An Isogeny of K3 Surfaces

In a recent paper Ahlgren, Ono and Penniston described the L-seriesof K3 surfaces from a certain one-parameter family in termsof those of a particular family of elliptic curves. The Tateconjecture predicts the existence of a correspondence betweenthese K3 surfaces and certain Kummer surfaces related to theseelliptic curves. A geometric construction of this correspondenceis given here, using results of D. Morrison on Nikulin involutions.2000 Mathematics Subject Classification 14J27, 14G25, 14J28.     

Small Deviations of Riemann-Liouville Processes In lq Spaces With Respect To Fractal Measures

We investigate Riemann–Liouville processes R_H, with H> 0, and fractional Brownian motions B_H, for 0 < H <1, and study their small deviation properties in the spacesL_q([0, 1], µ). Of special interest here are thin (fractal)measures µ, that is, those that are singular with respectto the Lebesgue measure. We describe the behavior of small deviationprobabilities by numerical quantities of µ, called mixedentropy numbers, characterizing size and regularity of the underlyingmeasure. For the particularly interesting case of self-similarmeasures, the asymptotic behavior of the mixed entropy is evaluatedexplicitly. We also provide two-sided estimates for this quantityin the case of random measures generated by subordinators. While the upper asymptotic bound for the small deviation probabilityis proved by purely probabilistic methods, the lower bound isverified by analytic tools concerning entropy and Kolmogorovnumbers of Riemann–Liouville operators. 2000 MathematicsSubject Classification 60G15 (primary), 47B06, 47G10, 28A80(secondary).     

Dealing with a local heating effect when measuring catalytic solids in a reactor with Raman spectroscopy

In continuation of our previous work on the applicability of the G(R(infinity)) correction factor for the quantification of Raman spectra of coke during propane dehydrogenation experiments (Phys. Chem. Chem. Phys., 2005, 7, 211), research has been carried out on the potential of this correction factor for the quantification of supported metal oxides during reduction experiments. For this purpose, supported chromium oxide catalysts have been studied by combined in situ Raman and UV-Vis spectroscopy during temperature programmed reduction experiments with hydrogen as reducing agent. The goal was to quantify on-line the amount of Cr(6+) in a reactor based on the measured in situ Raman spectra. During these experiments, a significant temperature effect was observed, which has been investigated in more detail with a thermal imaging technique. The results revealed a temperature 'on the spot' that can exceed 100 degrees C. It implies that Raman spectroscopy can have a considerable effect on the local reaction conditions and explains observed inconsistencies between the in situ UV-Vis and Raman data. In order to minimize this heating effect, reduction of the laser power, mathematical matching of the spectroscopic data, a different cell design and a change in reaction conditions has been evaluated. It is demonstrated that increasing the reactor temperature is the most feasible method to solve the heating problem. Next, it allows the application of in situ Raman spectroscopy in a reliable quantitative way without the need of an internal standard.     

Unusual coordination behavior of Cr3+ in microporous aluminophosphates

A CrAPO-5 molecular sieve has been investigated with X-ray absorption spectroscopy (EXAFS-XANES) as dehydrated material and after loading with water and ammonia to unravel the coordination geometries of Cr3+ in the framework of a microporous crystalline aluminophosphate, more particularly of the AFI-type. A comparison of the XANES data, a preedge analysis with crystal field multiplet calculations and EXAFS data, pointed toward the presence of framework Cr3+ which, on dehydration, takes on a distorted tetrahedral coordination state. Due to the 3d3 configuration of Cr3+, this unusual tetrahedral coordination environment strongly tends to transform into the more stable 6-fold coordination geometry by binding two extraframework water molecules during hydration. In the presence of ammonia, tetrahedral Cr3+ readily transforms into a 5-fold coordination geometry by binding one ammonia molecule. Therefore, depending on the environmental conditions, the Cr3+ ions can occur in a 4-, 5-, or 6-fold coordination. This observation underlines the flexibility of transition metal ions, such as Cr3+, to cope with unusual coordination geometries in inorganic hosts, making them interesting as potential active sites in heterogeneous catalysis.     

Novel Helmholtz-based photoacoustic sensor for trace gas detection at ppm level using GaInAsSb/GaAlAsSb DFB lasers

A new and compact photoacoustic sensor for trace gas detection in the 2-2.5 microm atmospheric window is reported. Both the development of antimonide-based DFB lasers with singlemode emission in this spectral range and a novel design of photoacoustic cell adapted to the characteristics of these lasers are discussed. The laser fabrication was made in two steps. The structure was firstly grown by molecular beam epitaxy then a metallic DFB grating was processed. The photoacoustic cell is based on a Helmholtz resonator that was designed in order to fully benefit from the highly divergent emission of the antimonide laser. An optimized modulation scheme based on wavelength modulation of the laser source combined with second harmonic detection has been implemented for efficient suppression of wall noise. Using a 2211 nm laser, sub-ppm detection limit has been demonstrated for ammonia.     

Short interval asymptotics for a class of arithmetic functions

Summary We provide a general asymptotic formula which permits applications to sums like <InlineEquation ID=IE"1"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"2"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"3"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"4"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"5"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"6"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"7"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"8"><EquationSource Format="TEX"><![CDATA[<InlineEquation ID=IE"9"><EquationSource Format="TEX"><![CDATA[$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation>$]]></EquationSource></InlineEquation>]]></EquationSource></InlineEquation> \sum_{x< n\le x+y} \big(d(n)\big)^2, \quad \sum_{x< n\le x+y} d(n^3),\quad \sum_{x< n\le x+y}\big(r(n)\big)^2, \quad \sum_{x< n\le x+y}r(n^3), $$ where $d(n)$ and $r(n)$ are the usual arithmetic functions (number of divisors, sums of two squares), and $y$ is small compared to~$x$.     

A Critical Look at 50 Years Particle Theory from the Perspective of the Crossing Property

The crossing property is perhaps the most subtle aspect of the particle-field relation. Although it is not difficult to state its content in terms of certain analytic properties relating different matrixelements of the S-matrix or formfactors, its relation to the localization- and positive energy spectral principles requires a level of insight into the inner workings of QFT which goes beyond anything which can be found in typical textbooks on QFT. This paper presents a recent account based on new ideas derived from “modular localization” including a mathematic appendix on this subject. Its main achievement is the proof of the crossing property from a two-algebra generalization of the KMS condition.     

Trajectory based non-markovian dissipative tunneling

The influence of a dissipative environment on scattering of a particle by a barrier is investigated by using the recently introduced bohmian mechanics with complex action [J. Chem. Phys. 125, 231103 (2006)]. An extension of this complex trajectory based formalism to include the interaction of the tunneling particle with an environment of harmonic oscillators with a continuous spectral density and at a certain finite temperature allows us to calculate transmission probabilities beyond the weak system bath coupling regime. The results display an increasing tunneling probability for energies below the barrier and a decreased transmission above the barrier due to the coupling. Furthermore, we demonstrate that solutions of a markovian master equation fail to do so in general.