Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.     

Surviving extrema for the action on the twisted SU(∞) one point lattice

We give a simplified construction of twist eating configurations, based on a theorem due to Frobenius. These configurations are defined through the equation:U U U ⁺ U ⁺ =exp(2in /N) withU SU(N), =1 tod andn an antisymmetric matrix with integer entries. In the (Twisted)-Eguchi-Kawai model they yield extrema some of which survive forN. Comparison is made with the Monte Carlo data of the internal energy in the small coupling region.     

Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model

We find the asymptotic decrease of correlations < _{A +y} , _B >,yZ ^v +1, |y|, in the Ising model at high temperatures. For the case when monomials _A and _B both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension . For even monomials _A , _B we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) =1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary . Here we use besides the saddle-point method, some arguments from scattering theory.     

Nonlinear Response of the Semiconductor Laser with Pump Current Modulation

The influence of tuning the lasing monochromatic radiation frequency _g within the amplification band on the nonlinear response of the semiconductor laser with harmonic modulation of pump current is investigated theoretically. It is established that the principal features of the behavior of the nonlinear amplitude-detuning characteristic (ADC) are determined by the relation between the current modulation frequency _m and the main resonance frequency of the laser _r. If _{m r}, then with increase in _g the response decreases monotonically mainly due to the decrease of its dynamic component. The exception is provided by the spectral regions where peaks on the ADC appear because of the explicitly nonlinear lasing regimes (period doubling, chaos, etc.) When _m < _r, the resonance conditions for induced oscillations are satisfied only for definite spectral intervals within the amplification band and a dip appears on the low-frequency side of the ADC. With decreasing _m, the dip boundary shifts to a more high-frequency region of the band corresponding to smaller local resonance frequencies. The peaks on the ADC corresponding to the radiation period doubling shift to the region of smaller values of _g on increase in _m.     

Analysis of the Vibrational-Rotational Structure of 2ν1, ν1 + ν3, and 2ν3 Bands of the D2Se Molecule

The absorption spectrum of the D₂Se molecule in the region of 2₁, ₁ + ₃, and 2₃ absorption bands is registered with a high-resolution Fourier spectrometer and is studied theoretically for a Hamiltonian model with allowance for resonant interactions among (200), (101), and (002) vibrational states.     

Additivity of vector gleason measures

We study the degree of additivity of orthogonal Hilbert-space-valued measures on the latticeL(H) of all projections acting on a Hilbert spaceH. We present criteria for such measures to be completely additive and we establish the connection between the additivity of orthogonal measures and the size of almost disjoint families on dimH. [For example, we show that everyH-valued orthogonal measure is weakly-additive iff (dimH) > dim H]. As a corollary we see that finitely additive orthogonal measures distinguish dimensions of Hilbert spaces (this can be viewed as a generalization of a theorem by Kruszynski). As a further corollary, we obtain that, for cardinals, with >,3, there is no Jordan homomorphism from a typeI -factor into a typeI -factor. Finally, we show that every latticeL(H) with (dimH) = dimH admits a nonzero free orthogonal measure with values inH. Our results contribute to the noncommutative probability theory and also may find applications in the theory of the representation ofC ^*-algebras.     

Phantom scalar fields in five-dimensional Kaluza-Klein theory

The existence of a so-called "phantom" scalar field in some Riemannian spaceV ₄, i.e., a field in which the effective energy momentum tensorT ^(sf) vanishes in the five-dimensional Kaluza-Klein theory, is investigated by means of the integrability conditions for relations of the form _;;=k_,,+bg found in [6]. Phantom fields are found in homogeneous isotropic cosmological models.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 50–56, February, 1996.     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.     

Low-temperature and long-time anomalies of a damped quantum particle

The time evolution of a damped quantum particle is discussed. Dissipation is modeled by the bilinear coupling to a set of harmonic oscillators. Using a functional integral technique that accounts for initial correlations between the particle and the reservoir, one can express the dynamics of the damped particle entirely in terms of equilibrium correlation functions. The long-time behavior of these correlations is determined for memory damping arising from the coupling to a reservoir with spectral densityI() at low frequencies, where > 0. The time evolution of nonequilibrium initial states of the damped particle is discussed. At finite temperatures an initially localized state is found to spread subdiffusively or superdiffusively, depending on . For > 2 the damping becomes ineffective for long times, and the width of a state grows kinematically. At zero temperature and for < 1, an initially localized state remains localized for all times. For 1 the state spreads, but with a slower rate than at finite temperatures. Study of arbitrary initial states indicates that the process is ergodic at finite temperatures only for 2 and at zero temperature for 1 2.     

Some Remarks on a Nongeometrical Interpretation of Gravity and the Flatness Problem

In a nongeometrical interpretation of gravity,the metric g(x) = + (x)is interpreted as an effective metric, whereas(x) is interpreted as afundamental gravitational field, propagated in spacetime which isactually flat. Some advantages and disadvantages of suchan interpretation are discussed. The main advantage isa natural resolution of the flatness problem.     

