Exact expressions for row correlation functions in the isotropicd=2 ising model

We present exact explicit expressions for the row spin-spin correlation functions _{00 n}0 in the isotropicd= 2 Ising model, in terms of elliptic integrals, forn 5. We also give a general structural formula for _{00 n}0.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

Asymptotic theory of multidimensional chaos

A delay-differential equationu(t)+u(t)=f(u(t–1)), 0t < , and its generalization are investigated in the limit 0, when the attractor's dimension increases infinitely. It is shown that a number of statistical characteristics are asymptotically independent of. As for the attractor, it can be regarded as a direct product ofO(1/) equivalent subattractors, their statistical characteristics being asymptotically independent of . The results enable one to predict some characteristics of the attractor with fractal dimensionD 1 for the case 1, when they are inaccessible numerically. The approach developed seems to be applicable for a wide class of spatiotemporal systems.     

Error performance analysis for an optical heterodyne FSK communication system with a limiter-discriminator-integrator detector

The error probability for a coherent optical heterodyne FSK system with a limiter-discriminator-integrator (LDI) detector is analysed. The analysis includes laser quantum phase noise, the correlated receiver additive white Gaussian noise (AWGN), Gaussian narrow-band IF filtering and intersymbol interference (ISI) caused by it. It is shown that, for 1 dBEb/N ₀penalty at bit error rate (BER) 10^–9, (i) the normalized IF beat spectral linewidth T0.35% for frequency deviation ratioh=0.5(MSK), and T0.5% forh=0.7 (the receiver is insensitive to laser quantum phase noise ath=1.0, if ISI is not included.); (ii) if ISI is incorporated, T0.15% forh=0.5, T0.5% forh=0.7, both with 3dB bandwidth-bit period product (3.0>BT1.5), and T0.5% forh=1.0 with BT1.0 ifT0.35% when ISI exists,h=0.7 is optimum;h=1.0 otherwise.     

ЗАТУХАНИЕ КОЛЕБАНИЙ ЧАСТИЦ В ОБЩЕМ ПОЛЕ С ПЕРИОДИЧЕСКОЙ СТРУКТУРОЙ I

, , . , . .

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The damping of particle oscillations in a general field with periodic structure I

A liner theory is derived, discussing the dynamics of particles in the region of an equilibrium orbit in a general electromagnetic field, which forms a periodic system. The total particle damping is determined from the Hamiltonian found and from dissipative forces brought out by a classical reaction radiation. Relations for the damping of the synchrotron oscillations are derived from the study of the appropriate phase space.

     

Asymptotic behaviour of spin-momentum distribution observables for fermion fields with cut-off self-coupling

In a previous paper asymptotic creation and annhilation operatorsa _± ^# have been constructed by the Kato-Mugibayashi method from the creation and annihilation operatorsa ^# for spin 1/2 fields with an interaction Hamiltonian density which is an evendegree polynomial in the field with ultra-violet cut-off and its derivatives. For any eigenvector of the total HamiltonianH=H ₀+H _I partial isometries _± have been defined so thata _± ^# equal _± a ^# *_± on the ranges _± of _±. Since the existence of a groundstate ofH has been proved, the existence of at least one pair _± follows. The purpose of this paper is to show that for any _± orthogonal to the distribution of spins and momenta of the interacting Schrödinger states exp[–itH]_± approaches fort the distributions of spins and momenta of the free state exp[–itH ₀] if a wave-amplitude renormalization is carried out in _±. This is achieved by studying the expectation values of the operators in themaximally abelian W*-algebra generated by operators of the form a*a, in terms of whichany information about spins and momenta can be expressed.Supported in part by the National Research Council of Canada.     

Polarization of photo-luminescence of ZnS: Cu monocrystals

Different models of luminescence centres are discussed on the basis of measurements of the composition of ZnS monocrystal photo-luminescence in different polarizations and temperature dependence of the degree of polarization. Those of the models submitted by Birman, which assume the polarization to be due to the different force of the oscillators for transitions withEc andEc, or models assuming luminescence polarization to be due to the orientation of the luminescence centres, agree with the results of experiments, i.e. the temperature independence of the degree of polarization and the conformable spectral composition of both polarizations. It is also shown that measurements made up to now of the degree of polarization must be taken as orientational as a consequence of the depolarizing influence of the diffused rays of luminescence on its value.

