The rate of growth of density perturbations in simple big-bang model universes

In this paper we present exact solutions to the density perturbation equation derived by Bonnor for the cases where = _c ,k=1 and = – _c ,k=–1. The solutions when =0,k=1 and =0,k=–1 have been previously published. Using these solutions a quantitative analysis has been carried out that has enabled us to estimate the size of the fluctuations that must be postulated at decoupling in order to explain the formation of the galaxies in these model universes.     

Plane-symmetric magnetofluid cosmological models

The solutions of the Einstein and Einstein-Maxwell equations for magnetofluid with cosmological constant are obtained for plane-symmetric space-time. We recover the results of Hojman and Santamarina in a special case when the magnetic field is made to vanish. It has also been shown that under a suitable transformation the cases =0 and 0 are mathematically equivalent.     

Anisotropic viscous universe with variableG and Λ

An anisotropic model with variableG and and bulk viscosity is considered. The model exhibits an inflationary behavior during which the coefficient of bulk viscosity varies lineraly with the energy density. This allows the anisotropy energy to decrease exponentially with time. Other results overlap with our earlier work with a different ansatz for . The gravitational constant was found to increase during the radiation and matter epochs.     

О влиянии флукаций электронной концентрации на меру дисперсии и мету вращения

, (DM) (RM). , DM RM N _e = n _e ds. M _e = n _e H cos ds ; . Lerche (1970a, b) , DM RM N _e M _e . .     

Оπорная селенодезическая система координат по гелиометрическим наБлюдениям луны В казани

, 1969–1975 .., 32 . , .     

Does the gravitational “constant” increase?

The possibility that the gravitational coupling constantG is an increasing function of the cosmic timet is discussed.In Section 1 the Maximal Power Hypothesis (MPH) stating that no power in Nature can exceed the upper boundc ⁵/G (Gunn's luminosity) is advocated.In Sections 2, 3, and 4 the MPH is employed on the cosmological scale to support the idea of an increasingG. In Section 2 the increasingG is obtained by two assumptions - the MPH and the energy conservation law - and by nothing else.In Section 3 the increasingG follows naturally from the MPH in the Einstein-Cartan theory of gravity. The arguments proposed in Sections 2 and 3 lead todG(t)/dt > 0 but cannot specify the form ofG(t). In Section 4 the MPH is applied to the energy of the vacuum and leads to a relation betweenG and the cosmological term,G S ³, valid in a matter-dominated universe (S =S(t) is the expansion factor). This relation plus the time-dependence law (suggested by many authors) t ² = constant, plustH > 2/3 (suggested by observations on the age of globular clusters;H is the Hubble parameter) implies an increasingG. One finds also GU, whereU is the mass density of the universe, in agreement with other studies.     

The nonlinear solar dynamo and differential rotation: A Taylor number puzzle?

We consider dynamically consistent mean-field dynamos in a spherical shell of incompressible fluid. The generation of magnetic field and differential rotation is parameterized by the - and -effects, respectively. Extending previous investigations, we include now the cases of moderate and rapid rotation in the sense that the inverse Rossby number can approach or exceed unity: This can lead to disk-shaped -contours, which are in better accordance with recent results of helioseismology than cylindrical -contours. On the other hand, in order to obtain -dynamo cycles the Taylor number has to be so large, that eventually cylindrical -contours become unavoidable (cf. Taylor-Proudman theorem). We discuss the different possibilities in a state diagram, where the inverse Rossby number and the relative correlation length are taken as the elementary parameters for mean-field dynamos.     

YO molecule in the sun

Vibrational transition probabilities, namely Franck—Condon factors and -centroids have been evaluated by an approximate analytical method for the (A–X), (A–X), and (A–X) system of YO molecule. Morse potential energy curves forX ²⁺,A ²₂,A²₂, andA²₂, states of YO have been constructed using the latest spectroscopic data. The value of -centroids for the band have been found to decrease linearly with the corresponding wavelengths. We show results for two new transitions of (A–X) and (A–X) and five new bands of (A–X) of YO in the umbral spectrum of the Sun.     

Evidence for a low-density inflationary universe?

The inflationary unvierse model predicts the density parameter ₀ to be 1.0 with the cosmological constant ₀ usually taken to be zero, whereas observational estimates give ₀0.2 and ₀10^-57 cm^–2. It was found, however, that the observed variation of angular diameter with redshift for extragalactic radio sources could be interpreted in terms of a low density universe with linear size evolution of the sources for either an inflationary model with 0 or an open model with =0.     

