The sampling theorem and coherent state systems

The Poisson Summation Formula and the sampling theorem for band limited signals, well known in the context of Fourier transformation theory, are analyzed from the perspective of the Zak basis and coherent state systems associated with the Heisenberg-Weyl group. In particular, we rephrase the content of the sampling theorem in terms coherent states and show that this in turn permits extensions, which allow us to make specific statements concerning standard and generalized coherent state systems on von Neumann or finer lattices. The text was submitted by the author in English.     

Shape evolution in odd-A 137 Pm

The odd mass nucleus ¹³⁷Pm has been studied to high spins through the ¹⁰⁹Ag(³²S, 2p2n)¹³⁷Pm reaction at an incident beam energy of 150 MeV. The de-exciting ??-rays were detected using an array of 18 Compton suppressed clover detectors. The level scheme of ¹³⁷Pm has been extended up to $J^\pi = \tfrac{{43}} {2}^ -$ and excitation energy of E _x ? 6 MeV with the observation of 42 new gamma transitions. The linear polarization (IPDCO) measurements for the ??-ray transitions have been done for the first time. The spin and parity assignments for most of the reported levels have been made using these results and the coincidence angular anisotropy (R_DCO) measurements. The nuclear shape evolution is discussed in the light of Total Routhian Surface (TRS) and Cranked Shell Model (CSM) calculations.     

Synthesis and Properties of Mixed Ligand Complexes of Diorganotin(IV): Part(VII) – Synthesis and Characterisation of Some Antibacterial Dibenzoylmethane Diorganotin(IV)‐O‐alkyl Trithiophosphates

A series of some new mixed ligand complexes have been synthesized with an objective for evaluation as antimicrobials. Reactions of diorganotin(IV) dichloride with dibenzoyl methane and O‐alkyl trithiophosphates in a 1:1:1 molar ratio in refluxing benzene yield products of the type [PhCOCHCOPh]R₂Sn‐[SSH(S)POR'] [where R = Me, Bu, Ph; R' = Me, Et, Prⁱ, Buⁱ, Ph]. The newly synthesized complexes are light yellow colored crystalline solids, non‐volatile, soluble in common organic solvents, monomeric in nature and highly sensitive towards atmospheric moisture. These complexes are characterized by elemental analysis, IR and multinuclear NMR (¹H, ³¹P and ¹¹⁹Sn) spectral studies. Spectral studies of these complexes indicate that dibenzoyl methane and O‐alkyl trithiophosphate moieties are bidentate and the central tin atom is hexacoordinated in nature. A few of these compounds were tested for their antibacterial activity using standard drugs.     

Privacy and pricing personal information

The issues we address here are – How should a firm (e.g. Internet service provider (ISP)) that is capable of collecting personal information (browsing information, purchase history, etc.) about consumers, price its service, given that consumers vary in their valuation for privacy, and also vary in terms of the value of their personal information to a third party (firms that need consumer information)? Should the firm have a blanket policy of never collecting, or a policy of always collecting and revealing information? Surprisingly we find that in some cases the collector of information may be no worse off in the asymmetric information case than in the full information case. The paper provides a justification for the strategy of some firms such as ISP’s which never collect information and also for the strategy of other firms, like grocery stores that do. We also find that it is non-optimal for the firm to design contracts where the consumer can choose an intermediate level of privacy.     

Triton-B catalyzed, efficient one-pot synthesis of dithiocarbazates

A quick and efficient, one-pot synthesis of dithiocarbazates was accomplished in high yields by the reaction of various primary, secondary, and tert. alkyl halides with a variety of substituted hydrazines using the benzyl-trimethylammonium hydroxide (Triton-B)/CS₂ system. The reaction conditions are mild with simpler work-up procedures than the reported methods.     

