On Transfer Operators for Continued Fractions with Restricted Digits

For any non-empty subset I of the natural numbers, let _I denotethose numbers in the unit interval whose continued fractiondigits all lie in I. Define the corresponding transfer operator for , where Re (rß) = _I is the abscissa of convergence of the series . When acting on a certain Hilbert space H_I, rß, weshow that the operator L_I, rß is conjugate to an integraloperator K_I, rß. If furthermore rß is real,then K_I, rß is selfadjoint, so that L_I, rß: H_I, rß H_I, rß has purely real spectrum.It is proved that L_I, rß also has purely real spectrumwhen acting on various Hilbert or Banach spaces of holomorphicfunctions, on the nuclear space C [0, 1], and on the Fréchetspace C [0, 1]. The analytic properties of the map rß L_I, rßare investigated. For certain alphabets I of an arithmetic nature(for example, I = primes, I = squares, I an arithmetic progression,I the set of sums of two squares it is shown that rß L_I, rß admits an analytic continuation beyond thehalf-plane Re rß > _I. 2000 Mathematics SubjectClassification 37D35, 37D20, 30B70.     

Long range ordering in self-assembled Ni arrays on patterned Si

We have succeeded in aligning self-assembled structures by using a lithographically defined stripe. The 140 nm wide by 100 nm high SiO₂ strip is shown to guide the assembly of 500 nm latex spheres so that spheres are aligned along the strip and are in registration on either side of the strip. This method can be used to increase long-range ordering in magnetic storage systems without compromising the density. Inverse sphere Ni arrays were made by electrodeposition through the latex template. We also show that the hexagonal symmetry of the resulting inverse sphere Ni arrays can be simulated using the approach presented below.     

The Stereochemistry of the Reaction of α-Silyl Lithium Reagents with Cyclic Tert-butyldimethylsilyl Acyloins

The reactions of the tert-butyldimethylsilylated acyloins of five-, six- and seven-membered rings with the lithium reagents of benzyltrimethylsilane, thiophenoxymethyltrimethylsilane and tri-methylsilyl acetonitrile were studied. These reactions favor formation of the substituted (Z) exo methylidene silyl ethers in moderate yields.     

A kinetic study of the reactions of sulfate and dihydrogen phosphate radicals with epicatechin,epicatechingallate, and epigalocatechingallate

The bimolecular rate constants for the reactions of sulfate radicals with epicatechin (EC), epicatechingallate (ECG), and epigallocatechingallate (EGCG) were found to be (1.46 ± 0.06) × 10⁹, (1.20 ± 0.08) × 10⁹, and (1.04 ± 0.07) × 10⁹, respectively. The activation energy [E_A = 9 ± 3 kJ mol^?1] and preexponential factor [A = (4.8 ± 0.6) × 10¹⁰] for the reaction of EC with the sulfate radical were measured in the temperature range 288–303 K. The phenoxyl radicals of EC (λ_max = 310 nm) were obtained both by the reaction of this flavonoid with the sulfate radicals and by photoionization. The measured bimolecular rate constants for the reactions of the dihydrogen phosphate radicals with EC, ECG, and EGCG were (7.8 ± 0.9) × 10⁸, (8.5 ± 0.4) × 10⁸, and (6.8 ± 0.4) × 10⁸, respectively. © 2010 Wiley Periodicals, Inc. Int J Chem Kinet 42: 391–396, 2010     

Nafion/tetraruthenated porphyrin glassy carbon-modified electrode: characterization and voltammetric studies of sulfite oxidation in water–ethanol solutions

In this work, the modification of a glassy carbon electrode with tetraruthenated porphyrins electrostatically assembled onto a Nafion film, previously adsorbed on the electrode surface, is reported. This modified electrode was characterized by scanning electron microscopy–energy-dispersive X-ray, Raman spectroscopy, UV-Vis spectroelectrochemistry, and cyclic voltammetry. The Nafion film onto the glassy carbon electrode shows a smooth disposition; when the tetraruthenated porphyrin is incorporated on the Nafion film, the complex is adsorbed in a homogeneous way. The modified electrode catalyzes HSO₃⁻ oxidation in water–ethanol solutions and shows an enhanced stability compared with the electrode modified with the dip coating method. Rotating disk electrode experiments showed a kinetic limitation to the electron transfer controlled by charge propagation in the film. I/E curves show a Tafel slope of 120 mV/decade corresponding to a first electron-transfer reaction, depending on the potential, as the determining step. Spectroelectrochemical experiments demonstrated that Ru(II) is the active site for the electrocatalysis.     

Martensitic transformation in Mn–Ni–Sn Heusler alloys

Three magnetic shape memory alloys: Mn₅₀Ni_50−x Sn _x (x = 5, 7.5, and 10) were produced as bulk polycrystalline ingots by arc melting. The structural austenite–martensite transformation was checked by calorimetry. The transformation temperatures decrease as increasing the Sn content. The same trend is found in the entropy and enthalpy changes related to the transformation. The control of the valence electron by atom e/a determines the transformation temperatures range in this kind of alloys and it is possible to develop alloys that can be candidates in applications as sensors and actuators. Furthermore, X-ray diffraction was performed to check the crystalline structure at room temperature.