Characteristic features of exact solutions of the problem of an electron in the quantized field of a plane wave

The physical and mathematical features of exact solutions of the problem of an electron moving in the field of a quantized, plane electromagnetic wave [1–4] are investigated. In particular, the problem of constructing solutions for all values of the total energy of the system is solved. A new interpretation is given to the limiting approach to Volkov solutions [5, 6]. The completeness and orthogonality of the solutions are proven in the reference plane formalism. The notation of [4] is used in this paper.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 3, pp. 7–14, March, 1977.     

A combination of Yang’s equations forSU(2) gauge fields and Charap’s equations for pion dynamics with exact solutions

Two sets of nonlinear partial differential equations originating from two different physical situations have been combined and a new set of nonlinear partial differential equations has been formed wherefrom the previous two sets can be obtained as particular cases. One of the two sets of equations was obtained by Yang [1] while discussing the condition of self-duality ofSU(2) gauge fields on Euclidean four-dimensional space. The second one was reported by Charap [2] for the chiral invariant model of pion dynamics under tangential parametrization. Using the same type of ansatz in each case De and Ray [16] and Ray [7] obtained physical solutions of the two sets of equations. Here exact solutions of the combined set of equations with particular values of the coupling constants have been obtained for a similar ansatz. These solutions too are physical in nature.     

N-fold Darboux Transformation for Integrable Couplings of AKNS Equations

For the integrable couplings of Ablowitz-Kaup-Newell-Segur(ICAKNS) equations, N-fold Darboux transformation(DT) TN, which is a 4 × 4 matrix, is constructed in this paper. Each element of this matrix is expressed by a ratio of the(4N + 1)-order determinant and 4N-order determinant of eigenfunctions. By making use of these formulae,the determinant expressions of N-transformed new solutions p~([N ]), q~([N ]), r~([N ])and s~([N ])are generated by this N-fold DT.Furthermore, when the reduced conditions q =-p*and s =-r*are chosen, we obtain determinant representations of N-fold DT and N-transformed solutions for the integrable couplings of nonlinear Schr?dinger(ICNLS) equations.Starting from the zero seed solutions, one-soliton solutions are explicitly given as an example.     

A benchmark comparison of Monte Carlo particle transport algorithms for binary stochastic mixtures

We numerically investigate the accuracy of two Monte Carlo algorithms originally proposed by Zimmerman [1] and Zimmerman and Adams [2] for particle transport through binary stochastic mixtures. We assess the accuracy of these algorithms using a standard suite of planar geometry incident angular flux benchmark problems and a new suite of interior source benchmark problems. In addition to comparisons of the ensemble-averaged leakage values, we compare the ensemble-averaged material scalar flux distributions. Both Monte Carlo transport algorithms robustly produce physically realistic scalar flux distributions for the benchmark transport problems examined. The base Monte Carlo algorithm reproduces the standard Levermore-Pomraning model [3] and [4] results. The improved Monte Carlo algorithm generally produces significantly more accurate leakage values and also significantly more accurate material scalar flux distributions. We also present deterministic atomic mix solutions of the benchmark problems for comparison with the benchmark and the Monte Carlo solutions. Both Monte Carlo algorithms are generally significantly more accurate than the atomic mix approximation for the benchmark suites examined.     

Some physical solutions of Yang’s equations forSU(2) gauge fields, Charap’s equations for pion dynamics and their combination

Some previously obtained physical solutions [1–3] of Yang’s equations forSU(2) gauge fields [4], Charap’s equations for pion dynamics [5,6] and their combination as proposed by Chakraborty and Chanda [1] have been presented. They represent different physical characteristics, e.g. spreading wave with solitary profile which tends to zero as time tends to infinity, spreading wave packets, solitary wave with oscillatory profile, localised wave with solitary profile which becomes plane wave periodically, and, wave packets which are oscillatory in nature.     

A class of exact solutions for coupled electromagnetic and scalar fields for Einstein-Rosen metric. Part IA

In the previous work [1] we have obtained a class of exact solutions for the nonstatic cylindrically symmetric Einstein-Rosen metric in the presence of combined electromagnetic and zero-rest-mass scalar meson fields. But, these solutions are restricted because of assuming certain conditions on the scalar field. The present work deals with all the solutions obtained in the previous paper without any such restriction. The class of exact solutions obtained thus is more general than that given in [1].     

