On the images of Sobolev spaces under the heat kernel transform on the Heisenberg group

The aim of this paper is to obtain certain characterizations for the image of a Sobolev space on the Heisenberg group under the heat kernel transform. We give three types of characterizations for the image of a Sobolev space of positive order H-m (H-n), m is an element of N-n, under the heat kernel transform on H-n, using direct sum and direct integral of Bergmann spaces and certain unitary representations of H-n which can be realized on the Hilbert space of Hilbert-Schmidt operators on L-2 (R-n). We also show that the image of Sobolev space of negative order H-s (H-n), s(> 0) is an element of R is a direct sum of two weighted Bergman spaces. Finally, we try to obtain some pointwise estimates for the functions in the image of Schwartz class on H-n under the heat kernel transform. (C) 2013 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Linear and nonlinear optical studies on 3,6-bis (2 pyridyl) pyridazine

3,6-Bis (2 pyridyl) pyridazine has been synthesized and characterized by NMR, XRD and elemental analyses. The vibrational studies were carried out by using FTIR and Raman spectroscopy and the modes of vibrations were analysed and compared with the theoretically calculated values. The nonlinear optical property of the title compound was examined by Kurtz-Perry method and Hyper Raleigh scattering with the fundamental wavelength of 1064nm. This compound possesses less SHG efficiency but large first hyperpolarizability. (C) 2013 Elsevier GmbH. All rights reserved.

Anthracene-Containing Conjugated Polymer Showing Four Optical Transitions Upon Doping: A Spectroscopic Study

An anthracene-containing poly(arylene-ethynylene)-alt-poly(arylene-vinylene) (PAE-PAV) of general constitutional unit (PhCCAnthrCCPhCHCHAnthrCHCH)(n) bearing two 2-ethylhexyloxy solubilizing side chains on each phenylene (Ph) unit has been synthesized and characterized. The basic electrochemical characterization was done, showing the existence of two non-reversible oxidation and one reversible reduction peaks. The optical properties, the real and imaginary part of the dielectric function, were probed using spectroscopic ellipsometry (SE). The vibrational structure of the undoped/doped polymer was investigated using Fourier transformed infrared spectroscopy. A strong change in the polaronic absorption was observed during the doping, which after modeling revealed the existence of two separated transitions. The optical changes upon doping were additionally recorded using the SE technique. Similar to the results from FT-IR spectroscopy, two new in-the-gap absorptions were found. Moreover, the electrical conductivity as well as the mobility of positive carriers were measured. In the undoped state, the conductivity of the polymer was found to be below the detection limit (

Image deconvolution research: its scope and importance in live cell microscopy

Fluorescence microscopy has become an indispensable tool in cell biology research due its exceptional specificity and ability to visualize subcellular structures with high contrast. It has highest impact when applied in 4D mode, i.e. when applied to record 3D image information as a function of time, since it allows the study of dynamic cellular processes in their native environment. The main issue in 4D fluorescence microscopy is that the phototoxic effect of fluorescence excitation gets accumulated during 4D image acquisition to the extent that normal cell functions are altered. Hence to avoid the alteration of normal cell functioning, it is required to minimize the excitation dose used for individual 2D images constituting a 4D image. Consequently, the noise level becomes very high degrading the resolution. According to the current status of technology, there is a minimum required excitation dose to ensure a resolution that is adequate for biological investigations. This minimum is sufficient to damage light-sensitive cells such as yeast if 4D imaging is performed for an extended period of time, for example, imaging for a complete cell cycle. Nevertheless, our recently developed deconvolution method resolves this conflict forming an enabling technology for visualization of dynamical processes of light-sensitive cells for durations longer than ever without perturbing normal cell functioning. The main goal of this article is to emphasize that there are still possibilities for enabling newer kinds of experiment in cell biology research involving even longer 4D imaging, by only improving deconvolution methods without any new optical technologies.

Next-generation optical microscopy

A new breed of microscopy techniques is coming to the forefront of optical imaging. They enhance the attainable 3D resolution of imaging in live and ``fixed'' cells' (with minimal structural perturbation) by greater than tenfold, bringing subcellular structures in sharp focus Along with long-term imaging, deep tissue and high throughput capablities, new insights in various fields of biology are being generated. The main set of these next-generation optical microscopy techniques along with select applications is described in this article.

