Implications of CP violation in hyperon decays

It is generally believed that the only known reaction in whichC _p violation definitely occurs is in the decay of the long-lived neutralK-mesonK _L ^+–,K _L ⁰⁰, andK _L e ^±± v (Christensonet al., 1964: Sivaram, 1982). No attempt has been made to studyC _p violation outside theK-system for quite a long time. Recently,C _p violation effects have been reported in the hyperon decays through the reaction (Bassompierre, 1990) with asymmetry at the level of 10^–3 to 10^–4.In this paper we examine the possible implications of hyperon decays asymmetry in some cosmic-ray sources. We identify cosmic-ray sources where such decays can occur. The signatures for measuring these asymmetries in both the laboratory and cosmic-ray sources are examined.It is found that there is a correlation between these signatures. We conclude that hyperon decays contribute significantly toC _p violation observed in cosmic-ray sources.     

General integral transform of the exponential integrals

General integral transform of the exponential integralsE _n is considered and will be denoted asB _(k) ⁿ (). Different expressions and the equations satisfied byB _(k) ⁿ are developed. Two-term recurrence formula forB _(k) ⁿ (0) and three-term recurrence formula forB _(k) ⁿ (); 0 will be established for a givenk1 andn=2,3, ...,N. The computational algorithms based on these formulae are also constructed for the casesk=1,2,3, andn2. Finally the numerical results fork=2,3 andn=2(1)25 are presented to 15-digit accuracy     

Unexplained empirical relations among certain scatterings

When the differential cross-section data of ⁺ -proton scattering are compared to the data of proton-alpha scattering at momenta related by 4p₄=p (where p₄ is the momentum of p-alpha scattering and p is the momentum of ⁺ -proton scattering) a correlation is observed between p=125 MeV/c and 1100 MeV/c. The correlation is most pronounced in the region of the lowest energy resonance of both scatterings (p210 MeV/c). A less pronounced correlation (in the lower energy regions) among four scatterings is observed when the differential cross-section data of ⁺ -p and p-alpha scatterings and the data of p-³He and protondeuteron scatterings are compared using relations 4p₄=3p₃=2p₂=p (where p₃ is the p-³He momentum and p₂ is the proton-deuteron momentum). The facts strongly suggest something of physical significance but no theoretical explanation is known. Indeed, an explanation seems to be beyond the scope of existing theory.     

Fourier analysis of the light curves of eclipsing variables-XXV: Error analysis in the frequency-domain

The aim of the present paper has been two-fold. In the first part (Sections 1–2), closed algebraic formulae will be set up furnishing the momentsA of the light curves of arbitrary index , and, due to arbitrary type of eclipses, in terms of the coefficientsa of Fourier cosine series obtained by least-squares fit to the given data; and the uncertainty of the momentsA deduced from that of thea 's.In the second part (Sections 3–4) we shall establish the explicit forms of the lincar functions r _1,2, (cosi) and L ₁ for the variation of the respective elements expressible likewise in terms of the Fourier coefficientsa . The probable errors of these elements can then be identified with those of the respective linear functions, and are obtainable from the same matrix of coefficients which furnished the most probable values of the elements.     

Exact cosmological solutions in the scalar-tensor theory with cosmological constant

Under the assumption of a power-law between the expansion factor of the Universe, and the scalar field (a ⁿ=c=const.) tensor theory with cosmological constant are reduced to quadrature. Several exact solutions are obtained, among them inflationary universes that have barotropic equation of state.     

A note on the instantaneous rotational velocity of Mercury

The fluctuation in the angular velocity of the present rotation of Mercury is investigated. The instantaneous rotational rate in terms of orbital mean motion at different positions along Mercury's orbit is given. At aphelion the rotational velocity decreases substantially because the solar gravitational torque on the two thermal bulges on Mercury's surface tends to retard the rotation of Mercury before aphelion passage. It is found that the difference between the rotational periods derived from the motions at perihelion and aphelion is 4.68 min and that the maximum rate of rotation occurs atf=/4 andf=7/4, wheref is the true anomaly.     

