BЛИЯHИE CBETA HA MOHOКPИCTAЛЛИЧECКИE ПЛACTИHКИ AgCl

The paper deals with the influence of light,=403 m, on the absorption of single-crystal plates of AgCl, grown by the capillary method. It was found that crystals with blue luminescence show no maximum in the region measured. For crystals with green luminescence a broad absorption maximum was found at – 590 m, which is partly bleached during further irradiation by light from the region of the absorption maximum. Measurements were preformed at room temperature.

---

---

. .     

Form of the NH3 spectral lines in the impact approximation and analytical expressions for the relaxation parameters

The half-width and cross-relaxation parameter are calculated for a series of rotational transitions on the basis of a rigorous theory taking account of the correlational broadening of the doublet components. The absorption of the doublet lines of the transition J = 4 5 for the system NH₃-N₂ and the transition J = 5 6 for NH₃-NH₃ is analyzed. For the vibrational ground state, analytical expressions are given for the parameters and .Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 3–7, June, 1984.     

Dynamical bifurcation with noise

It was shown by A. Neishtadt that dynamical bifurcation, in which the control parameter is varied with a small but finite speed , is characterized by adelay in bifurcation, here denoted _j and depending on . Here we study dynamical bifurcation, in the framework and with the language of Landau theory of phase transitions, in the presence of a Gaussian noise of strength . By numerical experiments at fixed = ₀, we study the dependence of _j on a for order parameters of dimension 3; an exact scaling relation satisfied by the equations permits us to obtain for this the behavior for general . We find that in the smallnoise regime _j() a(^–b ), while in the strong-noise regime _j() – ce(^–d); we also measure the parameters in these formulas.     

Electron microscope study of dislocations in slip bands of bent Fe-3·2% Si alloy single crystals

Dislocations in Fe-3·2% Si alloy single crystals deformed by bending are studied in this paper. The specimens were cut parallel to the slip plane into platelets, polished, and studied in places at various distances from the neutral plane with an electron microscope. A large number of jogs of various sizes was found on screw dislocations. Many loops are formed by the motion of dislocations with jogs and by the stopping of moving dislocations by obstacles. Some of them grow as a result of stress. The activity of sources on large jogs is stopped at an early stage by a cross slip. The formation and growth of loops increases the dislocation density and causes the growth of slip bands.

---

Fe-3,2% Si

Fe-3,2% Si, , , . . , . . . .

     

Symmetries and half-sided modular inclusions of von Neumann algebras

LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , _N , _N the modular operators to (, ), (N, ), resp (N , ). Assume now ^-it N ^it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups ^it , _N ^ir , _N ^is ,t, r, s generate a unitary representation of the group S1(2, )/Z ₂ of positive energy.Another result is related to two half-sided modular inclusions (₁ , ) and (₂ , ). Under proper conditions the three modular groups ^it , ₁ ^ir , ₂ ^is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

The Phase Transition in Statistical Models Defined on Farey Fractions

We consider several statistical models defined on the Farey fractions. Two of these models may be regarded as spin chains, with long-range interactions, while another arises in the study of multifractals associated with chaotic maps exhibiting intermittency. We prove that these models all have the same free energy. Their thermodynamic behavior is determined by the spectrum of the transfer operator (Ruelle–Perron–Frobenius operator), which is defined using the maps (presentation functions) generating the Farey tree. The spectrum of this operator was completely determined by Prellberg. It follows that these models have a second-order phase transition with a specific heat divergence of the form C [ ln² ]^–1. The spin chain models are also rigorously known to have a discontinuity in the magnetization at the phase transition.     

