Finite order solutions of linear differential equations in the unit disc

Necessary and sufficient conditions for the analytic coefficients of the complex linear differential equation

(†)     

Estimations of Hölder Regularities and Direction of Singularity by Hart Smith and Curvelet Transforms

Using Hart Smith’s and curvelet transforms, new necessary and new sufficient conditions for an L ²(?²) function to possess Hölder regularity, uniform and pointwise, with exponent α>0 are given. Similar to the characterization of Hölder regularity by the continuous wavelet transform, the conditions here are in terms of bounds of the transforms across fine scales. However, due to the parabolic scaling, the sufficient and necessary conditions differ in both the uniform and pointwise cases. We also investigate square-integrable functions with sufficiently smooth background. Specifically, sufficient and necessary conditions, which include the special case with 1-dimensional singularity line, are derived for pointwise Hölder exponent. Inside their “cones” of influence, these conditions are practically the same, giving near-characterization of direction of singularity.     

Neutrinoless Double-Beta Decay to Excited 0+ States

A considerable effort has been invested in studies of the two-neutrino double-beta decay to the first (and some others, too) excited 0⁺ states. These decay transitions have been considered favourable in terms of the nuclear matrix elements and the possibility to use -coincidence techniques in cleaning the background of the spectrum. A drawback in these studies is the diminished phase space for the emitted leptons due to the smaller Q value of the process. One positive result, namely the decay rate of ¹⁰⁰Mo to the first excited 0⁺ state in ¹⁰⁰Ru, already exists. Encouraged by this result one could argue that a similar situation could prevail also for the neutrinoless double-beta decay to excited 0 ⁺ states. In this article the situation has been studied for several nuclear systems with potential 0 decay to the low-lying 0⁺ states by using the quasiparticle random-phase approximation with realistic nucleon-nucleon interactions.     

Bi-Lipschitz concordance implies bi-Lipschitz isotopy

We modify the proof of an earlier result of ours to deforming topological, bi-Lipschitz, and quasiconformal embeddings of an open subsetU ofR ⁿ which now are of small uniform distance from the inclusion map. As an application we show that two bi-Lipschitz homeomorphismsf ₀,f ₁:R ⁿRⁿ are bi-Lipschitz isotopic if and only ifd(f ₀,f ₁)<.Research supported in part by a grant from the Institut Mittag-Leffler.     

Common fluorescent sunlamps are an inappropriate substitute for sunlight

Fluorescent sunlamps are commonly employed as convenient sources in photobiology experiments. The ability of Kodacel to filter photobiologically irrelevant UVC wavelengths has been described. Yet there still remains a major unaddressed issue--the over representation of UVB in the output. The shortest terrestrial solar wavelengths reaching the surface are approximately 295 nm with the 295-320 nm range comprising approximately 4% of the solar UV irradiance. In Kodacel-filtered sunlamps, 47% of the UV output falls in this range. Consequently, in studies designed to understand skin photobiology after solar exposure, the use of these unfiltered sunlamps may result in misleading, or even incorrect conclusions. To demonstrate the importance of using an accurate representation of the UV portion of sunlight, the ability of different ultraviolet radiation (UVR) sources to induce the expression of a reporter gene was assayed. Unfiltered fluorescent sunlamps (FS lamps) induce optimal chloramphenicol acetyltransferase (CAT) activity at apparently low doses (10-20 J/cm2). Filtering the FS lamps with Kodacel raised the delivered dose for optimal CAT activity to 50-60 mJ/cm2. With the more solar-like UVA-340 lamps somewhat lower levels of CAT activities were induced even though the apparent delivered doses were significantly greater than for either the FS or Kodacel-filtered sunlamp (KFS lamps). When DNA from parallel-treated cells was analyzed for photoproduct formation by a radioimmuneassay, it was shown that the induction of CAT activity correlated with the level of induced photoproduct formation regardless of the source employed.     

o-Alkyl-substituted aromatic phosphanes for hydroformylation studies: synthesis, spectroscopic characterization and ab initio investigations

In earlier hydroformylation studies modification of the rhodium catalyst with o-methyl-substituted or o-ethyl-substituted phosphane ligands have increased regioselectivity to branched aldehydes. The promising results achieved created a need for further studies. Hence, a wider group of o-substituted arylphosphane ligands, e.g. (2-cyclohexylphenyl)diphenylphosphane, (2-isopropylphenyl)diphenylphosphane, (2-methylnaphthyl)diphenylphosphane, (2,5-dimethylphenyl)diphenylphosphane and (2-phenylphenyl)diphenylphosphane were synthesized and tested in rhodium-catalyzed hydroformylation to support the previous findings. Characterization of the ligands was made by NMR spectroscopy (¹H, ³¹P{¹H}, ¹³C{¹H}, HSQC, COSY-90 and COLOC). Additional parameters for evaluation of the stereoelectronic properties of the ligands were provided by quantum mechanical calculations and by synthesizing Rh(acac)(CO)(PR₃) complexes. In the rhodium-catalyzed hydroformylation of propene and 1-hexene the ligands increased the formation of branched aldehydes compared to triphenylphosphane. Additionally the increasing size of the o-alkyl-substituent was found to effect favorably to the iso-selectivity.     

Mean growth and geometric zero distribution of solutions of linear differential equations

The aim of this paper is to consider certain conditions on the coefficient A of the differential equation f″ + Af = 0 in the unit disc which place all normal solutions f in the union of Hardy spaces or result in the zero-sequence of each non-trivial solution being uniformly separated. The conditions on the coefficient are given in terms of Carleson measures.