The circle method and bounds for L-functions - I

Let $f$ be a Hecke-Maass or holomorphic primitive cusp form of arbitrary level and nebentypus, and let $\chi $ be a primitive character of conductor $M$ . For the twisted $L$ -function $L(s, f\otimes \chi )$ we establish the hybrid subconvex bound $$\begin{aligned} L\left( \frac{1}{2}+it, f\otimes \chi \right) \ll (M(3+|t|))^{\frac{1}{2}-\frac{1}{18}+\varepsilon }, \end{aligned}$$ for $t\in \mathbb{R }$ . The implied constant depends only on the form $f$ and $\varepsilon $ .     

Identification of a new co-crystal of salicylic acid and benzamide of pharmaceutical relevance

Raman spectroscopy, X-ray powder diffraction/X-ray crystallography and differential scanning calorimetry have been used to study the phenomenon of co-crystal formation in stoichiometric mixtures of salicylic acid with benzamide. Raman spectroscopy was particularly useful for the characterization of the products and was used to determine the nature of the interactions in the co-crystals. It was observed that little change in the vibrational modes associated with the phenyl groups of the respective reactants took place upon co-crystal formation, but changes in intensities of the vibrational modes associated with the amide and the carboxylic acid groups were observed upon co-crystal formation. Several new vibrational bands were identified in the co-crystal which were not manifested in the physical mixture of both components and could be used as diagnostic features of co-crystal formation.     

Working group report: Heavy-ion physics and quark-gluon plasma

This is the report of Heavy Ion Physics and Quark-Gluon Plasma at WHEPP-09 which was part of Working Group-4. Discussion and work on some aspects of quark-gluon plasma believed to have created in heavy-ion collisions and in early Universe are reported.     

Effect of colour singletness of quark-gluon plasma in quark-hadron phase transition

Consequences of the constraint of SU(3) colour singletness of quark-gluon plasma are studied. This restriction increases the free energy barrier for the formation of hadronic bubble in supercooled phase and influences significantly the dynamics of the initial stage of quark-hadron phase transition. It also introduces terms dependent on the volume occupied by the plasma in the energy density and the pressure. These modifactions vanish in the limit of an infinite volume. The last stage of the hadronization of the QGP likely to be formed in relativistic heavy ion collisions is necessarily characterized by a decreasing volume containing the quark matter, and thus these corrections become important. The nucleation of plasma droplets at AGS energies is also seen to be strongly affected by the requirement of colour singletness, and the choice of prefactor. Received: 4 December 1997 / Published online: 15 May 1998     

Inequalities for divisor functions

We give certain optimal inequalities for the divisor function. Such inequalities are useful in estimating the sums of divisor functions which are required in many standard arguments in analytic number theory.     

Exploring the potential of fluoro-flavonoid derivatives as anti-lung cancer agents: DFT,molecular docking,and molecular dynamics techniques

The present investigation utilized in silico methodologies to explore the diverse pharmacological activities, toxicity profiles, and chemical reactivity of a series of fluoro-flavonoid compounds ( 1 – 14 ), which are secondary metabolites of plants known for their broad range of biological effects. A comprehensive strategy is utilized, incorporating methods such as prediction of activity spectra for substances (PASS) prediction, absorption, distribution, metabolism, excretion, and toxicity (ADMET) assessments, and density functional theory (B3LYP) calculations using three basis sets: 6-31G(d,p), 6-311G(d,p), and 6-311++G(d,p). Furthermore, the study employed molecular docking technique to identify target proteins, including HER2 (7JXH), EGFR (4UV7), FPPS (1YQ7), HPGDS (1V40), DCK (1P60), and KEAP1 on Nrf2 (1X2J), for the investigated compounds, with cianidanol and genistein serving as reference drugs for the docking process. The investigated fluoro-flavonoid compounds exhibited significantly greater binding affinities (ranging from −8.3 to −10.6 kcal mol⁻¹) toward HER2, HPGDS, and KEAP1 compared to the reference drugs, cianidanol and genistein, which displayed binding affinities ranging from −8.4 to −9.4 kcal mol⁻¹. Furthermore, molecular dynamics simulations were conducted to assess the stability of the protein-ligand interaction, using the root-mean-square deviation (RMSD), root-mean-square fluctuation (RMSF), Radius of gyration (Rg) parameters and principle component analysis (PCA). Among the tested fluoro-flavonoid analogs, analog 11 showed a RMSD value of .15 nm with the HER2 protein target, indicating a stable interaction. Based on in silico results, it appears that the fluoro-flavonoid compound 11 has the potential to serve as a targeted anti-lung cancer drug. However, additional in vivo and in vitro studies are necessary to confirm this hypothesis.     