Expansions of elliptic motion based on elliptic function theory

New expansions of elliptic motion based on considering the eccentricitye as the modulusk of elliptic functions and introducing the new anomalyw (a sort of elliptic anomaly) defined byw=u/2K–/2,g=amu–/2 (g being the eccentric anomaly) are compared with the classic (e, M), (e, v) and (e, g) expansions in multiples of mean, true and eccentric anomalies, respectively. These (q,w) expansions turn out to be in general more compact than the classical ones. The coefficients of the (e,v) and (e,g) expansions are expressed as the hypergeometric series, which may be reduced to the hypergeometric polynomials. The coefficients of the (q,w) expansions may be presented in closed (rational function) form with respect toq, k, k=(1–k ²)^1/2,K andE, q being the Jacobi nome relatedk whileK andE are the complete elliptic integrals of the first and second kind respectively. Recurrence relations to compute these coefficients have been derived.on leave from Institute of Applied Astronomy, St.-Petersburg 197042, Russia     

Propagation of spiral density waves in a magneto-active disk

The propagation of spiral density waves in a differentially rotating, self-gravitating, magnetoactive and highly flattened disk is investigated by using the asymptotic theory for tightly wound spirals developed by Lin and his collaborators. We adopt the continuum fluid model as the primary basis, and our treatment will be largely analytical. The disk plasma is studied in the frozen field approximation and inhomogenceous magnetic fields in the plane of the disk are considered in detail.In a differentially rotating disk with strong magnetic fields, the field lines will be considerably distorted and the mutual influence of magnetic fields and differential rotation is by no means obvious.In this paper we present a new asymptotic dispersion relation for tightly wound spiral density waves with magnetic fields along the spiral armsB (r). The effects of the magnetic fields lead to such terms likek ²(a ² +V _A ² ), wherek is the wave number,a represents the speed of sound,V _A = (B ²/4)^1/2 is the Alfvén speed,B denotes the field strength, and is the plasma density. These terms depict the well-known magnetoacoustic waves and could have been anticipated without a detailed computation. However the interaction of magnetic fields and differential rotation may give rise to other significant terms which are not so easy to foresee.We also present a more exact local dispersion relation by using the WKB approximation and study the effects of magnetic fields on the growth rate through the parametersQ andJ defined in the literature.Although the effects of the magnetic fields are rather insignificant for applications to Galactic dynamics, the effects of the magnetic fields are important for applications to star formation and problems related to the solar nebula.     

The equilibrium,stability and evolution of a rotating magnetized gaseous disk

The exact solutions for the equilibrium of rotating gaseous disk with poloidal magnetic field are obtained. The stability of the disk with respect to uniform expansion and contraction is investigated by means of the variational principle. It is shown that if the equilibrium is determined by gravitational and magnetic forces only, the disk is in neutral equilibrium with respect to perturbations of the form r=r. The instability to short-waves perturbations is studied by the quasi-classical method. The analysis shows that if the magnetic field isH>2G, where is the surface density, then these perturbations are stabilized. The configurations of the electrical field induced by the rotation of magnetized disk are found. In conclusion, the questions of the evolution of the disk are discussed in connection with the quasar model when pulsar-like radiation is taken into account.     

Magnetic and thermal pressures in the solar wind

Explorer 34 solar wind data for the period June to December, 1967 show that(a) The magnetic pressure, P _BB ²/8, and thermal pressure,P _kn _p kTp+n kT+n _e kTe,are variable and positively correlated on a scale of 2 days, but (b) changes in P _b and P _k are anticorrelated on a scale 1 hr (0.01 AU). Thus, dynamical hydromagnetic processes (dv/dto) must occur on the mesoscale, but the solar wind tends to be in equilibrium(P _B+P _Kconstant) on a smaller scale, the microscale. The 3-hr averages show that the most probable value of P _{k/P B} is =1.0±0.1, which implies that the most probable state of the solar wind at 1 AU is not one of equipartition between the thermal energy and magnetic energy. The average total pressure for a given bulk speed(P(V)=P ^k+P _k+P _B) is essentially independent of V, implying that P is not determined by the heating or acceleration mechanisms of the solar wind; the average pressure is P=(2.9±1.5)×10^-10dyne/cm².     