Абсолютная система высот в краевой зоне луны по наблениям покрытий звэзд

. , .     

Electrical conductivity of neutron star cores in the presence of a magnetic field

General theory of electrical conductivity of a multicomponent mixture of degenerate fermions in a magnetic fieldB, developed in the preceding article (this volume), is applied to a matter in neutron star interiors at densities ₀, where ₀ = 2.8×10¹⁴ g cm^–3 is the standard nuclear matter density. A model of free-particle mixture ofn, p, e is used, with account for appearance of ^–-hyperons at > _c , where _c 4₀. The electric resistivities along and acrossB, and , and the Hall resistivity _H are calculated and fitted by simple analytical formulae at _c and > _c for the cases of normal or superfluid neutrons provided other particles are normal. Charge transport alongB is produced by electrons, due to their Coulombic collisions with other charged particles; is independent ofB and almost independent of the neutron superfluidity. Charge transport acrossB at largeB may be essentially determined by other charged particles. If _c , one has = [1 + (B/B ₀)²] for the normal neutrons, and for the superfluid neutrons, while _H = B/B _e for both cases. HereB _e 10⁹ T ₈ ² G,B ₀10¹¹ T ₈ ² G, andT ₈ is temperature in units of 10⁸ K. Accordingly for the normal neutrons atBB ₀, the transverse resistivity suffers an enhancement, _{1/4 1}. When 5₀ andB varies from 0 toBB _p 10¹³ T ₈ ² G, increases by a factor of about 10³–10⁴ and _H changes sign. WhenBB _p , remains constant for the superfluid neutrons, and _H B ² for the normal neutrons, while _H B for any neutron state. Strong dependence of resistivity onB, T, and may affect evolution of magnetic fields in neutron star cores. In particular, the enhancement of at highB may noticeably speed up the Ohmic decay of those electric currents which are perpendicular toB.     

Набλюдатрльльй подхои к ранним ста диям эволюции звезд

. . u . . . ]qi . , , . . (, , , , -). . , . , . FU ) - ).     

Models of clusters of point masses with large central redshifts

Conclusions In the Newtonian case we have obtained an isotropic self-consistent distribution of gravitationally interacting point masses which satisfies the transport equation without collisions, and the gravitational equation for an arbitrary powerfunction density distribution =r^–s, s<3.For =r^–2 the analogous self-consistent solution was obtained for the anisotropic distribution function both in Newtonian and GTR cases.The GTR solutions with =r^–2 have central redshifts which increase without limit in accordance with the law 1+zr^–1/ as we approach the center. In the isotropic case, they appear to be stable when the mean velocities are much less than the velocity of light u<0.2c, >21.The hydrodynamic GTR solution was found for a perfect gas at constant temperature (but variable T=T(g₀₀)^1/2) which also has z for r0.We should like to thank K. Thorne, L. Hazin, and M. Podurets for valuable discussions. K. Thorne was particularly helpful in supplying unpublished results on circular orbits obtained by American authors.Astrofizika, Vol. 5, No. 2, pp. 223–234, 1969     

Перенос поляризации излучения В магнитоактивной космической плазме

u , . , .. (1.10), (1.2) ( (1.2)) . (1964) . (1.10), , , , (1.13). , , S _iq ,R _iglm ,K _iqlm (1.10) . , . . , (1.3), (2.3); (2.8)–(2.10). , , , , z (2.20), .. , , (. (2.15)). (K _{e, 0} ) . ^S , ( (2.24)). (2.24a) ^S ±/4. , , (K _{e, o}<0). L, — , , ; , . .     

Horizontal-branch star models

Evolutionary tracks of 0.9M , 0.7M and 0.6M models for Population II stars have been computed in the post-red giant phase. The stars are initially composed of a helium core containing a mass fraction equal to 0.9 and of a hydrogen-rich envelope. They represent hypothetical remnants of stars after substantial mass loss in previous evolutionary phases or/and at the helium flash.u 0,9M , 0,7M 0,6M . , 90% , . , .Riassunto È stata calcolata per modelli di stelle di 0,9M , 0,7M e 0,6M di Popolazione II l'evoluzione successiva allo stadio di gigante rossa. Inizialmente i modelli constano di un nucleo di elio contenente il 90% della massa totale e di un inviluppo idrogenico. Essi possono interpretarsi come i resti di stelle che abbiano perso una frazione di massa considerevole in fasi evolutive precedenti, o all'innesco violento dell'elio al centro.     

