Non-compact generalized variational inequalities for quasi-monotone and hemi-continuous operators with applications

Some results are obtained for non-compact cases in topological vector spaces for the existence problem of solutions for some set-valued variational inequalities with quasi-monotone and lower hemi-continuous operators, and with quasi-semi-monotone and upper hemi-continuous operators. Some applications are given in non-reflexive Banach spaces for these existence problems of solutions and for perturbation problems for these set-valued variational inequalities with quasi-monotone and quasi-semi-monotone operators. This revised version was published online in June 2006 with corrections to the Cover Date.     

Studies on recoil proton tracks in NTA films with the T(d,n)He reaction

Recoil proton tracks in nuclear emulsion are counted by scanning them using strip, square or circular field of view of optical microscope. In this paper, the overestimate due to the edge effects in counting recoil proton tracks at different neutron energies produced from the T(d,n)⁴He reaction has been determined by measuring the true track density in NTA film. The overestimate has also been calculated using the measured value of the mean projected track length (L) in the film. The percentage of measured overestimates has been compared with those obtained by calculation and the results agree reasonably well. Fading effect in NTA film has been studied and found to be 22% more in the summer than in the winter season. A great reduction in fading rate could be achieved if the films are desiccated and sealed in highly pure dry nitrogen maintained at an over-pressure of 1000 Pa to reduce water vapour ingress. After the edge effect correction, the sensitivity of NTA film has been calculated from (1.72±0.08)×10⁻³ tracksn⁻¹ to (1.97±0.16)×10⁻³ tracksn⁻¹ in the neutron energy ranges from 15.91 to 18.88 MeV. The response was found to be from 0.24±0.02 trackscm⁻² permSv to 0.26±0.01 trackscm⁻² permSv in the same energy range.     

Second Dissociation Constant of Bis-[(2-hydroxyethyl)amino]acetic Acid (BICINE) and pH of Its Buffer Solutions from 5 to 55 °C

The values of the second dissociation constant, K ₂, and related thermodynamic quantities of the ampholyte bis[(2-hydroxyethyl)amino]acetic acid (BICINE) have been determined at temperatures from 5 to 55 ^∘C. The pH values of six equimolal buffer solutions, and four buffer solutions having ionic strengths (I = 0.16 mol⋅kg⁻¹) similar to those in blood plasma, have been evaluated at 12 temperatures from 5 to 55 ^∘C using the Bates–Guggenheim convention. The liquid junction potentials (E _j ) between the buffer solutions of BICINE and saturated KCl solution of the calomel electrode at 25 and 37 ^∘C have been estimated by measurement with a flowing junction cell. These values of E _j have been used to ascertain the operational pH values at 25 and 37 ^∘C. The pK ₂ values at 25 and 37 ^∘C are 8.333 and 8.156, respectively. The thermodynamic quantities associated with the second acid dissociation have been calculated from the values of pK ₂ as a function of temperature. The zwitterionic buffer BICINE was shown to be useful as a pH standard in the region close to that of blood serum.     

Higgs and SUSY searches at LHC

I start with a brief introduction to Higgs mechanism and supersymmetry. Then I discuss the theoretical expectations, current limits and search strategies for Higgs boson(s) at LHC — first in the SM and then in the MSSM. Finally I discuss the signatures and search strategies for the superparticles.     

Breathers in ferrimagnetic systems

Breathers in discrete nonlinear ferrimagnetic spin lattices are investigated for both easy-axis and easy-plane configurations. The region in frequency space of the formation of breathers is determined and the anticontinuum limit discussed. The monochromatic and the coloured breathers are found out numerically for different parameters and different conditions of excitations.     