Optical microscopy methods for understanding learning and memory

Structural dynamics of dendritic spines is one of the key correlative measures of synaptic plasticity for encoding short-term and long-term memory. Optical studies of structural changes in brain tissue using confocal microscopy face difficulties of scattering. This results in low signal-to-noise ratio and thus limiting the imaging depth to few tens of microns. Multiphoton microscopy (MpM) overcomes this limitation by using low-energy photons to cause localized excitation and achieve high resolution in all three dimensions. Multiple low-energy photons with longer wavelengths minimize scattering and allow access to deeper brain regions at several hundred microns. In this article, we provide a basic understanding of the physical phenomena that give MpM an edge over conventional microscopy. Further, we highlight a few of the key studies in the field of learning and memory which would not have been possible without the advent of MpM.

Nanostructured CexZn1-xO thin films: Influence of Ce doping on the structural, optical and electrical properties

Thin films of CexZn1-xO thin films were deposited on glass substrates at 400 degrees C by nebulizer spray pyrolysis technique. Ce doping concentration (x) was varied from 0 to 10%, in steps of 2.5%. X-ray diffraction reveals that all the films have polycrystalline nature with hexagonal crystal structure and high preferential orientation along (002) plane. Optical parameters such as; transmittance, band gap energy, refractive index (n), extinction coefficient (k), complex dielectric constants (epsilon(r), epsilon(i)) and optical conductivity (sigma(r), sigma(i)) have been determined and discussed with respect to Ce concentration. All the films exhibit transmittance above 80% in the wavelength range from 330 to 2500 nm. Optical transmission measurements indicate the decrease of direct band gap energy from 3.26 to 3.12 eV with the increase of Ce concentration. Photoluminescence spectra show strong near band edge emission centered similar to 398 nm and green emission centered similar to 528 nm with excitation wavelength similar to 350 nm. High resolution scanning electron micrographs indicate the formation of vertical nano-rod like structures on the film surface with average diameter similar to 41 nm. Electrical properties of the Ce doped ZnO film have been studied using ac impedance spectroscopy in the frequency range from 100 Hz-1 MHz at different temperatures. (C) 2013 Elsevier B.V. All rights reserved.

Projection Error Propagation-based Regularization (PEPR) method for resistivity reconstruction in Electrical Impedance Tomography (EIT)

A novel Projection Error Propagation-based Regularization (PEPR) method is proposed to improve the image quality in Electrical Impedance Tomography (EIT). PEPR method defines the regularization parameter as a function of the projection error developed by difference between experimental measurements and calculated data. The regularization parameter in the reconstruction algorithm gets modified automatically according to the noise level in measured data and ill-posedness of the Hessian matrix. Resistivity imaging of practical phantoms in a Model Based Iterative Image Reconstruction (MoBIIR) algorithm as well as with Electrical Impedance Diffuse Optical Reconstruction Software (EIDORS) with PEPR. The effect of PEPR method is also studied with phantoms with different configurations and with different current injection methods. All the resistivity images reconstructed with PEPR method are compared with the single step regularization (STR) and Modified Levenberg Regularization (LMR) techniques. The results show that, the PEPR technique reduces the projection error and solution error in each iterations both for simulated and experimental data in both the algorithms and improves the reconstructed images with better contrast to noise ratio (CNR), percentage of contrast recovery (PCR), coefficient of contrast (COC) and diametric resistivity profile (DRP). (C) 2013 Elsevier Ltd. All rights reserved.

Effect of substituent position on optical properties of boron-dipyrromethane isomers

Three isomeric meso-SiMe3C6H4 substituted BODIPYs have been synthesized and their optical properties studied. The constitutional isomers show similar absorption properties but vastly different emissive properties as a result of their different conformational flexibility. Fluorine-19 NMR study is used to unravel the conformational state of the BODIPY isomers at a molecular level. (C) 2013 Elsevier B. V. All rights reserved.

Trends in aerosol optical depth over Indian region: Potential causes and impact indicators

The first regional synthesis of long-term (back to similar to 25 years at some stations) primary data (from direct measurement) on aerosol optical depth from the ARFINET (network of aerosol observatories established under the Aerosol Radiative Forcing over India (ARFI) project of Indian Space Research Organization over Indian subcontinent) have revealed a statistically significant increasing trend with a significant seasonal variability. Examining the current values of turbidity coefficients with those reported similar to 50 years ago reveals the phenomenal nature of the increase in aerosol loading. Seasonally, the rate of increase is consistently high during the dry months (December to March) over the entire region whereas the trends are rather inconsistent and weak during the premonsoon (April to May) and summer monsoon period (June to September). The trends in the spectral variation of aerosol optical depth (AOD) reveal the significance of anthropogenic activities on the increasing trend in AOD. Examining these with climate variables such as seasonal and regional rainfall, it is seen that the dry season depicts a decreasing trend in the total number of rainy days over the Indian region. The insignificant trend in AOD observed over the Indo-Gangetic Plain, a regional hot spot of aerosols, during the premonsoon and summer monsoon season is mainly attributed to the competing effects of dust transport and wet removal of aerosols by the monsoon rain. Contributions of different aerosol chemical species to the total dust, simulated using Goddard Chemistry Aerosol Radiation and Transport model over the ARFINET stations, showed an increasing trend for all the anthropogenic components and a decreasing trend for dust, consistent with the inference deduced from trend in Angstrom exponent.

