定轴转动带电体的磁场分布

类比定轴转动刚体转动贯量以及电偶极子电场的计算方法得出定轴转动带电体的磁矩及其磁场分布。     

Two-loop Majorana neutrino mass and magnetic moment in a gauge model

Two-loop contributions to Majorana mass and transition magnetic moment in a gauge model not in conflict with decaying neutrino dark matter (DDM) hypothesis have been studied. Another variant of an earlier model [J Dhar and S Dev,Pramana — J. Phys. 39 541 (1992)] consistent with the DDM hypothesis is proposed and is shown to lead to large enough neutrino magnetic moment and consistent with the phenomenological constraints on neutrino mass.     

Comparison of variants of the bi-conjugate gradient method for compressible Navier-Stokes solver with second-moment closure

Variants of the bi-conjugate gradient (Bi-CG) method are used to resolve the problem of slow convergence in CFD when it is applied to complex flow field simulation using higher-order turbulence models. In this study the Navier-Stokes and Reynolds stress transport equations are discretized with an implicit, total variation diminishing (TVD), finite volume formulation. The preconditioning technique of incomplete lower-upper (ILU) factorization is incorporated into the conjugate gradient square (CGS), bi-conjugate gradient stable (Bi-CGSTAB) and transpose-free quasi-minimal residual (TFQMR) algorithms to accelerate convergence of the overall itertive methods. Computations have been carried out for separated flow fields over transonic bumps, supersonic bases and supersonic compression corners. By comparisons of the convergence rate with each other and with the conventional approximate factorization (AF) method it is shown that the Bi-CGSTAB method gives the most efficient convergence rate among these methods and can speed up the CPU time by a factor of 2·4–6·5 as compared with the AF method. Moreover, the AF method may yield somewhat different results from variants of the Bi-CG method owing to the factorization error which introduces a higher level of convergence criterion.     

Relaxation phenomena of polar non-polar liquid mixtures under low and high frequency electric field

Simultaneous calculation of the dipole moment μ_j and the relaxation time τ_j of a certain number of non-spherical rigid aliphatic polar liquid molecules (j) in non-polar solvents (i) under 9.8 GHz electric field is possible from real ε′_ij and imaginary ε″_ij parts of the complex relative permittivity ε*_ij. The low frequency and infinite frequency permittivities ε_0ij and ε_∞ij measured by Purohitet al [1,2] and Srivastava and Srivastava [3] at 25, 35 and 30°C respectively are used to obtain static μ_s. The ratio of the individual slopes of imaginary σ″_ij and real σ′_ij parts of high frequency (hf) complex conductivity σ*_ij with weight fractionsw _jatw _j → 0 and the slopes of σ″_ij— σ′_ij curves for differentw _js [4] are employed to obtain τ_js. The former method is better in comparison to the existing one as it eliminates polar-polar interaction. The hf μ_js in Coulomb metre (C m) when compared with static and reported μs indicate that μ_s s favour the monomer formations which combine to form dimers in the hf electric field. The comparison among μs shows that a part of the molecule is rotating under X-band electric field [5]. The theoretical μ_theos from available bond angles and bond moments of the substituent polar groups attached to the parent molecules differ from the measured μ_js and μs to establish the possible existence of mesomeric, inductive and electromeric effects in polar liquid molecules.     

