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

New Structural Topologies in a Series of 3d Metal Complexes with Isomeric Phenylenediacetates and 1,3,5-Tris(1-imidazolyl)benzene Ligand: Syntheses, Structures, and Magnetic and Luminescence Properties

In this article we present the syntheses, characterizations, magnetic and luminescence properties of five 3d-metal complexes, Co(tib)(1,2-phda)](n)center dot(H2O)(n) (1), Co-3(tib)(2)(1,3-phda)(3)(H2O)](n)center dot(H2O)(2n) (2), Co-5(tib)(3)(1,4-phda)(5)(H2O)(3)](n)center dot(H2O)(7n) (3), Zn-3(tib)(2)(1,3-phda)(3)](n)center dot(H2O)(4n) (4), and Mn(tib)(2)(H2O)(2)](n)center dot(1,4-phdaH)(2n)center dot(H2O)(4n) (5), obtained from the use of isomeric phenylenediacetates (phda) and the neutral 1,3,5-tris(1-imidazolyl)benzene (tib) ligand. Single crystal X-ray structures showed that 1 constitutes 3,5-connected 2-nodal nets with a double-layered two-dimensional (2D) structure, while 2 forms an interpenetrated 2D network (3,4-connected 3-nodal net). Complex 3 has a complicated three-dimensional structure with 10-nodal 3,4,5-connected nets. Complex 4, although it resembles 2 in stoichiometry and basic building structures, forms a very different overall 2D assembly. In complex 5 the dicarboxylic acid, upon losing only one of the acidic protons, does not take part in coordination; instead it forms a complicated hydrogen bonding network with water molecules. Magnetic susceptibility measurements over a wide range of temperatures revealed that the metal ions exchange very poorly through the tib ligand, but for the Co(II) complexes the effects of nonquenched orbital contributions are prominent. The 3d(10) metal complex 4 showed strong luminescence with lambda(max) = 415 nm (lambda(ex) = 360 nm).

Cu(In,Al)Se-2 thin films by one-step electrodeposition for photovoltaics

Chalcopyrite Cu(In,Al)Se-2 (CIAS) thin films are grown on stainless steel substrate through one-step electrodeposition at room temperature. Indium is partially replaced with aluminum to increase the band gap of CuInSe2 without creating significant change in the original structure. The deposition potential is optimized at -0.8 V (vs. SCE) and annealing of the films is performed in vacuum to remove binary phases present in the as-deposited films. In/Al ratio is varied from 1/9 to 8/2, to find the suitability for solar cell fabrication. For In/Al ratio of less than 8/2, CuAlSe2 phase is formed in the film in addition to the CIAS phase. Depth profile X-ray photoelectron spectroscopy analysis of the CIAS sample prepared with In/Al ratio of 8/2 in the precursor solution confirmed the existence of single phase CIAS throughout the film. This film showed p-type conductivity while the rest of the samples with In/Al ratio less than 8/2 showed n-type conductivity. The band gap of the film varied from 1.06 to 1.45 eV, with variation in deposition potential. Structural, optical, morphological, compositional and electrical characterizations are carried out to establish the suitability of this film for solar cell fabrication. (C) 2013 Elsevier B.V. All rights reserved.

Self propagating combustion synthesis and luminescent properties of nanocrystalline CeO2: Tb3+ (1-10 mol%) phosphors

Undoped and Tb3+ (1-10 mol%) doped CeO2 nanophosphors were synthesized by low temperature solution combustion method. The combustion derived products were well studied by Powder X-ray diffraction (PXRD), Scanning electron microscopy (SEM), transmission electron microscopy (TEM), Fourier transform infrared spectroscopy (FTIR) and Ultraviolet visible (UV-Vis) characterizations. The thermoluminescence (TL) glow curves of CeO2: Tb3+ (1-10 mol%) nanophosphors exposed to c source (60Co) for various doses were discussed for the first time. Two TL glow peaks recorded at 182 and 262 degrees C respectively. The TL intensity at 262 degrees C peak increases linearly in the dose range 0.5-7 kGy. Further, this peak was well defined, intense and glow peak structure does not change with c-dose as a result, it was quite useful in TL dosimetry of ionizing radiations. The kinetic parameters associated with the glow peak were estimated using Chen's half width method. The photoluminescence emission (PLE) spectra consists of characteristic peaks at 544 and 655 nm which were attributed to D-5(4) -> F-7(5) and D-5(4) -> F-7(2) transitions of Tb3+ ions. The optimal concentration of Tb3+ ions was found to be 7 mol%. The color co-ordinates of CeO2: Tb3+ (1-10 mol%) located in green region. Hence, this phosphor was quite useful for display applications. (C) 2013 Elsevier B. V. All rights reserved.

