Holomorphic Sobolev spaces, Hermite and special Hermite semigroups and a Paley-Wiener theorem for the windowed Fourier transform

The images of Hermite and Laguerre-Sobolev spaces under the Hermite and special Hermite semigroups (respectively) are characterized. These are used to characterize the image of Schwartz class of rapidly decreasing functions f on R-n and C-n under these semigroups. The image of the space of tempered distributions is also considered and a Paley-Wiener theorem for the windowed (short-time) Fourier transform is proved.

Worldwide outdoor round robin study of organic photovoltaic devices and modules

Accurate characterization and reporting of organic photovoltaic (OPV) device performance remains one of the important challenges in the field. The large spread among the efficiencies of devices with the same structure reported by different groups is significantly caused by different procedures and equipment used during testing. The presented article addresses this issue by offering a new method of device testing using “suitcase sample” approach combined with outdoor testing that limits the diversity of the equipment, and a strict measurement protocol. A round robin outdoor characterization of roll-to-roll coated OPV cells and modules conducted among 46 laboratories worldwide is presented, where the samples and the testing equipment were integrated in a compact suitcase that served both as a sample transportation tool and as a holder and test equipment during testing. In addition, an internet based coordination was used via plasticphotovoltaics.org that allowed fast and efficient communication among participants and provided a controlled reporting format for the results that eased the analysis of the data. The reported deviations among the laboratories were limited to 5% when compared to the Si reference device integrated in the suitcase and were up to 8% when calculated using the local irradiance data. Therefore, this method offers a fast, cheap and efficient tool for sample sharing and testing that allows conducting outdoor measurements of OPV devices in a reproducible manner.

Long-term Accelerated Multistress Aging of Composite Outdoor Polymeric Insulators

Polymeric outdoor insulators are being increasingly used for electrical power transmission and distribution in the recent years. One of the current topics of interest for the power transmission community is the aging of such outdoor polymeric insulators. A few research groups are carrying out aging studies at room temperature with wet period as an integral part of multistress aging cycle as specified by IEC standards. However, aging effect due to dry conditions alone at elevated temperatures and electric stress in the presence of radiation environment has probably not been explored. It is interesting to study and understand the insulator performance under dry conditions where wet periods are either rare or absent and to estimate the extent of aging caused by multiple stresses. This paper deals with the long-term accelerated multistress aging on full-scale 11 kV distribution class composite silicone rubber insulators. In order to assess the long-term synergistic effect of electric stress, temperature and UV radiation on insulators, they are subjected to accelerated aging in a specially designed multistress-aging chamber for 3800 hours. All the stresses are applied at an accelerated level. Using a data acquisition system developed for the work, leakage current has been monitored in LabVIEW environment. Chemical changes due to degradations have been studied using Energy Dispersive X-Ray analysis, Scanning Electron Microscope and Fourier transform Infrared Spectroscopy. Periodically different parameters like low molecular weight (LMW) molecular content, hydrophobicity, leakage current and surface morphology were monitored. The aging study is under progress and only intermediate results are presented in this paper.

Proximinality in Banach spaces

In this paper, we study approximatively τ-compact and τ-strongly Chebyshev sets, where τ is the norm or the weak topology. We show that the metric projection onto τ-strongly Chebyshev sets are norm-τ continuous. We characterize approximatively τ-compact and τ-strongly Chebyshev hyperplanes and use them to characterize factor reflexive proximinal subspaces in τ-almost locally uniformly rotund spaces. We also prove some stability results on approximatively τ-compact and τ-strongly Chebyshev subspaces.

Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

Semigroups on Frechet spaces and equations with infinite delays

In this paper, we show existence and uniqueness of a solution to a functional differential equation with infinite delay. We choose an appropriate Frechet space so as to cover a large class of functions to be used as initial functions to obtain existence and uniqueness of solutions.

Support theorems on R-n and non-compact symmetric spaces

We consider convolution equations of the type f * T = g, where f, g is an element of L-P (R-n) and T is a compactly supported distribution. Under natural assumptions on the zero set of the Fourier transform of T, we show that f is compactly supported, provided g is. Similar results are proved for non-compact symmetric spaces as well. (C) 2010 Elsevier Inc. All rights reserved.

Chemistry in Confined Spaces: High-Energy Conformer of a Piperidine Derivative is Favored Within a Water-Soluble Capsuleplex

Propyloxy-substituted piperidine in solution adopts a conformation in which its alkoxy group is equatorially positioned Surprisingly, two conformers of it that do not interconvert in the NMR time scale at room temperature have been found within an octa-acid capsule The serendipitous finding of the axial conformer of propyloxy-substituted piperidine within a supramolecular capsule highlights the value of confined spaces in physical organic chemistry.

On the relation between rotation increments in different tangent spaces

In computational mechanics, finite rotations are often represented by rotation vectors. Rotation vector increments corresponding to different tangent: spaces are generally related by a linear operator, known as the tangential transformation T. In this note, we derive the higher order terms that are usually left out in linear relation. The exact nonlinear relation is also presented. Errors via the linearized T are numerically estimated. While the concept of T arises out of the nonlinear characteristics of the rotation manifold, it has been derived via tensor analysis in the context of computational mechanics (Cardona and Geradin, 1988). We investigate the operator T from a Lie group perspective, which provides a better insight and a 1-1 correspondence between approaches based on tensor analysis and the standard matrix Lie group theory. (C) 2010 Elsevier Ltd. All rights reserved.

Properties of Toeplitz operators on analytic function spaces : from function symbols to distributions

Toeplitz operators are among the most important classes of concrete operators with applications to several branches of pure and applied mathematics. This doctoral thesis deals with Toeplitz operators on analytic Bergman, Bloch and Fock spaces. Usually, a Toeplitz operator is a composition of multiplication by a function and a suitable projection. The present work deals with generalizing the notion to the case where the function is replaced by a distributional symbol. Fredholm theory for Toeplitz operators with matrix-valued symbols is also considered. The subject of this thesis belongs to the areas of complex analysis, functional analysis and operator theory. This work contains five research articles. The articles one, three and four deal with finding suitable distributional classes in Bergman, Fock and Bloch spaces, respectively. In each case the symbol class to be considered turns out to be a certain weighted Sobolev-type space of distributions. The Bergman space setting is the most straightforward. When dealing with Fock spaces, some difficulties arise due to unboundedness of the complex plane and the properties of the Gaussian measure in the definition. In the Bloch-type spaces an additional logarithmic weight must be introduced. Sufficient conditions for boundedness and compactness are derived. The article two contains a portion showing that under additional assumptions, the condition for Bergman spaces is also necessary. The fifth article deals with Fredholm theory for Toeplitz operators having matrix-valued symbols. The essential spectra and index theorems are obtained with the help of Hardy space factorization and the Berezin transform, for instance. The article two also has a part dealing with matrix-valued symbols in a non-reflexive Bergman space, in which case a condition on the oscillation of the symbol (a logarithmic VMO-condition) must be added.