A comparison of approximate gravitational lens equations and a proposal for an improved new one

Keeping the exact general relativistic treatment of light bending as a reference, we compare the accuracy of commonly used approximate lens equations. We conclude that the best approximate lens equation is the Ohanian lens equation, for which we present a new expression in terms of distances between observer, lens and source planes. We also examine a realistic gravitational lensing case, showing that the precision of the Ohanian lens equation might be required for a reliable treatment of gravitational lensing and a correct extraction of the full information about gravitational physics.Comment: 11 pages, 6 figures, to appear on Physical Review

Spin multistability of cavity polaritons in a magnetic field

Spin transitions are studied theoretically and experimentally in a resonantly excited system of cavity polaritons in a magnetic field. Weak pair interactions in this boson system make possible fast and massive spin flips occurring at critical amplitudes due to the interplay between amplitude dependent shifts of eigenstates and the Zeeman splitting. Dominant spin of a condensate can be toggled forth and back by tuning of the pump intensity only, which opens the way for ultra-fast spin switchings of polariton condensates on a picosecond timescale.Comment: 4 pages, 4 figure

The weakly perturbed Schwarzschild lens in the strong deflection limit

We investigate the strong deflection limit of gravitational lensing by a Schwarzschild black hole embedded in an external gravitational field. The study of this model, analogous to the Chang & Refsdal lens in the weak deflection limit, is important to evaluate the gravitational perturbations on the relativistic images that appear in proximity of supermassive black holes hosted in galactic centers. By a simple dimensional argument, we prove that the tidal effect on the light ray propagation mainly occurs in the weak field region far away from the black hole and that the external perturbation can be treated as a weak field quadrupole term. We provide a description of relativistic critical curves and caustics and discuss the inversion of the lens mapping. Relativistic caustics are shifted and acquire a finite diamond shape. Sources inside the caustics produce four sequences of relativistic images. On the other hand, retro-lensing caustics are only shifted while remaining point-like to the lowest order.Comment: 12 pages, 1 figure

Situación moderna de pequeñas promociones e problemas del desarrollo empresarial en Rusia

The article describes the current state of small business development prospects and problems in Russia and, in particular, some aspects of small business development in Primorsky Krai and the city of Vladivostok. The article analyzes the main economic indicators of small enterprise activity in Russia. The analysis of small enterprise state allows us to conclude that, small businesses have incentives for their development despite significant changes in the external environment, which make an ambiguous impact on the activities of small businesses, and an unstable economic situation in the country. Despite the general reduction of small enterprise number in Russian Federation, the number of employees, the level of wages has increased insignificantly among the workers of small enterprises, and the turnover of small enterprises has also increased both in Russia as a whole and in small enterprises of Primorsky Krai. However, some of the problems that prevent the full-fledged development of small business continue to be unresolved. Understanding the prospects and the trends of small business development, as well as the solution of the problems limiting its development, is of great importance for the development of Russia and in particular for the development of the region strategic potential.El artículo describe el estado actual de las perspectivas y problemas de desarrollo de pequeñas empresas en Rusia y, en particular, algunos aspectos del desarrollo de pequeñas empresas en Primorsky Krai y la ciudad de Vladivostok. El artículo analiza los principales indicadores económicos de la actividad de la pequeña empresa en Rusia. El análisis del estado de la pequeña empresa nos permite concluir que las pequeñas empresas tienen incentivos para su desarrollo a pesar de los cambios significativos en el entorno externo, que tienen un impacto ambiguo en las actividades de las pequeñas empresas y una situación económica inestable en el país. A pesar de la reducción general del número de pequeñas empresas en la Federación de Rusia, el número de empleados, el nivel de los salarios ha aumentado insignificativamente entre los trabajadores de las pequeñas empresas, y el volumen de negocios de las pequeñas empresas también ha aumentado tanto en Rusia como en las pequeñas empresas de Primorsky Krai. Sin embargo, algunos de los problemas que impiden el desarrollo completo de las pequeñas empresas continúan sin resolverse. Comprender las perspectivas y las tendencias del desarrollo de pequeñas empresas, así como la solución de los problemas que limitan su desarrollo, es de gran importancia para el desarrollo de Rusia y, en particular, para el desarrollo del potencial estratégico de la región.O artigo descreve o e stado atual das perspectivas e problemas do desenvolvimento de pequenas empresas na Rússia e, em particular, alguns aspectos do desenvolvimento de pequenas empresas em Primorsky Krai e na cidade de Vladivostok. O artigo analisa os principais indicadores econômicos da atividade de pequenos negócios na Rússia. A análise do estado da pequena empresa nos permite concluir que as pequenas empresas têm incentivos para o seu desenvolvimento, apesar das mudanças significativas no ambiente externo, que têm um impacto ambíguo nas atividades das pequenas empresas e uma situação econômica instável na economia. país Apesar da redução geral no número de pequenas empresas na Federação Russa, o número de funcionários, o nível de salários aumentou insignificantemente entre os trabalhadores de pequenas empresas, e o volume de negócios de pequenas empresas também aumentou tanto na Rússia como nos pequenos negócios de Primorsky Krai. No entanto, alguns dos problemas que impedem o pleno desenvolvimento de pequenas empresas permanecem sem solução. Compreender as perspectivas e tendências do desenvolvimento das pequenas empresas, bem como a solução dos problemas que limitam o seu desenvolvimento, é de grande importância para o desenvolvimento da Rússia e, em particular, para o desenvolvimento do potencial estratégico da região

Gravitational lensing in fourth order gravity

Gravitational lensing is investigated in the weak field limit of fourth order gravity in which the Lagrangian of the gravitational field is modified by replacing the Ricci scalar curvature R with an analytical expression $f(R)$. Considering the case of a pointlike lens, we study the behaviour of the deflection angle in the case of power law Lagrangians, i.e. with f(R) = f_0 R^n. In order to investigate possible detectable signatures, the position of the Einstein ring and the solutions of the lens equation are evaluated considering the change with respect to the standard case. Effects on the amplification of the images and the Paczynski curve in microlensing experiments are also estimated.Comment: 10 pages, 3 figures, accepted for publication on Physical Review

Can an electric current orient spins in quantum wells?

A longstanding theoretical prediction is the orientation of spins by an electrical current flowing through low-dimensional carrier systems of sufficiently low crystallographic symmetry. Here we show by means of terahertz transmission experiments through two-dimensional hole systems a growing spin orientation with an increasing current at room temperature.Comment: 5 pages, 2 figure

On the mean width of log-concave functions

In this work we present a new, natural, definition for the mean width of log-concave functions. We show that the new definition coincide with a previous one by B. Klartag and V. Milman, and deduce some properties of the mean width, including an Urysohn type inequality. Finally, we prove a functional version of the finite volume ratio estimate and the low-M* estimate.Comment: 15 page

Magnetic field induced 3D to 1D crossover in type II superconductors

We review and analyze magnetization and specific heat investigations on type-II superconductors which uncover remarkable evidence for the magnetic field induced fnite size effect and the associated 3D to 1D crossover which enhances thermal fluctuations.Comment: 26 pages, 19 figure