Integrability of the Yang-Mills Hamiltonian system

This paper considers the integrability of generalized Yang-Mills system with the HamiltonianH _a (p, q)=1/2(p ₁ ² +p ₂ ² +a ₁ q ₁ ² +a ₂ q ₂ ² )+1/4q ₁ ⁴ +1/4a ₃ q ₂ ⁴ + 1/2a ₄ q ₁ ² q ₂ ² . We prove that the system is integrable for the cases: (A)a ₁=a ₂,a ₃=a ₄=1; (b)a ₁=a ₂,a ₃=1,a ₄=3; (C)a ₁=a ₂/4,a ₃=16,a ₄=6. Our main result is the presentation of these integrals. Only for cases A and B does the Yang-Mills Hamiltonian possess the Painlevé property. Therefore the Painlevé test does not take account of the integrability for the case C.     

Interstellar Extinction and the Intrinsic Colors of Classical Cepheids in the Galaxy, the LMC, and the SMC

New methods are applied to samples of classical cepheids in the galaxy, the Large Magellanic Cloud, and the Small Magellanic Cloud to determine the interstellar extinction law for the classical cepheids, R _B:R _V:R _I:R _J:R _H:R _K= 4.190:3.190:1.884:0.851:0.501:0.303, the color excesses for classical cepheids in the galaxy, E(B-V)=-0.382-0.168logP+0.766(V-I), and the color excesses for classical cepheids in the LMC and SMC, E(B-V)=-0.374-0.166logP+0.766(V-I). The dependence of the intrinsic color (B-V)₀ on the metallicity of classical cepheids is discussed. The intrinsic color (V-I)₀ is found to be absolutely independent of the metallicity of classical cepheids. A high precision formula is obtained for calculating the intrinsic colors of classical cepheids in the galaxy: (<B>-<V>)₀=0.365(±0.011)+0.328(±0.012)logP.     

A study of the variability of the Delta Scuti-stars

A total of 321 observations of the Delta Scuti star BD –6°4932, obtained in 1968 by Hall and Mallama (1970), are analyzed. We find four frequencies which represent the light curves satisfactorily.The three periods:P ₁=0 _. ^d 240,P ₃=0 _. ^d 182 andP ₄=0 _. ^d 114 seem to correspond to the radial modes of pulsation withK=0, 1, and 3, respectively. The last periodP ₂=0 _. ^d 220 can be related to a non-radial mode.     

Effect of perturbation on the location of libration point in the robe restricted problem of three bodies

The effect of small perturbation in the Coriolis and centrifugal forces on the location of libration point in the ‘Robe (1977) restricted problem of three bodies’ has been studied. In this problem one body,m ₁, is a rigid spherical shell filled with an homogeneous incompressible fluid of densityϱ ₁. The second one,m ₂, is a mass point outside the shell andm ₃ is a small solid sphere of densityϱ ₃ supposed to be moving inside the shell subject to the attraction ofm ₂ and buoyancy force due to fluidϱ ₁. Here we assumem ₃ to be an infinitesimal mass and the orbit of the massm ₂ to be circular, and we also suppose the densitiesϱ ₁, andϱ ₃ to be equal. Then there exists an equilibrium point (−μ + (ɛ′μ)/(1 + 2μ), 0, 0).     

On a difference of the chromospheric background intensity between the equatorial and polar regions of the sun

Small chromospheric emission centres (here defined as flocculi) were studied photometrically on K _{2, 3, 2} spectroheliograms taken at the Arcetri Observatory. The intensity ratio between I _fl, the flocculus brightness, and I _chr, the brightness of the chromospheric background, was determined. A difference was found between the polar and the equatorial limb values of the ratio I _fl/I _chr.     

On the number of central configurations in the N-body problem

Central configurations are critical points of the potential function of the n-body problem restricted to the topological sphere where the moment of inertia is equal to constant. For a given set of positive masses m ₁,..., m _n we denote by N(m ₁, ..., m _n, k) the number of central configurations' of the n-body problem in ^k modulus dilatations and rotations. If m _{n 1},..., m _n, k) is finite, then we give a bound of N(m ₁,..., m _n, k) which only depends of n and k.     