A Donor-Acceptor-Donor Structured Organic Conductor with S center dot center dot center dot S Chalcogen Bonding

A novel thiophene derivative 7,9-di(thiophen-2-yl)-8H-cyclopentaa]acenaphthylen-8-one (DTCPA) is shown to exhibit high electrical conductivity (1.97 x 10(-2) +/- 0.0018 S/cm at RT) in the crystalline state. The material shows two orders of increase in conductivity from normal solid to single crystalline state. The crystal structure has S center dot center dot center dot S chalcogen bonding, C-H center dot center dot center dot O hydrogen bonding, and pi center dot center dot center dot pi stacking as the major intermolecular interactions. The nature and strength of the S center dot center dot center dot S interactions in this structure have been evaluated by theoretical charge density analysis, and its contribution to the crystal packing quantified by Hirshfeld surface analysis. Further, thermal and morphological characterizations have been carried out, and the second harmonic generation (SHG) efficiency has been measured using the Kurtz-Perry method.

Investigation on the Sr-doped ceria Ce1-xSrO2-delta (x=0.05-0.2) as an electrolyte for intermediate temperature SOFC

The effect of Sr doping in CeO2 for its use as solid electrolytes for intermediate temperature solid oxide fuel cells (IT-SOFCs) has been explored here. Ce1-xSrxO2-delta (x = 0.05-0.2) are successfully synthesized by citrate-complexation method. XRD, Raman, FT-IR, FE-SEM/EDX and electrochemical impedance spectra are used for structural and electrical characterizations. The formation of well crystalline cubic fluorite structured solid solution is observed for x = 0.05 based on XRD and Raman spectra. For compositions i.e., x > 0.05, however, a secondary phase of SrCeO3 is confirmed by the peak at 342 cm(-1) in Raman spectra. Although the oxygen ion conductivity was found to decrease with increase in x, based on ac-impedance studies, conductivity of Ce0.95Sr0.05O2-delta was found to be higher than of Ce0.95Gd0.1O2-delta and Ce0.8Gd0.2O2-delta. The decrease in conductivity of Ce1-xSrxO2-delta with increasing dopant concentration is ascribed to formation of impurity phase SrCeO3 as well as the formation of neutral associated pairs, Se `' Ce V-o. The activation energies are found to be 0.77, 0.83, 0.85 and 0.90 eV for x = 0.05, 0.1, 0.15 and 0.20, respectively. (C) 2014 Elsevier B.V. All rights reserved.

Specroelectrochemical, Switching Kinetics, and Chronoamperometric Studies of Dibenzyl Derivative of Poly(3,4-propylenedioxythiophene) Thin-Film-Based Electrochromic Device

The dibenzyl derivative of poly(3,4-propylenedioxythiophene) (PProDOT-Bz(2)) thin film is deposited onto ITO-coated glass substrate by electropolymerization technique. The electropolymerization of ProDOT-Bz(2) is carried out by a three-electrode electrochemical cell. The cyclic voltammogram shows the redox properties of electrochemically prepared films deposited at different scan rates. The thin films prepared were characterized for its morphological properties to study the homogeniety. Classic six-layer structure of PProDOT-Bz(2) electrochromic device using this material was fabricated and reported for the first and its characterizations such as spectroelectrochemical, switching kinetics, and chronoamperometric studies are performed. The color contrast of the thin film and the device achieved are 64 and 40%, respectively, at lambda(max) (628 nm). The switching time is recorded and the observed values are 5 s from the coloring state to the bleaching state and vice versa. The chronoamperometry shows that the device performed up to 400 cycles, and it is capable of working up to 35 cycles without any degradation. (C) 2014 Wiley Periodicals, Inc.

Synthesis of benzimidazole-grafted graphene oxide/multi-walled carbon nanotubes composite for supercapacitance application

We are reporting the fabrication, characterizations and supercapacitance performance of benzimidazole-grafted graphene oxide/multi-walled carbon nanotubes (BI-GO/MWCNTs) composite. The synthesis of BI-GO materials involves cyclization reaction of carboxylic groups on GO among the hydroxyl and amino groups on o-phenylenediamine. The BI-GO/MWCNTs composite has been fabricated via in situ reduction of BI-GO using hydrazine in presence of MWCNTs. Scanning electron microscopy (SEM), Transmission electron microscopy (TEM), Raman spectroscopy, X-ray diffraction (XRD) and Fourier transform infrared spectroscopy (FTIR) have been used to characterize its surface and elemental composition. The uniform dispersion of MWCNTs with BI-GO helps to improve the charge transfer reaction during electrochemical process. The specific capacitance of BI-GO/MWCNTs composite is 275 and 460 F/g at 200 and 5 mV/s scan rate in 1 mol/L aqueous solution of H2SO4. This BI-GO/MWCNTs composite has shown 224 F/g capacitance after 1300 cycles at 200 mV/s scan rate, which represents its good electrochemical stability. (C) 2014 Elsevier B.V. All rights reserved.

An Algorithmic Characterization of Polynomial Functions over Z(pn)

In this paper we consider polynomial representability of functions defined over , where p is a prime and n is a positive integer. Our aim is to provide an algorithmic characterization that (i) answers the decision problem: to determine whether a given function over is polynomially representable or not, and (ii) finds the polynomial if it is polynomially representable. The previous characterizations given by Kempner (Trans. Am. Math. Soc. 22(2):240-266, 1921) and Carlitz (Acta Arith. 9(1), 67-78, 1964) are existential in nature and only lead to an exhaustive search method, i.e. algorithm with complexity exponential in size of the input. Our characterization leads to an algorithm whose running time is linear in size of input. We also extend our result to the multivariate case.