Determination of Optical Spectra by a Modified Kramers Kronig Integral

A new modified Kramers Kronig Integral is derived and shown to produce excellent results when k data is only known over a limited range. By considering the effect of resonance features simulated using the Dirac-Delta function, the new integral is shown to be more rapidly converging than both the conventional Kramers Kronig integral and a modified (Subtractive Kramers Kronig – SKK) integral introduced by Ahrenkiel (1971). The new integral does not require extensive extrapolation of reflectance data outside the measured region in order to produce reliable results. By extending the above procedure to include n data points, it is shown that at wavelength ₀, \[ n(_0)=\sum_{i=1}^{\rm n}(-1)^{\rm n+1}\prod_{\stackrel{j=1}{j \not=i}}^{\rm n} \frac{(_j^2-_0^2)}{(_i^2- _j^2)}n(_i)+\frac{2}{\pi}P\int_{0}^{\infty}(-1)^{\rm n+1} \frac{\prod_{i=1}^{\rm n}(_i^2-_0^2)}{\prod_{i=0}^{\rm n}(^2-_i^2)} k()d \] with relative error given by, \[ R_n(_0)=\prod_{i=1}^{\rm n}\frac{_i^2- _0^2}{_^2-_i^2} . \] This n^th order expression should prove useful in establishing the internal self-consistency of data sets for which both optical coefficients have been theoretically derived.     

Circular Polarization of Starlight

Of the 7500 stars cited in the Catalog of starlight polarization, those which satisfy the condition P _obs % and A _V 0^m.5 are selected. It is presumed that the selected stars (n=216) have circularly polarized light.     

Magnetic reconnection in high-temperature plasma of solar flares

Quasi-steady high-temperature current sheets are an energy source during the main or hot phase of solar flares. Such sheets are shown to be stabilized with respect to the tearing instability by a small transverse component of magnetic field existing in the sheets.     

Possible selection effects and their consequences on the determination of the model of the Universe from the redshift-magnitude relation of the brightest cluster galaxies

Because of a suspicion that a positive correlation exists between the luminosity of the first-class galaxies and the richness of the clusters, an attempt is made of taking into account the difference in richness (and presumably in total population) between the clusters withz<0.1 and the ones with 0.1<z0.2 (all being in the list of Peach, 1969) in the analysis of the redshift-magnitude relation of the brightest members.This analysis carried out with the clusters of richness 1 and 2, both present in the intervals of redshift 0.0–0.1 and 0.1–0.2 supports the steady-state model of the Universe in comparison with the category of the models with =0.This result induces another kind of selection effect, due to difference in the mean space density of the data points between the region withz<0.1 and the one with 0.1<z0.2, the mean volume occupied by the observed cluster being correlated with the luminosity of its brightest galaxy: also in this case the analysis supports the steady-state cosmology, while the tendency is clearly towards lower value ofq ₀.The last result brings into consideration the models of the Universe with 0: the results obtained are compatible with those obtained by the analysis of other relations i.e. logN-logS of the 3C sources;N-z relation of the quasistellar objects;m-z for brightest quasars.     

The ‘critical inclination’: Another look

The occurrence and uniqueness of the critical inclination in satellite theory is discussed.An infinite set of canonical transformations in Hill variables are shown to exist whereby the first order secular part of the disturbing function can be changed into an alternative form. As a result of such a transformation the critical inclination can become (a)any other real or complex inclination or a function independent of the satellite's orbital inclination and (b) a function dependent on the semi-major axis, eccentricity and inclination of the satellite's orbit. It is also shown that all transformations of types (a) and (b) are only valid for short intervals of time of the order of a few satellite revolutions. Furthermore if such transformations are modified so that they become valid for greater intervals of time, then the resulting solutions in all cases containno singular divisor other than the critical inclination.It is concluded that the singularity at the critical inclination is unique and that it represents an actual physical resonance rather than something resulting from the method of solution or the type of variable used in the analysis. This conclusion is supported by numerical evidence which shows that a satellite's perigee height does suffer resonant changes when the orbital inclination is equal to the critical inclination of 63.°4.