Normality and shared values

LetF be a family of meromorphic functions on the unit disc Δ and leta andb be distinct values. If for everyf∈F,f andf′ sharea andb on Δ, thenF is normal on Δ. The first author was supported by NNSF of China approved no. 19771038 and by the Research Institute for Mathematical Sciences, Bar-Ilan University.     

Bounded type Siegel disks of finite type maps with few singular values

Let U be an open subset of the Riemann sphere \(\hat {\mathbb{C}}\). We give sufficient conditions for which a finite type map f: U → \(\hat {\mathbb{C}}\) with at most three singular values has a Siegel disk compactly contained in U and whose boundary is a quasicircle containing a unique critical point. The main tool is quasiconformal surgery à la Douady-Ghys-Herman-?wi?tek. We also give sufficient conditions for which, instead, Δ has not compact closure in U. The main tool is the Schwarzian derivative and area inequalities à la Graczyk-?wi?tek.     

Periodic orbits, damped transitions and targeted energy transfers in oscillators with vibro-impact attachments

We study complex damped and undamped dynamics and targeted energy transfers (TETs) in systems of coupled oscillators, consisting of single-degree-of-freedom primary linear oscillators (LOs) with vibro-impact attachments, acting, in essence, as vibro-impact nonlinear energy sinks (VI NESs). First, the complicated dynamics of such VI systems is demonstrated by computing the VI periodic orbits of underlying Hamiltonian systems and depicting them in appropriate frequency–energy plots (FEPs). Then, VI damped transitions and distinct ways of passive TETs from the linear oscillators to the VI attachments for various parameter ranges and initial conditions are investigated. As in the case of smooth stiffness nonlinearity [Y. Lee, G. Kerschen, A. Vakakis, P. Panagopoulos, L. Bergman, D.M. McFarland, Complicated dynamics of a linear oscillator with a light, essentially nonlinear attachment, Physica D 204 (1–2) (2005) 41–69], both fundamental and subharmonic TET can be realized in the VI systems under consideration. It is found that the most efficient mechanism for VI TET is through the excitation of highly energetic VI impulsive orbits (IOs), i.e., of periodic or quasiperiodic orbits corresponding to zero initial conditions except for the initial velocities of the linear oscillators. In contrast to NESs with smooth essential nonlinearities considered in previous works, VI NESs are capable of passively absorbing and locally dissipating significant portions of the energies of the primary systems to which they are attached, at fast time scale. This renders such devices suitable for applications, like seismic mitigation, where dissipation of vibration energy in the early, highly energetic regime of the motion is a critical requirement.     

Effect of hydrogen on surface texturing and crystallization of a-Si:H thin film irradiated by excimer laser

Hydrogenated amorphous silicon (a-Si:H) thin films have been considered for use in solar cell applications because of their significantly reduced cost compared to crystalline bulk silicon. However, their overall efficiency and stability are lower than that of their bulk crystalline counterpart. Limited work has been performed on simultaneously solving the efficiency and stability issues of a-Si:H. Previous work has shown that surface texturing and crystallization on a-Si:H thin film can be achieved through a single-step laser processing, which can potentially alleviate the disadvantages of a-Si:H in solar cell applications. In this study, hydrogenated and dehydrogenated amorphous silicon thin films deposited on glass substrates were irradiated by KrF excimer laser pulses and the effect of hydrogen on surface morphologies and microstructures is discussed. Sharp spikes are focused only on hydrogenated films, and the large-grained and fine-grained regions caused by two crystallization processes are also induced by presence of hydrogen. Enhanced light absorptance is observed due to light trapping based on surface geometry changes of a-Si:H films, while the formation of a mixture of nanocrystalline silicon and original amorphous silicon after crystallization suggests that the overall material stability can potentially improve. The relationship between crystallinity, fluence and number of pulses is also investigated. Furthermore, a step-by-step crystallization process is introduced to prevent the hydrogen from diffusing out in order to reduce the defect density, and the relationship between residue hydrogen concentration, fluence and step width is discussed. Finally, the combined effects show that the single-step process of surface texturing and step-by-step crystallization induced by excimer laser processing are promising for a-Si:H thin-film solar cell applications.     

The NiII,HgII and CuII complexes of 12‐membered‐ring mixed‐donor macrocycles

The structures of di­aqua(1,7‐dioxa‐4‐thia‐10‐aza­cyclo­do­decane)­nickel dinitrate, [Ni(C₈H₁₇NO₂S)(H₂O)₂](NO₃)₂, (I), bis­(nitrato‐O,O′)(1,4,7‐trioxa‐10‐aza­cyclo­do­decane)­mercury, [Hg(NO₃)₂(C₈H₁₇NO₃)], (II), and aqua­(nitrato‐O)(1‐oxa‐4,7,10‐tri­aza­cyclo­do­decane)copper nitrate, [Cu(NO₃)(C₈H₁₉N₃O)(H₂O)]NO₃, (III), reveal each macrocycle binding in a tetradentate manner. The conformations of the ligands in (I) and (III) are the same and distinct from that identified for (II). These differences are in agreement with molecular‐mechanics predictions of ligand conformation as a function of metal‐ion size.     

