The Spinning Particles as a Nonlinear Realizations of the Superworldline Reparametrization Invariance

The superdiffeomorphisms invariant description of $N$ - extended spinning particle is constructed in the framework of nonlinear realizations approach. The action is universal for all values of $N$ and describes the time evolution of $D+2$ different group elements of the superdiffeomorphisms group of the $(1,N)$ superspace. The form of this action coincides with the one-dimensional version of the gravity action, analogous to Trautman's one.Comment: 4 pages, RevTe

The Einstein 3-form G_a and its equivalent 1-form L_a in Riemann-Cartan space

The definition of the Einstein 3-form G_a is motivated by means of the contracted 2nd Bianchi identity. This definition involves at first the complete curvature 2-form. The 1-form L_a is defined via G_a = L^b \wedge #(o_b \wedge o_a). Here # denotes the Hodge-star, o_a the coframe, and \wedge the exterior product. The L_a is equivalent to the Einstein 3-form and represents a certain contraction of the curvature 2-form. A variational formula of Salgado on quadratic invariants of the L_a 1-form is discussed, generalized, and put into proper perspective.Comment: LaTeX, 13 Pages. To appear in Gen. Rel. Gra

Scientific and technological development of the modern cardiological science: Global and Russian trends

In this article are presented the results of research aimed at defining scientific and technological development trends in cardiology, their differences in Russia in comparison with the global reality. For determination the tasks a proprietary multidisciplinary approach was applied in social-economic studies to estimate academic and technological development of cardiology, which allows integrating the results of the national and foreign theoretical research to the maximum in this area. Analysis showed that nowadays, the focus is on studying the mechanisms of originating and development of the cardiovascular diseases and studying the pathogenic basis, biological functioning of the organ system and heart under normal and pathological conditions and innovative methods of predicting and such diseases therapy. Russian scientists conduct research in the area of cardiology almost in every actual direction. Russian scientists are successfully finding solutions to the top problems in diagnostics, treatment and prevention of chronic ischemic heart disease, dyslipoproteinemia, arterial hypertension, type two diabetes, cardiomyopathy, employing modern achievements in the medical science and practice. Besides, there are remarkable scientific centers, conducting independent research and developing unique self-engineered products. Conducted classification and description of the material allows to form a conclusion about the current develop level of the studied science industry in Russia, in addition it allows to say about the degree of conformity with the develop level of the leading global practices in the field of cardiology. Attained results became a basis for drawing conclusions about the development prospects of some certain fields which study cardiovascular diseases and the therapy methods in Russian and world science

Einstein equations in the null quasi-spherical gauge III: numerical algorithms

We describe numerical techniques used in the construction of our 4th order evolution for the full Einstein equations, and assess the accuracy of representative solutions. The code is based on a null gauge with a quasi-spherical radial coordinate, and simulates the interaction of a single black hole with gravitational radiation. Techniques used include spherical harmonic representations, convolution spline interpolation and filtering, and an RK4 "method of lines" evolution. For sample initial data of "intermediate" size (gravitational field with 19% of the black hole mass), the code is accurate to 1 part in 10^5, until null time z=55 when the coordinate condition breaks down.Comment: Latex, 38 pages, 29 figures (360Kb compressed

Lagrangian and Hamiltonian for the Bondi-Sachs metrics

We calculate the Hilbert action for the Bondi-Sachs metrics. It yields the Einstein vacuum equations in a closed form. Following the Dirac approach to constrained systems we investigate the related Hamiltonian formulation.Comment: 8 page

Connections and dynamical trajectories in generalised Newton-Cartan gravity I. An intrinsic view

The "metric" structure of nonrelativistic spacetimes consists of a one-form (the absolute clock) whose kernel is endowed with a positive-definite metric. Contrarily to the relativistic case, the metric structure and the torsion do not determine a unique Galilean (i.e. compatible) connection. This subtlety is intimately related to the fact that the timelike part of the torsion is proportional to the exterior derivative of the absolute clock. When the latter is not closed, torsionfreeness and metric-compatibility are thus mutually exclusive. We will explore generalisations of Galilean connections along the two corresponding alternative roads in a series of papers. In the present one, we focus on compatible connections and investigate the equivalence problem (i.e. the search for the necessary data allowing to uniquely determine connections) in the torsionfree and torsional cases. More precisely, we characterise the affine structure of the spaces of such connections and display the associated model vector spaces. In contrast with the relativistic case, the metric structure does not single out a privileged origin for the space of metric-compatible connections. In our construction, the role of the Levi-Civita connection is played by a whole class of privileged origins, the so-called torsional Newton-Cartan (TNC) geometries recently investigated in the literature. Finally, we discuss a generalisation of Newtonian connections to the torsional case.Comment: 79 pages, 7 figures; v2: added material on affine structure of connection space, former Section 4 postponed to 3rd paper of the serie

