Erratum: Solution of periodic Poisson's equation and the Hartree-Fock approach for solids with extended electron states: application to linear augmented plane wave method

Erratum to Int. J. Quantum Chem. v. 89, pp. 57-85 (2002)Comment: 1 pag

On the upper bound of the size of the r-cover-free families

Let T (r; n) denote the maximum number of subsets of an n-set satisfying the condition in the title. It is proved in a purely combinatorial way, that for n sufficiently large log 2 T (r; n) n 8 \Delta log 2 r r 2 holds. 1. Introduction The notion of the r-cover-free families was introduced by Kautz and Singleton in 1964 [17]. They initiated investigating binary codes with the property that the disjunction of any r (r 2) codewords are distinct (UD r codes). This led them to studying the binary codes with the property that none of the codewords is covered by the disjunction of r others (Superimposed codes, ZFD r codes; P. Erdos, P. Frankl and Z. Furedi called the correspondig set system r-cover-free in [7]). Since that many results have been proved about the maximum size of these codes. Various authors studied these problems basically from three different points of view, and these three lines of investigations were almost independent of each other. This is why many results were ..

LHC Bellows Impedance Calculations

To compensate for thermal expansion the LHC ring has to accommodate about 2500 bellows which, together with beam position monitors, are the main contributors to the LHC broad-band impedance budget. In order to reduce this impedance to an acceptable value the bellows have to be shielded. In this paper we compare different designs proposed for the bellows and calculate their transverse and longitudinal wakefields and impedances. Owing to the 3D geometry of the bellows, the code MAFIA was used for the wakefield calculations; when possible the MAFIA results were compared to those obtained with ABCI. The results presented in this paper indicate that the latest bellows design, in which shielding is provided by sprung fingers which can slide along the beam screen, has impedances smaller tha those previously estimated according to a rather conservative scaling of SSC calculations and LEP measurements. Several failure modes, such as missing fingers and imperfect RF contact, have also been studied

Results of Theoretical Studies to Substantiate the Parameters of Multi-blade Rotary-type Working Bodies

The article presents the results of theoretical studies of the technological process of operation of multi-blade working bodies of rotary type, intended for the distribution of solid organic fertilizers. To determine the length of the blades of the last row of rotors, and accordingly the overall dimensions of the spreader, theoretical dependences of the range of fertilizer particles on the radius of the blades are obtained, which made it possible to determine the size of the blades that provide the required performance of the rotary spreader. Considering the uniform distribution of fertilizer particles over the sieving width, the dependences of the “limiting” zone of loading of the blades (the maximum thickness of the layer of fertilizers captured by one blade) on the angle of their inclination at different lengths of the blades were obtained, which showed that when applying fertilizers with medium and large doses, several rows of blades. Computational experiments were carried out, during which, the number of rows of blades and the ratio of the lengths of the blades of different rows were determined to obtain the smallest unevenness depending on different doses of fertilizer application. As a result of mathematical modeling, the dependences of the working insertion width on the angle of inclination of the blades of the rotor rows relative to the radial position are obtained for various second-time supply of material, using which rational values of the angle of inclination of the blades are found

Индуктивное моделирование объектов и явлений методом группового учёта аргументов: недостатки и способы их устранения

Original results of a research of an efficient computing method - group method of data han-dling are presented. Key shortcomings on each significant procedure of a classical algorithm arerevealed and systematized, and also ways of their elimination, including author’s modificationsare presented. In particular, the use of dispersion and an assessment of dispersion (Fischer’scriterion) is proposed as an assessment of accuracy of the received result, additional “internal”criterion for evaluation of adequacy of model in various tests during the fixing of input dataand changing of characteristics of an algorithm, and determining the optimal complexity of themodel. To solve the convergence problem of the classical algorithm, it was proposed to usethe methods of dispersion, factor and correlation analysis to eliminate non-informative features,modify the criterion for stopping the algorithm. The use of regularizing functionals is suggestedto solve the problem of multicollinearity of input characteristics and increase the stability of theobtained model, etc. A complex of computer modeling programs was developed, realizing an ef-ficient modified algorithm of GMDH with the considered modifications and also methods of adispersion analysis, correlation analysis, component analysis, elements of the regression analy-sis and others. The conducted researches and the received practical results can become a basisfor development with use of Machine Learning and Data Science technologies of the automaticsystem of computer modeling, the intellectual analysis and the data processing.Представлены оригинальные результаты исследования эффективного вычислительного метода - метода группового учёта аргументов. Выявлены и систематизированы ключевые недостатки на каждой значимой процедуре классического алгоритма, а также представлены способы их устранения, в том числе авторские модификации. В частности, предложено использование дисперсии и её оценки (критерий Фишера) в качестве оценки точности полученного результата, дополнительного «внутреннего» критерия оценки адекватности модели в различных тестах при фиксации исходных данных и изменении характеристик алгоритма, а также определения оптимальной сложности модели. Для решения проблемы сходимости классического алгоритма было предложено использование методов дисперсионного, факторного и корреляционного анализов для исключения неинформативных признаков, модификации критерия остановки алгоритма. Предложено использование регуляризирующих функционалов для разрешения проблемы мультиколлинеарности входных признаков и повышения устойчивости полученной модели и др. Разработан комплекс программ компьютерного моделирования, реализующий модифицированный эффективный алгоритм метода группового учёта аргументов с рассмотренными авторскими модификациями, а также методами дисперсионного анализа, корреляционного анализа, факторного анализа, элементы регрессионного анализа и др. Проведённые исследования и полученные практические результаты могут стать основой для разработки с применением современных технологий Machine Learning и Data Science автоматизированной системы компьютерного моделирования, интеллектуального анализа и обработки данных