Resonances, scattering theory, and rigged Hilbert spaces

The problem of decaying states and resonances is examined within the framework of scattering theory in a rigged Hilbert space formalism. The stationary free,''in,'' and ''out'' eigenvectors of formal scattering theory, which have a rigorous setting in rigged Hilbert space, are considered to be analytic functions of the energy eigenvalue. The value of these analytic functions at any point of regularity, real or complex, is an eigenvector with eigenvalue equal to the position of the point. The poles of the eigenvector families give origin to other eigenvectors of the Hamiltonian: the singularities of the ''out'' eigenvector family are the same as those of the continued S matrix, so that resonances are seen as eigenvectors of the Hamiltonian with eigenvalue equal to their location in the complex energy plane. Cauchy theorem then provides for expansions in terms of ''complete'' sets of eigenvectors with complex eigenvalues of the Hamiltonian. Applying such expansions to the survival amplitude of a decaying state, one finds that resonances give discrete contributions with purely exponential time behavior; the background is of course present, but explicitly separated. The resolvent of the Hamiltonian, restricted to the nuclear space appearing in the rigged Hilbert space, can be continued across the absolutely continuous spectrum; the singularities of the continuation are the same as those of the ''out'' eigenvectors. The free, ''in'' and ''out'' eigenvectors with complex eigenvalues and those corresponding to resonances can be approximated by physical vectors in the Hilbert space, as plane waves can. The need for having some further physical information in addition to the specification of the total Hamiltonian is apparent in the proposed framework. The formalism is applied to the Lee–Friedrichs model and to the scattering of a spinless particle by a local central potential. Journal of Mathematical Physics is copyrighted by The American Institute of Physics.

Axisymmetric free vibration of thick annular plates

Free vibrationo f annularp latesh asb eens tudiedu singt he methodo f initial functionsN. umericalr esultso f the naturalf requencieasr e obtainedfo r two typicals upportc onditionsT. he presenrt esultsd epartf rom the classicapll atet heoryf or higherm odesa s wella sf or thickerp latesb, ut is in gooda greemenwt ith Mindlin's improve,pdl ateth eory.

Grain boundary sliding during diffusion and dislocation creep in a Mg-0.7 pct Al alloy

Early studies on grain boundary sliding (GBS) in Mg alloys have suggested frequently that the contribution of GBS to creep is high even under conditions corresponding to dislocation creep. The role of creep strain and grain size in influencing the experimental measurements has not been clearly identified. Grain boundary sliding measurements were conducted in detail over experimental conditions corresponding to diffusion creep as well as dislocation creep in a single-phase Mg-0.7 wt pet Al alloy. The results indicated clearly that the GBS contribution to creep was Very high during,, diffusion creep at low stresses (similar to 75 pct) and substantially reduced during dislocation creep at high stresses (similar to 15 pct). These measurements were consistent with the observation of significant intragranular slip band activity observed in most grains at high stresses and very little slip band activity at low stresses. The experimental measurements and analysis indicated also that the GBS contribution to creep was high during the initial stages of creep and decreased to a steady-state value at large strains.

Studies in terpenoids-XIII. Magnetic anisotropy2 in and stereochemistry of some gem-dimethylcyclobutanoids related to pinonic acid

The chemical shifts of “axial” vs “equatorial” Me protons of some gem-dimethylcyclobutanoids derived from α-pinene, arising from magnetic anisotropy of the ring and as influenced by vicinal substituents, are discussed. Conformational aspects of some cis- and trans-pinonic, pinononic and pinic acids have been elucidated on the basis of NMR evidence.

Signal characterization using fractal dimension

Fractal Dimensions (FD) are one of the popular measures used for characterizing signals. They have been used as complexity measures of signals in various fields including speech and biomedical applications. However, proper interpretation of such analyses has not been thoroughly addressed. In this paper, we study the effect of various signal properties on FD and interpret results in terms of classical signal processing concepts such as amplitude, frequency, number of harmonics, noise power and signal bandwidth. We have used Higuchi's method for estimating FDs. This study may help in gaining a better understanding of the FD complexity measure itself, and for interpreting changing structural complexity of signals in terms of FD. Our results indicate that FD is a useful measure in quantifying structural changes in signal properties.

