Statistics of the One-Dimensional Riemann Walk

The Riemann walk is the lattice version of the Lévy flight. For the one-dimensional Riemann walk of Lévy exponent 0<<2 we study the statistics of the support, i.e., set of visited sites, after t steps. We consider a wide class of support related observables M(t), including the number S(t) of visited sites and the number I(t) of sequences of adjacent visited sites. For t we obtain the asymptotic power laws for the averages, variances, and correlations of these observables. Logarithmic correction factors appear for =2/3 and =1. Bulk and surface observables have different power laws for 1<2. Fluctuations are shown to be universal for 2/3 <2. This means that in the limit t the deviations from average M(t)M(t)–M-0304;(t-0304;) are fully described either by a single M independent stochastic process (when 2/3 <1) or by two such processes, one for the bulk and one for the surface observables (when 1<<2).     

Влияние переменного магнитного поля на остаточное состоя ние магнитно — Мягких материалов

. .

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The influence of an alternating magnetic field on the remanent state of magnetically soft materials

A study is made of the influence of an alternating magnetic field of varying maximum amplitude on the remanent state, or rather, apparent remanent state of toroidal and open samples of metallic and non-metallic magnetically soft ferromagnetics. An interpretation of the corresponding dependences is given on the basis of Kondorski's conception of the composition of a polycrystalline jerromagnetic material.

     

Quantum measurements,sequential and latent

The results of a hypothetical experiment requiring a sequence of quantum measurements are obtained retrospectively, after the experiment has been completed, from a single reading of an apparatus register. The experiment is carried out reversibly and Schrödinger's equation is satisfied until the terminal reading of the register. The technique is illustrated using a feasible method of measuring photon spin as the quantum object observable and using the photon energy as the apparatus register. The technique is used to discuss the watchdog effect, the effect of repeated measurements inhibiting quantum jumps.     

The optical constants of single crystals of hexagonal selenium

The optical constants of single crystals of hexagonal selenium in the region of the intrinsic absorption edge in polarized light were investigated. The absorption edge for light polarized normal to the optical axis of the crystal is displaced towards longer wavelengths. The absorption maximum of hexagonal selenium for a wavelength of 0·6 is interpreted as the maximum corresponding to interaction between neighbouring chains and in connection with this the position of the absorption edge of different modifications of selenium is discussed.

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. , , . 0,6 , .

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In conclusion the author wishes to thank Dr. E. Klier and R. Kuel for valuable discussions and advice. He thanks laboratory assistants J. Ontl and O. Kundrátová for help in the work.     

The critical point indices of ferroelectric and ferromagnetic phase transitions

Magnetic transitions are described by the critical indices0,1/3,4/3 while some ferroelectric transitions appear to give0,R~1/2,1. It is pointed out that these two sets of values for the critical indices are allowed by the scaling laws and stability conditions near the phase transitions.The authors thank Prof. R. S. Krishnan for his encouragement and Mr. B. Viswanathan for some discussions. The financial assistance from DAE and CSIR is also acknowledged.     

НИЗКОЧАСТОТНЫЕ КОЛЕ БАНИЯ ПРЯМОУГОЛЬНЫХ ПЛАСТИНОК ADP

- — . , - NH₄H₂PO₄,- ADP. ; - .     

Bunching phenomena during electron injection into the betatron II. Theory of starting conditions

A theory of the azimuthal bunching of electrons injected into the betatron is presented and compared with the experiments described in [1]. The bunching is treated as a small perturbation of the stationary beam.The stationary injected beam is replaced by the corresponding equilibrium beam of the same perveance so that the angular velocity spread of the injected electrons is proportional to the square root of the injection perveance.Self-consistent wave solutions for the perturbation of the stationary solution are then found. Equations giving the amplification of small density or energy disturbances along the beam are derived. These disturbances are assumed to be introduced by density or velocity modulation of the injected beam. The condition for the spontaneous occurrence of bunching is deduced by assuming that the disturbances do not vanish even when there is no modulation of the injected beam. The resulting expressions for the threshold perveance and the rise-time of the disturbance are in reasonably good agreement with the experiments. Such agreement may be considered as further verification of the statement made in [1] that the amplification of the disturbances is caused by the negative mass instability mechanism.

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, . , [1]. . . , , . . , ., . , , . . , , [1].

     

MultipletSO(n+1) scalar fields driving eternal expansion in closed (D+1)-dimensional FLRW cosmologies

The possibility of having a de Sitter asymptotic stage free of choice of the value of the positive cosmological constant (no critical ) is analyzed in a closed FLRW universe which starts from a quiescent phase of evolution and ends into a textured phase by taking into account multipletSO(n+1) scalar fields.On leave of absence from Universidade Federal do Rio de Janeiro, RJ, Brazil     

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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1- , 1964., , .

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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.     

ВОЗМОЖНОСТЬ ИССЛЕДО ВАНИЯ ХОДА ИСКАЖЕНИЙ РЕШЕТКИ В КРИСТАЛЛИКАХ ПРИ ПО МОЩИ РЕНТГЕНОВСКИХ Л УЧЕЙ РАЗНОЙ ДЛИНЫ ВОЛНЫ

, . , (K , , ), - , -. -, 25 a 1956.     