On Rosen's bi-metric theory of gravitation

The field equations of Rosen's bi-metric theory of gravitation [1] are solved exactly. The solutions are the same as in the author's theory of gravitation [2]. These solutions are, however, incompatible with Rosen's conservation laws and his second (flat) metric. Incompatibility with the conservation laws arises in second order. Incompatibility with the flat metric arises in first order but only for time-dependent fields. Rosen's theory is defensible only as a static first order theory and predicts the red shift light deflection and time-delay correctly.     

Some remarks on finite-gap solutions of the Ernst equation

The relationship between the class of algebro-geometrical (finite-gap) solutions of the Ernst equation constructed by Korotkin and Matveev [Theor. Math. Phys. 77 (1989) 1018; St. Petersburg Math. J. 1 (1990) 379] and the solutions recently constructed by Meinel and Neugebauer [Phys. Lett. A 210 (1996) 160] is discussed. A new formula for the general algebro-geometrical solution is obtained.     

Localization expansions. I. Functions of the “background” configurations

Expansions of the type described in the inductive hypothesis (H.5) in the paper [1] are constructed for local functions of the “background” configurations, i.e., solutions of the variational problems studied in the previous paper [3]. A main part of this construction is a further analysis of a local structure of the solutions. This work has been partially supported by the NSF Grant DMS-9102639     

标准芳烃及其混合溶液的同步荧光光谱分析

为了提供区分标准芳烃的实验依据,并为环境中芳烃污染检测提供参考.对10个标准芳烃样品(萘、芴、蒽、菲、荧蒽、苊、芘、1,2-苯并[A]蒽、苯并[k]荧蒽、苯并菲)及其混合溶液(蒽、萘、芴混合溶液,苊、荧蒽、菲混合溶液和芘、1,2-苯并[A]蒽、苯并[k]荧蒽、苯并菲混合溶液)的同步荧光特性进行了分析,获得10种标准芳烃标志峰最好时对应的Δλ值及其标志峰位.在此基础上,通过同步荧光光谱分析区分了三种标准芳烃混合溶液的组分,实验发现对蒽、萘、芴混合溶液,Δλ=3 nm时最易区分三种组分|对苊、荧蒽、菲混合溶液,Δλ=3 nm或Δλ=10 nm均可区分三种组分,相对而言,Δλ=10 nm更简便些|对芘、1,2-苯并[A]蒽、苯并[k]荧蒽、苯并菲混合溶液,Δλ=5 nm时是最好的,但也仅能区分芘、1,2-苯并[A]蒽、苯并[k]荧蒽三种组分,苯并菲不确定.     

Solution of the thermoelastoplastic problem for a thin disk of plastically compressible material subjected to thermal loading

Elastoplastic solutions for thin plates and disks are sensitive to loading and plasticity conditions [1–5]. The plasticity condition for a number of metal materials depends on the mean stress [6–8]. In this case, when using the associated flow rule, plastic deformations do not satisfy the incompressibility condition, which is commonly accepted in statements of boundary-value problems for thin elastoplastic plates and disks [9–13]. It is of interest to determine the effect of plastic compressibility on the behavior of solutions for such structures. In this paper, a hollow disk in a rigid container subjected to a uniform temperature field is considered. The plasticity condition proposed in [14] is accepted. A general study of the set of equations including this plasticity condition and the associated flow rule was performed in [15]. The solution under the Mises plasticity condition was obtained in [1].     

Bulk and boundary S-matrices for the SU(N) chain

We consider both closed and open integrable antiferromagnetic chains constructed with the SU(N)-invariant R-matrix. For the closed chain, we extend the analyses of Sutherland and Kulish — Reshetikhin by considering also complex “string” solutions of the Bethe ansatz equations. Such solutions are essential to describe general multiparticle excited states. We also explicitly determine the SU(N) quantum numbers of the states. In particular, the model has particle-like excitations in the fundamental representations [k] of SU(N), with k = 1, …, N − 1. We directly compute the complete two-particle S-matrices for the cases [1] ⊗ [1] and [1] ⊗ [N − 1 ]. For the open chain with diagonal boundary fields, we show that the transfer matrix has the symmetry SU(l) × SU(N−l) × U(1), as well as a new “duality” symmetry which maps l→N−l. With the help of these symmetries, we compute by means of the Bethe ansatz for particles of types [1] and [N − 1 ] the corresponding boundary S-matrices.     

The equivalence of perfect fluid space-times and viscous magnetohydrodynamic space-times in general relativity

The work of a previous article [1] is extended to show that space-times which are the exact solutions of the field equations for a perfect fluid also may be exact solutions of the field equations for a viscous magnetohydrodynamic fluid. Conditions are found for this equivalence to exist and viscous magnetohydrodynamic solutions are found for a number of known perfect fluid space-times.     

