A method of visualization of surface and volumetric caustics of reflected and refracted light on mirror surfaces in volume and on functionally specified surfaces consisting of patches of free forms is proposed. Caustics are surfaces near which the intensity of the light field increases sharply. The visualization method tracks the rays of light in the light space when displaying mirror surfaces. Light rays are projected from light sources onto patches of free-form scenes. The limiting volumes of caustic rays are determined, thereby reducing the number of calculations. Only caustic rays are calculated, which make the main contribution to the resulting image.
This work is the result of research and modeling of a set of forces that create the movement of the object with acceleration in a certain direction. The proposed analytical dependences determine the values of the coordinates of spatial locations of technological object, for example, when machining or in the medical diagnosis of pathological formations. An analytical model of maintaining stable spatial coordinates of the object, taking into account the peculiarities of the object's motion, is presented. Further research on the creation of analytical dependences that take into account the influence of external forces on the stability of the object’s spatial coordinates is proposed. This will increase the accuracy of determining the location of the object, which is very important in determining the positioning of the workpiece in the processing of parts, and in determining the spatial coordinates of pathology in the mass of a living organism.
In this article, we discuss an extensive class of channel codes called turbo codes. These error correction methods will achieve very good results in terms of error rates, which may be close to the bandwidth limit of the Shannon channel. The article begins with a brief discussion on the coding of the turbo, and then describes the form of the iterative decoder most often used to decode the turbo codes. This article proposes a new optimal modification of the log-MAP-log decoding algorithm. This method (PL-log-MAP) is based on a partial linear approximation of the correction function in the Jacobean logarithm. Using the proposed approximation, the complex functions of ln (.) I exp (.) In the log-MAP algorithm can be estimated with high accuracy and lower computational complexity. The effectiveness of the proposed approximation is tested and demonstrated by applying it to the digital communication system for transmission images in MatLab. It seems that the performance of the PL-log-MAP algorithm has the closest efficiency to the original log-MAP solution.
The law of conservation and transformation of energy proves one of the fundamental laws of nature. In mechanics, this law is defined as the law of conservation of mechanical energy. It states that the total mechanical energy of a closed system of bodies, where solely conservative forces interact, remains constant. Consideration is given to the methodical recommendations related to implementing laboratory experiments for the experimental verification of the law of the energy conservation in a closed system. The paper is aimed at theoretically substantiating the use of innovative techniques of carrying out laboratory experiments in physics under the present-day conditions of training military students of higher military educational establishments which will contribute to developing their professional competence under the conditions of the fundamental and professional training integration.
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