Generalized Hardy inequalities and pseudocontinuable functions

Given positive integersn ₁<n ₂<... we show that the Hardy-type inequality $$\sum\limits_{k = 1}^\infty {\frac{{\left| {\hat f(n_k )} \right|}}{k}} \leqslant const\left\| f \right\|1$$ holds true for allf∈H ¹, provided that then _k 's, satisfy an appropriate (and indispensable) regularity condition. On the other hand, we exhibit inifinite-dimensional subspaces ofH ¹ for whose elements the above inequality is always valid, no additional hypotheses being imposed. In conclusion, we extend a result of Douglas, Shapiro and Shields on the cyclicity of lacunary series for the backward shift operator.     

Conditions for obtaining backward collinear isotropic acousto-optic interaction in germanium and iodic acid crystals

The possibility of experimentally obtaining backward collinear isotropic acousto-optic interaction based on bulk ultrasonic waves and terahertz electromagnetic waves is considered. The magnitudes of the acousto-optic figure of merit and the corresponding acoustic frequencies are calculated for the basic crystallographic axes in germanium and iodic acid crystals. The acousto-optic parameters of both crystals are compared.     

Weighted Bloch Spaces, Hp, and BMOA

It is determined which Bloch-type conditions on a function f _0<p<H^p ensure that f BMOA.     

Organic p-i-n solar cells

We introduce a p-i-n-type heterojunction architecture for organic solar cells where the active region is sandwiched between two doped wide-gap layers. The term p-i-n means here a layer sequence in the form p-doped layer, intrinsic layer and n-doped layer. The doping is realized by controlled co-evaporation using organic dopants and leads to conductivities of 10^-4 to 10^-5 S/cm in the p- and n-doped wide-gap layers, respectively. The photoactive layer is formed by a mixture of phthalocyanine zinc (ZnPc) and the fullerene C₆₀ and shows mainly amorphous morphology. As a first step towards p-i-n structures, we show the advantage of using wide-gap layers in M-i-p-type diodes (metal layer–intrinsic layer–p-doped layer). The solar cells exhibit a maximum external quantum efficiency of 40% between 630-nm and 700-nm wavelength. With the help of an optical multilayer model, we optimize the optical properties of the solar cells by placing the active region at the maximum of the optical field distribution. The results of the model are largely confirmed by the experimental findings. For an optically optimized device, we find an internal quantum efficiency of around 82% under short-circuit conditions. Adding a layer of 10-nm thickness of the red material N,N-dimethylperylene-3,4:9,10-dicarboximide (Me-PTCDI) to the active region, a power-conversion efficiency of 1.9% for a single cell is obtained. Such optically thin cells with high internal quantum efficiency are an important step towards high-efficiency tandem cells. First tandem cells which are not yet optimized already show 2.4% power-conversion efficiency under simulated AM 1.5 illumination of 125 mW/cm² . PACS 73.61.Ph; 78.30.Jw; 89.30.Cc     

Holomorphic functions and quasiconformal mappings with smooth moduli

We discuss the implication , where f is a holomorphic function (resp., a quasiconformal mapping) on a domain (resp., ) and Λ_ω(G) is the Lipschitz space associated with a majorant ω.     

Temperature and pressure dependences of EPR spectra of Gd ion doped in the EuAl3(BO3)4 monocrystal

The ground state of Gd³⁺ ions substituting for trivalent europium in the EuAl₃(BO₃)₄ single crystal was studied by electron paramagnetic resonance (EPR) over the temperature range of 300-4.2 K and at pressures up to 9 kbar. The EPR spectra were analysed using the spin Hamiltonian of axial symmetry. The following parameters are reported: g=1.981±0.002, b₂⁰=280.18±0.12, b₄⁰=−12.95±0.08 and b₆⁰=0.61±0.12 (at Т=298 K). The distortions of the nearest environment of Gd³⁺ ion were analysed within the framework of the superposition model of crystal field.     

Observation of bi-polarons in blends of conjugated copolymers and fullerene derivatives

From a fundamental and application point of view it is of importance to understand how charge carrier generation and transport in a conjugated polymer (CP):fullerene blend are affected by the blend morphology. In this work light-induced electron spin resonance (LESR) spectra and transient ESR response signals are recorded on non-annealed and annealed blend layers consisting of alkyl substituted thieno[3,2-b]thiophene copolymers (pATBT) and the soluble fullerene derivative [6,6]-phenyl-C61-butyric acid methyl ester (PCBM) at temperatures ranging from 10 to 180 K. Annealing of the blend sample leads to a reduction of the steady state concentration of light-induced PCBM anions within the blend at low temperatures (T = 10 K) and continuous illumination. This is explained on the basis of the reducing interfacial area of the blend composite on annealing, and the high activation energy for electron diffusion in PCBM blends leading to trapped electrons near the interface with the CP. As a consequence, these trapped electrons block consecutive electron transfer from an exciton on a CP to the PCBM domain, resulting in a relatively low concentration charge carriers in the annealed blend. Analysis of the transient ESR data allows us to conclude that in annealed samples diamagnetic bi-polaronic states on the CPs are generated at low temperature. The formation of these states is related to the generation and interaction of multiple positive polarons in the large crystalline polymer domains present in the annealed sample.