Almost periodic Jacobi matrices associated with Julia sets for polynomials

Let be the Jacobi matrix associated with polynomialT(z) of degreeN2. The spectrum of is the Julia set associated withT(z) which in many cases is a Cantor set. Let ⁽¹⁾ denote the result of omitting the first row and column ofJ. Then it is shown that the spectrum of ⁽¹⁾ may be purely discrete.It is also shown that forT(z)= ^NC_N(z/) for > , whereC _N is a Chebychev polynomial the coefficients of and ⁽¹⁾ are limit periodic extending the work of Bellissard, Bessis, and Moussa (Phys. Rev. Lett.49, 701–704 (1982)).Supported in part by N.S.F. grant DMS-8401609Supported in part by N.S.F. grant MCS-8203325     

Generating fields from data onH − ⋃H +andH − ⋃I +

There are series solutions for characteristic boundary value problems for fields on black hole backgrounds that converge when the data are given on =^{– +}, or on =^{– +}, but may not converge when the data are given on ^{– –}, or on ^{+ +}. We specialize to oscillatory data of frequency and calculate approximate reflection and transmission coefficientsR() andT(), using a field generated by data on =^{– +}, and again, using a field generated by data on ^{– –}. The first calculation gives qualitatively good results at all frequencies at each order of approximation, and quantitatively better results at higher orders of approximation; the second calculation, using the series which may not converge, gives bad results except at very high frequencies. Thus for the physically unnatural case of a field that vanishes on ^– and goes toe ^iv on ⁺ we have a series that is convergent, and uniformly so with respect to frequency, while for the natural case of a field that vanishes on ^– and goes toe ^iv on ^– we are limited to high frequencies. It is argued that a frequency-dependent renormalization of a series of the first type provides an approximation scheme that is convergent, and uniformly so with respect to frequency, for the physically important problems of the second type. The difficulties posed by the -dependent renormalization for the study of incident pulses are discussed.     

The tangent bundle of a Calabi-Yau manifold-deformations and restriction to rational curves

The tangent bundle _X of a Calabi-Yau threefoldX is the only known example of a stable bundle with non-trivial restriction to any rational curve onX. By deforming the direct sum of _X and the trivial line bundle one can try to obtain new examples. We use algebro-geometric techniques to derive results in this direction. The relation to the finiteness of rational curves on Calabi-Yau threefolds is discussed.     

A remark on null infinity

It is shown that to each choice of conformal factor for the conformal metric on future null Infinity (₊) there is associated an equivalence class of slicings of ₊. Each slicing in turn gives rise to a family of null hypersurfaces in the physical space-time.Supported by NSF Grant No. GP-35773X1.     

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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A particle model for spinodal decomposition

We study a one-dimensional lattice gas where particles jump stochastically obeying an exclusion rule and having a small drift toward regions of higher concentration. We prove convergence in the continuum limit to a nonlinear parabolic equation whenever the initial density profile satisfies suitable conditions which depend on the strengtha of the drift. There is a critical valuea _c ofa. Fora<a _c, the density values are unrestricted, while foraa _c, they should all be to the right or to the left of a given interval (a). The diffusion coefficient of the limiting equation can be continued analytically to (a), and, in the interior of (a), it has negative values which should correspond to particle aggregation phenomena. We also show that the dynamics can be obtained as a limit of a Kawasaki evolution associated to a Kac potential. The coefficienta plays the role of the inverse temperature. The critical value ofa coincides with the critical inverse temperature in the van der Waals limit and (a) with the spinodal region. It is finally seen that in a scaling intermediate between the microscopic and the hydrodynamic, the system evolves according to an integrodifferential equation. The instanton solutions of this equation, as studied by Dal Passo and De Mottoni, are then related to the phase transition region in the thermodynamic phase diagram; analogies with the Cahn-Hilliard equations are also discussed.This paper is dedicated to Jerry Percus with great affection on the occasion of his 65th birthday.     