Some results of the cooperative photometric observations of the UV Cet-type flare stars in the years 1967–71

The list of the cooperative photometric observations of the UV Cet-type flare stars that have been organized during the years 1967 to 1971 by the Working Group on Flare Stars of the IAU Commission 27 is given. The completeness and reliability of the data obtained are evaluated by comparing simultaneous observations at different observatories. the statistical analysis of the UV Cet, YZ CMi, EV Lac and AD Leo flares observed in the B-band is carried out. The flare energy spectrum in the energy range where observational selection effects are small is found to be d lnv/d lnE _B=–1.4 to –1.9,v is an occurrence of flares with radiation energy ofE _B. The total flares' radiation is equal to 1.7%, 1.2%, 0.3% and 0.4% of the quiet radiation in the B-band of the stars listed, and the main part of this total radiation is due to the strongest flares. Distributions of flare rise times (t _r) and of rates of flare absolute luminosity increase (d² E _B/dt _r ²Ë _r) are considered; these parameters of flare are independent statistically for all stars studied. Correlation coefficientsr (E _B,t _r) andr (E _B,r(E _B,Ë _r)) are rather small except r (E _B,t _r)=0.86 for the AD Leo flares. Contradictory conclusions on temporal distribution of flares infered by different investigators are noted.     

Photometric Inference of the Corotation Radii of Ten Barred Galaxies

We have used photometric images of ten barred galaxies in the B and I bands to infer the geometrical and dynamical parameters of their bars: Their length, (R _bar), their strengths, (S _b), and their corotation radii, (R _CR).These parameters have been obtained studying azimuthal profiles from the B and I band images of the galaxies. We find that R _CR is in all cases slightly larger than R _bar, with mean values close to 1.2 R _bar. We have also found a dependence of the ratio R _CR/R _bar on S _bar. This revised version was published online in July 2006 with corrections to the Cover Date.     

The extinction curve in the visible and the value of RV

This article discusses the interstellar extinction curve in the visible and the value of the ratio of absolute to selective extinction R_V = A_V/E (B – V). It is concluded that the visible extinction curve is likely to be linear in the visible and that indirect estimates of R_V from tentative determinations of A_V or from infrared and UV observations are questionable. There is currently no evidence of any variation of R_V with direction. If R_V is close to 3, as it has been inferred from mid‐infrared data, starlight in the visible is extinguished by a factor F /F₀ = (2.5 e^–2μm/λ)^{E (B –V)}. But if the visible wavelength range alone is considered, 4 appears as its most natural and probable value and F /F₀ = e^{–2E (B –V)/λ} (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the Tetrad Formulation of the Equations of Motion in General Relativity

It is shown that the equation of motion Du _j/Ds = (e/mc ²)F _ji u ⁱ , a natural generalization to the curved spacetime of the Heaviside-Lorentz law of ponderomotive force, is equivalent to the metric independent and covariant Van Dantzig's equations of motion dx ^j _[jpi] = 0 or L _v p _i = 0, where p _i is the conjugate momentum 4-vector and v a vector determined by the condition p _i v ⁱ, only with respect to holonomic coordinates. With respect to an anholonomic system, the Heaviside-Lorentz equation is a particular case of the VD equations valid for a privileged class of anholonomic frames, those consisting of orthogonal unit vectors.     

Perturbation equations of the elements of Vinti's intermediate orbit

Perturbation equations of the elements a, e, s, M_s, Ψ_s,Ω_sof Vinti's intermediate orbit are derived here correct to the second-order. Poisson terms have been eliminated from these equations.     

On a relation between the indices of solar activity in the photosphere and the corona

In the first part a new index of solar activity in the photosphere is introduced i.e. the areas index I _a defined with the help of the relation, where A and f are the total areas of the sunspots and faculae respectively corrected for foreshortening.In the second part a relation of the form: is proposed, where S represents the intensity of solar radio-emission in the frequency range 1000 f < 10000 MHz, i _f is the index of solar flares, S ₀o is the corresponding value of s for I _a = 0 and K is a constant.In the third part a relation of the form: is proposed, where I 5303 is the mean intensity of the coronal line 5303 Å for each quarter of the years 1954–1964, n _pf is the corresponding number of proton flares, I ₀ is the value of I ₅₃₀₃ corresponding to I = 0 and K is a constant.     

