Digital Sums and Divide-and-Conquer Recurrences: Fourier Expansions and Absolute Convergence

We propose means for computing the Fourier expansions of periodic functions appearing in higher moments of the sum-of-digits function and in the solutions of some divide-and-conquer recurrences. The expansions are shown to be absolutely convergent. We also give a new approach to efficiently compute numerically the coefficients involved to high precision.     

Thermoanalytische Untersuchungen an Schichtmaterialien: Der Einfluβ der Kationen auf das thermische Verhalten

Aluminium-free layered silicates of the metal silicate hydrate type (M-SH) comprise an interesting supplement to the well-known zeolite-like porous materials. Their specific properties allow these materials to be used as catalysts, adsorbents and ion-exchangers. Comparative X-ray diffraction and thermoanalytical investigations (TG and DSC) have shown that the thermoanalytical methods are useful to follow the process of structure formation of ilerite. The interlayer cations influence the properties of the different ilerites. In particular, the hydration behaviour of ilerite is affected. Thus, H⁺- and DTMA⁺-ilerite are stable up to temperatures of about 800°C, while the as-synthesized Na-form loses water irreversibly at about 150°C, is dehydroxylated, and is then desomposed structurally at about 400°C. The course of the dehydration exhibits significant differences for the various cation forms.This revised version was published online in November 2005 with corrections to the Cover Date.     

Photoreactivity of psoralen derivatives in micelles: the roles of hydrophobicity and heavy atom substitution

Intersystem crossing quantum yields of two psoralen derivatives, bromopsoralen (BrMOP) and hexylpsoralen (8-HOP) were measured in ethanol and water by means of laser flash photolysis. Compared to 8-methoxypsoralen (8-MOP), the triplet quantum yields of BrMOP and 8-HOP in ethanol are increased by a factor of 5 and 30, respectively, while BrMOP in aqueous solution shows a twofold enhancement with respect to 8-MOP. Radical cations and hydrated electrons were generated by photoionization in micellar solution upon excitation at 266nm. A nonlinear relationship between transient yield and photon fluence was obtained for each compound, indicating that a two-photon mechanism is predominant in the photoionization of the sensitizers. The photoionization efficiencies are significantly higher in anionic sodium dodecyl sulfate (SDS) than in cationic cetyltrimethylammonium bromide (CTAB) micelles, reflecting the influence of micelle charge on the efficiency of the separation of the photoproduced charge carriers. The photoionization efficiencies of 8-HOP and 8-MOP are similar. It is concluded that the intersystem crossing properties of BrMOP show a substantial heavy atom effect, whereas the effects of hydrophobic substitution on photoionization efficiency are minor.     

Chloride-catalyzed oxidation of phenol in pulsed-laser irradiation titanium dioxide sols

The kinetics of photolysis of phenol in presence of two kinds of TiO₂ colloid in acid aqueous solution medium was studied by transient absorption spectroscopy. The absorbance and quantum yield of the phenoxyl radicals is strongly influenced by the chloride ions. The process of laser flash photolysis of phenol in the presence of chloride has been discussed.     

Structure and properties of Na-magadiite dependent on temperature

The mechanism of the thermal behaviour of Na-magadiite at a temperature range from 293–573 K was developed based on X-ray diffraction, DTA, DTL, Q-TG, and gravimetric measurements. A structure model (BRANDT et al.) previously proposed was additionally used. It is possible to show that there probably is a connection between the typical modifications of basal spacing and significant shiftings of silicate sheets. Different steps of dehydration, decrystallization and structure variations can be ascribed to the several thermal transitions. The results depend on sample treatment such as the existent or not existent solid-water vapour interaction and the establishment of equilibrium. It seems that there is a predominance of the first mentioned influence.     

Additive Functions with Respect to Numeration Systems on Regular Languages

Asymptotic formulae for the summatory function of additive arithmetic functions related to numeration systems given by regular languages are derived.     

Additive Functions with Respect to Numeration Systems on Regular Languages

Asymptotic formulae for the summatory function of additive arithmetic functions related to numeration systems given by regular languages are derived.This author is supported by the START project Y96-MAT of the Austrian Science Fund.This author warmly thanks P. Grabner for his kind invitation to Graz and his hospitality.Received February 18, 2002; in revised form September 20, 2002 Published online May 15, 2003     

On The Sum of Digits Function for Number Systems with Negative Bases

Let q 2 be an integer. Then –q gives rise to a number system in , i.e., each number n has a unique representation of the form n = c ₀ + c ₁ (–q) + ... + c _h (–q) ^h , with c _i {0,..., q – 1}(0 i h). The aim of this paper is to investigate the sum of digits function _–q (n) of these number systems. In particular, we derive an asymptotic expansion for

Analyzing the sustainability of harvesting behavior and the relationship to personality traits in a simulated Lotka–Volterra biotope

For the analysis presented in this paper we use experiments to study human behavior in a simulation environment based on a simple Lotka–Volterra predator–prey ecology. The aim is to study the influence of different harvesting strategies and of certain personality traits derived from the Hamburg Personality Inventory (HPI) [Andresen, B., 2002. HPI – Hamburger Persönlichkeitsinventar. Hogrefe, Göttingen] on the outcome in terms of sustainability and economic performance.     

Photoablation by UV and visible laser radiation of native and doped biological tissue

Photoablation studies of biological material (human cornea) with UV and visible laser light show that effective, apparently non-conventional thermal photoablation can be achieved by introducing energy absorbing dopants in the tissue. Previously unknown high ablation rates of 80 Gmm/pulse have been observed. The results allow one to clearly postulate different ablation mechanisms for increasing laser fluence. The results are compared with the photoablation rates observed with 193 nm UV laser light on undoped human cornea. Explosive desorption has been found the dominant process involved.