On the existence of solutions to Einstein's equation with non-zero Bondi news

It is shown that theC-metric (with parameters chosen to lie in suitable intervals) admits a conformal completion such that the space of generators of null infinity, , is a 2-sphere. This structure of is both necessary and sufficient for the analysis of gravitational radiation in exact general relativity. Bondi news (as well as the electromagnetic radiation field, in the charget case) is examined and found to be non-zero. Thus the issue of existence of exact solutions to the Einstein (and Einstein-Maxwell) equations admitting radiation (in the sense of Bondi, Sachs, and Penrose) is resolved. In addition, the analysis clarifies the sense in which the vacuumC-metric represents the gravitational field of two accelerating black-holes.     

A possible test of quantum electrodynamics by means of polarization effects in electron-nucleon scattering

The differential cross-section is given for the electromagnetic scattering of polarized relativistic electrons on polarized nucleons. The finite size of each particle is taken into account by means of two form-factors. The effect of the possible non-punctiform structure of the electron on the polarization effects in scattering is discussed. It is shown that the internal structure of the anomalous magnetic moment of the electron would show itself in the cross-section by terms depending on the transversal polarization of the incident electrons.

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Summary of results of a diploma-thesis for the degree of graduate physicist.

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In conclusion the author wishes to express his sincere gratitude to prof. V. Votruba and J. Kvasnica for suggesting this problem, for helpful discussions and valuable advice.     

ИЗЛУЧЕНИЕ ЭЛЕКТРИЧЕ СКОГО ДИПОЛЯ НАД ГРАН ИЦЕЙ ДВУХ СРЕД

, , . , - - . - . -, - , . , - ; , , .     

Energy and momentum in general relativity

In general relativity, conservation of energy and momentum is expressed by an equation of the form /x= 0, where –gT represents the total energy, momentum, and stress. This equation arises from the divergence formula dV _v = (/x ^v )d ⁴ d. Here we show that this formula fails to account properly for the system of basis vectors e(x). We obtain the (invariant) divergence formula e dV _v = e (/x ^v + )d ⁴ d. Conservation of energy and momentum is therefore expressed by the covariant equation (/x ^v ) + = 0. We go on to calculate the variation of the action under uniform displacements in space-time. This calculation yields the covariant equation of conservation, as well as the fully symmetric energy tensor . Finally, we discuss the transfer of energy and momentum, within the context of Einstein's theory of gravitation.     

Globally noncausal space-times. II. Naked singularities and curvature conditions

In this paper we prove that if there is a naked singularity, then there will be some null geodesic, reaching ⁺ from the singularity, which does not satisfy the strong curvature condition regardless of whether causality is violated or not. Assuming that a naked singularity is a strong curvature singularity only sufficiently far to the future, we prove that strong causality is violated arbitrarily close to ⁺.Work partially supported by the Nuffield Foundation and by the Consiglio Nazionale delle Ricerche of Italy under contract N.CT 81.00532.02.     

КРУЧЕНИЕ ПРИЗМАТИЧЕ СКИХ СТЕРЖНЕЙ ШВЕЛЛЕ РНОГО ПОПЕРЕЧНОГО СЕЧЕНИЯ

- [3], [4], U(x, y) . - U(x, y) -, . B § 10 - . , - , - D, . - .     

Honeycomb domain structure

A theory is given of a new structure produced when demagnetizing uniaxial single crystals (e.g. magnetoplumbite) in a field normal to thec axis. The experimental results fully support the theory on the assumption that domain structures produced under normal conditions are metastable. Methods are given by which stable structures can be prepared from such metastable ones. On the basis of these results opinions are expressed as to the nucleation of plate and honeycomb structures, produced either by reducing the field from saturation or by cooling below the Curie point.

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, (, ) , c. , , , , , . , . , .

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In conclusion the authors would like to thank C. Novák from the Institute of Technical Physics, Czechoslovak Academy of Sciences, for checking the calculation of the harmonic analysis and Z. Málek and J. Eousek for carefully reading the paper and for valuable remarks.     

Новый метод измерени я магнитокалорическ ого эффекта у ферромагни тных полупроводнико в

, .     