Effect of coriolis force on acceleration covariance in MHD turbulent flow of a dusty incompressible fluid

In the present problem, acceleration covariance in MHD turbulent flow of dusty fluid with Coriolis force have been obtained.The obtained result shows that the defining scalars (r,t), (r, t), (r, t) of the acceleration covariance in the presence of Coriolis force depends on the defining scalars of tensorsQ _ij, H_ij, _i,j,S _ik,jandT _ij,kalready defined in the text.     

Linear current instability in loop prominences

By use of the dispersion equation given by Song, Wu, and Dryer (1987) for a cylinder plasma with mass motion and gravity included, we investigate the linear current instabilities developed in loop prominences. The results indicate that the mode of linear instability depends mainly on whetherv _s ² > or not, wherev _s is the sonic velocity at heightz, =GM/(R +z) is the gravity potential,G the gravitational constant,M andR the mass and the radius of the Sun respectively. Ifv _s ² > , then the sausage instability will be dominant. Otherwise, the kink instability will be more important. A possible explanation of knot structure, which appears sometimes in solar loop prominences has been given.     

A discussion of Hill's method of secular perturbations and its application to the determination of the zero-rank effects in non-singular vectorial elements of a planetary motion

Knowledge of the perturbations of zero-rank is essential for the understanding of the behavior of a planetary or cometary orbit over a long interval of time. Recent investigations show that these zero-rank perturbations can cause large oscillations in both the shape and position of the orbit. At present we lack a complete analytical theory of these perturbations that can be applied to cases where either the eccentricity or inclination is large or has large oscillations. For this reason we here develop formulas for the numerical integration of the zero-rank effects, using a modified Hill's theory and suitable vectorial elements. The scalar elements of our theory are the two components of Hamilton's vector in a moving ideal reference frame and the three components of Gibb's rotation vector in an inertial system. The integration step can be taken to be several hundred years in the planetary or cometary case, and a few days in the case of a near-Earth space probe. We re-discuss Hill's method in modern symbolism and by applying the vectorial analysis in a pseudo-euclidean spaceM ₃, we obtain a symmetrical computational scheme in terms of traces of dyadics inM ₃. The method is inapplicable for two orbits too close together. In Hill's method the numerical difficulty caused by such proximity appears in the form of a small divisor, whereas in Halphen's method it appears as a slow convergence of a hypergeometric series. Thus, in Hill's method the difficulty can be watched more directly than in Halphen's method. The methods of numerical averaging have, at the present time, certain advantages over purely analytical methods. They can treat a large range of eccentricities and orbital inclinations. They can also treat the free secular oscillations as well as the forced ones, and together with their mutual cross-effects. At the present time, no analytical theory can do this to the full extent.Basic Notations m the mass of the disturbed body - M the mass of the Sun - f the gravitational constant - f(M+m) - r the heliocentric position vector of the disturbed body - r |r| - r ⁰ the unit vector alongr - n ⁰ the unit vector normal tor and lying in the orbital plane of the disturbed body - a the semi-major axis of the orbit of the disturbed body - e the eccentricity of the orbit of the disturbed body - g the mean anomaly of the disturbed body - the eccentric anomaly of the disturbed body - p a(1–e ²) - P ₁ the unit vector directed from the Sun toward the perihelion of the disturbed body - P ₂ the unit vector normal toP ₁ and lying in the orbital plane of the disturbed body - s - the true orbital longitude of the disturbed body, reckoned from the departure point of the ideal system of coordinates - X the true orbital longitude of the perihelion of the disturbed body in the ideal system of coordinates reckoned from the departure point - the angular distance of the ascending node from the departure point - R ₁,R ₂,R ₃ the unit vectors along the axes of the ideal system of coordinates,R ₁ andR ₂ are in the osculating orbital plane of the disturbed body,R ₃ is normal to this plane. The intersection ofR ₁ with the celestial sphere is the departure point - R ₃ P ₁×P ₂ - S ₁,S ₂,S ₃ the initial values ofR ₁,R ₂,R ₃, respectively - q the Gibb's vector. This vector defines the rotation of the orbital plane of the disturbed body from its initial position to the position at the given timet - m the mass of the disturbing body - r the heliocentric position vector of the disturbing body - a the semi-major axis of the orbit of the disturbing body - e the eccentricity of the orbit of the disturbing body - g the mean anomaly of the disturbing body - the eccentric anomaly of the disturbing body - P₁ the unit vector directed from the Sun toward the perihelion of the disturbing body - P₂ the unit vector normal toP₁ and lying in the orbital plane of the disturbing body - A₁ a P₁ - A₂ - |r–r|     