Frustrations in low-dimensional magnetic systems

On the basis of exact analytical solutions for spin-spin correlation functions in the one-dimensional 3-state [1] and 4-state [2] standard Potts models and Ising model [3] with allowance for the interactions between nearest neighbors J and next-nearest neighbors J′, phenomena of the appearance and disappearance of frustrations have been investigated, depending on the signs of J and J′ and the ratio of the interactions. In the Ising model, these phenomena have been studied on triangular, hexagonal, and kagomé lattices on the basis of exact analytical solutions for the maximum values of the Kramers-Wannier matrices obtained in [4, 5].     

Selective etching of InP in NaF solution

The crossing porous structure of InP has been obtained by electrochemical etching in NaF solutions. The behavior of the periodic oscillation occurs at different potential ranges for the different concentrations of solutions, and it will disappear with the concentration of the solution decreased. The scanning electron microscope (SEM) image shows that the pores have two directions on the surface and are perpendicular to each other. The two directions are assigned to [0 1 1] and [], respectively. The SEM image of the cross-section also shows that the two directions are assigned to [1 1 1]B and []B. Both are due to the selective etching of F⁻ ions. The crossing porous structure of InP is a very promising feature for the three-dimensional structure of III-V compound semiconductors for photonic band gap materials.     

Temperature dependence of the dislocation starting stress in Ni+17 at.% Cr

The K state can [1–7] have a marked effect on the mechanical parameters of homogeneous solid solutions containing transition elements. The K state is seen as a rise in resistance in low-temperature annealing after quenching from high temperatures and has been ascribed to the formation of short-range order [4, 5, 8–10] or of imperfect long-range order [6, 7]. The mechanical properties are also substantially affected. We have examined the effects on the dislocation starting stress as a function of temperature, as measured by mechanical hysteresis [18–20], in the K state range for Ni+17% Cr.     

Structure Elucidation and Assignment of 1H and 13C Spectra of the New Fused Cyclobutane-Naphthofuran Derivative by Two-Dimensional NMR in Different Solvents

One of the major product from the photodimerization of 2-[2-(2-methyl-phenyl)ethenyl)]naphtho[2. 1-b]furan (1) is a new fused cyclobutane-naphthofuran derivative, 6-(2-methylphenyl)-1-[2-(2-methylphenyl)ethenyl]-7-(2-naphtho-[2,1-b]furyl)-3-[2,1]naphtho-2-oxabicyclo[3.2.0]hept-3-ene (2). Its ¹H and ¹³C NMR spectra were fully assigned by the application of COSY, LR COSY, NOESY, APT and HETCOR experiments in deuterated chloroform, acetone and benzene solutions.     

托卡马克中逃逸电子分布函数和波能密度计算

本文用非等距有限差分法,求解了准线性微分方程组,获得了在电子平行速度区间,逃逸电子分布函数和波能密度的二维演化图象。这一结果比文[1]和[2]在稳态情形下所得到的解析结果以及文[1]在一维情形下演化的解析结果,较完整地反映了逃逸电子分布函数的特征。可供对逃逸电子的进一步研究参考。     

Asymptotic properties of the solutions of linear and nonlinear spin field equations in Minkowski space

In this paper I will first derive, based on energy estimations and geometric invariance, the asymptotic behavior of solutions of linear spin field equations in Minkowski space. It generalizes the result in [3] where it was proved for the spin-1 and spin-2 cases. The techniques are then applied to Yang-Mills equations, the result improves the previous one in [1] by allowing the initial data to have charge, dipole and quadrupole moments. The Lie derivative operator for spinors and some properties will be also discussed; they can be used to simplify some algebraic calculations of [4].This research is partially supported by a grant from NSF under DMS-8610730     

Excitonic nature of the dual fluorescence of 2,3-diazabicyclo[2.2.2]oct-2-ene and 1,4-dimethyl-(2,3-diazabicyclo[2.2.2]oct-2-ene)

Absorption, fluorescence excitation, and fluorescence spectra and the dependence of the degree of fluorescence polarization on the emission wavelength are measured for glass-like ethanol solutions of 2,3-diazabicyclo[2.2.2]oct-2-ene and 1,4-dimethyl-(2,3-diazabicyclo[2.2.2]oct-2-ene) at a temperature of 77 K. The analysis of the spectral polarization data shows that two excited electronic states S₁ and S₂ that contribute to the emission of the compounds are related to the exciton splitting and correspond to the symmetric (S₂) and antisymmetric (S₁) wave functions.