Solving game problems using recursion

The article describes the methodology to game problems of Olympiads in informatics using recursive numbers generation. The study is based on the sequential solution of increasingly complex tasks. For each task, the following materials are given: the condition of the task, the idea of the solution with a proposal to come up with an independent implementation, the solution in the Pascal programming language. Distance learning system DL.GSU.BY is the effective technical base for teaching. It allows offer the student a condition of the task; send the solution for review; get a verdict from the system — a correct or incorrect solution; for incorrect solutions, the number of the test on which the solution did not pass is indicated. A student can take a test (input and output data), on which his solution did not pass, figure out what the error is in his program, correct and send the solution again. In addition, for each problem there is a link on it to the topic in the forum at site, where you can ask a question on solving this problem and / or read the answer if the questions have already been asked before.

A method of designing equipment for heat processing of polymer workpieces

The paper describes a method of designing heating equipment that maintains a predetermined temperature field. The method consists in sequential solution of two problems. At the first stage, the heat generation field was calculated using the stationary heat conduction equation. At the second stage, parametric optimization of the temperature field was performed with reference to the power and configuration limits of the heaters. To test this method, the problem of maintaining a predetermined non-uniform temperature field was solved. A practical example of the application of the method for designing a uniform heating plate used in vulcanizing presses was given. To assess the efficiency of the plate, the results of modeling the heat processing of a workpiece from a rubber mixture were presented.

Optimal Space Trajectories with Multiple Coast Arcs Using Modified Equinoctial Elements

The detection of optimal trajectories with multiple coast arcs represents a significant and challenging problem of practical relevance in space mission analysis. Two such types of optimal paths are analyzed in this study: (a) minimum-time low-thrust trajectories with eclipse intervals and (b) minimum-fuel finite-thrust paths. Modified equinoctial elements are used to describe the orbit dynamics. Problem (a) is formulated as a multiple-arc optimization problem, and additional, specific multipoint necessary conditions for optimality are derived. These yield the jump conditions for the costate variables at the transitions from light to shadow (and vice versa). A sequential solution methodology capable of enforcing all the multipoint conditions is proposed and successfully applied in an illustrative numerical example. Unlike several preceding researches, no regularization or averaging is required to make tractable and solve the problem. Moreover, this work revisits problem (b), formulated as a single-arc optimization problem, while emphasizing the substantial analytical differences between minimum-fuel paths and problem (a). This study also proves the existence and provides the derivation of the closed-form expressions for the costate variables (associated with equinoctial elements) along optimal coast arcs.

Solution of tasks using recursive numbers generation

The article describes the methodology to solve tasks of Olympiads in informatics using recursive numbers generation. The study is based on the sequential solution of increasingly complex tasks. For each task, the following materials are given: the condition of the task, the idea of the solution with a proposal to come up with an independent implementation, the solution in the Pascal programming language. Distance learning system DL.GSU.BY is the effective technical base for teaching. It allows offer the student a condition of the task; send the solution for review; get a verdict from the system — a correct or incorrect solution; for incorrect solutions, the number of the test on which the solution did not pass is indicated. A student can take a test (input and output data), on which his solution did not pass, figure out what the error is in his program, correct and send the solution again. In addition, for each task there is a link on it to the topic in the forum, where you can ask a question on solving this problem and / or read the answer if the questions have already been asked before.

SILAR deposition of bismuth vanadate photoanodes for photoelectrochemical water splitting

Bismuth vanadate coatings are fabricated via a sequential solution-based method and used as photoanodes for water oxidation achieving exceptional performances.