Search

Relevance of the study is that qualitative and quantitative results of solving of its tasks suitable for developing of me­thodic of decreasing of methodical errors of determination of values of mass hourly emission of particulate matter in exhaust gas flow of reciprocating internal combustion engine with using of conversion formula and readings of opa­ci­meter and gas ana­ly­zer. Purpose of the study is obtaining of pa­rameters of beta-distribution that approximate the empirical law of dis­tri­bution of values of mass hou­r­ly emission of particulate matter in exhaust gas flow of recipro­ca­ting internal combustion engine which achieved by in­di­rect measur­ing with taking into ac­count the accuracy of direct measuring of its components that has nonlinear im­pact. Task of the study is obtaining of rational values of number of multiple measuring of coefficient of ate­nuation of light flux and volume concentration of unburned hydrocarbons in ex­haust gas on individual opera­ti­o­nal regime of diesel en­gine during bench motor tests for case of automation of mea­suring process. Methodic of the study is in consistently appli­ca­tion of following methods: ana­ly­sis of sci­enti­fic and te­chnical literature, analysis of data of bench motor tests, ap­pli­cation of prof. Parsadanov conversion formula, mathematical ap­paratus of beta-distribution, nu­me­ri­cal calculation studies. It was detected that empirical distri­bu­ti­on of values of mass hourly emission of particulate matter in exhaust gas flow of reciprocating internal combustion engine which obtained with using of one of known conver­si­on formula of prof. Parsadanov as the function of indica­tor of opacity and toxicity of exhaust gas, has a sig­ni­ficant difference from the normal distribution law at number of mea­su­re­ments less than 50 even in case of confir­ma­tion of the hypo­the­sis of normality of distribution law of readings of opacimeter into limits of its passport measuring errors. That re­sults were described by the mathema­ti­cal apparatus of beta-distribution by carrying out the numerical cal­cu­lation stu­dies with using of pro­gram product written of the lan­guage Borland Pascal 7.0. The parameters of beta-distribu­tion were obtain as the function of nu­m­ber of multiple measuring., Актуальность исследования заключается в том, что количественные и ка­че­ственные результаты решения задач исследования пригодны для создания методики снижения методической погрешности определения величины массового часового выброса твердых час­тиц с потоком отработанных газов поршневого двигателя внутреннего сгорания с испо­ль­зо­ванием формул пересчета и показаний дымомера и газоанализатора. Целью исследования является по­лучение пара­ме­тров бета-плотности, аппроксимирующей эмпирический закон распределения значений часо­вых мас­совых выбросов ТЧ с потоком ОГ поршневого ДВС, полученных косвен­ными измере­ни­ями с учетом точности прямых измерений их сос­тавляющих, оказывающих не­линейный влия­ние. За­дачей исследования является получение рациональных значений ко­ли­че­с­тва многократ­ных из­мерений коэффициента ослабления светового потока и объемной концен­трации несгоревших углеводородов в ОГ на одном режиме ра­боты дизеля в стен­до­вых мотор­ных исследованиях для случая автоматизации процесса изме­ре­ний. Методика выпо­л­нения дан­ной научной работы состояла в последовательном исполь­зова­нии следу­ющих мето­дов: анализ научно-технической литературы, методика анализа данных мо­торных стендо­вых ис­пытаний, ме­тодика применения формулы пересчета Парсаданова, мате­ма­тический аппа­рат бе­та-распре­деления, метод чис­лен­ных расчетных исследований. Установлено, что эмпирическое распределение значений массового ча­со­вого выброса ТЧ с ОГ поршневого ДВС, полученных при применении одной из известных формул пересчета проф. И.В. Парсаданова как фун­к­ция по­казателей дымности и токсичности ОГ существенно отлича­ется от нормаль­ного закона при ко­личеству изме­ре­ний, меньшем 50, даже при подтверждении гипо­тезы о нор­мальности распре­де­ления показаний дымомера в пре­делах паспортной пог­реш­ности измерений. Результаты описаны мате­ма­тическим аппа­ратом бе­та-распре­деления пу­тем расчетного исследования с использованием про­граммного продукта, разработанного в среде Bor­land Pascal 7.0. Полу­че­ны параметры бета-плотности для описания изучаемого показателя эколо­ги­ческой безопаснос­ти и их зави­си­мости от количества измерений.