Synthesis of Novel C/D Ring Modified Bile Acids

Bile acid receptors have been identified as important targets for the development of new therapeutics to treat various metabolic and inflammatory diseases. The synthesis of new bile acid analogues can help elucidate structure–activity relationships and define compounds that activate these receptors selectively. Towards this, access to large quantities of a chenodeoxycholic acid derivative bearing a C-12 methyl and a C-13 to C-14 double bond provided an interesting scaffold to investigate the chemical manipulation of the C/D ring junction in bile acids. The reactivity of this alkene substrate with various zinc carbenoid species showed that those generated using the Furukawa methodology achieved selective α-cyclopropanation, whereas those generated using the Shi methodology reacted in an unexpected manner giving rise to a rearranged skeleton whereby the C ring has undergone contraction to form a novel spiro–furan ring system. Further derivatization of the cyclopropanated steroid included O-7 oxidation and epimerization to afford new bile acid derivatives for biological evaluation.     

Ring current effects in crystals. Evidence from 13C chemical shift tensors for intermolecular shielding in 4,7-di-t-butylacenaphthene versus 4,7-di-t-butylacenaphthylene

13C chemical shift tensor data from 2D FIREMAT spectra are reported for 4,7-di-t-butylacenaphthene and 4,7-di-t-butylacenaphthylene. In addition, calculations of the chemical shielding tensors were completed at the B3LYP/6-311G** level of theory. While the experimental tensor data on 4,7-di-t-butylacenaphthylene are in agreement with theory and with previous data on polycyclic aromatic hydrocarbons, the experimental and theoretical data on 4,7-di-t-butylacenaphthene lack agreement. Instead, larger than usual differences are observed between the experimental chemical shift components and the chemical shielding tensor components calculated on a single molecule of 4,7-di-t-butylacenaphthene, with a root mean square (rms) error of +/-7.0 ppm. The greatest deviation is concentrated in the component perpendicular to the aromatic plane, with the largest value being a 23 ppm difference between experiment and theory for the 13CH2 carbon delta11 component. These differences are attributed to an intermolecular chemical shift that arises from the graphitelike, stacked arrangement of molecules found in the crystal structure of 4,7-di-t-butylacenaphthene. This conclusion is supported by a calculation on a trimer of molecules, which improves the agreement between experiment and theory for this component by 14 ppm and reduces the overall rms error between experiment and theory to 4.0 ppm. This intermolecular effect may be modeled with the use of nuclei independent chemical shieldings (NICS) calculations and is also observed in the isotropic 1H chemical shift of the CH2 protons as a 4.2 ppm difference between the solution value and the solid-state chemical shift measured via a 13C-1H heteronuclear correlation experiment.     

ELECTRON TRANSFER FROM CHLOROPHYLL a TO QUINONE IN MONO- AND MULTILAYER ARRAYS

Abstract— Mono- and multilayers of chlorophyll a (Chl a )– lecithin have been prepared on quartz slides, by means of the Blodgett-Langmuir technique, for fluorescence studies. Self-quenching of the Chl a fluorescence has been observed in Chl a -lecithin single layer excited with a laser light at 632.8 nm. The fluorescence yield is reduced by 50% at a concentration of 7 ± 10¹² Chl a molecules cm⁻². Chl a fluorescence quenching, by adding N,N -distearoyl-1,4-diaminoanthraquinone (SAQ), has been studied. in a single layer, in pure Chl a and also at various dilutions of Chl a in lecithin. The results are explained in terms of a dynamic quenching rather than in terms of a permanent complex formation, at the ground state, between Chl a and SAQ. The fluorescence quenching has been interpreted as the result of an electron transfer from excited Chl a to SAQ, and rate constants of 8.3 ± 10⁻⁵ cm² molecule⁻¹ S⁻¹ and 2.4 ± 10⁻⁴ cm² molecule⁻¹ s⁻¹ have been found for pure diluted Chl a , respectively. Ten per cent of the diluted Chl a fluorescence always remains unquenchable and independent of the quinone concentration. In multilayers, where SAQ and Chl a are in different layers, there is no fluorescence quenching for pure or diluted Chl a even when the chromophores are in two adjacent layers. This happens only if SAQ is not able to diffuse from one layer to another. A minimum value of 22.4 nm has been found for the singlet exciton diffusion length in pure Chl a multilayers.