Structural, dielectric and ferroelectric properties of multilayer lithium tantalate thin films prepared by sol-gel technique

Multilayer lithium tantalate thin films were deposited on Pt-Si Si(111)/SiO2/TiO2/Pt(111)]substrates by sol-gel process. The films were annealed at different annealing temperatures (300, 450 and 650 degrees C) for 15 min. The films are polycrystalline at 650 degrees C and at other annealing conditions below 650 degrees C the films are in amorphous state. The films were characterized using X-ray diffraction, atomic force microscopy (AFM) and Raman spectroscopy. The AFM of images show the formation of nanograins of uniform size (50 nm) at 650 degrees C. These polycrystalline films exhibit spontaneous polarization of 1.5 mu C/cm(2) at an application of 100 kV/cm. The dielectric constant of multilayer film is very small (6.4 at 10 kHz) as compared to that of single crystal. (C) 2010 Elsevier B.V. All rights reserved.

New triquinane-based host molecules : binding with diamines

Synthesis of several shape-specific hosts through heteroaromatic annulation on cis,syn,cis-triquinanedione 1 and X-ray crystal structure determination of one of them, 4a, is reported. Preliminary results of complexation between cleft 5a and diamines are reported.

A total synthesis of 11-O-methyldebenzoyltashironin

A concise total synthesis of 11-O-methyldebenzoyltashironin is reported in which oxidative dearomatization-IMDA-RCM triad constitutes the key ring forming steps, while an unorthodox DIBAL-H mediated stereo- and regioselective reductive epoxide openings and implementation of the vinyl bromide-carbonyl equivalency concept were pivotal to the success of this endeavor. (C) 2011 Elsevier Ltd. All rights reserved.

Polyethylene stibinite phosphate esters: Novel flame-retardant plasticizers for PVC

A new series of multielement flame-retardant plasticizers containing polyethylene stibinite phosphate esters have been prepared by bulk polymerization from ethylene glycol with various antimony (III) aryloxydichlorides and arylphosphorodichloridates possessing various combinations of substituent [Cl,Br,NO2]. All the polymers are pink-coloured viscous fluids. They were characterized by inherent viscosity, density, IR, H-1, C-13 and P-31 NMR spectroscopy. The thermal behaviour of the polymers was compared by thermogravimetric analysis and correlated with their structures. The flammability studies were carried out by the limiting oxygen index test. The polymers containing P, Sb, N and Pr elements in their backbone show superior thermal-and flame-retardant characteristics than the other polymers. A comparative study was carried out with one of the synthesized polymers as a polymeric flame-retardant additive to plasticized PVC. The results showed improved LOI and mechanical properties to that of the conventional flame-retardant additive composition. (C) 1997 Elsevier Science Ltd.

Self-Assembly and Catalytic Activity of Metal Nanoparticles Immobilized in Polymer Membrane Prepared via Layer-by-Layer Approach

Densely packed nanoparticles distributed in a stable and robust thin film is a highly preferred system for utilizing the various applications of nanoparticles. Here, we report covalent bond mediated layer-by-layer (LbL) self-assembled thin films of nanoparticles embedded in polymer membrane. Polymer with complementary functional group is utilized for fabrication of thin film via covalent bonding. UV-visible spectroscopy, atomic force microscopy (AFM) and scanning electron microscopy (SEM) were used to monitor the growth of LbL thin film. Subsequently, the composite thin film is used for catalysis of an organic electron transfer reaction of p-nitrophenol to p-aminophenol by sodium borohydride. The catalytic activity of these composite films is assayed multiple times, proving its applicability as a catalyst. The kinetic data obtained by monitoring reduction of p-nitrophenol suggest that the reaction rates are directly related to the sizes of the nanoparticle and porosity of the membrane.

Power Controlled Reverse Channel Training Achieves an Infinite Diversity Order in a TDD-SIMO System with Perfect CSIR

In this letter, we analyze the Diversity Multiplexinggain Tradeoff (DMT) performance of a training-based reciprocal Single Input Multiple Output (SIMO) system. Assuming Channel State Information (CSI) is available at the Receiver (CSIR), we propose a channel-dependent power-controlled Reverse Channel Training (RCT) scheme that enables the transmitter to directly estimate the power control parameter to be used for the forwardlink data transmission. We show that, with an RCT power of (P) over bar (gamma), gamma > 0 and a forward data transmission power of (P) over bar, our proposed scheme achieves an infinite diversity order for 0 <= g(m) < L-c-L-B,L-tau/L-c min(gamma, 1) and r > 2, where g(m) is the multiplexing gain, L-c is the channel coherence time, L-B,L-tau is the RCT duration and r is the number of receive antennas. We also derive an upper bound on the outage probability and show that it goes to zero asymptotically as exp(-(P) over bar (E)), where E (sic) (gamma - g(m)L(c)/L-c-L-B,L-tau), at high (P) over bar. Thus, the proposed scheme achieves a significantly better DMT performance compared to the finite diversity order achieved by channel-agnostic, fixed-power RCT schemes.