К ТЕОРИИ РЕЗОНАНСНОЙ МИГРАЦИИ ЭНЕРГИИ ВОЗ БУЖДЕНИЯ В ТВЕРДЫХ ТЕЛАХ

- - . - .     

Monochromator unit with high resolving power

The paper describes a double-crystal monochromator unit. The influence of vertical divergence of the beam on the luminosity and degree of monochromatization is discussed in detail and experimentally proved. Finally, the author shows how to apply a double-crystal monochromator unit (using analyzing crystals of germanium (111)) in fluorescent X-ray emission analysis, especially for an X-ray quantometer.

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. . ( (111)) , .

     

БЕТАТРОННЫЕ КОЛЕБАН ИЯ В УСКОРИТЕЛЕ С ОБЩИМ ПО ЛЕМ II

, , . , I. . . , .

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Betatron oscillations in an accelerator with a general field. II

In the second part of the theory of an accelerator with a generalized field the author solves the dynamics of particles in a stationary approximation (without acceleration). The trajectories of the particles in the neigbourhood of the equilibrium orbit are related to it as betatron oscillations. An analysis of betatron oscillations includes the region of stability determined by means of Routh-Hurwitz criterion, damping, resonance effects and field perturbations. A general matrix method is presented permiting the inclusion of all the focusing structures used in accelerators.

     

ВЛИЯНИЕ СПЕКТРАЛЬНО ГО ПРОФИЛЯ ДУБЛЕТАKα 1 α 2 И ДИФРАКЦИОННОГО РАС ШИРЕНИЯ НА ИНТЕГРАЛЬ НУЮ ИНТЕНСИВНОСТЬ ДИФРА КЦИЙ ПРИ ВЫСОКИХ УГЛА Х БРЭГГА

, K _{1 2} LP . 75°85° K , . , <80°. ( , ) <83°. , 90° , , , . >83° , , .

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The influence of the spectral profile of theK₁₂ doublet and diffraction broadening on the integrated intensities of high angle diffractions

Relations are derived giving the influence of the spectral profile of theK _{1 2} doublet and the influence of diffraction broadening on the productLP of the Lorentz and polarization factor. The relations are used to calculate the numerical values of the corresponding corrections for the theoretical values of the integrated intensities of diffractions in the angular region 75°85° and for the most frequently usedK radiation of copper, cobalt and iron.It follows from the calculated values of the corrections that, due to the accuracy at present attainable in experimental measurements, the influence of the spectral profile in diffractions with an angle<80° can be neglected when calculating the theoretical values of the integrated intensities. The influence of diffraction broadening need not be taken into account in diffractions with an angle<83° even when the broadening is large (e. g. five-fold). As the angle approaches 90°, of eourse, the corrections for both above influences suddenly increase, particularly those for diffraction broadening, and their limitation becomes difficult and is not single-valued. For this reason the use of diffractions with angles>83° does not appear very suitable for solving problems based on exact measurement of the integrated intensities and their comparison with the corresponding theoretical values.

     

Atomic versus ionized states in many-particle systems and the spectra of reduced density matrices: A model study

We study the spectrum of appropriate reduced density matrices for a model consisting of one quantum particle (electron) in a classical fluid (of protons) at thermal equilibrium. The quantum and classical particles interact by a shortrange, attractive potential such that the quantum particle can form atomic bound states with a single classical particle. We consider two models for the classical component: an ideal gas and the cell model of a fluid. We find that when the system is at low density the spectrum of the electron-proton pair density matrix has, in addition to a continuous part, a discrete part that is associated with atomic bound states. In the high-density limit the discrete eigenvalues disappear in the case of the cell model, indicating the existence of pressure ionization or a Mott effect according to a general criterion for characterizing bound and ionized electron-proton pairs in a plasma proposed recently by M. Girardeau. For the ideal gas model, on the other hand, eigenvalues remain even at high density.     

ПРИМЕНЕНИЕ ПАРАМАГН ИТНОГО РЕЗОНАНСА ДЛЯ ИССЛЕДОВАНИЯ РЕАКЦИЙ СВОБОДНЫХ РА ДИКАЛОВ

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The use of paramagnetic resonance in studying the reactions of free radicals

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

, .     

The probability distribution of the velocities of gas molecules after collision with a rapidly moving rigid body

The above problem is met, for example, in the case of the collision of molecules of the atmosphere with an artificial earth satellite and leads to the problem of determining the probability distribution of the absolute value of the vector sum of a constant vector and a Maxwell vector (the latter being a vector, whose rectangular components are distributed normally, with the same standard deviation and mean value zero). The resultant probability density is given by equation (18), the complement to the distribution function by (24), the mean value by (27) and the variance by (31). These results are obtained by transforming the corresponding three-dimensional normal distribution to spherical co-ordinates and integrating over the co-ordinate angles and , which yields the required probability density; the other results are then obtained from it by the usual methods.

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, , (. . , ). (18), -(24), -(27) (31). , ; .

     

Мезонные распады лег ких гиперфрагментов

, . . , °. K^–- , .

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The meson decay of light hyperfragments

The binding energies of five types of light hyperfragments, i. e. of atomic nuclei of light elements containing one hyperon instead of one neutron, were measured. The hyperfragments originated by means of the interaction of K^– mesons with the nuclei of light elements, contained in the emulsion.