The action of the satellite 1981 S13, and the optical depth profile of the Encke-gap ringlet in the Saturn A ring

The radial optical depth profile of the Encke ringlet obtained by the occultation experiment of the Voyager photopolarimeter (PPS data) is explained to be caused by the gravitational action of the recently discovered stallite 1981 S13 and a second smaller moonlet orbiting near one of its either libration points — L₄ or L₅. To this aim the results of previous and new numerical particle simulations as well as an extension of the scattering theory concerning a single moonlet to a pair of satellites have been used leading to a triple-peaked ringlet near the orbits of the moonlets. The width and the shape of that ringlet and its separate peaks depend on the mass ratio of both moonlets and on their orbital eccentricites. The best resemblance between the PPS data and the theoretical profile is obtained if the mass ratio of the either moonlets takes M₂/M_1981S13 ≈ (0.8 … 3.0) × 10⁻² and the eccentricities hold: e_1981S13 < h_1981S13; e₂ ≈ h₂ (the values h are the Hill scales of either moonlets defined by h_1981S13/2 ≈ (M_1981S13/2/3M_h)^1/3, M_h = Saturn mass). Furthermore, our results yield a size of 1981 S13 of < 15 km in diameter.     

Lymanα forests and the evolution of the universe

The Lyα forest absorption lines in the spectra of quasars are interpreted as caused by the crossings of the light beam with the walls of a bubble structure (expanding with the Hubble flow only). Then, the typical separation between the absorption lines is proportional to the mean size of the bubbles. The variable factor is the expansion rate H[z]. The Friedmann regression analysis of the observed line separations determines the density parameter ω₀ and the normalized cosmological term λ₀ = λc²/3H²₀ of the appropriate cosmological model: ω₀ = 0.014 ± 0.002, λ₀ = 1.080 ± 0.006. Depending on the Hubble parameter this method reveals the values of the present mean matter density pm,0 = 2.6 h² · 10⁻²⁸ kg m⁻³ and of the cosmological constant Λ = 3.77 h² · 10⁻⁵² m⁻² (with h = H₀/(100 km/s·Mpc)). According to our analysis all models with Λ = 0 must be excluded. The curvature of space is positive. The curvature radius R₀ is 3.3 times the Hubble radius (c/H₀). The age t₀ is 2.8 times the Hubble age (H₀⁻¹).     

A study of the degradation of daytime astronomical images due to turbulence in the lower atmosphere by measurement of the standard deviation of the angle of arrival

Fluctuations in the angle-of-arrival of a luminous wavefront are investigated by placing a narrow slit over the image of the solar limb, and observing the entrance pupil through this diaphragm. Measurement of the standard deviation _AA of these fluctuations, in a direction perpendicular to the solar limb, provides sufficient information to estimate an absolute parameter characterizing the seeing, i.e. Fried's parameter r ₀ or the equivalent parameter _L C _N ²(h) dh which gives the integral, over an atmosphere thickness L which depends on the spatial and angular filterings performed by the slit, of the structure constant C _N ² characterizing fluctuations in the air's refractive index. Simultaneous estimations of _AA ² and _L C _N ² (h) dh permit a linear relationship to be established between these two quantities. The result is interpreted theoretically by integration of the two-dimensional power spectrum for the angle-of-arrival fluctuations. The influence of filtering effects is discussed.Such a calibration can be performed for a given telescope and slit, enabling the system to be used as a seeing monitor.     

Basic Functions of the Light Curve Analysis of Eclipsing Variables in the Frequency Domain

An analytically tractable method of transforming the problem of light curve analysis of eclipsing binaries from the time domain into the frequency domain was introduced by Kopal (1975, 1979, 1990). This method uses a new general formulation of eclipse functions α, the so-called moments A _2m , and their combinations as g _2m = A _2m+2/(A _2m A _2m+4) functions for the basic spherical model. In this paper, I will review the use of these functions in the light curve analysis of eclipsing binaries.     

Meteoroid Stream Searching: The Use of the Vectorial Elements

In this initial study, we propose a new distance function D _V involving heliocentric vectorial orbital elements. The function measures differences between: the orbital energies, the angular momentums vectors and the Laplace vectors. In comparison with the widely used D _SH criterion of Southworth and Hawkins, D _D criterion of Drummond and their hybrid D _H by Jopek, the new function contains one invariant with respect to the principal secular perturbation: the orbital energy. The new function proved to be useful in the classification amongst the IAU2003 meteoroids which we searched for streams by D _V function and also using D _SH and D _N -function given by Valsecchi et al. For major streams, the results agree very well. For minor, and near-ecliptical streams the results sometimes differ markedly.     