Te-waves guided by arbitrary nonlinear dielectrics bounded by linear media

Considerable interest is currently being devoted to nonlinear propagation in dielectric slab waveguides for integrated optics and millimetric applications. Much of the current work is based on Kerr-like ( E ²) nonlinear media and numerically discussed. We present a exact solution of TE-waves for arbitrary nonlinear dielectric ( |E| ). We applicate this solution to the planar nonlinear optic waveguides and the dispersion relations are given. The results show that the propagation constants are a function of the field magnitude.Supported by deutscher akademischer austauschdienst (DAAD)He is now with Dept. Electrical Engineering, Duisburg University, 4100 Duisburg, Germany     

Layering transition in SOS model with external magnetic field

For the SOS model defined by the Hamiltonian , where _x , _x ,{1,2,...},h>0,x ^d ,d2 it is shown that in the low-temperature region an infinite sequence of first-order phase transitions takes place whenh»0 and the temperature is fixed.     

p-adic Heisenberg group and Maslov index

A system of coordinates on a set of selfdual lattices in a two-dimensionalp-adic symplectic space (V,) is suggested. A unitary irreducible representation of the Heisenberg group of the space (V,) depending on a lattice (an analogue of the Cartier representation) is constructed and its properties are investigated. By the use of such representations for three different lattices one defines the Maslov index =(₁,₂,₃) of a triple of lattices. Properties of the index are investigated and values of in coordinates for different triples of lattices are calculated.     

Existence,uniqueness, and nondegeneracy of positive solutions of semilinear elliptic equations

We study positive solutions of the Dirichlet problem: u(x)+f(u(x))=0,xD ⁿ ,u(x)=0,xD ⁿ , whereD ⁿ is ann-ball. We find necessary and sufficient conditions for solutions to be nondegenerate. We also give some new existence and uniqueness theorems.Research supported in part by NSF Contract Number MCS 80-02337     

THe mechanism of the amplification of moving striations in a d-c discharge

To determine the mechanism of the amplification of moving striations one starts out from the processes which [3] showed to be decisive for the production of stratification of the plasma of a positive column. An analysis of the influence of other processes shows that the main processes leading to the decay of space charges and thus to a smoothing out of the inhomogeneities and thereby to the attenuation of the periodic structure, cannot by overcome by ionization phenomena caused by changes in the concentration of electrons but only partially compensated.It was found that the process which can lead to the predomination of the processes of amplification over the attenuation is the process of the spatial shift of the temperature deflections of the electrons with respect to the additional electric field, which is expressed in a simplified way by Eq. (12).By solving the extremely simplified basic equations it is proved that under favourable conditions this displacement can lead to both a time and a spatial amplification of the striations. Such a possibility is also verified quantitatively by substituting numerical values into the formulae obtained.

---

, [3] . , , , , , ., , (12). , , . .

     

On the Eisenbud-Wigner formula for time-delay

It is shown that the Eisenbud-Wigner relation for time-delay holds for potentials V(r) that are O(r ^-5/2-) at . This improves previous results in which V was required to be O(r ^-4-) and O(r ^-3-), respectively.     

Absolute Continuity of Vitali–Hahn–Saks Measure Convergence Theorems

In this paper, we prove the following improved Vitali–Hahn–Saks measure convergence theorem: Let (L, 0, 1) be a Boolean algebra with the sequential completeness property, (G, ) be an Abelian topological group, be a nonnegative finitely additive measure defined on L, {_n: n N} be a sequence of finitely additive s-bounded G-valued measures defined on L, too. If for each a L, {_n(a)}_{n N} is a -convergent sequence, for each nN, when { (a)} convergent to 0, {_n(a)} is -convergent, then when { (a)} convergent to 0, {_n(a)} are -convergent uniformly with respect to nN     

Ballistic annihilation and deterministic surface growth

A model of deterministic surface growth studied by Krug and Spohn, a model of the annihilating reactionA+Binert studied by Elskens and Frisch, a one-dimensional three-color cyclic cellular automaton studied by Fisch, and a particular automaton that has the number 184 in the classification of Wolfram can be studied via a cellular automaton with stochastic initial data called ballistic annihilation. This automaton is defined by the following rules: At timet=0, one particle is put at each integer point of . To each particle, a velocity is assigned in such a way that it may be either +1 or –1 with probabilities 1/2, independent of the velocities of the other particles. As time goes on, each particle moves along at the velocity assigned to it and annihilates when it collides with another particle. In the present paper we compute the distribution of this automaton for each timet . We then use this result to obtain the hydrodynamic limit for the surface profile from the model of deterministic surface growth mentioned above. We also show the relation of this limit process to the process which we call moving local minimum of Brownian motion. The latter is the processB _x ^min ,x , defined byB _x ^min min{B _y ;x–1yx+1} for everyx , whereB _x ,x , is the standard Brownian motion withB ₀=0.     