Nanofibrous polyaniline thin film prepared by plasma‐induced polymerization technique for detection of NO2 gas

A nanofibrous polyaniline (PANI) thin film was fabricated using plasma‐induced polymerization method and explored its application in the fabrication of NO₂ gas sensor. The effects of substrate position, pressure, and the number of plasma pulses on the PANI film growth rate were monitored and an optimum condition for the PANI thin film preparation was established. The resulting PANI film was characterized with UV–visible spectrophotometer, FTIR, scanning electron microscopy (SEM), and transmission electron microscopy (TEM). The PANI thin film possessed nanofibers with a diameter ranging from 15 to 20 nm. The NO₂ gas sensing behavior was studied by measuring the change in electrical conductivity of PANI film with respect to NO₂ gas concentration and exposure time. The optimized sensor exhibited a sensitivity factor of 206 with a response time of 23 sec. The NO₂ gas sensor using nanofibrous PANI thin film as sensing probe showed a linear current response to the NO₂ gas concentration in the range of 10–100 ppm. Copyright © 2009 John Wiley & Sons, Ltd.     

Nonlinear Dynamics of the 3D Pendulum

A 3D pendulum consists of a rigid body, supported at a fixed pivot, with three rotational degrees of freedom. The pendulum is acted on by a gravitational force. 3D pendulum dynamics have been much studied in integrable cases that arise when certain physical symmetry assumptions are made. This paper treats the non-integrable case of the 3D pendulum dynamics when the rigid body is asymmetric and the center of mass is distinct from the pivot location. 3D pendulum full and reduced models are introduced and used to study important features of the nonlinear dynamics: conserved quantities, equilibria, relative equilibria, invariant manifolds, local dynamics, and presence of chaotic motions. The paper provides a unified treatment of the 3D pendulum dynamics that includes prior results and new results expressed in the framework of geometric mechanics. These results demonstrate the rich and complex dynamics of the 3D pendulum.     

Studies of synthesis, structural features of Cu(I) thiophene-2-thiocarboxylates and unprecedented desulfurization of Cu(II) thiocarboxylate complexes

Thiophene-2-thiocarboxylate complexes of Cu(I), [(Ph(3)P)(2)Cu(SCOth)] (1) and H[(Ph(3)P)(2)Cu(SCOth)(2)] (2) (where th = thiophene) were synthesized and characterized structurally by X-ray crystallography. Electronic absorption and emission spectral properties of the two compounds have been studied. Cu(II) complexes, [(TMEDA)Cu(SCOth)(2)] (3b) and [(Phen)Cu(SCOth)(2)] (4a) (where TMEDA = tetramethylethylenediamine; Phen = 1,10-phenanthroline) were prepared and characterized by spectroscopic measurements. 3b and 4a underwent desulfurization under ambient conditions readily yielding the corresponding carboxylate complexes [(TMEDA)Cu(O(2)Cth)(2)] (3a) and [(Phen)Cu(O(2)Cth)(2)·H(2)O] (4b). 3a and 4b have been characterized crystallographically.     

Electrocatalytic Hydrogen Evolution Using A Molecular Antimony Complex under Aqueous Conditions: An Experimental and Computational Study on Main-Group Element Catalysis

Electrocatalytic hydrogen gas production is considered a potential pathway towards carbon-neutral energy sources. However, the development of this technology is hindered by the lack of efficient, cost-effective, and environmentally benign catalysts. In this study, a main-group-element-based electrocatalyst, SbSalen , is reported to catalyze the hydrogen evolution reaction (HER) in an aqueous medium. The heterogenized molecular system achieved a Faradaic efficiency of 100 % at −1.4 V vs. NHE with a maximum current density of −30.7 mA/cm². X-ray photoelectron spectroscopy of the catalyst-bound working electrode before and after electrolysis confirmed the molecular stability during catalysis. The turnover frequency was calculated as 43.4 s⁻¹ using redox-peak integration. The kinetic and mechanistic aspects of the electrocatalytic reaction were further examined by computational methods. This study provides mechanistic insights into main-group-element electrocatalysts for heterogeneous small-molecule conversion.     

On sequential procedures for the point estimation of the mean of a normal population

The sequential procedures developed by Starr (1966, Ann. Math. Statist., 37, 1173–1185) for estimating the mean of a normal population are further analyzed. Asymptotic properties of the regret and first two moments of the stopping rules are studied and second-order approximations are derived.