The article deals with a method of simulation modeling, that takes into account the peculiarities of its use in the conditions of a frame-monolithic building erection. The method of simulation modeling is developed. The essence of this method is in usage a Monte Carlo method for performing one work and construction of the entire object for a two-factor beta distribution. The empirical regularities that characterize the duration of individual works anderection stages of a frame-monolithic building are obtained., В статті розглянуто метод імітаційного моделювання, який враховує особливості його використання в умовах зведення каркасно-монолітного будинку. Розроблено методику імітаційного моделювання з використанням методу Монте-Карло для виконання однієї роботи і будівництва об'єкта в цілому для двофакторного бета-розподілу. Отримані емпіричні закономірності, що характеризують тривалості окремих робіт та етапів зведення каркасно-монолітного будинку.

We describe two parametric classification tree methods, which allow formal selection of a member of a class of generalised distributions. In the paper we consider generalised Beta distributions for non-negative random variables and the generalised skew-Student distribution for random variables distributed on the real line. We introduce a class of symmetric generalised multivariate Student distributions, members of which may also be selected using the classification trees. We present two versions of the parametric classification tree: specific to general and general to specific. We apply the classification methods to daily returns on stocks from a selection of 15 major, mid-cap and emerging markets. The results show that the majority of return distributions follow Student's t, but that a non-negligible minority follow a symmetric generalised Student distribution. We confirm a well-known stylised fact about skewness: it tends not to be persistent. By contrast, kurtosis is persistent. Using the symmetric generalised multivariate Student distribution, we present a risk management study based on efficient portfolios constructed from UKFTSE250 stocks and specifically concerned with the computation of value at risk. The case study demonstrates that the model selection procedures based on the classification trees lead to more accurate computation of VaR than those based on the normal distribution or on non-parametric approaches. The study also shows that the normal distribution may be used for VaR computations for larger portfolios when the holding period is longer.

Admixture diffusion flows are investigated in two-phase randomly nonhomogeneous multilayered strips with non-uniform distributions of inclusions. Cases where the most probable disposition of layered inclusions is located near the body boundary on which the mass source acts in the neighborhood of another boundary and in the middle of the body are considered. The initial-boundary value problem is formulated for the function of rand om mass flow under conditions of a constant flow on the upper surface and zero concentration of the admixture on the lower surface. Calculation formulae are obtained for the diffusion flow averaged over the ensemble of phase configurations in the particular cases of beta-distribution at zero and nonzero initial concentrations. The dependences of the averaged admixture flows on medium characteristics are established. It is shown that if the admixture diffusion coefficient in inclusions is greater than in the matrix, consolidation of inclusions in the middle of the body leads to an increasing diffusion flow. Simulation of the averaged diffusion flows of the admixture in the multilayered strip is performed for different model variants of a probable disposition of phases in the body and their comparative analysis is carried out.

