Accretion disks around a mass with quadrupole QUADRUPOLE

In this work, we consider the exterior static axisymmetric gravitational of compact objects. We investigate the properties of the q-metric which is the simplest generalization of the Schwarzschild solution that contains a quadrupole parameter. The geodesic line equation is derived from the field equations and the orbits of the test particle are investigated. We consider the stability properties of test particles moving along circular orbits around a mass with quadrupole. We show that the quadrupole modifies drastically the properties of an accretion disk made of such test particles.

Coulomb Potential as Metrics of Hyperbolic Space

Representation of the Coulomb field as a metrics of the hyperbolic space within the Beltrami- Poincare model of hyperbolic geometry is done. In order to connect the potential of the electric field with the length of a geodesic line a new characteristics of the Coulomb field, the entropy, is introduced.

ОЦЕНКА РИСКА ВОЗДЕЙСТВИЯ ОПАСНЫХ ПРИРОДНЫХ ПРОЦЕССОВ НА ПОБЕРЕЖЬЕ ОСТРОВОВ РУССКИЙ И ШКОТА (ЗАЛИВ ПЕТРА ВЕЛИКОГО, ЯПОНСКОЕ МОРЕ)

В береговой зоне отмечается проявление наиболее опасных природных катастрофических событий. Изучение этой зоны необходимо для более верного выбора оптимального пути ее развития. Очень ограниченное число исследований концентрируются на оценке опасности аномальных природных процессов. В данной работе была выполнена балльная оценка потенциальной опасности воздействия аномальных природных процессов на береговую зону островов Русский и Шкота. Для этого была проведена типология берегов островов Русский и Шкота. Всего на о. Русский выделено четыре типа и двенадцать подтипов берегов. На о. Шкота было выявлено четыре типа и восемь подтипов берегов. На обоих островах были определены коэффициенты расчлененности берегов. Этот показатель равен отношению между длиной берега и геодезической линии, соединяющей концы участка берега. Рассмотрены особенности воздействия опасных природных процессов (цунами, штормовых нагонов, оползней, обвалов, абразии) на побережье островов Русский и Шкота. На обоих островах эти процессы распространены в полной мере. Цунами подвержено в основном восточное побережье островов, штормовые нагоны развиты на всем протяжении берегов островов, а оползни и обвалы распространены достаточно дисперсно на обоих островах. Используя балльную систему оценки от 1 до 3, где 1 это наличие процесса (его слабое проявление), 2 среднее проявление, а 3 потенциальная опасность (для оползней и обвалов), были выявлены наиболее опасные типы и подтипы берегов островов. На о. Русский наиболее опасными подтипами берегов являются абразионноденудационные берега с обрывистым типом берегового уступа и узкими валунногалечными пляжами восточного побережья. На о. Шкота также наиболее опасными подтипами берегов являются абразионноденудационные берега с обрывистым типом берегового уступа и с узкими валунногалечными пляжами.The coastal zone researching is an important direction of geomorphology. In this zone is existed many hazardous natural processes. Coastal zone is a most important contact geosystem, where interacting different types of a nature use. In common, very important to investigate this zone for more correcting choice of optimal way of its solution. One of the main limited factors, that confine it are hazardous natural processes. Very limited number of scientists concentrates on hazardous anomalous natural processes estimation. It is revealed a scorecard method of potential hazard of natural processes influence on the Russky and Shkota coastal zone. It is given the coastal typology of Russky and Shkota islands. It is dedicated four coast types and twelve coast subtypes in Russky island. It is identified four coast types and eight coast subtypes in Shkota island. It is explicated a number of permeable intervals. This indicator is equal to relation between coastal length and geodesic line that connect both termination of a coast. Are examined special aspects of a hazardous natural processes influence (tsunami, storm surges, landslides, avalanches, abrasion) on Russky and Shkota Islands coast. These processes diffuse on both islands in full degree. Tsunami segregate on eastern islands coast, storm surges manifest on all stretch of islands coasts. Landslides and avalanches concentrate dispersily on both islands. By the use scorecard method from 1 to 3, where 1 is a process availability, but 3 is a potential hazard (for landslides and avalanches), it is revealed the most hazardous types and subtypes of islands coasts. The most hazardous subtypes of coasts for Russky Island are abrasion and denudation coasts with a steep type of coastal bench and narrow boulder and gravel beaches of eastern coast. The most hazardous subtypes of coasts for Shkota Island also are abrasion and denudation coasts with a steep type of coastal bench and narrow boulder and gravel beaches.

Improved Neural Networks Based on Mutual Information via Information Geometry

This paper presents a new algorithm based on the theory of mutual information and information geometry. This algorithm places emphasis on adaptive mutual information estimation and maximum likelihood estimation. With the theory of information geometry, we adjust the mutual information along the geodesic line. Finally, we evaluate our proposal using empirical datasets that are dedicated for classification and regression. The results show that our algorithm contributes to a significant improvement over existing methods.

On Algorithms of Graphical Plotting of Geodesic Line on a Ruled Surface

Geodesic lines find interesting applications when solving many tasks of fundamental sciences (mathematicians, physics, etc.) and engineering practice. In differential geometry geodesic lines are characteristic lines for determination of internal properties of surface. However, the construction of geodesic line on a surface presents certain complications, mainly solved by the methods of calculating mathematics and descriptive geometry. In this article the development of a simple and comfortable algorithm of construction of geodesic line is considered on linear surfaces. In general case, the spatial model of algorithm of construction of geodesic line on a ruled surface is expressed in the following: a ruled surface we replace with averged surface, and at any side of the viewed verge, the intersection point of the geodesic with the rib of fracture (line of bending of dihedral angle) will be determined as the intersection of contiguous generatrix with the surface of cone of rotation – the congruence of directions of geodesic laying with the top at initial point, axis of rotation, incident to the considered generatrix, and the corner at the top of cone, equal to the doubled corner between the axis of rotation and direction of the geodesic laying. Next, as an initial parameters the contiguous with reviewed generatrix are accepted, determined higher point, lying on it, and the direction of geodesic is a corner between a segment obtained from geodesic and contiguous generatrix. Thus, repeatedly reiterating the described cycle, we will get the multitude number of points, making the required geodesic line.

Passing the Einstein–Rosen bridge

A test particle moving along geodesic line in a spacetime has three physical propagating degrees of freedom and one unphysical gauge degree. We relax the requirement of geodesic completeness of a spacetime. Instead, we require test particles trajectories to be smooth and complete only for physical degrees of freedom. Test particles trajectories for Einstein–Rosen bridge are proved to be smooth and complete in the physical sector, and particles can freely penetrate the bridge in both directions.