On the existence of J 2 invariant relative orbits from the dynamical system point of view

The present paper addresses the existence of J ₂ invariant relative orbits with arbitrary relative magnitude over the infinite time using the Routh reduction and Poincaré techniques in the J ₂ Hamiltonian problem. The current research also proposes a novel numerical searching approach for J ₂ invariant relative orbits from the dynamical system point of view. A new type of Poincaré mapping is defined from different central manifolds of the pseudo-circular orbits (parameterized by the Jacobi energy E, the polar component of momentum H _z and the measure of distance Δr between the fixed point and its central manifolds) to the nodal periods T _d and the drifts of longitude of the ascending node during one period (ΔΩ), which differs from Koon et al.’s (AIAA 2001) definition on central manifolds parameterized by the same fixed point. The Poincaré mapping is surjective because it compresses the three-dimensional variables into two-dimensional images, and the mapping degenerates into a bijective mapping in consideration of the fixed points. An iteration algorithm to the degenerated bijective mapping is proposed from the continuation procedure to perform the ergodic representation of E- and H _z -contour maps on the space of T _d –ΔΩ. For the surjective mapping with Δr ≠ 0, different pseudo-circular or elliptical orbits may share the same images. Hence, the inverse surjective mapping may achieve non-unique variables from a single image, which makes the generation of J ₂ invariant relative orbits possible. The pseudo-circular or elliptical orbits generated from the surjective mapping will be defined in different meridian planes. Hence, the critical contribution of the present paper is the assignment of J ₂ invariant relative orbits to different invariant parameters E and H _z depending on the E- and H _z -contour map, which will hold J ₂ invariant relative orbits for extended durations. To investigate the high-order nonlinearity neglected by previous studies, a formation configuration with a large magnitude of 500 km is successfully generated from the theory developed in the present work, which is beyond the scope of the linear conditions of J ₂ invariant relative orbits. Therefore, the existence of J ₂ invariant relative orbit with an arbitrary relative magnitude over the infinite time is achieved from the dynamical system point of view.     

UBV photometry of the WR binary CQ Cephei

Photoelectric observations of the WR binary CQ Cephei (WN6+O9) are presented. the depths of the eclipses in the light curves are best represented by an inclination of the orbit i = (68°.8±0.6) and the width of the very asymmetric eclipse curves can be represented by only an overcontact configuration (Ω₁ = Ω₂ = 3.65 ± 0.05, and f = 27%). Simultaneous solution of the light and radial velocity curves strongly supports CQ Cep's membership of the Cep OB1 association. By considering this membership we obtained absolute dimensions of the system, which lead to a consistent physical model for CQ Cephei. The more luminous WR primary turns out to be the hotter but slightly less massive component: M_WR = 20.8 M⊙, R_WR = 8.2R⊙, T_eff(WR) = 43600 K, and M_o = 21.4 M⊙, R_o = 8.3 R⊙, T_eff(O) = 37000 K.     

The Schwabe and Gleissberg Periods in the Wolf Sunspot Numbers and the Group Sunspot Numbers

Three wavelet functions: the Morlet wavelet, the Paul wavelet, and the DOG wavelet have been respectively performed on both the monthly Wolf sunspot numbers (R_z) from January 1749 to May 2004 and the monthly group sunspot numbers (R_g) from June 1795 to December 1995 to study the evolution of the Gleissberg and Schwabe periods of solar activity. The main results obtained are (1) the two most obvious periods in both the R_z and R_g are the Schwabe and Gleissberg periods. The Schwabe period oscillated during the second half of the eighteenth century and was steady from the 1850s onward. No obvious drifting trend of the Schwabe period exists. (2) The Gleissberg period obviously drifts to longer periods the whole consideration time, and the drifting speed of the Gleissberg period is larger for R_z than for R_g. (3) Although the Schwabe-period values for R_z and R_g are about 10.7 years, the value for R_z seems slightly larger than that for R_g. The Schwabe period of R_z is highly significant after the 1820s, and the Schwabe period of R_g is highly significant over almost the whole consideration time except for about 20 years around the 1800s. The evolution of the Schwabe period for both R_z and R_g in time is similar to each other. (4) The Gleissberg period in R_z and R_g is highly significant during the whole consideration time, but this result is unreliable at the two ends of each of the time series of the data. The evolution of the Gleissberg period in R_z is similar to that in R_g.