Stability of planar oscillations of a satellite in an elliptic orbit

A problem of stability of odd 2-periodic oscillations of a satellite in the plane of an elliptic orbit of arbitrary eccentricity is considered. The motion is supposed to be only under the influence of gravitational torques.Stability of plane oscillations was investigated earlier (Zlatoustovet al., 1964) in linear approximation. In the present paper a problem of stability is solved in the non-linear mode. Terms up to the forth order inclusive are taken into consideration in expansion of Hamiltonian in a series.It is shown that necessary conditions of stability obtained in linear approximation coincide with sufficient conditions for almost all values of parameters ande (inertial characteristics of the satellite and eccentricity of the orbit). Exceptions represent either values of the parameters ,e when a problem of stability cannot be solved in a strict manner by non-linear approximation under consideration, or values of the parameters which correspond to resonances of the third and fourth orders. At the resonance of the third order oscillations are unstable, but at the resonance of the fourth order both unstability and stability of the satellite's oscillations take place depending on the values of the parameters ,e.     

Hydrodynamic models for population-II cepheids

The nonlinear self-excited pulsations of population-II stars with mass 0.6M and luminosities from 128 to 1280L are studied. The pulsation periods are found to be in the range of 1.3 to 19 days. An increase of the stellar luminosity is shown to be accompanied by an increasing nonadiabaticity and decreasing efficiency of the radiative damping region. This leads to both an increase of the growth rate while pulsations are exciting and an increase of the oscillation amplitude of the limit cycle. In the models withL800L the efficiency of the radiative damping region becomes so small that amplitude growth ceases due to a dissipation of the mechanical energy by shocks in the stellar atmosphere. The models with periods of from 1.3 to 3 days show the bump on their light curves. The bump is connected with a travelling pulse generated at the antinode of the second overtone at maximum compression. The time delays estimated for the pulses reflected of the stellar core are in a good agreement with the pulse resonance condition proposed by Aikawa and Whitney (1983). The model with the period of 2.1 days revealed double resonance ₀ = 2₂, 2₀ = 3₁ causing alternating oscillations with slightly different periods and amplitudes. The models with period of 10 days and longer reveal the resonance ₀ = 2₁. This resonance causes the flat top on the light curve at a period of about 10 days and appearance of a shallow alternating minimum at longer periods, as is observed in RV Tau variables. The theoretical period-luminosity relation proposed for population-II cepheids is in good agreement with that obtained from observations.     