Limiting distributions of two random sequences

For fixed p (0 ≤ p ≤ 1), let {L₀, R₀} = {0, 1} and X₁ be a uniform random variable over {L₀, R₀}. With probability p let {L₁, R₁} = {L₀, X₁} or = {X₁, R₀} according as $\text{X}{}_1\text{≥}\text{1}\text{2}\text{(L}{}_0\text{+ R}{}_0\text{)}\text{or}\text{<}\text{1}\text{2}\text{(L}{}_0\text{+ R}{}_0\text{)}$; with probability 1 ? p let {L₁, R₁} = {X₁, R₀} or = {L₀, X₁} according as $\text{X}{}_1\text{≥}\text{1}\text{2}\text{(L}{}_0\text{+ R}{}_0\text{)}\text{or}\text{<}\text{1}\text{2}\text{(L}{}_0\text{+ R}{}_0\text{)}$, and let X₂ be a uniform random variable over {L₁, R₁}. For n ≥ 2, with probability p let {L_n, R_n} = {L_{n ? 1}, X_n} or = {X_n, R_{n ? 1}} according as $\text{X}{}_{\mathrm{n}}\text{≥}\text{1}\text{2}\text{(L}{}_{\mathrm{n\; ?\; 1}}\text{+ R}{}_{\mathrm{n\; ?\; 1}}\text{)}\text{or}\text{<}\text{1}\text{2}\text{(L}{}_{\mathrm{n\; ?\; 1}}\text{+ R}{}_{\mathrm{n\; ?\; 1}}\text{)}$, with probability 1 ? p let {L_n, R_n} = {X_n, R_{n ? 1}} or = {L_{n ? 1}, X_n} according as $\text{X}{}_{\mathrm{n}}\text{≥}\text{1}\text{2}\text{(L}{}_{\mathrm{n\; ?\; 1}}\text{+ R}{}_{\mathrm{n\; ?\; 1}}\text{)}\text{or}\text{<}\text{1}\text{2}\text{(L}{}_{\mathrm{n\; ?\; 1}}\text{+ R}{}_{\mathrm{n\; ?\; 1}}\text{)}$, and let X_{n + 1} be a uniform random variable over {L_n, R_n}. By this iterated procedure, a random sequence {X_n}_{n ≥ 1} is constructed, and it is easy to see that X_n converges to a random variable Y_p (say) almost surely as n → ∞. Then what is the distribution of Y_p? It is shown that the Beta, (2, 2) distribution is the distribution of Y₁; that is, the probability density function of Y₁ is g(y) = 6y(1 ? y) I_0,1(y). It is also shown that the distribution of Y₀ is not a known distribution but has some interesting properties (convexity and differentiability).     

The stochastic heat equation: Feynman-Kac formula and intermittence

We study, in one space dimension, the heat equation with a random potential that is a white noise in space and time. This equation is a linearized model for the evolution of a scalar field in a space-time-dependent random medium. It has also been related to the distribution of two-dimensional directed polymers in a random environment, to the KPZ model of growing interfaces, and to the Burgers equation with conservative noise. We show how the solution can be expressed via a generalized Feynman-Kac formula. We then investigate the statistical properties: the two-point correlation function is explicitly computed and the intermittence of the solution is proven. This analysis is carried out showing how the statistical moments can be expressed through local times of independent Brownian motions.     

Seminormality of operators from their tensor product

The question of seminormality of tensor products of nonzero
bounded linear operators on Hilbert spaces is investigated. It is shown that is subnormal if and only if so are and .

     

Heuristic solutions to polynomial moment problems with some convex entropic objectives

We are asking to estimate a nonnegative density on ^m , given some of its algebraic or trigonometric moments. The maximum entropy method is to introduce an entropy-like objective function and then solve a convex minimization programming with some linear constraints. In the existing literature, Newton's method or some other iteration methods are used to solve its dual problem. In this paper, special structures of the problem have been discovered when we use some particular entropies, which include Boltzmann-Shannon entropy and Burg's entropy. Useful linear relationships among the moments help us to set up very fast and effective algorithms. Numerical computations and comparison are also presented.     

Synthesis and characterization of mixed iodide-naphthalene complexes of lanthanides

The [LnI₂(THF)₃]₂(-C₁₀H₈) complexes were obtained by reactions of LnI₃(THF)₃ (Ln = Ce, Pr, Nd, or Gd) with lithium and excess naphthalene. The magnetic moments of these complexes correspond to the oxidation state +3 of the metal atoms. The Yb^II complex, [YbI(DME)₂]₂(-C₁₀H₈), was synthesized by the reaction of YbI₂(DME)₂ with an equimolar amount of naphthalenelithium.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 10, pp. 2573–2574, October 1996.