Evolution of microstructure and texture during deformation and recrystallization of heavily rolled Cu-Cu multilayer

A Cu-Cu multilayer processed by accumulative roll bonding was deformed to large strains and further annealed. The texture of the deformed Cu-Cu multilayer differs from the conventional fcc rolling textures in terms of higher fractions of Bs and RD-rotated cube components, compared with the volume fraction of Cu component. The elongated grain shape significantly affects the deformation characteristics. Characteristic microstructural features of both continuous dynamic recrystallization and discontinuous dynamic recrystallization were observed in the microtexture measurements. X-ray texture measurements of annealing of heavily deformed multilayer demonstrate constrained recrystallization and resulted in a bimodal grain size distribution in the annealed material at higher strains. The presence of cube- and BR-oriented grains in the deformed material confirms the oriented nucleation as the major influence on texture change during recrystallization. Persistence of cube component throughout the deformation is attributed to dynamic recrystallization. Evolution of RD-rotated cube is attributed to the deformation of cube components that evolve from dynamic recrystallization. The relaxation of strain components leads to Bs at larger strains. Further, the Bs component is found to recover rather than recrystallize during deformation. The presence of predominantly Cu and Bs orientations surrounding the interface layer suggests constrained annealing behavior.

Seismic hazard analysis of Lucknow considering local and active seismic gaps

The Himalayas are one of very active seismic regions in the world where devastating earthquakes of 1803 Bihar-Nepal, 1897 Shillong, 1905 Kangra, 1934 Bihar-Nepal, 1950 Assam and 2011 Sikkim were reported. Several researchers highlighted central seismic gap based on the stress accumulation in central part of Himalaya and the non-occurrence of earthquake between 1905 Kangra and 1934 Bihar-Nepal. The region has potential of producing great seismic event in the near future. As a result of this seismic gap, all regions which fall adjacent to the active Himalayan region are under high possible seismic hazard due to future earthquakes in the Himalayan region. In this study, the study area of the Lucknow urban centre which lies within 350 km from the central seismic gap has been considered for detailed assessment of seismic hazard. The city of Lucknow also lies close to Lucknow-Faizabad fault having a seismic gap of 350 years. Considering the possible seismic gap in the Himalayan region and also the seismic gap in Lucknow-Faizabad fault, the seismic hazard of Lucknow has been studied based on deterministic and the probabilistic seismic hazard analysis. Results obtained show that the northern and western parts of Lucknow are found to have a peak ground acceleration of 0.11-0.13 g, which is 1.6- to 2.0-fold higher than the seismic hazard compared to the other parts of Lucknow.

Thermodynamics of NdRhO3 and phase relations in the system Nd-Rh-O

Phase equilibrium experiments indicate that NdRhO3 is the only ternary oxide in the system Nd-Rh-O at 1273 K; it has orthorhombically-distorted perovskite structure. By employing a solid-state electrochemical cell incorporating calcia-stabilized zirconia as the electrolyte, thermodynamic properties of NdRhO3 are determined. The standard Gibbs energy of formation of NdRhO3 from its component binary oxides in the temperature ranges from 900 to 1300 K can be expressed as: 1/2Rh(2)O(3) (ortho)+1/2Nd(2)O(3)(hex)=NdRhO3(ortho), Delta(f(o,x))G(0)/J mol(-1)( +/- 197) = - 66256+5.64 (T/K). The decomposition temperature of NdRhO3 computed from extrapolated thermodynamic data is 1803 (+/- 4) K in pure oxygen and 1692 (+/- 4) K in air at standard pressure. Oxygen partial pressure-composition diagram and three-dimensional chemical potential diagram at 1273 K are developed from thermodynamic data obtained in this study and auxiliary information from the literature. Equilibrium temperature-composition phase diagrams at constant oxygen partial pressures are also constructed. (C) 2013 Elsevier Ltd. All rights reserved.