Isospin symmetry violation, meson production and η-nucleus interaction studies

We have studied isospin symmetry violation in nuclear reactions by measuring simultaneously the cross-section of the following two reactionsp +d →³H π⁺ andp +d →³He π⁰. The experiment was perfomed at the cooler synchrotron accelerator COSY, Jülich at several beam energies close to the correspondingη production threshold. We also have ongoing programmes onη-nucleus final-state interaction studies viap+⁶ Li →⁷ Be +η reactions, high resolution search for dibaryonic resonances and lambda-proton final state interaction studies. The experimental details and results obtained so far are presented here     

A comparison of spin relaxation and local motion between symmetrically and asymmetrically ring-substituted bisphenol units in dissolved polycarbonates

Carbon-13 and proton spin-lattice relaxation times were measured at two field strengths on solutions 10% by weight of two polycarbonates in C₂D₂Cl₄ from ?20 to +120°C. The first polycarbonate is an asymmetrically substituted form with one chlorine on one of the two phenylene aromatic rings of the bisphenol unit, whereas the second polycarbonate is symmetrically substituted with two chlorines on each of the two rings. The nuclear spin relaxation data are interpreted in terms of several local motions likely in these polymers. Segmental motion was described by the Hall–Helfand correlation function. Segmental motion in the monosubstituted polycarbonate is somewhat slower than in unsubstituted polycarbonate, whereas segmental motion in the tetrasubstituted polycarbonate is considerably slower. Phenylene ring rotation is observed in unsubstituted polycarbonate and in the monosubstituted polycarbonate above 40°C. Below 40°C in the monosubstituted species, and at all temperatures in the tetrasubstituted species, ring rotation is replaced by ring libration as the predominant motion contributing to spin lattice relaxation. In addition, the rotational motion of the two types of rings in the asymmetric monosubstituted form are very similar although not identical. The substituted ring is slightly less mobile than the rings of unsubstituted polycarbonate. This indicates a strong coupling of ring motion, although the coupling leads to less than synchronous motion. Methyl group rotation is present in both polymers and is little affected by the various structural modifications.     

Fluctuation study of pionisation in ultrarelativistic nucleus-nucleus interaction

The scaled factorial moments and the multifractal moments have been investigated in differentη-intervals to study the dynamical fluctuation of pions produced in 200 AGeV³²S-Ag/Br interaction. In order to investigate the detail characteristics of intermittency behaviour, theF-moments are extracted up to the eighth order of moments in differentM-intervals. The analysis indicates a non-thermal phase transition and different regime of particle production during the hadronisation process.     

An isothermal equation of state for solids

An isothermal equation of state (EOS) for solids, recently suggested by the authors in the realistic form, V/V₀=f(P), with relative volume as the dependent and the pressure as the independent variable, was shown to have an advantage for some close-packed materials in that it allows B′_∞=(∂B_s/∂P)_s(P→∞) to be fitted, and this is where the usual standard equations fail. In the present study, our EOS is applied to a number of inorganic as well as organic solids, including alloys, glasses, rubbers and plastics; varying widely in their bonding and structural characteristics, as well as in their bulk modulus values. A very good agreement is observed between the data and fits. The results obtained are compared with those from two well-known equations, expressible in the realistic form, proposed by Murnaghan and Luban. Further, the results are also compared with those from the widely used two- and three-parameter EOSs, expressible in the unrealistic form only, P=f(V/V₀), proposed by Birch—and also with those from the EOS model of Keane in which B′_∞ is explicitly expressed as an equation of state parameter. The results obtained from our model compare well to these EOSs. Our EOS, in general, yields the smallest mean-squared deviations between data and fits. The values of B′_∞calculated from our EOS are compared with those from Keane's model. Further, we have studied the variation of B′_∞with temperature using the experimental isotherms of Mo and W at 10 different temperatures ranging from 100 to 1000 K, and observed that the values of B′_∞ yielded by our model and that of Keane vary, as expected, within a narrow range. Furthermore, our EOS is applied to study the stability of the fit parameters with variation in the pressure ranges with reference to the isothermal compression data on Mo and W—and also to study the variation of isothermal bulk modulus with pressure, with reference to the ultrasonic data on NaCl and noted a very good agreement with experiment. In addition, our model is applied, with B₀ and B′₀ constrained to the theoretical values, to the five theoretical isotherms of MgO at 300, 500, 1000, 1500 and 2000 K obtained on the basis of a first principles approach—a good agreement is observed with the predictions, and the values of B′_∞ inferred at different temperatures tend to converge to a constant value.