zhai＇s approach to a wider range of quadratic fields etc.     

On limit distribution of the Hurwitz zeta-function

The distribution of the vector (|ζ(s, α)|; ζ(s, α)), where ζ(s, α) is the Hurwitz zeta-function with transcendental parameter α, is considered and a probabilistic limit theorem is obtained. Also, the dependence between |ζ(s, α)| and ζ(s, α) in terms of m-characteristic transforms is discussed.     

On convergence rate of a rectangular partition based global optimization algorithm

The convergence rate of a rectangular partition based algorithm is considered. A hyper-rectangle for the subdivision is selected at each step according to a criterion rooted in the statistical models based theory of global optimization; only the objective function values are used to compute the criterion of selection. The convergence rate is analyzed assuming that the objective functions are twice- continuously differentiable and defined on the unit cube in d-dimensional Euclidean space. An asymptotic bound on the convergence rate is established. The results of numerical experiments are included.     

Electronic transport mechanism in polydiacetylene crystals — variable range hopping or phonon-assisted tunnelling

Experimental results on the current-voltage characteristics of polydiacetylene (PDA) single crystals reported by Aleshin et al [Phys. Rev. Vol. B 69, (2004) art. 214203] are reinterpreted in terms of the phonon-assisted electron tunnelling model. It is shown that the experimental results, measured in the temperature range from 1.8 K to 300 K are consistent with the tunnelling rate dependence on field strength, computed for the same range of temperatures. An advantage of this model over that of Aleshin et al, using the variable range hopping (VRH) model, is the possibility of describing the behaviour of I — V data measured at both high and low temperatures with the same set of parameters characterizing this material. This assertion is confirmed by comparison of the temperature-dependent current-voltage data extracted from Aleshin et al’s work with tunnelling rate dependence on temperature, computed using two different expressions of the phonon-assisted tunnelling theory. The temperature dependence of the conductivity of an ion implanted PDA crystals [B. S. Elman et al, Appl. Phys. Lett., Vol. 46, (1985) p. 100] and polypyrrole [P. Dutta et al, Synth. Met., Vol. 139 (2003) p. 201] are also explained on the basis of this model.      

Globally-biased Disimpl algorithm for expensive global optimization

Direct-type global optimization algorithms often spend an excessive number of function evaluations on problems with many local optima exploring suboptimal local minima, thereby delaying discovery of the global minimum. In this paper, a globally-biased simplicial partition Disimpl algorithm for global optimization of expensive Lipschitz continuous functions with an unknown Lipschitz constant is proposed. A scheme for an adaptive balancing of local and global information during the search is introduced, implemented, experimentally investigated, and compared with the well-known Direct and Direct l methods. Extensive numerical experiments executed on 800 multidimensional multiextremal test functions show a promising performance of the new acceleration technique with respect to competitors.     

A limit theorem for the Hurwitz zeta-function with an algebraic irrational parameter

We prove a limit theorem in the complex plane for the Hurwitz zeta-function with algebraic irrational parameter. Received: 14 June 2004; revised: 12 April 2005     

Temperature dependence of compositional changes of SiO2 surface during ion and electron bombardment

The influence of ion (Ar⁺ 0.5 keV, 2 microA/cm²) and electron (2 keV, 2 mA/cm²) bombardment on the elemental composition of SiO₂ was investigated in the temperature range of 270–790 K. Elemental composition was controlled by AES. It was found that both ion and electron bombardment resulted in an increasing amount of Si₉₂ (elemental silicon) and in decreasing amounts of both O₅₁₀ and Si₇₈ (silicon bound to oxygen). The temperature influence on the composition of SiO₂ is negligible under ion bombardment while the amount of Si₉₂ strongly increases under electron bombardment at temperatures exceeding 600 K. The mechanism of temperature dependence is discussed.     

Structural and electrical investigation of (Ag3AsS3)x(As2S3)1?x superionic glasses

Structural studies of (Ag₃AsS₃) _x (As₂S₃)_1−x chalcogenide superionic glasses in the compositional range x = 0.3–0.9 were performed by scanning electron microscopy. Temperature and compositional dependences of transmission coefficient, electrical conductivity, and activation energy were investigated     

Generalizations of a discrete universality theorem for Hurwitz zeta-functions

It is well known that the Hurwitz zeta-function ζ(s, α) with transcendental or rational parameter α is universal in the sense that the shifts ζ(s + iτ ), t ? \mathbbR \tau \in \mathbb{R} (continuous case), and ζ(s + imh), m ? \mathbbN è{ 0 } m \in \mathbb{N} \cup \left\{ 0 \right\} , with fixed h > 0 (discrete case) approximate any analytic function. In the paper, the discrete universality is extended for some classes of the functions F(ζ(s, α)).     

A discrete version of the Mishou theorem

H. Mishou proved that the Riemann zeta-function and Hurwitz zeta-function with transcendental parameter are jointly universal, i.e., their shifts (continuous) approximate any pair of analytic functions. In the paper, a discrete version of the Mishou theorem is presented. In this case, the parameter of the Hurwitz zeta-function and the step of discrete shifts are connected by a certain independence relation.