ВЛИЯНИЕ СОДЕРЖАНИЯ К ИСЛОРОДА НА ЭЛЕКТРИЧЕСКИЕ И ТЕ РМОЭЛЕКТРИЧЕСКИЕ СВОЙСТВА ТРОЙНОЙ СИС ТЕМЫ Вi2Те3−x Sе x

, Bi₂Te_3–x Se _x . , , . , , . .

---

Influence of oxygen content on electric and thermoelectric properties of ternary system Bi₂Te_3–x Se _x

A study is made of the influence of oxygen, contained in the semi-conducting system Bi₂Te_3–x Sé _x , on the electric and thermoelectric properties. It is shown that the addition of oxygen to the prepared samples Bi₂Te_2.4Se_0.6 causes a decrease in electric conductivity while the thermoelectric force remains unchanged. This influence is connected with a decrease in the mobility of the electrons but their concentration is not influenced by the presence of oxygen. Conclusions are reached as to the influence of oxygen on the efficiency of the conversion of thermal energy into electric energy and vice versa.

     

The chiral determinant and the eta invariant

For { _y },y, a one parameter family of invertible Weyl operators of possibly non-zero index acting on spinors over an even dimensional compact manifoldX, we express the phase of the chiral determinant det _– in terms of the invariant of a Dirac operator acting on spinors over ×X.Supported in part by NSF Grant No. PHY-82-15249Supported in part by NSF Grant PHY 8605978 and the Robert A. Welch Foundation     

A contribution to the theory of the triple crystal diffractometer

The first part of the paper gives a general equation for triple-crystal arrangement with perfect crystals on the assumption that the third crystal is rotated. It is shown that in the case of perfect crystals the shape of the reflection curve is practically independent of the vertical divergence. The case of mosaic crystals is also solved and the possibility of rotation by other than the third crystal is considered. A method is proposed for investigating the imperfection of a crystal which is different from methods used up to now. The paper is supplemented by some experimental results.

---

, . , . , , . , . .

     

Self and mutual admittance of slot antennas on a dielectric half-space

In this paper, an efficient implementation of the spectral domain moment technique is presented for computing the self and mutual coupling between slot antennas on a dielectric half-space. It is demonstrated that by the proper selection of the weighting functions in the method of moments, the analytic evaluation or simplification of the transverse moment integrals is enabled. This results into a significant reduction of the required computational labor. The method is then utilized in order to provide design data for the self and mutual admittances between two slot antennas on a dielectric substrate lens in the case of fused quartz ( _r =3.80), crystal quartz ( _r =4.53), silicon ( _r =11.9) and GaAs ( _r =12.8). The presented technique and associated results are useful when designing twin slot quasi-optical receivers, imaging arrays, phased arrays or power-combining arrays of slot elements at millimeter-wave frequencies.     

W-Algebras,new rational models and completeness of thec=1 classification

Two series ofW with two generators are constructed from chiral vertex operators of a free field representation. Ifc=1–24k, there exists aW(2, 3k) algebra for k ₊/2 and aW(2, 8k) algebra for k ₊/4. All possible lowest-weight representations, their characters and fusion rules are calculated proving that these theories are rational. It is shown, that these non-unitary theories complete the classification of all rational theories with effective central chargec _eff=1. The results are generalized to the case of extended supersymmetric conformal algebras.     

Adiabatic hyperspherical approach to the Coulomb three-body problem: Theory and numerical method

The adiabatic hyperspherical (AH) approach to the three-body Coulomb bound-state problems is considered. The variational method of computation of the AH harmonics potential curves and coupling matrix elements is developed. The method takes into account the asymptotic behaviour of the AH harmonics at large and small values of the hyperradius . The developed method allows to perform calculations with high accuracy and stability for any hyperradius (0,) with only a few AH harmonics. The efficiency of the method and its convergence is illustrated by calculations of energy levels of the mesic moleculesdd anddt.