On the growth of universal functions

In this paper, we study the growth of universal functions (Taylor series) on the unit discD. We describe a class of growth types prohibited for such a function. By investigating the relation between growth and value distribution, we prove that every universal function assumes every complex value, with at most one exception, on sequences inD that approach ϖD rather slowly. We use this to get a large class of equations, including polynomials with Nevanlinna coefficients and equations of iterates, that no universal function satisfies. Finally, we produce a universal function whose growth is bounded by

A lower bound for sums of eigenvalues of the Laplacian

Let be the th Dirichlet eigenvalue of a bounded domain in . According to Weyl's asymptotic formula we have

The optimal in view of this asymptotic relation lower estimate for the sums has been proven by P.Li and S.T.Yau (Comm. Math. Phys. 88 (1983), 309-318). Here we will improve this estimate by adding to its right-hand side a term of the order of that depends on the ratio of the volume to the moment of inertia of .

     

Biotechnological progress in producing fuels and valuable chemicals and in bioremediating environmental impacts

Applied Biochemistry and Biotechnology - The 71 poster papers presented at the 16th Symposium on Biotechnology for Fuels and Chemicals provided new information on ethanol production, feedstock...     

Induced cosmology on a regularized brane in six-dimensional flux compactification

We consider a six-dimensional Einstein–Maxwell system compactified in an axisymmetric two-dimensional space with one capped regularized conical brane of codimension one. We study the cosmological evolution which is induced on the regularized brane as it moves in between known static   bulk and cap solutions. Looking at the resulting Friedmann equation, we see that the brane cosmology at high energies is dominated by a five-dimensional ρ²${\rho }^2$ energy density term. At low energies, we obtain a Friedmann equation with a term linear to the energy density with, however, negative coefficient in the small four-brane radius limit (i.e., with negative effective Newton's constant). We discuss ways out of this problem.     

A theoretical approach to the interpretation of the transient data in scanning laser ablation inductively coupled plasma mass spectrometry: Consideration of the geometry of the scanning area

This paper represents a further development of the theoretical basis for the interpretation of transient data obtained by scanning laser ablation inductively coupled plasma mass spectrometry (LA-ICP-MS) to overcome the non-linear distortion of the transient signal as well as to improve spatial resolution. The reconstruction of the relative concentration profile from transient data is suggested in terms of simple models of analytical information gathering for extreme cases of depth distribution of the analyte. The main attention is focused on the geometry of the overlap between the laser spot and the concentration profile, the consideration of which allows defining explicitly the response function necessary for the deconvolution procedure. The profile of the transient signal simulated according the proposed model for a real system (copper conductor lines in polymer matrix) is in good agreement with the measured data. The feasibility of the deconvolution procedure to reconstruct the relative concentration profile for a model system is demonstrated. The suggested analytical framework is intended to overcome certain limitations of scanning LA-ICP-MS which are caused by the measuring process independently from the optimization of hardware and experimental conditions.     

Free electron transfer from xanthenyl- and fluorenylsilanes (Me3 or Ph3) to parent solvent radical cations: effects of molecule dynamics

Parent radical cations of nonpolar solvents (alkanes and alkyl chlorides) ionize 9-(trimethylsilyl)xanthenes and 9-(trimethylsilyl)fluorenes in a diffusion-controlled electron transfer. The actual electron jump as the deciding part of the process does not require a defined encounter complex, and therefore the reactants are not subjected to any geometry optimization. Considering the molecule dynamics of the donors, bending motions of the silyl group are concerted with fluctuations of the highest occupied molecular orbital electrons. Ionizing such a standing conformer mixture creates metastable (microsecond) as well as dissociative donor radical cations. A mobility restriction of the benzylic silane group in positions vertical to the phenyl plane stabilizes the radical cations and accounts for a declining amount of dissociative radical cations, which undergo C-Si bond fragmentation in the order benzylsilane > xanthenylsilane > fluorenylsilane.     

Studies on pyrrolidinones. On the carbamoylation of some pyroglutamic derivatives

The carbamoylation of some lactams derivatived from pyroglutamic acid as been studied; better yields were obtained starting from the unsubstitued lactam (toluene, 80°) rather than starting with the N-silyllactam (room temperature), although these latter reaction conditions could be interesting for heat sensitive compounds. Methyl and phenyl isothiocyanate react only with the sodium salt of methyl pyroglutamate, giving 1,5-diaddition products.     

Studies on pyrrolidinones. Synthesis of some N-fatty acylpyroglutamic acids

Starting from readily available pyroglutamic acid 1 , some N-fatty acylpyroglutamic acids were synthesized and characterized by their spectral data. A preliminary pharmacological study showed that N-stearoylpyroglutamic acid 4c displays a CNS stimulating effect on mice.     

Recent research efforts in the area of biotechnology for fuels and chemicals

Applied Biochemistry and Biotechnology -     

TiO2 nanoparticles as a soft X-ray molecular probe

This communication reports the development of a TiO2-streptavidin nanoconjugate as a new biological label for X-ray bio-imaging applications; this new probe, used in conjunction with the nanogold probe, will make it possible to obtain quantitative, high-resolution information about the location of proteins using X-ray microscopy.