By exploiting the theory of ordinary differential equations together with certain properties of higher transcendental functions, a useful analytical expression for the integral transform of the Green's function for motion in Coulomb–Yamaguchi potential is derived via the r-space approach. This integral transform is applied to construct an analytical expression for off-shell Jost solution in its ‘maximal reduced form’ involving confluent and Gaussian hypergeometric functions. Corresponding Jost functions auto-matically follow from this solution. Finally, as another application of the off-shell Jost solution, the off-shell T-matrix is calculated by using a modified relation between offshell physical wave function and T-matrix which does not involve the potential explicitly, thereby avoiding certain difficult integrals, and expressed it in terms of rational functions and simple hypergeometric functions which is in exact agreement with the results given previously by other authors.

In mechanics of the mass point passage from one frame of reference to another moving with velocity $\vec{u}$ consists in subtracting this vector from the velocity of the particle. In general case the vector $\vec{u}$ is not constant, as, for example, when passing through a rotating frame, this operation creates inertial forces. Analysis of this phenomenon from the point of view of Lagrangian and Hamiltonian mechanics is interesting from the general relativistic point of view due to Einstein's principle of equivalence. We show that the vector $\vec{u}$ plays the role of vector potential which, however, essentially differs from vector potential known in classical electrodynamics. Comparative analysis of the two kinds of vector potentials is completed.

We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein–Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal Universe. We show that the mass corresponds to the values obtained previously for quark stars when anisotropy and charge are present.

We study the effect of parameter fluctuations and the resultant multiplicative noise on the synchronization of coupled chaotic systems. We introduce a new quantity, the fluctuation rate 𝜙 as the number of perturbations occurring to the parameter in unit time. It is shown that 𝜙 is the most significant quantity that determines the quality of synchronization. It is found that parameter fluctuations with high fluctuation rates do not destroy synchronization, irrespective of the statistical features of the fluctuations. We also present a quasi-analytic explanation to the relation between 𝜙 and the error in synchrony.

We demonstrate that the nilpotent Becchi–Rouet–Stora–Tyutin (BRST) and anti-BRST symmetry invariance of the Lagrangian density of a four $(3 + 1)$-dimensional (4D) non-Abelian 1-form gauge theory with Dirac fields can be captured within the frame-work of the superfield approach to BRST formalism. The above 4D theory, where there is an explicit coupling between the non-Abelian 1-form gauge field and the Dirac fields, is considered on a (4,2)-dimensional supermanifold, parametrized by the bosonic 4D space-time variables and a pair of Grassmannian variables. We show that the Grassmannian independence of the super-Lagrangian density, expressed in terms of the (4,2)-dimensional superfields, is a clear signature of the presence of the (anti-)BRST invariance in the original 4D theory.

One of the most interesting areas of current research in molecular physics is the study of the vibrationally excitated states of medium and large molecules. In view of the considerable amount of experimental activity in this area, one needs theoretical models within which to interpret experimental data. Using Lie algebraic method, the vibrational energy levels of nickel metalloporphyrins like Ni(OEP), Ni porphyrin and Ni(TPP) are calculated for 16 vibrational modes. The algebraic Hamiltonian $H = E_{0} + \sum_{i=1}^{n} A_{i}C_{i} + \sum_{i < j} A_{ij}C_{ij} + \sum_{i < j}^{n} \lambda_{ij}M_{ij}$, where $A_{i}$, $A_{ij}$ and $\lambda_{ij}$ are the algebraic parameters which vary from molecule to molecule and $C_{i}$, $C_{ij}$ and $M_{ij}$ are algebraic operators. The vibrational energy levels are calculated using algebraic model Hamiltonian and the results are compared with the experimental values. The results obtained by this model are very accurate.

Fragmentation of ground state ortho-positronium (Ps) in collision with Li ion (Li⁺) is studied in the framework of post-collisional Coulomb distorted eikonal approximation (CDEA), giving special emphasis on the dynamics of the electron loss to the continuum (ELC) that occurs when the electron (𝑒) and the positron ($e^{+}$) are very close to each other in the velocity space $(v_{e} \approx v_{p})$. The present model takes account of the two-centre effect on the ejected 𝑒 which is crucial for a proper description of the ELC phenomena. Both the fully differential cross-section (TDCS) and the doubly differential cross-section (DDCS) (energy spectra) are investigated at intermediate and high incident energies. A broad distinct ELC peak centred around $v_{e} \approx v_{p}$ is noted in the 𝑒 energy spectrum in contrast to the sharp ELC peak for a heavy projectile, corroborating the experimental findings. Two salient features are noted in the present study: (i) the shift of the 𝑒 DDCS peak (summed over $e^{+}$ angles) towards higher ejection energy with respect to half the residual energy of the system, (ii) comparison of the 𝑒 and $e^{+}$ energy spectra reflect a strong $e-e^{+}$ asymmetry with respect to the ratio $v_{e}/v_{p} = 1$. Both these features are in qualitative agreement with the experimental observations due to Armitage et al for Ps–He atom system and could be attributed to the post-collisional two-centre effect on 𝑒 due to its parent nucleus $(e^{+})$ and the screened target ion. Two different wave functions of the Li ion are chosen in order to test the sensitivity of the present results with respect to the choice of the wave function.