The evolution of the polar coronal holes

He i 10830 Å synoptic maps, obtained at the Kitt Peak National Observatory during 1974–1979, show that the Sun's polar coronal holes have contracted significantly during 1977–1978. Prior to the accelerated increase of sunspot activity in mid-1977, the area of each polar cap was on the order of 8% of the Sun's total surface area (4R ²), whereas toward the end of 1978 these areas fell below 2% of 4R ². Synoptic polar plots show that the vestigual holes had irregular shapes and were often well removed from the poles themselves. These results are consistent with the changes that one would expect when the polar magnetic fields are weakening just prior to sunspot maximum.     

A model cosmology based on gravity-electromagnetism unification

In this article the GEM (Brandenburg, 1992; Brandenburg, 1988) theory is applied to the problem of the cosmos in which most of the matter is hydrogen, spacetime is flat, and a Cosmic Background Radiation CBR field exists. Using the two postulates of the GEM theory: 1. That gravity fields are equivalent to an array ofE ×B drifts or a spacially varying Poynting field, such that spacetime is determined by EM fields so that the stress tensor of ultrastrong fields is self-canceling; 2. That EM and gravity fields and protons and electrons are unified at the Planck scale of lengths and energies and split apart to form distinct fields and separate particles at the Mesoscale of normal particle rest energies and classical radii. A new derivation is made of the formula forG found previously:G =e ²/(m _p m _e ) exp(-2R ^1/2) = 6.668 × 10^–8 dynes cm² g^–2wherem _p andm _e are the proton and electron masses respectively,R =m _p /m _e and is the fine structure constant, shows that quantum processes may occur which make the vacuum unstable to appearance of hydrogen thus allowing matter creation and a steady state universe to occur. The value for the Hubble Time calculated from this model isT _o = (3/((2)(R ^1/2)⁴))^1/3(r _e /c)(e ²/Gm _p m _e )= 19 Gyr wherer _e =e ² / (m _e c ²)and follows the form first hypothesized by Dirac(1937). The CBR is traced to this process of matter creation and its temperature is calculated as beingT _CBR = ((3/4)Gm _e ² c/( ² _o ))^1/4 = 2.66K where is the Thomson cross section of the electron and _o is the Stefan-Boltzman constant.     

Effect of drift-resonance broadening on radial diffusion in the magnetosphere

In the quasilinear theory of magnetospheric radial diffusion caused by fluctuating electrostatic (E) or magnetic (B) fields, the diffusion coefficientD _LLis proportional to the spectral density of E or B at the particle drift frequency ₃/2. Since ₃ varies withL at fixedM andJ (adiabatic invariants), the drift resonance =₃ can be maintained only transiently, and therefore is not perfectly sharp. Its bandwidth ^* is approximately (16D _LL /L ²₃)^1/3₃. In magnetospheric radial diffusion caused mainly by electrostatic fluctuations, the value of ^*₃ typically exceeds 0.4 for particle energiesE40 keV. However, the numerical value ofD _LLis correctly given (within 1% in all cases) by quasilinear theory because the spectrum of E is rather flat at resonance frequencies for which the bandwidth is an appreciable fraction of ₃. (Numerical conclusions are based on a quasilinear model forD _LLused successfully by Cornwall in 1972.)     

Gravitational radiation and spiralling time of close binary systems (V)

Forty-six binary systems with their primary component masses between 2M and 3M have been considered for gravitational radiation study. Power output by gravitational radiation (P _B ) and spiral time ₀ for all individual systems have been evaluated. A relation has been given betweenP _B and ₀. The rate of decrease of orbital period (P) has also been given for 10 eccentric orbit systems.     

Gravitational radiation and spiralling time of close binary systems (IV)

Binary systems with their primary and secondary component masses less than 2M have been investigated to evaluate the rate of emission of gravitational energy (P _B) and spiralling time (₀) for them. In all twenty-two binary systems have been considered. It is found that in spite of the same mass range, these systems form two distinct groups. New relations have been given betweenP _B and (₀) for each group. For a few eccentric orbit systems the rate of decay of orbital periods due to the loss of energy from the system via gravitational radiation emission has also been given and compared with a short-period binary pulsar.