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ZnS: Cu

ZnS , . , . . , , , E E, , . , , - .

     

Un phénomène de concentration évanescente pour des flots non-stationnaires incompressibles en dimension deux

We consider a sequencev of non-stationary solutions of the incompressible 2D-Euler equation, locally bounded inL ². We prove that if the defect measure is supported in a one-dimensional set (³) of some special type (which we call finite type), the weak limitv ofv is a solution of the Euler equations: our theorem is of the type concentration-cancellation.     

On the asymptotic behaviour of infinite gradient systems

We consider gradient systems of infinitely many particles in one-dimensional space interacting via a positive invariant pair potential with a hard core. The main assumption is that is strictly convex within the rangeR of (whereR is a fixed number ). Under some technical conditions we prove the following theorems: Let the initial distribution be given by a translation invariant point process onR ¹. Then there exists only one extreme equilibrium state with a given intensityI() satisfyingI()R ^–1, and all ergodic initial distributions with an intensityI()R ^–1 converge weakly ast to the extreme equilibrium state with the same intensity.     

Lorentzian Warped Products and Singularity

We show that to any convex function f: ⁿ there correspondinfinitely many geodesically complete metricsds² such that Ric() 0 for anynonspacelike vector . These metrics are constructedas the warped products of the natural metric in and the inner metric of a convexhyperface (the graph of f) in ^{n + 1}.     

Analysis of the order parameter for uniform nearest particle system

The uniform nearest particle system (UNPS) is studied, which is a continuoustime Markov process with state space . The rigorous upper bound ^(mf) = ( – 1)/ for the order parameter ₂, is given by the correlation identity and the FKG inequality. Then an improvement of this bound ^(mf) is shown in a similar fashion; C( – 1)/|log( – 1) for >1. Recently, Mountford proved that the critical value _c=1. Combining his result and our improved bound implies that if the critical exponent exists, it is strictly greater than the mean-field value 1 in the weak sense.     

ФИЗИЧЕСКИЕ ОСНОВЫ ИЗ МЕРЕНИЯ НАПРАВЛЕНИЯ ВОЗДУШНОГО ПОТОКА МЕ ТОДОМ НАКАЛЕННОЙ ПРО ВОЛОКИ ПРИ ВЫСОКНХ ПОДЗВУКО ВЫХ СКОРОСТЯХ

d - l - t _d R _max - J , ( ) - - , . . - ( ) - - R R _max —R. ,      

Studies on the microstructure of phase transitions in two kinds of liquid crystals by PAT and DSC

The positron lifetime and DSC measerments for EBBA and DOBAMBC have been made with heating and cooling clycles. The experimental results show that a shorter lifetime (₁) is essentially independent of temperature while the longer lifetime (₂) and the intensity (I ₂) change abruptly double or triple with temperature. Consequently, the EBBA has only nematic phases while the DOBAMBC has two liquid-crystalline phases (smectic C* and smectic A) with transition temperatures as follows: for EBBA, solid nematic (304.5 K), nematic isotropic (356.5 K), isotropic nematic (356.5 K), nematic solid (301 K); and for DOBAMBC, solid smectic C* (346 K), smectic C* smectic A (357.5 K), smectic A isotropic (389 K). These critical temperatures are in accordance with the transition temperatures measured by DSC. In addition, the difference in the solid-nematic transition temperature in the heating and cooling cycles was also observed. A discussion about the correlation of the observed changes in lifetime (₂) with the changes in molecular orientational order (S) and dielectric anisotropy () is presented.     

Current distributions in a two-dimensional random-resistor network

The current and logarithm-of-the-current distributionsn(i) andn(ln i) on bond diluted two-dimensional random-resistor networks at the percolation threshold are studied by a modified transfer matrix method. Thek th moment (–9k8) of n(ln i) i.e., ln i&^k, is found to scale with the linear sizeL as (InL)^(k). The exponents (k) are not inconsistent with the recent theoretical prediction (k)=k, with deviations which may be attributed to severe finitesize effects. For small currents, ln n(y)–, yielding information on the threshold below which the multifractality of (i) breaks down. Our numerical results for the moments of the currents are consistent with other available results.     