A new scheme of binary half adder and full adder is proposed. It realizes a kind of all-optical computation which is based on the polarization coding technique and the nonlinear total reflectional optical switches.

We have prepared, characterized and investigated a new PEG-2000 based solid polymer electrolyte (PEG)$_{x}$NH₄I. Ionic conductivity measurements have been made as a function of salt concentration as well as temperature in the range 265–330 K. Selected compositions of the electrolyte were exposed to a beam of 8 MeV electrons to an accumulated dose of 10 kGy to study the effect on ionic conductivity. The electrolyte samples were also quenched at liquid nitrogen temperature and conductivity measurements were made. The ionic conductivity at room temperature exhibits a characteristic double peak for the composition $x = 20$ and 70. Both electron beam irradiation and quenching at low temperature have resulted in an increase in conductivity by 1–2 orders of magnitude. The enhancement of conductivity upon irradiation and quenching is interpreted as due to an increase in amorphous region and decrease in crystallinity of the electrolyte. DSC and proton NMR measurements also support this conclusion.

The EPR parameters (𝑔 factors $g\parallel$, $g\perp$ and zero-field splitting 𝐷) of Mn⁴⁺ ion in h-BaTiO₃ crystal are calculated from the complete high-order perturbation formulas based on a two-mechanism model for the EPR parameters of $3d^{3}$ ions in trigonal symmetry. In the model, not only the widely used crystal-field mechanism, but also the charge-transfer mechanism (which is not considered in crystal-field theory) are included. The calculated results are in reasonable agreement with the experimental values. The relative importance of charge-transfer mechanism to EPR parameters and the defect structure of Mn⁴⁺ centre in h-BaTiO₃ crystal obtained from the calculations are discussed.

The reduction mechanism of Ni²⁺ into Ni particles using different precursors such as NiCl₂ solution, NiO powder and Ni[(NH₃)₆]Cl₂ complex has been established. Different particle sizes can be designed from these precursors. The smallest crystallite size (12 nm) can be obtained from Ni[(NH₃)₆]Cl₂ complex in the presence of the stabilizing ligand (oleic acid). The field-cooled (FC) and zero-field-cooled (ZFC) magnetization of Ni particles obtained from Ni[(NH₃)₆]Cl₂ complex in the temperature range 5–300 K established the ferromagnetic interaction up to 300 K. The magnetization values at three different temperatures 5, 70 and 300 K are 50.2, 49.5 and 45.5 Oe respectively at $3 \times 10^{4}$ Oe applied field and such values are less than that of the bulk value. The Curie temperature $(T_{c})$ decreases slightly with the decrease of particle size. This study will provide guidance in the preparation of metal nanoparticles from different precursors.

In this paper, we study the effects of short channel on double gate MOSFETs. We evaluate the variation of the threshold voltage, the subthreshold slope, the leakage current and the drain-induced barrier lowering when channel length $L_{\text{CH}}$ decreases. Further- more, quantum effects on the performance of DG-MOSFETs are addressed and discussed. We also study the influence of metal gate work function on the performance of nanoscale MOSFETs. We use a self-consistent Poisson–Schrödinger solver in two dimensions over the entire device. A good agreement with numerical simulation results is obtained.

Capability to compute neutron dose rate is introduced for the first time in the new version of the CASCADE.04 code. Two different methods, `track length estimator' and `collision estimator' are adapted for the estimation of neutron fluence rate needed to calculate the ambient dose rate. For the validation of the methods, neutron dose rates are experimentally measured at different locations of a 5Ci Am–Be source, shielded in Howitzer-type system and these results are compared with those estimated using (i) modified CASCADE.04.d and (ii) MCNP4A codes and it is found that the agreement is good. The paper presents details of modification and results of the comparative study.

We construct the expression for the ground state eigenfunction of the Schrödinger equation for a particle inside an arbitrary planar triangle under the influence of a potential.