Research Progress Report: Fox-Pheasant Relationships in South Dakota, 1965

A 5-year cooperative study designed to obtain information regarding effects of foxes on pheasant populations in eastern South Dakota was initiated in 1964. Specific objectives were to determine (1) population fluctuations of foxes and pheasants, (2) fox food habits and reproductive characteristics and (3) effectiveness and cost of fox reduction to increase pheasant abundance. Studies were conducted on four pairs of 100-square-mile areas. Fox populations were reduced on one member of each pair beginning in January 1965, and individual foxes were removed on a complaint basis on the other. Each pair of areas is referred to as a unit. When summer pheasant data on the fox-reduction and check areas are considered, significant differences are noted in adult pheasants per mile, broods per mile, and brood size from 1964 to 1965. Changes in adult pheasants per mile in Unit 2 showed the decline in the fox-reduction area was significantly (0. 01) less than in the check area. However, in Units 1 and 4 the declines in the check areas were significantly (0. 01) less than those in the fox-reduction areas. The difference in decline in broods per mile in the fox-reduction compared to the check area from 1964 to 1965 was negligible in Unit 1. In Unit 2 the fox-reduction area showed a slight increase compared to a decrease in the check area. This difference is significant (0. 01). In Unit 4 a smaller decline occurred in the fox-reduction area than in the check area. The difference in Unit 4 is significant (0. 05). The proportion of hens with broods showed an increase from 1964 to 1965 in the fox-reduction areas of Units 1, 2, and 4 and a lesser increase or a decrease in the corresponding check areas. A significant (0. 01) increase in brood size occurred from 1964 to 1965 in the fox-reduction compared to the check area of Unit 1. A non-significant increase occurred in the check area compared to the fox-reduction area in Unit 2. The adult pheasant-per-mile averages during the spring of 1965 showed more birds in the fox-reduction area than in the check area of Unit 1, and the reverse in Unit 2. Neither difference is significant. Units 3 and 4 showed significantly (0. 01) more adults per mile in the fox reduction than in the check areas during this same period. Fox data revealed that counting tracks in snow along transects is the best of three methods for determining fox activity in an area. Such counts in reduction and check areas within each unit showed that fox activity was sufficiently comparable in each pair of areas prior to fox reduction. Methods used to reduce fox populations also reduced to some extent other predators, including nest robbers. Grasses, mice, pheasants, rabbits, and insects, in descending order, respectively, were the most frequently occurring items found in stomachs of foxes taken in the study areas from January to June 1965. Grasses were found in stomachs that also contained mice and insects. Pheasants were the item composing the greatest volume, followed by rabbits and mice. Prairie deer mice made up the majority of small mammal remains. (See more in Text

Post-Newtonian extension of the Newton-Cartan theory

The theory obtained as a singular limit of General Relativity, if the reciprocal velocity of light is assumed to tend to zero, is known to be not exactly the Newton-Cartan theory, but a slight extension of this theory. It involves not only a Coriolis force field, which is natural in this theory (although not original Newtonian), but also a scalar field which governs the relation between Newtons time and relativistic proper time. Both fields are or can be reduced to harmonic functions, and must therefore be constants, if suitable global conditions are imposed. We assume this reduction of Newton-Cartan to Newton`s original theory as starting point and ask for a consistent post-Newtonian extension and for possible differences to usual post-Minkowskian approximation methods, as developed, for example, by Chandrasekhar. It is shown, that both post-Newtonian frameworks are formally equivalent, as far as the field equations and the equations of motion for a hydrodynamical fluid are concerned.Comment: 13 pages, LaTex, to appear in Class. Quantum Gra

Linear Einstein equations and Kerr-Schild maps

We prove that given a solution of the Einstein equations $g_{ab}$ for the matter field $T_{ab}$, an autoparallel null vector field $l^{a}$ and a solution $(l_{a}l_{c}, \mathcal{T}_{ac})$ of the linearized Einstein equation on the given background, the Kerr-Schild metric $g_{ac}+\lambda l_{a}l_{c}$ ($\lambda$ arbitrary constant) is an exact solution of the Einstein equation for the energy-momentum tensor $T_{ac}+\lambda \mathcal{T}_{ac}+\lambda ^{2}l_{(a}\mathcal{T}_{c)b}l^{b}$. The mixed form of the Einstein equation for Kerr-Schild metrics with autoparallel null congruence is also linear. Some more technical conditions hold when the null congruence is not autoparallel. These results generalize previous theorems for vacuum due to Xanthopoulos and for flat seed space-time due to G\"{u}rses and G\"{u}rsey.Comment: 9 pages, accepted by Class. Quant. Gra

On quasi-local charges and Newman--Penrose type quantities in Yang--Mills theories

We generalize the notion of quasi-local charges, introduced by P. Tod for Yang--Mills fields with unitary groups, to non-Abelian gauge theories with arbitrary gauge group, and calculate its small sphere and large sphere limits both at spatial and null infinity. We show that for semisimple gauge groups no reasonable definition yield conserved total charges and Newman--Penrose (NP) type quantities at null infinity in generic, radiative configurations. The conditions of their conservation, both in terms of the field configurations and the structure of the gauge group, are clarified. We also calculate the NP quantities for stationary, asymptotic solutions of the field equations with vanishing magnetic charges, and illustrate these by explicit solutions with various gauge groups.Comment: 22 pages, typos corrected, appearing in Classical and Quantum Gravit