Sagnac delay in the Kerr-dS space-time: Implications for Mach's principle

Relativistic twin paradox can have important implications for Mach's principle. It has been recently argued that the behavior of the time asynchrony (different aging of twins) between two flying clocks along closed loops can be attributed to the existence of an absolute spacetime, which makes Mach's principle unfeasible. In this paper, we shall revisit, and support, this argument from a different viewpoint using the Sagnac delay. This is possible since the above time asynchrony is known to be exactly the same as the Sagnac delay between two circumnavigating light rays re-uniting at the orbiting source/receiver. We shall calculate the effect of mass $M$ and cosmological constant $\Lambda$ on the delay in the general case of Kerr-de Sitter spacetime. It follows that, in the independent limits $M\rightarrow 0$, spin $a\rightarrow 0$ and $\Lambda\rightarrow 0$, while the Kerr-dS metric reduces to Minkowski metric, the clocks need not tick in consonance since there will still appear a non-zero observable Sagnac delay. While we do not measure spacetime itself, we do measure the Sagnac effect, which signifies an absolute substantive Minkowski spacetime instead of a void. We shall demonstrate a completely different limiting behavior of Sagnac delay, heretofore unknown, between the case of non-geodesic and geodesic source/observer motion.Comment: 15 pages. arXiv admin note: text overlap with arXiv:1709.0841

Optimization of Adams-type difference formulas in Hilbert space W2(2,1)(0,1)W_2^{(2,1)}(0,1)

In this paper, we consider the problem of constructing new optimal explicit and implicit Adams-type difference formulas for finding an approximate solution to the Cauchy problem for an ordinary differential equation in a Hilbert space. In this work, I minimize the norm of the error functional of the difference formula with respect to the coefficients, we obtain a system of linear algebraic equations for the coefficients of the difference formulas. This system of equations is reduced to a system of equations in convolution and the system of equations is completely solved using a discrete analog of a differential operator $d^2/dx^2-1$. Here we present an algorithm for constructing optimal explicit and implicit difference formulas in a specific Hilbert space. In addition, comparing the Euler method with optimal explicit and implicit difference formulas, numerical experiments are given. Experiments show that the optimal formulas give a good approximation compared to the Euler method

As investigações de ligante para fundição de investimento

The paper presents a study of binders of different composition for investment casting, which are safe from the point of view of ecology and safety for human life and health, have a long life-span, stable properties, provide increased gas permeability of forms and a lesser tendency to cracking, and as a result, ensure the production of quality castings. The proposed binder can be used on a par with the traditional, if you introduce spirit into it as a solvent. The introduction of acetone is impractical, because it promotes gelation of the solution, which makes it difficult to continue working with the binder. The gelling process is the coalescence of colloidal particles which causes an increase in the viscosity of the solution. The proposed binder has the following advantages over the traditional ones: it is water-based, non-flammable, non-toxic, environmentally safe; suspensions based on them have longer vitality, more permanent properties and require minimal maintenance; provide increased gas permeability of forms and their less tendency to cracking.El artículo presenta un estudio de los aglutinantes de diferente composición para la fundición de inversión, que son seguros desde el punto de vista de la ecología y la seguridad para la vida y la salud humanas, tienen una vida útil prolongada, propiedades estables, proporcionan una mayor permeabilidad al gas de las formas y una menor tendencia al agrietamiento, y como resultado, asegura la producción de piezas fundidas de calidad. El aglutinante propuesto se puede usar a la par con el tradicional, si se introduce el espíritu como un disolvente. La introducción de la acetona es poco práctica, ya que promueve la gelificación de la solución, lo que dificulta el trabajo continuo con el aglutinante. El proceso de gelificación es la coalescencia de partículas coloidales que causa un aumento en la viscosidad de la solución. El aglutinante propuesto tiene las siguientes ventajas sobre los tradicionales: es a base de agua, no inflamable, no tóxico, seguro para el medio ambiente; las suspensiones basadas en ellas tienen una mayor vitalidad, propiedades más permanentes y requieren un mantenimiento mínimo; proporcionan mayor permeabilidad al gas de las formas y su menor tendencia al agrietamiento.O trabalho apresenta um estudo de ligantes de diferentes composições para fundição, que são seguros do ponto de vista da ecologia e segurança para a vida e saúde humanas, possuem longa vida útil, propriedades estáveis, proporcionam maior permeabilidade a gases de formas e menor tendência a rachaduras e, como resultado, garantir a produção de peças fundidas de qualidade. O fichário proposto pode ser usado em pé de igualdade com o tradicional, se você introduzir o espírito nele como um solvente. A introdução de acetona é impraticável, pois promove a gelificação da solução, o que dificulta continuar trabalhando com o aglutinante. O processo de gelificação é a coalescência de partículas coloidais que causa um aumento na viscosidade da solução. O aglutinante proposto tem as seguintes vantagens em relação às tradicionais: é à base de água, não inflamável, não-tóxico, ambientalmente seguro; suspensões baseadas neles têm maior vitalidade, propriedades mais permanentes e requerem manutenção mínima; proporcionam maior permeabilidade a gases das formas e menor tendência a rachaduras

CCD Photometry of Standard Stars at Maidanak Astronomical Observatory in Uzbekstan: Transformations and Comparisons

Observation of standard stars is of crucial importance in stellar photometry. We have studied the standard transformation relations of the UBVRI CCD photometric system at the Maidanak Astronomical Observatory in Uzbekistan. All observations were made with the AZT-22 1.5m telescope, SITe 2k CCD or Fairchild 486 CCD, and standard Bessell UBVRI filters from 2003 August to 2007 September. We observed many standard stars around the celestial equator observed by SAAO astronomers. The atmospheric extinction coefficients, photometric zero points, and time variation of photometric zero points of each night were determined. Secondary extinction coefficients and photometric zero points were very stable, while primary extinction coefficients showed a distinct seasonal variation. We also determined the transformation coefficients for each filter. For B, V, R, and I filters, the transformation to the SAAO standard system could be achieved with a straight line or a combination of two straight lines. However, in the case of the U filter and Fairchild 486 CCD combination, a significant non-linear correction term - related to the size of Balmer jump or the strength of the Balmer lines - of up to 0.08 mags was required. We found that our data matched well the SAAO photometry in V, B-V, V-I, and R-I. But in U-B, the difference in zero point was about 3.6 mmag and the scatter was about 0.02 mag. We attribute the relatively large scatter in U-B to the larger error in U of the SAAO photometry. We confirm the mostly small differences between the SAAO standard UBVRI system and the Landolt standard system. We also attempted to interpret the seasonal variation of the atmospheric extinction coefficients in the context of scattering sources in the earth's atmosphere.Comment: 14 pages, 13 figure