On the mean square of standard L-functions attached to Ikeda lifts

By using estimates on the frequency of large values of the Riemann zeta-function and modular L-functions attached to the full modular group SL(2, ℤ), we prove sharp upper and lower estimates of the mean square of standard L-functions attached to Siegel cusp forms which are Ikeda lifts, on boundaries and the central line of the critical strip. The mean square of spinor L-functions attached to Saito-Kurokawa lifts is also studied.     

Magnetization studies in niobium and YBa2Cu3O7 samples

The results of experimental studies on hysteresis in magnetization, thermomagnetic history effects, anomalous variations in magnetic hysteresis curves and the decay rates of magnetization obtained under different thermomagnetic histories in specimens of conventional and high temperature superconductors are presented. The Bean’s critical state model is considered adequate to explain magnetic behaviour in conventional hard superconductors. The similarity in the general features of the results of different experiments on specimens of the two families of superconductors underscores the efficacy of the said model to understand some aspects of the macroscopic magnetic response of high temperature superconductors as well. For instance, the isothermal magnetization hysteresis loop which comprises of magnetization curves along forward (−H _max to +H _max) and reverse (+H _max to −H _max) paths define an envelop within which all isothermal magnetization data along different thermomagnetic histories lie. There exist inequality relationship between various field values identified asH _peak,H _I,H _II etc. in isothermal magnetization hysteresis as well as magnetic relaxation data. The entire field span of an isothermal magnetization hysteresis data set can be considered to comprise of three parts corresponding to (M _rem(H)−M _FC(H)+M _ZFC(H)) being equal to, less than or greater than zero, whereM _rem(H) are the remanent magnetization values obtained on reducing field to zero after having the specimen in different applied field (H) values. There are, however some situations amongst thermomagnetic history effects in specimens which show incomplete flux trapping on field cooling, where the critical state model has been found inadequate.     

Raman and infrared spectra of ammonium selenate and lithium ammonium selenate

The Raman and infrared absorption spectra of (NH₄)₂ SeO₄, (ND₄)₂ SeO₄ and Li (NH₄) SeO₄ have been recorded at 300° K; while the spectra of the non-deuterated compounds have been recorded at 110° K also. (NH₄)₂ Se0₄ crystal exhibits 33 Raman lines, while LiNH₄SaO₄ shows 30 Raman lines at 300° K. Proper assignments have been given to the observed vibration frequencies. The SeO₄ ^?? ions and the (NH₄)⁺ ions are found to be highly distorted in these selenates. There is lowering of the N-H vibration frequencies due to hydrogen bonding. The present spectroscopic investigations do not reveal the existence of any phase transition in these selenates in the temperature region investigated.     

On a sum involving Fourier coefficients of cusp forms

We improve the existing upper bound for the quantity |∑ _n⩽x a(n ²)|, where a(n ²) is the n ²th Hecke eigenvalue of a normalized holomorphic cusp form (Hecke eigenform) of the full modular group SL(2, ℤ), whenever the weight of the original holomorphic cusp form (Hecke eigenform) lies in a certain range. Published in Lietuvos Matematikos Rinkinys, Vol. 46, No. 4, pp. 565–583, October–December, 2006.     

Level structures of 95,97Mo — A comparative study

High-spin states of ^95,97Mo (Z=42, N=53,55) nuclei have been investigated through ⁸²Se(¹⁸O, xn) reaction at Eb=60 MeV. The level scheme in ⁹⁵Mo has been observed upto ≏ 10 MeV in the present experiment. The level structure shows mainly single particle character. In ⁹⁷Mo, the ground state level sequence has been extended to ≏ 4.5 MeV while the previous information had been up to 2.4 MeV. A negative parity band built on 1437 keV (11/2⁻) excited state has been extended to 5.5 MeV. The structure seems to show a coexistence of single particle and collective modes of excitation. Properties of both the nuclei have been compared with shell model calculations using OXBASH.     

High spin rotational bands in 65Zn

The nucleus ₃₀ ⁶⁵ Zn was studied using the ⁵²Cr(¹⁶O, 2pn)⁶⁵Zn reaction at a beam energy of 65 MeV. The level scheme is extended up to an excitation energy of 10.57 MeV for spin-parity (41/2?) with several newly observed transitions placed in it.     