Al3+-Ion-Triggered Conformational Isomerization of a Rhodamine B Derivative Evidenced by a Fluorescence Signal - A Crystallographic Proof

A newly designed rhodamine B anisaldehyde hydrazone exhibits Al3+-ion-induced cis (L) to trans (L) conformational isomerization with respect to the xanthene moiety through a rotation about a N-N bond; the isomerization is indicated by a detectable naked-eye color change and a turn-on red fluorescence in 4-(2-hydroxyethyl)-1-piperazineethanesulfonic acid (HEPES) buffer (EtOH/Water 1:9 v/v; pH 7.4) at 25 degrees C. In support of this observation, detailed spectroscopic and physicochemical studies along with density function theory (DFT) calculations have been performed. This cis-to-trans conformational isomerization is due to Al3+ ion coordination, which induces this visual color change and the turn-on fluorescence response. To strengthen our knowledge of the conformational isomerization, detailed structural characterizations of the cis and trans isomers in the solid state were performed by single-crystal X-ray diffraction. To the best of our knowledge, this is the first structural report of both cis and trans conformational isomers for this family of compounds. Moreover, this noncytotoxic probe could be used to image the accumulation of Al3+ ions in HeLa and MCF-7 cell lines.

A Family of Domains Associated with mu-Synthesis

We introduce a family of domains-which we call the -quotients-associated with an aspect of -synthesis. We show that the natural association that the symmetrized polydisc has with the corresponding spectral unit ball is also exhibited by the -quotient and its associated unit `` -ball''. Here, is the structured singular value for the case Specifically: we show that, for such an E, the Nevanlinna-Pick interpolation problem with matricial data in a unit `` -ball'', and in general position in a precise sense, is equivalent to a Nevanlinna-Pick interpolation problem for the associated -quotient. Along the way, we present some characterizations for the -quotients.

New symmetrical dinucleating ligand based assembly of bridged dicopper(II) and dizinc(II) centers: Synthesis, structure, spectroscopy, magnetic properties and glycoside hydrolysis

Two dinuclear copper(II) complexes Li(H2O)(3)(CH3OH)](4)Cu2Br4]Cu-2(cpdp)(mu-O2CCH3)](4)(OH)(2) (1), Cu (H2O)(4)]Cu-2(cpdp)(mu-O2CC6H5)](2)Cl-2 center dot 5H(2)O (2), and a dinuclear zinc(II) complex Zn-2(cpdp)(mu-O2CCH3)] (3) have been synthesized using pyridine and benzoate functionality based new symmetrical dinucleating ligand, N, N'-Bis2-carboxybenzomethyl]-N, N'-Bis2-pyridylmethyl]-1,3-diaminopropan-2-ol (H(3)cpdp). Complexes 1, 2 and 3 have been synthesized by carrying out reaction of the ligand H3cpdp with stoichiometric amounts of Cu-2(O2CCH3)(4)(H2O)(2)], CuCl2 center dot 2H(2)O/C6H5COONa, and Zn(CH3COO)(2)center dot 2H(2)O, respectively, in methanol in the presence of NaOH at ambient temperature. Characterizations of the complexes have been done using various analytical techniques including single crystal X-ray structure determination. The X-ray crystal structure analyses reveal that the copper(II) ions in complexes 1 and 2 are in a distorted square pyramidal geometry with Cu-Cu separation of 3.455(8) angstrom and 3.492(1)angstrom, respectively. The DFT optimized structure of complex 3 indicates that two zinc(II) ions are in a distorted square pyramidal geometry with Zn-Zn separation of 3.492(8)angstrom. UV-Vis and mass spectrometric analyses of the complexes confirm their dimeric nature in solution. Furthermore, H-1 and C-13 NMR spectroscopic investigations authenticate the integrity of complex 3 in solution. Variable-temperature (2-300 K) magnetic susceptibility measurements show the presence of antiferromagnetic interactions between the copper centers, with J = -26.0 cm(-1) and -23.9 cm(-1) ((H) over cap = -2JS(1)S(2)) in complexes 1 and 2, respectively. In addition, glycosidase-like activity of the complexes has been investigated in aqueous solution at pH similar to 10.5 by UV-Vis spectrophotometric technique using p-nitrophenyl-alpha-D-glucopyranoside (4) and p-nitrophenyl-beta-D-glucopyranoside (5) as model substrates. (C) 2015 Elsevier B.V. All rights reserved.

Ancilla-assisted measurements on quantum ensembles: general protocols and applications in NMR quantum information processing

Quantum ensembles form easily accessible architectures for studying various phenomena in quantum physics, quantum information science and spectroscopy. Here we review some recent protocols for measurements in quantum ensembles by utilizing ancillary systems. We also illustrate these protocols experimentally via nuclear magnetic resonance techniques. In particular, we shall review noninvasive measurements, extracting expectation values of various operators, characterizations of quantum states and quantum processes, and finally quantum noise engineering.