On two “self-creation” cosmologies

An attempt to produce a continuous creation theory by adapting the Brans-Dicke theory is described. The universe is seen to be created out of self-contained gravitational, scalar, and matter fields. However, the solution of the one-body problem reveals unsatisfactory characteristics of the theory, and in particular the principle of equivalence is severely violated. A second theory is described which retains the attractive features of the first theory and which does not fall foul of its objections. There do exist empirical tests for the theory which are described and which will require further examination. In the limit this theory approaches general relativity in every respect.Notation ² gf the invariant d'Alembertian - t ₀ Hubble time - H Hubble's constant - scalar field - coupling constant - T _M energy-momentum tensor of matter and nongravitational energy, and nonscalar field energy - T _M energy-momentum tensor of scalar field energy - T _M covariant form - T _M contravariant form - T _M mixed form - T _M T _M trace - T _{M ;} covariant differentiation - contravariant differentiation - T Ricci tensor - R curvature scalar (in tensorial equations) - Kronecker symbol - () a function of used in the text - density - p pressure - g the metric tensor - R(t) scale factor (in cosmological equations) - U the fluid 4-velocity (covariant) - U the fluid 4-velocity (contravariant) - functions differentiated once with respect to time ( , differenciated twice) - k the Robertson-Walker curvature constant=+1, 0, or –1 - proportional to - g gravitational coefficient - parameter - angle of deflection, or coordinate - angle of precession or coordinate - angle of precession - G _v the force density - ³( – _n (t)) the Dirac delta function - proper time - K an unknown function definingG - total angle of deflection - r ₀ minimum radius of approach of a light ray grazing the sun     

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.

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Zur Frage derZ-Zentren bei der Exoelektronenemission aus Alkalihalogeniden

Zusammenfassung Es wurde das Maximum des Exoelektronenemissionsstroms untersucht, das an NaCl infolge Verunreinigung durch Kalzium auftritt, und die Möglichkeit, dieses Maximum denZ-Zentren zuzuordnen, diskutiert.

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Z-

, NaCl . Z-.

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Wir danken herzlichst Herrn Dr. A. Bohun für das gefällige überlassen des NaCl: Ca-Materials.     

The application of the thermodynamics of irreversible processes to welding arcs

The self-regulation of an inert gas shielded metal welding arc is dealt with briefly. A thermodynamic equation is derived for the self-regulation of such an arc.

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. .

     

Magnetization coils without iron core for high field intensities

A new theory of rectangular coils without an iron core is described which amends the old one of Fabry and Bitter. It enables us to compute field intensities in coils having very small openings, which the old theory could not do.

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New interpretation of experiments on the intermediate meson

A new theory of weak interactions is proposed in which the coupling between theV-A currents j(X) and j(X) is achieved not by vector mesons [by a propagator D ^c (X-X)], but by a scalar functionR(X – X), a fermion-antifermion loop which plays the role of a unique film joining two different pointsX andX of completely uncoupled space-times (as a result of which the space becomes a continuum). The existence of the actual currents j results from correlations between the two different spinor layers of Dirac layer formation.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 25–40, February, 1996.     

Ferromagnetic resonance in thin cobalt films

The paper gives the results of measuring ferromagnetic resonance on thin cobalt films, vacuum deposited on unheated glass slides. The values of the (g-factor, the width of the curve, the effective stress and uniaxial induced anisotropy were determined as a function of the thickness of the film from measurements of the ferromagnetic absorption in a magnetic field normal and parallel to the surface of the film. Measurements were carried out on a frequency of 9200 MHz and on film thicknesses of 180 to 1800 Å. A qualitative explanation of the observed dependences is given.

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, . , , g-, , , . 9200 MHz 180–1800 Å. .

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The author thanks V. Kamberský and Z. Málek, C. Sc., for providing some of the cobalt films and for help in depositing and measuring the thicknesses, S. Kadeková and M. Polcarová for valuable advice in determining the structure of the films, J. Míová for carefully plotting the results of measurements and Z. Málek and O. tirand for carefully reading the paper and for valuable discussions.     

The effect of oxygen on the electric conductivity of a cuprous oxide single crystal

The effect of an excess of oxygen on the electric conductivity of a pre-illuminated and heated single crystal of Cu₂O is investigated. It is found that the influence of illumination on the electric conductivity, together with the concentration of impurities, increases with increasing oxygen pressure during annealing.

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, Cu₂O. , .

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In conclusion the author thanks E. Klier and J. Pastrak for valuable remarks and discussion.     

МОДЕЛИРОВАНИЕ ЭЛЕКТ РОННО-ОПТИЧЕСКИХ СИС ТЕМ С ОСЕВОЙ СИММЕТРИЕЙ П РИ ПОМОЩИ СЕТИ СОПРОТИВЛЕНИЙ

The paper explains the theory of modelling electrostatic fields by a resistance network. The conditions, which the resistance network must satisfy, are derived and the question of modelling electrodes of different shapes is solved. The finished network and the results obtained on it when modelling a jet for a linear h-f accelerator of electrons are described. Particular attention is paid to the influence of a space charge, the modelling of which is an advantage of this method.

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Strict inequalities for some critical exponents in two-dimensional percolation

For 2D percolation we slightly improve a result of Chayes and Chayes to the effect that the critical exponent for the percolation probability isstrictly less than 1. The same argument is applied to prove that ifL():={(x, y):x=r cos, y=r sin for some r0, or} and():=limpp _c [log(p–p _c )]^–1 log P_cr {itO is connected to by an occupied path inL()}, then() is strictly decreasing in on [0, 2]. Similarly, lim_n [–logn]^–1 logP _cr {itO is connected by an occupied path inL()() to the exterior of [–n, n]×[–n, n] is strictly decreasing in on [0, 2].