Unidirectional seeded single crystal growth from solution of benzophenone

A novel crystal growth method has been established for the growth of single crystal with selective orientation at room temperature. Using volatile solvent, the saturated solution containing the material to be crystallized was taken in an ampoule and allowed to crystallize by slow solvent evaporation assisted with a ring heater. The orientation of the growing crystal was imposed by means of a seed fixed at the bottom of the ampoule. By selecting a suitable ring heater voltage and by controlling the ring heater voltage, nucleation and the growth rate of the crystal were controlled more effectively. By employing this novel method, benzophenone single crystal ingots of diameters 10 and 20 mm and length more than 50 mm were successfully grown using xylene as solvent. The ease in scaling up of diameter from 10 to 20 mm shows the vital advantage of this technique. It was possible to achieve solute–crystal conversion efficiency of 100 percent. The grown benzophenone crystal was characterized by FTIR, TG and DTA, powder X-ray diffraction, X-ray rocking curve, optical transmission study and powder SHG measurement. The results show that the crystal quality is at least as good as the quality of the crystal grown by other known methods. Also, microbial growth was naturally avoided in this method, as the fresh solution is constantly made available for the growing crystal.     

Selective formation of triplet alkyl nitrenes from photolysis of beta-azido-propiophenone and their reactivity

Photolysis of beta-azido propiophenone derivatives, 1, with built-in sensitizer units, leads to selective formation of triplet alkyl nitrenes 2 that were detected directly with laser flash photolysis (lambdamax = 325 nm, tau = 27 ms) and ESR spectroscopy (|D/hc| = 1.64 cm-1, |E/hc| = 0.004 cm-1). Nitrenes 2 were further characterized with argon matrix isolation, isotope labeling, and molecular modeling. The triplet alkyl nitrenes are persistent intermediates that do not abstract H-atoms from the solvent but do decay by dimerizing with another triplet nitrene to form azo products, rather than reacting with an azide precursor. The azo dimer tautomerizes and rearranges to form heterocyclic compound 3. Nitrene 2a, with an n,pi* configuration as the lowest triplet excited state of the its ketone sensitizer moiety, undergoes intramolecular 1,4-H-atom abstraction to form biradical 6, which was identified by argon matrix isolation, isotope labeling, and molecular modeling. beta-Azido-p-methoxy-propiophenone, with a pi,pi* lowest excited state of its triplet sensitizer moiety, does not undergo any secondary photoreactions but selectively yields only triplet alkyl nitrene intermediates that dimerize to form 3b.     

Effect of annealing on the surface and band gap alignment of CdZnS thin films

Effects of the annealing temperature on structural, optical and surface properties of chemically deposited cadmium zinc sulfide (CdZnS) films were investigated. X-ray diffraction (XRD) results showed that the grown CdZnS thin films formed were polycrystalline with hexagonal structure. Atomic force microscopy (AFM) studies showed that the surface roughness of the CdZnS thin films was about 60-400 nm. Grain sizes of the CdZnS thin films varied between 70 and 300 nm as a function of annealing temperature. The root mean square surface roughness of the selected area, particular point, average roughness profile, topographical area of roughness were measured using the reported AFM software. The band gaps of CdZnS thin films were determined from absorbance measurements in the visible range as 300 nm and 1100 nm, respectively, using Tauc theory.     

Triplet-sensitized photoreactivity of a geminal diazidoalkane

Photolysis of 1 in chloroform yielded 2 as the major product and a small quantity of 3. Laser flash photolysis demonstrated that upon irradiation, the first excited triplet state of the ketone (T(1K)) of 1 is formed and decayed to form radical 4, which has a λ(max) at 380 nm (τ = 2 μs). Radical 4 expelled a nitrogen molecule to yield imine radical 5 (λ(max) at 300 nm). Density functional theory (DFT) calculations showed that the transition state barrier for the formation of 5 is approximately 4 kcal/mol. In comparison, photolysis of 1 in argon matrices resulted in triplet nitrene 6, which was further characterized with (15)N and D isotope labeling and DFT calculations. Prolonged irradiation of 6 yields triplet imine nitrene 7.