Nilpotent Subgroups of Groups with All Subgroups Subnormal

It is proved that in groups with all subgroups subnormal everynilpotent subgroup is contained in a normal nilpotent subgroup.     

On Nonlinear Integro-differential Operators in Generalized Orlicz–Sobolev Spaces

A nonlinear integral operator T of the form (Tf)(s)=∫_G K(t, f (σ(s, t))) dμ(t), for sG, is defined and investigated in the measure space (G, Σ, μ), where f and K are vector-valued functions with values in normed linear spaces E and F, respectively. The results are applied to the case of integro-differential operators in generalized Orlicz–Sobolev spaces. There are studied problems of existence, embeddings, and approximation by means of T.     

Towards a nonperturbative foundation of the dipole picture: II. High energy limit

This is the second of two papers in which we study real and virtual photon-proton scattering in a nonperturbative framework. In the first paper we have identified the leading contributions to this process at high energies and have derived expressions for them which take into account the renormalisation of the photon-quark-antiquark vertex. In the present paper we investigate the approximations and assumptions that are necessary to obtain the dipole model of high energy scattering from the results derived in the first paper. We discuss the gauge invariance of different contributions to the scattering amplitude and point out some subtleties related to gauge invariance in the correct definition of a perturbative photon wave function. As a phenomenological consequence of the dipole picture we derive a bound on the ratio of the cross sections for longitudinally and transversely polarised photons. This bound is independent of any particular model for the dipole-proton cross section and allows one to test the validity of the assumptions leading to the dipole picture in particular at low photon virtualities. We conclude that the naive dipole model formula should be supplemented by two additional terms which can potentially become large at small photon virtualities.     

Substrates for flexible electronics: A practical investigation on the electrical,film flexibility,optical, temperature,and solvent resistance properties

Designing and developing flexible electronics requires a thorough investigation of the substrates available for the fabrication of devices. Here, we present a practical study on a variety of significant substrates: polyethylene terephthalate (PET), its heat‐stabilized (HS) derivative, HS‐PET, and polyethylene naphthalate (PEN) plastic insulating films; indium tin oxide (ITO)‐coated ITO/PEN and ITO/PET transparent conducting films; rigid ITO/glass and FTO/glass substrates; stainless steel and titanium foils. We put the substrates through a range of tests these actually undergo during device fabrication to determine their optical, mechanical flexibility (under different types of tensile and compressive stress bending with and without a PEDOT:PSS conducting polymer layer), solvent resistance, stability to temperature treatment (conductivity and deformation), and to UV irradiation. We highlight issues and propose solutions to improve substrate response. The results and thresholds extracted reveal limitations and windows of opportunity useful for the designer of flexible optoelectronics in determining manufacturing processes and the final applications under everyday operation. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Asymptotic formulae for multivariate Kantorovich type generalized sampling series

In this paper an asymptotic formula of Voronovskaja type for a multivariate extension of the Kantorovich generalized sampling series is given. Moreover a quantitative version in terms of some moduli of smoothness is established. Finally some particular examples of kernels are discussed, as the Bochner-Riesz kernel and the multivariate splines.     

Multivalency as a Chemical Organization and Action Principle

Multivalent interactions can be applied universally for a targeted strengthening of an interaction between different interfaces or molecules. The binding partners form cooperative, multiple receptor–ligand interactions that are based on individually weak, noncovalent bonds and are thus generally reversible. Hence, multi‐ and polyvalent interactions play a decisive role in biological systems for recognition, adhesion, and signal processes. The scientific and practical realization of this principle will be demonstrated by the development of simple artificial and theoretical models, from natural systems to functional, application‐oriented systems. In a systematic review of scaffold architectures, the underlying effects and control options will be demonstrated, and suggestions will be given for designing effective multivalent binding systems, as well as for polyvalent therapeutics.     

A novel simplified synthesis of acivicin

This report describes an efficient synthesis of the natural isomer of acivicin, which is the only one provided with a noteworthy biological activity. The present procedure allowed the synthesis of (+)-1 in just five steps with a 34% overall yield. Due to the easy separation of the two diastereomers and to the availability of the starting material at low cost, the present procedure can be scaled-up to gram quantities.