A note on a class of singular integro-differential equations

A simplified analysis is employed to handle a class of singular integro-differential equations for their solutions     

Exact Bianchi type V imperfect fluid solutions

It is shown that it is sufficient to solve a single first order differential equation to determine exact Bianchi type V imperfect fluid solutions of Einstein's field equations. Two exact solutions are presented in this paper. One of these two solutions corresponds to the case when the anisotropic pressure tensor is proportional to the shear tensor. This proportionality, it is shown, is a necessary but not a sufficient condition for the absence of heat flow in a Bianchi type V universe. It is also observed that the presence of heat flow necessarily introduces anisotropy in a Bianchi type V universe.     

Evidence of Dynamical Fluctuation of Target Residues in Relativistic Nuclear Interaction at 14.5 AGeV

An analysis of data of target fragments of ²⁸Si-AgBr (at 14.5 AGeV) reveals the existence of emission asymmetry in the azimuthal plane, which is found to depend on the number of target fragments. The comparison with the data of ³²S-AgBr (at 200 AGeV) and ¹⁶O-AgBr (at 60 AGeV) interactions indicates that emission asymmetry depends on the projectile mass and energy.     

Atom Capture by Nanotube and Scaling Anomaly

The existence of bound state of the polarizable neutral atom in the inverse square potential created by the electric field of a single walled charged carbon nanotube (SWNT) is shown to be theoretically possible. The consideration of inequivalent boundary conditions due to self-adjoint extensions lead to this nontrivial bound state solution. It is also shown that the scaling anomaly is responsible for the existence of such bound state. Binding of the polarizable atoms in the coupling constant interval η ²∈[0,1) may be responsible for the smearing of the edge of steps in quantized conductance, which has not been considered so far in the literature.     

Infrared and Raman spectroscopies of InP/II–VI core-shell nanoparticles

We use infrared (IR) and Raman spectroscopies to investigate the optically active phonon modes in InP nanoparticles and InP/II–VI core-shell nanoparticles fabricated by similar colloidal chemistry methods. The IR transmission spectra of several InP nanoparticle samples exhibit a common absorption feature, which we assign to the Fröhlich mode. The Raman results for the same samples show transverse and longitudinal optical phonon peaks, and scattering strength in between due to surface optical (SO) modes. Infrared spectra of the InP/ZnSe core-shell nanoparticles () exhibit three absorption features, one due to the InP core, and the others associated with the ZnSe shell layer. Raman measurements (12–292 K) also show three phonon-related peaks, whose intensities vary sharply with temperature. The frequencies of the IR and Raman lines are in approximate accord with dielectric continuum theory.     

Study of precipitation in NaCl:Pb2+ by light scattering and ultramicroscopy

The formation and dissolution behaviour of precipitates in NaCl : Pb²⁺ single crystals is studied by light scattering and ultramicroscopy. Measurements of Rayleigh ratio together with ultramicroscopic observations during isochronal annealing indicate the presence of two types of precipitates in as-grown crystals. Isochronal annealing after suitable thermal and thermomechanical treatments shows that precipitates of first type (I) which form and dissolve at lower temperatures, are due to homogeneous nucleation. Precipitates of the second category (II) which form and dissolve at higher temperatures are aligned along crystallographic directions and have their origin in stress-assisted processes. Isothermal annealing has been used to study the dissolution kinetics of the precipitated fraction, and it is found that the kinetics is of first order. The enthalpy of solution is determined from a study of the temperature dependence of the kinetic rate constant, in conjunction with available information on the migration energy of Pb²⁺ in NaCl. The enthalpy so deduced is in good agreement with the value as usually obtained from the concentration dependence of the dissolution temperature.     

Solution of singular integral equations with logarithmic and Cauchy kernels

A direct method of solution is presented for singular integral equations of the first kind, involving the combination of a logarithmic and a Cauchy type singularity. Two typical cases are considered, in one of which the range of integration is a single finite interval and, in the other, the range of integration is a union of disjoint finite intervals. More such general equations associated with a finite number (greater than two) of finite, disjoint, intervals can also be handled by the technique employed here.     

Simple modification of a protein database for mass spectral identification of N-linked glycopeptides

We describe an algorithm which modifies a protein database such that during a database search deamidation is limited to asparagines strictly contained within the N-glycosylation consensus sequence. The modified database was evaluated using a dataset created from the shotgun proteomic analysis of N-linked glycopeptides from human blood serum. We demonstrate that the application of the modified database eliminates incorrect glycopeptide assignments, reduces the peptide false-discovery rate, and eliminates the need for manual validation of glycopeptide identifications.