Immer ��fter treten Naturkatastrophen auf, die weltweitem CO2-Aussto�� und dem daraus resultierenden Klimawandel zugeordnet werden. Gro��e Hoffnung wird in die erneuerbaren Energien gesetzt, um die Emissionen zu reduzieren; vor allem Sonnen- und Windenergie werden verst��rkt forciert und ausgebaut. Diese Diplomarbeit soll einen Beitrag leisten, um die noch vielen offenen Fragen und ungel��sten Probleme rund um die volatilen, erneuerbaren Energietr��ger schrittweise behandeln und letztendlich auch l��sen zu k��nnen. Wir haben f��r unsere Simulationen die Auswirkung der Korrelation zweier Windparks und deren Lasteinspeisung betrachtet. Mit der Korrelation wird die geographische Distanz beider Standorte als Windabh��ngigkeit modelliert. Die Erzeugungscharakteristik eines Windparks kann sehr gut durch eine Verteilung dargestellt werden. Daher stand die Erzeugung von verteilten Zufallsvariablen mit einer bestimmten Korrelation im Mittelpunkt. Wir wenden das DC-Lastfluss Modell auf ein kleines Testsystem an. Dieses besteht aus zwei Windparks, einer Last mit Weibull-Verteilung und einem Slack. Die Berechnungen wurden f��r alle wichtigen Leitungen und zwei Szenarien durchgef��hrt. Einerseits wurden zwei Parks mit gleicher Wahrscheinlichkeitsverteilung f��r den gesamten Bereich von keiner bis zur vollen Korrelation simuliert. Andererseits haben wir zwei unterschiedliche Windparks betrachtet und von keiner bis zur maximal m��glichen Korrelation der beiden Verteilungen untersucht. Diese h��ngt von der ��hnlichkeit der beiden Verteilungen ab. Als weiteres Szenario wurden noch Speicher und Leitungslimits einbezogen. Die Speicher wurden bei jedem Knoten angebunden und erm��glichen eine ungek��rzte Produktion bei Einf��hrung von Limits. Es wurde keine Einschr��nkungen auf eine bestimmte Speichertechnologie vorgenommen. Mit unserer Korrelationsmethode k��nnen wir Gruppen von beta-verteilten Zufallszahlen mit einer exakten, vorgegebenen Korrelation erzeugen. Unsere Simulationen ergeben, dass relativ einfach die minimale und maximale Belastung der Leitung ermittelt werden kann - dazu m��ssen die Lastfluss-Ergebnisse f��r keine und maximale Korrelation ��berlagert werden., This master thesis deals with probabilistic power flow analysis for correlated, beta-distributed wind power injections. The importance of renewable energies steadily increases over time. Wind and solar energy are playing an ever increasingly significant role in the field of climate change and smart grid applications. In this research we focused on wind energy. We looked specifically at the correlation between wind power injections of different wind power farms. The correlation models the geographical distance between these wind power plant sites. The output of wind power plant farms can be described best by the means of probability density functions with beta-distributions. We developed an algorithm to generate a set of beta-distributed random variables to fit the desired correlation as closely as possible. Our simulation method is DC-load flow and uses power transfer distribution factors. We applied our method to a small grid with two wind power injections and one load with Weibull distribution as well as a slack. We investigated the power flow on the important branches for a range from non to maximum correlation for two scenarios with different input densities. Firstly, we investigated the situation for two equal wind parks and calculated the line flow for the correlation range from zero to full correlation. Secondly, we repeated the simulations with differing beta-distributed power outputs for both of the wind farms. The range of correlation does not even come to full correlation. The maximum correlation level depends on the similarity of the input probability densities. We also took certain line limits into account and used storage devices for keeping the energy surplus to avoid curtailment of energy production or overloading of lines. The storage devices are placed at each bus, but do not represent a specific technology. With our methodology of correlation we can generate exact sets of correlated, beta-distributed random variables. Our simulation method can easily find the absolute maximum and minimum load on a given line just by combining the outcome of the maximum correlation and the uncorrelated result.

Description of random sequences in strongly-correlated systems with the help of β - distribution has been considered. This new method was applied to analysis of CCD-matrix noises recorded at different temperatures. Every noise sequence was "read" in terms of fitting parameters of the β - distribution. Relative fitting error does not exceed the value of 2.2% with the value of Pearson correlation coefficient close to 1. The fitting parameters are rather stable to a difference in treatment procedures. In first treatment method the procedure was applied to the mean values of the noise sequence, while in the second - to each separate sampling with subsequent averaging in the end. For the first method the relative error is located in the vicinity of 1%, while for the second approach this value is about 2.2%. This simple comparison confirms that the self-averaging phenomenon occurs as a result of repetition of the same measurement. With the help of the ECs method we recognized a hypothesis for temperature behavior of the mean values that were calculated for each sampling. This hypothesis represents itself in a linear combination of two exponential functions. One can judge about the temperature stability of the CCD device analyzing the fitting parameters with respect to the temperature. The method has potential application in device calibration or in determination its readiness to a normal work. © 2011 SPIE.

The method of sequential improvement of beta-distribution approximation for small parameter values suggested in [I. N. Volodin, Theory Probab. Appl., 15 (1970), pp. 546-549] is developed. An asymptotic of the approximation error is established in terms of uniform distance between distributions.© 2010 Society for Industrial and Applied Mathematics.

Moment spaces, weak convergence, large deviations, canonical moments, range of the moment space, beta-distribution