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.     

ТЕПЛОВАЯ ЭНЕРГИЯ ДИССОЦИАЦИИ И ОСНОВН ОЕ СОСТОЯНИЕF 2 + -ЦЕНТРОВ

+ - , , g - . , . .F ₂ ⁺ -. .     

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].

     

Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

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A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

An interpretation of the conditions for the existence of Shockley surface states

A study is made of the Shockley surface states in a linear chain of equal atoms, joined by alternately strong bonds. If the simple MO LCAO method is used, which considers the exchange integrals between nearest neighbours and next nearest neighbours, we get the surface states for a semi-infinite chain if the stronger bond is interrupted. The connection between Shockley and Tamm surface states is shown and the hypothesis is put forward that the condition for the existence of Shockley surface states has a generally simple physical interpretation, the validity of which is proved on the models of a semi-infinite crystal studied up to now.

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, . MO LCAO, , , . , , , .

     

О взаимодействии экс итонов с колебаниями кристаллической реш етки

, - . : - . - .     

ИспОльжОВАНИЕ ФлУОР ЕсцЕНтНОгО РЕНтгЕНО ВскОгО ИжлУЧЕНИь Дль кОНтАк тНОИ МИкРОРАДИОгРАФ ИИ

( )K- Fe, Ti Ca . , , , . , , , K- , .

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The use of fluorescent X-rays for contact microradiography

The possibilities of using fluorescentK-radiation of the elements Fe, Ti and Ca for contact microradiography of thin, little absorbing samples were studied and a simple set-up for carrying out this method, which uses a common type of microstructural X-ray tube as a source of the exciting radiation, was proposed. The experiments performed showed that if large magnifications are not required secondary-excitedK-radiation of the above-mentioned elements can be advantageously used for contact microradiography without the exposure times becoming impracticably long.

     

MV and Heyting Effect Algebras

We review the fact that an MV-algebra is the same thing as a lattice-ordered effect algebra in which disjoint elements are orthogonal. An HMV-algebra is an MV-effect algebra that is also a Heyting algebra and in which the Heyting center and the effect-algebra center coincide. We show that every effect algebra with the generalized comparability property is an HMV-algebra. We prove that, for an MV-effect algebra E, the following conditions are mutually equivalent: (i) E is HMV, (ii) E has a center valued pseudocomplementation, (iii) E admits a central cover mapping such that, for all p, qE, pq=0(p)q=0.     

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.

     

Radiation losses in completely ionized plasma

The losses caused by bremsstahlung during electron-ion and electron-electron collisions in a completely ionized plasma (in Born's approximation) are calculated. The calculation can be carried out analytically for a sufficiently dilute plasma (plasma with infinitely large Debay-Hückel radius). This assumption is satisfied very well by the known classification to actual controlled thermonuclear reaction. A dependence of the formI=an ². (1+3/2), wherea=0·73×10^–16 MeV.cm³.sec^–1,n is the number of ions per cm³ and =kT/mc ², is determined for the amount of energy radiated from 1 cm³ of plasma per sec. In the relativistic temperature regionkTmc ² the influence of electron-electron collisions begins to predominate. A number of important results concerning radiation losses in relativistic plasma will be published in a later paper.

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, ( ). ( -). . , I=an ². (1+3/2), =0,73. 10^–16 MeVcm²s^–1,n — =kT/mc ². kTmc ² . , .

     

ПОГЛОЩЕНИЕ И РАССЕЯНИЕ МОНОКРИСТАЛЛОВ NaCl ∶ Ni

NaCl Cd [10]. , NaCl Ni , .

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Absorption and dispersion on NaCl Ni crystals

The results of measuring the absorption and dispersion of light on NaCl Cd crystals were compared with the X-ray diffraction measurements by Toman [10]. The comparison showed that under certain conditions micro-regions of segregated impurities are produced in NaCl Ni crystals, apparent in an increased dispersion of light in the ultra-violet region.

     

Angular distribution of gamma quanta in the capture of polarized μ−-mesons by atomic nuclei

The capture of a polarized ^–-meson from theK-orbit of a mesic atom is investigated for the case when the nucleus after ^–-capture is in an excited state and emits a -quantum of multipolarityL (any type). The angular distribution of circular polarized -quanta with respect to the direction of the polarization of the ^–-meson on theK-orbit is obtained for the case of allowed transitions (according to the Morita-Fujii classification).

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- ^–-

^–- K- ^–- - L ( ). - ^–- K- ( -).

     

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

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

ЭЛЕКТРИЧЕСКАЯ ЭКВИВ АЛЕНТНАЯ СХЕМА ЗАТУХАЮЩИХ КОЛЕБАНИ Й СДВИГА ПЬЕЗОЭЛЕКТРИЧЕСКИХ СТЕРЖНЕЙ

n - , - .     

Determination of accuracy in measuring the parameters of tetragonal and hexagonal lattices

The procedure for determining the accuracy when measuring the parameters of tetragonal and hexagonal lattices is described. The accuracy can easily be calculated for all common methods by means of graphically represented functions. The relations derived can be used as quantitative criteria for the suitability of the combination of lines from which the lattice parameters are to be determined.

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. , . , .

     

Gentle perturbations

By introducing a specific type of perturbation,A, in the Hamiltonian, we define a class of gently perturbed states, ,A, of a canonical ensemble, . The perturbations are chosen so as to preserve a relationship of the form ,A constant ×. Applications in ergodic theory and phase transitions are described.     

ИЗОТОПЫ ФТОРА F19 И F21 В МОДЕЛИ НИЛЬССОНА

Energy levels and electromagnetic properties of fluorin isotopes in the Nilsson's model with Coriolis mixing are investigated. Position of the F¹⁹ levels is satisfactorily explained up to the energy of 4·5 MeV. Concerning the F²¹ it seems that the shell model will better correspond to the F²¹ nucleus.

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. , .     

The formation of dislocations by a spark discharge

The arrangement of dislocations formed in a single crystal of the alloy Fe-4·2% Si by a spark discharge in air is studied. The dislocations are made visible by etching on the surfaces perpendicular and parallel to the axis of the crater. The results of the observations are explained on the basis of microphysical conceptions of plastic deformation.

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, Fe— 4,2% Si . , . .

     

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.

     

Photostability of Molecules of Aromatic Amines in a Polymeric Matrix

In the temperature range T = 5–295 K, the spectralluminescent properties and curves of thermostimulated luminescence (TSL) of molecules of triphenylamine (TPA), trirtolylamine (TTA), triranisolamine (TAA), and N,N'diphenylbis(3methylphenyl)(1,1'biphenyl)4,4'diamine (TPD) in polystyrene and 4Brpolystyrene matrices have been investigated. It has been found that photoirradiation at room temperature in the region of the lowest electron transition of molecules leads to a decrease in the intensities of the luminescence, photoluminescence, and TSL bands, as well as to the formation of new deep traps for charge carriers. At equal irradiation doses these changes in TPD are noticeably less pronounced than in TPA, TTA, and TAA. The higher photochemical stability of TPD molecules compared to TPA, TTA, and TAA is attributed to the difference in the mechanisms of nonradiative deactivation of the triplet states of molecules.