Double quantum transitions in paramagnetic resonance

The theory of double quantum transitions of the M=±2 type, with regard to inhomogeneously broadened spin systems is studied in this paper with the approximation ²T₂T₃ 1. We suppose that the inhomogeneous broadening is formed by an inhomogeneous crystal field. The obtained results describe the magnitude of absorption as a function of the h.f. power and also describe the shape of the absorption curve. It is demonstrated that in inhomogeneously broadened spin systems the absorption curve of double quantum transitions has the form of the difference of two different Lorentz's curves and that at the saturation ( ²T₂T₁ 1) the absorption increases with the cube of the h.f. field intensity. The shape of the curves is expressed by means of phenomenological relaxation constants of the system.

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M=±2 ²T₂T₃ 1. , - . . , ( ²T₂T₁ 1) . .

     

On the probability of double beta decay

Double beta decay is discussed in relation to parity non-conservation. Two possible ways of neutrino-less double beta decay (allowed and forbidden) are investigated and the half-life of decay is calculated. For allowed transitions we obtain for Ca⁴⁸ an estimatedT1/2=2×10¹⁹ years. The negative results of the experiments by Lukjanov et al., who give the valueT1/2=0.7×10¹⁹ years for the lower limit of the half-life of double beta decay of Ca⁴⁸, cannot therefore be regarded as a definitive solution of the question, whether the neutrino is a Dirac or Majorana particle. Further study of double beta decay, aimed at finding higher values of the lower limit of half-life, are of considerable importance for theory.

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- . - ( ) . ⁴⁸ T1/2210¹⁹ . - . [1] ( - ⁴⁸ T1/2 0,710¹⁹ ), , . - .

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In conclusion the author thanks Prof. I. S. apiro for suggesting this work and help in elaborating it.     

ДАЛЬНЕЙШИЕ ИССЛЕДОВ АНИЯ ФИЛЬТРА ДВОЙНОГ О ЛУЧЕПРЕЛОМЛЕНИЯ

, 4, (1954), 53. . .     

Hermiticity of Quantum Observables Versus Commutation Relations

In order to obtain sum rules and spectral representations the Hermiticity property , A = A, of observables is used. It is shown that for certain and the property turns out to be inconsistent with the commutation relations that contain A. The known Schwinger paradox is explained by this inconsistency.     

Representation of fuzzy quantum posets of types I,II

Let (,M) be a fuzzy quantum poset of type I, II, or FQP of type I, II for short. For Boolean representations of fuzzy quantum spaces, by a representation of (,M) we mean a quantum logic (i.e., an orthocomplemented-orthocomplete orthomodular poset with a homomorphismh: such that for any states onM and any observable ¯X on there is a state ¯s on and observableX onM such that the following diagram commutes [where () is a Borel-algebra of the real line ]: We prove that a representation of FQP of type I always exists and a representation of FQP of type II exists in some cases.     

Contribution of quantum corrections and superconducting fluctuations to the magnetic field and temperature dependence of the conductivity in amorphous CuTi and CuZr alloys

We report conductivity measurements on Cu _x Ti_100–x and Cu _x Zr_100–x glasses as a function of magnetic field (0B6T) and temperature (1.5–5. At low temperatures the measured conductivity(T,B)= ₀+(T)+(B,T) is compared quantitatively with the predictions of diagrammatic perturbation theories including quantum interference effects, spin-orbit scattering and electron-electron interaction. We obtain a set of characteristic fields for inelastic and spin orbit scattering from both the magnetic field and the temperature dependence of the measured (T, B). Below about 4K the Coulomb interaction determines (T) in consistence with the Hall effect, whereas quantum interference processes and spin-orbit scattering dominate the magnetic field dependence. In case of Cu _x Zr_100–x , (B, T) can be explained by taking into account superconducting fluctuations (Maki-Thompson and Aslamasov-Larkin parts) in addition. Superconducting fluctuations dominate the temperature dependence as well. For high magnetic fields and lower temperatures (B/T>1T/K) we find discrepancies between experiment and calculations from perturbation theory.