On the properties of contact binary stars

A catalogue of light curve solutions of contact binary stars has been compiled. It contains the results of 159 light curve solutions. Properties of contact binary stars were studied by using the catalogue data. As it is well known since Lucy's (1968a,b) and Mochnacki's (1981) works, primary components transfer their own energy to the secondary star via the common envelope around the two stars. This transfer was parameterized by a transfer parameter (ratio of the observed and intrinsic luminosities of the primary star). We proved that this transfer parameter is a simple function of the mass and luminosity ratio. This newly found relation is valid for all systems except H type systems which have a different relation. We introduced a new type of contact binary stars: H subtype systems which have a large mass ratio ($q>0.72$). These systems show highly different behaviour on the luminosity ratio - transfer parameter diagram from other systems and according to our results the energy transfer rate is less efficient in them than in other type of contact binary stars. We also show that different types of contact binaries have well defined locations on the mass ratio - luminosity ratio diagram. All contact binary systems do not follow Lucy's relation ($L_2/L_1 = (M_2/M_1)^{0.92}$). No strict mass ratio - luminosity ratio relation of contact binary stars exists.Comment: 5 pages, 4 figures, accepted for publication in A&

Global Operator Calculus on Spin Groups

Acknowledgements The work of P. Cerejeiras, M. Ferreira, and U. Kähler was supported by Portuguese funds through CIDMA-Center for Research and Development in Mathematics and Applications, and FCT– “Fundação para a Ciência e a Tecnologia”, within project UIDB/04106/2020 and UIDP/04106/2020. The present paper was supported by the project “Global operator calculi on compact and non-compact Lie groups”, Ações Integradas Luso-Alemãs – Acção No. A-42/16. Funding Open access funding provided by FCT|FCCN (b-on).n this paper, we use the representation theory of the group Spin(m) to develop aspects of the global symbolic calculus of pseudo-differential operators on Spin(3) and Spin(4) in the sense of Ruzhansky–Turunen–Wirth. A detailed study of Spin(3) and Spin(4)-representations is made including recurrence relations and natural differential operators acting on matrix coefficients. We establish the calculus of left-invariant differential operators and of difference operators on the group Spin(4) and apply this to give criteria for the subellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of first and second order globally hypoelliptic differential operators are given, including some that are locally neither invertible nor hypoelliptic. The paper presents a particular case study for higher dimensional spin groups.info:eu-repo/semantics/publishedVersio

Generalized Gauge Theories and Weinberg-Salam Model with Dirac-K\"ahler Fermions

We extend previously proposed generalized gauge theory formulation of Chern-Simons type and topological Yang-Mills type actions into Yang-Mills type actions. We formulate gauge fields and Dirac-K\"ahler matter fermions by all degrees of differential forms. The simplest version of the model which includes only zero and one form gauge fields accommodated with the graded Lie algebra of $SU(2|1)$ supergroup leads Weinberg-Salam model. Thus the Weinberg-Salam model formulated by noncommutative geometry is a particular example of the present formulation.Comment: 33 pages, LaTe

A wavelet based numerical method for nonlinear partial differential equations

The purpose of this paper is to present a wavelet–Galerkin scheme for solving nonlinear elliptic partial differential equations. We select as trial spaces a nested sequence of spaces from an appropriate biorthogonal multiscale analysis. This gives rise to a nonlinear discretized system. To overcome the problems of nonlinearity, we apply the machinery of interpolating wavelets to obtain knot oriented quadrature rules. Finally, Newton’s method is applied to approximate the solution in the given ansatz space. The results of some numerical experiments with different biorthogonal systems, confirming the applicability of our scheme, are presented.Instituto de Cooperação Científica e Tecnológica Internacional - Acções Integradas Luso-Alemãs (DAAD/ICCTI) - Projecto DAAD/ICCTI nº 01141

A condensed matter interpretation of SM fermions and gauge fields

We present the bundle Aff(3) x C x /(R^3), with a geometric Dirac equation on it, as a three-dimensional geometric interpretation of the SM fermions. Each C x /(R^3) describes an electroweak doublet. The Dirac equation has a doubler-free staggered spatial discretization on the lattice space Aff(3) x C (Z^3). This space allows a simple physical interpretation as a phase space of a lattice of cells in R^3. We find the SM SU(3)_c x SU(2)_L x U(1)_Y action on Aff(3) x C x /(R^3) to be a maximal anomaly-free special gauge action preserving E(3) symmetry and symplectic structure, which can be constructed using two simple types of gauge-like lattice fields: Wilson gauge fields and correction terms for lattice deformations. The lattice fermion fields we propose to quantize as low energy states of a canonical quantum theory with Z_2-degenerated vacuum state. We construct anticommuting fermion operators for the resulting Z_2-valued (spin) field theory. A metric theory of gravity compatible with this model is presented too.Comment: Minimal modifications in comparison with the published versio

Dirac-K\"ahler approach connected to quantum mechanics in Grassmann space

We compare the way one of us got spinors out of fields, which are a priori antisymmetric tensor fields, to the Dirac-K\"ahler rewriting. Since using our Grassmann formulation is simple it may be useful in describing the Dirac-K\"ahler formulation of spinors and in generalizing it to vector internal degrees of freedom and to charges. The ``cheat'' concerning the Lorentz transformations for spinors is the same in both cases and is put clearly forward in the Grassmann formulation. Also the generalizations are clearly pointed out. The discrete symmetries are discussed, in particular the appearance of two kinds of the time-reversal operators as well as the unavoidability of four families.Comment: 36 page

Note on Dirac--K\"ahler massless fields

We obtain the canonical and symmetrical Belinfante energy-momentum tensors of Dirac--K\"{a}hler's fields. It is shown that the traces of the energy-momentum tensors are not equal to zero. We find the canonical and Belinfante dilatation currents which are not conserved, but a new conserved dilatation current is obtained. It is pointed out that the conformal symmetry is broken. The canonical quantization is performed and the propagator of the massless fields in the first-order formalism is found.Comment: 16 pages, minor corrections in the text, published versio