The quantum theory of the spontaneous magnetization of ferrimagnetics,anti-ferromagnetics and thin films with arbitrary spin at high temperatures

Using Van Vleck's modification of the Heisenberg theory of ferro-magnetism for substances with arbitrary spin per atom, a generalization of the theory is given for the case of ferrimagnetics, anti-ferromagnetics and thin films with an arbitrary number of sub-lattices and with arbitrary spin per atom. The exchange part of the energy operator is formulated by means of rotated spin operators. The theory contains the quantum-mechanical generalization of non-quantum theories given by Néel and later generalized by Yafet and Kittel. It also contains the theory of thin films proposed recently by the author. The magnetization laws are completely analogous to the relations derived from the theory of molecular fields. The constants of the molecular fields are interpreted by means of exchange integrals. For the special case of spin S=1/2the theory agrees with the results of the work of Vlasov and Imuchametov for ferrimagnetics and anti-ferromagnetics and with the author's for thin films.

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,

, , , . . - , . , . , . . S=1/2 .

     

A new geometrical gravitational theory

A geometrical gravitational theory based on the connection ={ } + ln + ln –g ln is developed. The field equations for the new theory are uniquely determined apart from one unknown dimensionless parameter ₂. The geometry on which our theory is based is an extension of the Weyl geometry, and by the extension the gravitational coupling constant and the gravitational mass are made to be dynamical and geometrical. The fundamental geometrical objects in the theory are a metricg and two gauge scalars and. Physically the gravitational potential corresponds tog in the same way as in general relativity, the gravitational coupling constant to ^–2, and the gravitational mass tou(, ), which is a coscalar of power –1 algebraically made of and. The theory satisfies the weak equivalence principle, but breaks the strong one generally. We shall find outu(, )= on the assumption that the strong one keeps holding good at least for bosons of low spins. Thus we have the simple correspondence between the geometrical objects and the gravitational objects. Since the theory satisfies the weak one, the inertial mass is also dynamical and geometrical in the same way as is the gravitational mass. Moreover, the cosmological term in the theory is a coscalar of power –4 algebraically made of andu(, ), so it is dynamical, too. Finally we give spherically symmetric exact solutions. The permissible range of the unknown parameter ₂ is experimentally determined by applying the solutions to the solar system.     

Local and non-local conserved quantities for generalized non-linear Schrödinger equations

It is shown how to construct infinitely many conserved quantities for the classical non-linear Schrödinger equation associated with an arbitrary Hermitian symmetric spaceG/K. These quantities are non-local in general, but include a series of local quantities as a special case. Their Poisson bracket algebra is studied, and is found to be a realization of the half Kac-Moody algebrak _R [], consisting of polynomials in positive powers of a complex parameter which have coefficients in the compact real form ofk (the Lie algebra ofK).     

A remark on the decay rate of bound muons

The probability of the decay of a bound -meson is calculated using the theory of weak interactions with an intermediate boson. It is found that this theory, like all the others, cannot explain the experimental maximum atZ=26.

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- K-

- K- . , , , Z=26.

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I wish to acknowledge my indebtedness to Professor V. Votruba for suggesting the problem and for valuable discussions.     

К ПРОБЛЕМЕ МАГНИТНОЙ ФОКУСИРОВКИ ПУЧКОВ ЭЛЕКТРОНОВ, ЭМИТТИРО ВАННЫХ С ТЕПЛОВЫМИ СКОРОСТЯМИ

, . — , , — - . , - -. - .     

On the electroluminescence of powdered zinc sulphide layers

The experimental study of the dependence of the electroluminescence brightness on the voltage confirms the correctness of the mechanism of electroluminescence, based on impact ionization in parts of the crystal where the electric field is concentrated. A study of the photoluminescent and electroluminescent spectra of phosphors containing two activators (copper and an element of rare earth) permits the determination of the magnitude of the volume of the crystal in which electroluminescence occurs. A study of the influence of the stored light sum on the brightness of electroluminescence and a study of the rate of growth of the variable and constant components of electroluminescence point to the fact that the excitation is transferred from the region of field concentration to the whole volume of the crystal.

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, . - , ( ), , . .