Optical, Electrochemical, and Structural Properties of Spray Coated Dihexyl Substituted Poly (3,4 propylene dioxythiophene) Film for Optoelectronics Devices

The dihexyl substituted poly (3,4-propylenedioxythiophene) (PProDOT-Hx(2)) thin films uniformly deposited by cost effective spray coating technique on transparent conducting oxide coated substrates. The electro-optical properties of PProDOT-Hx(2) films were studied by UV-Vis spectroscopy that shows the color contrast about 45% with coloration efficiency of approximate to 185cm(2)/C. The electrochemical properties of PProDOT-Hx(2) films were studied by cyclic voltammetry and AC impedance techniques. The cyclic voltammogram shows that redox reaction of films are diffusion controlled and ions transportation will be faster on the polymer film at higher scan rate. Impedance spectra indicate that polymer films are showing interface charge transfer process as well as capacitive behavior between the electrode and electrolyte. The XRD of the PProDOT-Hx(2) thin films revealed that the films are in amorphous nature, which accelerates the transportation of ions during redox process.

Nonlinear optical second harmonic generation in ZnS quantum dots and observation on optical properties of ZnS/PMMA nanocomposites

ZnS quantum dots (QDs) of different sizes are synthesized by a simple chemical co-precipitation method at room temperature, by varying pH value of the reaction mixture. Samples are characterized by an X-ray diffractometer, transmission electron microscope, energy-dispersive X-ray analysis, etc. Linear optical properties, including UV-visible absorption and photoluminescence emission characteristics, of as-prepared QDs are measured. Size dependent nonlinear optical property, such as second harmonic generation (SHG) of 1064 nm Nd:YAG laser fundamental radiation in the synthesized ZnS QDs, is reported for the first time, to the best of our knowledge, by using the standard Kurtz-Perry powder method. In not to study the possibility of the synthesized ZnS QDs in different device applications ZnS/PMMA (polymethylmethacrylate) nanocomposites are also synthesized. The presence of weak chemical interaction between the polymer matrix and ZnS QDs is confirmed by Fourier transform infrared spectroscopy. Thermal properties of the nanocomposites are studied by differential scanning calorimetry and thermo-gravimetric analysis techniques, which show that the composites are stable up to similar to 300 degrees C temperature. (C) 2013 Elsevier B.V. All rights reserved.

Triarylborane conjugated acacH ligands and their BF2 complexes: facile synthesis and intriguing optical properties

A facile synthetic route for a new class of organoborane compounds (Mes)(2)B-arene-acacH and (Mes)(2)Barene-acacBF2 (Mes = mesityl and arene = C6H4 or C6Me4) is reported. The new dyads exhibit intriguing photophysical properties. A small structural change in spacer connecting the two chromophores leads to fine tuning of photophysical properties. The dyad containing 2,3,5,6-tetramethyl phenyl spacer acts as a selective ``turn-on'' chemodosimetric sensor for cyanide ion. Steric crowding around the boron centre significantly alters anion binding events. From NMR titration studies it is established that fluoride and cyanide follow different binding mechanisms which lead to intriguing optical properties in the reported probes.

Simulation of inhomogeneous distributions of ultracold atoms in an optical lattice via a massively parallel implementation of nonequilibrium strong-coupling perturbation theory

We present a nonequilibrium strong-coupling approach to inhomogeneous systems of ultracold atoms in optical lattices. We demonstrate its application to the Mott-insulating phase of a two-dimensional Fermi-Hubbard model in the presence of a trap potential. Since the theory is formulated self-consistently, the numerical implementation relies on a massively parallel evaluation of the self-energy and the Green's function at each lattice site, employing thousands of CPUs. While the computation of the self-energy is straightforward to parallelize, the evaluation of the Green's function requires the inversion of a large sparse 10(d) x 10(d) matrix, with d > 6. As a crucial ingredient, our solution heavily relies on the smallness of the hopping as compared to the interaction strength and yields a widely scalable realization of a rapidly converging iterative algorithm which evaluates all elements of the Green's function. Results are validated by comparing with the homogeneous case via the local-density approximation. These calculations also show that the local-density approximation is valid in nonequilibrium setups without mass transport.