AMPLITUDE DISTRIBUTION OF LINEAR ANTENNA SYSTEMS WITH CONTINUOUS APERTURES

Проведены исследования известных амплитудных распределений для линейных непрерывных раскрывов, а также получен ряд новых распределений с наилучшим соотношением коэффициента использования поверхности раскрыва для заданного уровня боковых лепестков. Среди рассмотренных известны амплитудные распределения типа “косинус m-й степени”. Отмечены амплитудные распределения из данного класса, диаграммы направленности которых обладают противофазными боковыми лепестками. Предложен новый класс амплитудных распределений для непрерывных раскрывов типа суперпозиции “косинус m-й степени” и “косинус m-2 степени” с разными весовыми коэффициентами, диаграммы направленности которых с противофазными боковыми лепестками дают результирующую с узким главным лепестком, меньшим значением уровня боковых лепестков и более высоким коэффициентом использования поверхности раскрыва в сравнении с классическим распределением “косинус m-й степени”. Приведен сравнительный анализ полученных непрерывных распределений с Дольф-Чебышевскими амплитудными распределениями для дискретных структур по критерию максимального коэффициента использования поверхности раскрыва для заданного уровня боковых лепестков. Показано, что коэффициент использования поверхности раскрыва сравниваемых амплитудных распределений при высоком уровне боковых лепестков отличается на 35%. Предложенный класс амплитудных распределений позволяет получать высокие значения коэффициента использования поверхности раскрыва для непрерывных структур и, следовательно, высокий коэффициент направленного действия We carried out investigations of the known amplitude distributions for linear continuous apertures and obtained a number of new distributions with the best ratio of the utilization factor of the aperture surface for a given level of side lobes. Among the considered, there are the well-known amplitude distributions of the “cosine of the m-th degree” type. We note amplitude distributions from this class, the directional patterns of which have antiphase side lobes. We propose a new class of amplitude distributions for continuous apertures of the superposition type “cosine of the m-th degree” and “cosine of the m-2 degree” with different weight coefficients, the radiation patterns of which with antiphase side lobes give the resultant with a narrow main lobe, a lower value of the level of side lobes and a higher utilization of the aperture surface in comparison with the classical distribution “cosine of the m-th degree”. We present a comparative analysis of the obtained continuous distributions with the Dolph-Chebyshev amplitude distributions for discrete structures according to the criterion of the maximum utilization of the aperture surface for a given level of side lobes. We show that the utilization factor of the aperture surface of the compared amplitude distributions at a high level of side lobes differs by 35%. The proposed class of amplitude distributions allows one to obtain high values of the coefficient of use of the aperture surface for continuous structures and, therefore, a high coefficient of directional action

Probability and Random Processes

Phenomena, systems, and processes are rarely purely deterministic, but contain stochastic,probabilistic, or random components. For that reason, a probabilistic descriptionof most phenomena is necessary. Probability theory provides us with the tools for thistask. Here, we provide a crash course on the most important notions of probabilityand random processes, such as odds, probability, expectation, variance, and so on. Wedescribe the most elementary stochastic event—the trial—and develop the notion of urnmodels. We discuss basic facts about random variables and the elementary operationsthat can be performed on them. We learn how to compose simple stochastic processesfrom elementary stochastic events, and discuss random processes as temporal sequencesof trials, such as Bernoulli and Markov processes. We touch upon the basic logic ofBayesian reasoning. We discuss a number of classical distribution functions, includingpower laws and other fat- or heavy-tailed distributions.

Determination of partition surface of grained material by means of non-classical approximation methods of distributions functions of particle size and density

In this paper, the grained material analyzed was hard coal collected from one of the mines located in Upper Silesia. Material was collected from a dust jig where it was separated in industrial conditions by concentrate and waste. It was then screened in sieves and it was separated in dense media into density fractions. Both particle size distribution and particle density distribution for feed and concentrate were approximated by several classical distribution functions. The best results were obtained by means of the Weibull (RRB) distribution function. However, because of the unsatisfying quality of approximations it was decided to apply non-parametric statistical methods, which became more and more popular alternative methods in conducting statistical investigations. In the paper, the kernel methods were applied to this purpose and the Gauss kernel was accepted as the kernel function. Kernel method, which is relatively new, gave much better results than classical distribution functions by means of the least squared method. Both classical and non-parametric obtained distribution functions were evaluated by means of mean standard error, the values of which proved that they sufficiently well approximate the empirical data. Such function forms were then applied to determine the theoretical distribution function for vector (D, P), where D is the random variable describing particle size and P – its density. This approximation was sufficiently acceptable. That is why it served to determine the equation of partition surface dependent on particle size and particle density describing researched material. The obtained surface proves that it is possible to evaluate material separation which occurs during mineral processing operations, such as jigging, by means of more than one feature of researched material. Furthermore, its quality confirms that it is justified to apply non-parametric statistical methods instead of commonly used classical ones.