In situ formation of ruthenium catalysts for the homogeneous hydrogenation of carbon dioxide

A total of 44 different phosphines were tested, in combination with [RuCl(2)(C(6)H(6))](2) and three other Ru(II) precursors, for their ability to form active catalysts for the hydrogenation of CO(2) to formic acid. Half (22) of the ligands formed catalysts of significant activity, and only 6 resulted in very high rates of production of formic acid. These were PMe(3), PPhMe(2), dppm, dppe, and cis- and trans-Ph(2)PCH=CHPPh(2). The in situ catalysts prepared from [RuCl(2)(C(6)H(6))](2) and any of these 6 phosphine ligands were found to be at least as efficient as the isolated catalyst RuCl(O(2)CMe)(PMe(3))(4). There was no correlation between the basicity of monophosphines (PR(3)) and the activity of the catalysts formed from them. However, weakly basic diphosphines formed highly active catalysts only if their bite angles were small, while more strongly basic diphosphines had the opposite trend. In situ (31)P NMR spectroscopy showed that trans-Ru(H)(2)(dppm)(2), trans-RuCl(2)(dppm)(2), trans-RuHCl(dppm)(2), cis-Ru(H)(O(2)CH)(dppm)(2), and cis-Ru(O(2)CH)(2)(dppm)(2) are produced as the major metal-containing species in reactions of dppm with [RuCl(2)(C(6)H(6))](2) under catalytic conditions at 50 degrees C.     

Void-fraction reconstruction with stochastic data

The technique of computerized tomography has been used earlier to measure point density (or void-fraction) distribution in air-water flows. The interrogation source used in the measurement system was a gamma ray source, Cs-137. The inherent nature of such sources is the Poisson nature of the emmitted radiation. This Poisson corruption leads to imperfections in the projection data, i.e., the data no longer represents the line integral of the desired property being measured. The present study was conducted to assess the sensitivity of the tomographic reconstruction process to the statistical (Poisson) uncertainity in the projection data. Reconstruction experiments performed on six different sets of data indicate that influence of Poisson errors on reconstruction profiles is much more pronounced near the centre of the pipe in all the cases indicating the need for stronger gamma ray sources than the 13.6 milli-Curie used in the earlier investigations.On leave from: Indian Institute of Technology, Kanpur 208016, India     

Influence of non-proportional loading on ratcheting responses and simulations by two recent cyclic plasticity models

Aubin and her coworkers conducted a unique set of experiments demonstrating the influence of loading non-proportionality on ratcheting responses of duplex stainless steel. In order to further explore their new observation, a set of experiments was conducted on stainless steel (SS) 304L under various biaxial stress-controlled non-proportional histories. This new set of data reiterated Aubin and her coworkers’ observation and illustrated many new responses critical to model development and validation. Two recent and different classes of cyclic plasticity models, the modified Chaboche model proposed by Bari and Hassan and the version of the multi-mechanism model proposed by Taleb and Cailletaud, are evaluated in terms of their simulations of the SS304L non-proportional ratcheting responses. A modeling scheme for non-proportional ratcheting responses using the kinematic hardening rule parameters in addition to the conventionally used isotropic hardening rule parameter (yield surface size change) in the modified Chaboche model is evaluated. Strengths and weaknesses of the models in simulating the non-proportional ratcheting responses are identified. Further improvements of these models needed for improving the non-proportional ratcheting simulations are suggested in the paper.     

Detection of cancer affected cell using Sagnac interferometer based photonic crystal fiber refractive index sensor

Optical and Quantum Electronics - A complex studies of optoelectronics, non-linear optical and laser stimulated piezoelectric features of chalcogenide powder-like chalcogenide crystals pure and...