Classes of Ordinary Differential Equations Obtained for the Probability Functions of inverse Rayleigh Distribution

Differential calculus was used to obtain the ordinary differential equations (ODE) of the probability density function (PDF), Quantile function (QF), survival function (SF), inverse survival function (ISF), hazard function (HF) and reversed hazard function (RHF) of inverse Rayleigh distribution. The parameters and support that define the distribution inevitably determine the nature, existence, uniqueness and solution of the ODEs. The method can be extended to other probability distributions, functions and can serve an alternative to estimation and approximation. Computer codes and programs can be used for the implementation

The Transmuted Exponentiated Additive Weibull Distribution: Properties and Applications

A new generalization of the transmuted additive Weibull distribution is proposed by using the quadratic rank transmutation map, the so-called transmuted exponentiated additive Weibull distribution. It retains the characteristics of a good model. It is more flexible, being able to analyze more complex data; it includes twenty-seven sub-models as special cases and it is interpretable. Several mathematical properties of the new distribution as closed forms for ordinary and incomplete moments, quantiles, and moment generating function are presented, as well as the MLEs. The usefulness of the model is illustrated by using two real data sets

Experimental study of combustion and scalar mixing in swirling jet flows

Turbulent mixing of passive scalar field and combustion of gaseous fuel were studied in the context of a non-premixed isothermal and reacting swirling jets discharged from a swirl-stabilised burner, as a function of swirl number. The rate of molecular mixing, which was quantified by the scalar dissipation rate was computed from measured scalar fields that were recorded by using Planar Laser Induced Fluorescence (PLIF) of acetone. The influence of the swirl number on the scalar mixing, unconditional and conditional scalar dissipation rate statistics was investigated. Scalar fields were measured with an average error of 3%. Scalar dissipation rate was measured with an average error of 12% after de-nosing. The influence of swirl number on combustion characteristics was examined by using Rayleigh scattering with accuracy of 90%. The flow fields in non-reacting and reacting swirling jets were investigated by using Particle Image Velocimetry (PIV). The effect of swirl number on a recirculation zone was shown and discussed. The flow structures were evaluated by using Proper Orthogonal Decomposition. Experimental assessment of presumed filtered density function and subgrid scale (SGS) scalar variance models that are being developed in the context of Large Eddy Simulation (LES) was performed by using the data obtained from measured scalar fields. Measurements were performed in a flow formed by discharging a central jet in the annular stream of swirling air. This is a typical geometry used in swirl-stabilised burners where the central jet is the flow. The measurements were performed at a constant Reynolds number of 28662, based on the area-averaged velocity of 8.46 (m/s) at the exit of the swirl-stabilised burner and the diameter of the annular swirling stream of 50.8(mm). Three swirl numbers S = {0.3, 0.58, 1.07} of the annular swirling stream were considered.Open Acces

Radiation dose optimization based on personalized numerical voxel models of exposure area

Целью исследования является воксельный метод в лучевой терапии с учетом элементного состава ткани. Цель работы - исследование воксельного метода планирования внешней лучевой терапии с использованием анализа элементного состава.The object of research is voxel-based method in radiotherapy accounting elemental composition of the tissue substance. Purpose of work – investigation of the voxel-based method of external radiation therapy planning using elemental composition analysis

Computational applications in stochastic operations research

Several computational applications in stochastic operations research are presented, where, for each application, a computational engine is used to achieve results that are otherwise overly tedious by hand calculations, or in some cases mathematically intractable. Algorithms and code are developed and implemented with specific emphasis placed on achieving exact results and substantiated via Monte Carlo simulation. The code for each application is provided in the software language utilized and algorithms are available for coding in another environment. The topics include univariate and bivariate nonparametric random variate generation using a piecewise-linear cumulative distribution, deriving exact statistical process control chart constants for non-normal sampling, testing probability distribution conformance to Benford\u27s law, and transient analysis of M/M/s queueing systems. The nonparametric random variate generation chapters provide the modeler with a method of generating univariate and bivariate samples when only observed data is available. The method is completely nonparametric and is capable of mimicking multimodal joint distributions. The algorithm is black-box, where no decisions are required from the modeler in generating variates for simulation. The statistical process control chart constant chapter develops constants for select non-normal distributions, and provides tabulated results for researchers who have identified a given process as non-normal The constants derived are bias correction factors for the sample range and sample standard deviation. The Benford conformance testing chapter offers the Kolmogorov-Smirnov test as an alternative to the standard chi-square goodness-of-fit test when testing whether leading digits of a data set are distributed according to Benford\u27s law. The alternative test has the advantage of being an exact test for all sample sizes, removing the usual sample size restriction involved with the chi-square goodness-of-fit test. The transient queueing analysis chapter develops and automates the construction of the sojourn time distribution for the nth customer in an M/M/s queue with k customers initially present at time 0 (k ≥ 0) without the usual limit on traffic intensity, rho \u3c 1, providing an avenue to conduct transient analysis on various measures of performance for a given initial number of customers in the system. It also develops and automates the construction of the sojourn time joint probability distribution function for pairs of customers, allowing the calculation of the exact covariance between customer sojourn times

Experimental study of combustion and scalar mixing in swirling jet flows

Turbulent mixing of passive scalar field and combustion of gaseous fuel were studied in the context of a non-premixed isothermal and reacting swirling jets discharged from a swirl-stabilised burner, as a function of swirl number. The rate of molecular mixing, which was quantified by the scalar dissipation rate was computed from measured scalar fields that were recorded by using Planar Laser Induced Fluorescence (PLIF) of acetone. The influence of the swirl number on the scalar mixing, unconditional and conditional scalar dissipation rate statistics was investigated. Scalar fields were measured with an average error of 3%. Scalar dissipation rate was measured with an average error of 12% after de-nosing. The influence of swirl number on combustion characteristics was examined by using Rayleigh scattering with accuracy of 90%. The flow fields in non-reacting and reacting swirling jets were investigated by using Particle Image Velocimetry (PIV). The effect of swirl number on a recirculation zone was shown and discussed. The flow structures were evaluated by using Proper Orthogonal Decomposition. Experimental assessment of presumed filtered density function and subgrid scale (SGS) scalar variance models that are being developed in the context of Large Eddy Simulation (LES) was performed by using the data obtained from measured scalar fields. Measurements were performed in a flow formed by discharging a central jet in the annular stream of swirling air. This is a typical geometry used in swirl-stabilised burners where the central jet is the flow. The measurements were performed at a constant Reynolds number of 28662, based on the area-averaged velocity of 8.46 (m/s) at the exit of the swirl-stabilised burner and the diameter of the annular swirling stream of 50.8(mm). Three swirl numbers S = {0.3, 0.58, 1.07} of the annular swirling stream were considered

Efficient control chart-based monitoring of scale parameter for a process with heavy-tailed non-normal distribution

Statistical process control is a procedure of quality control that is widely used in industrial processes to enable monitoring by using statistical techniques. All production processes are faced with natural and unnatural variations. To maintain the stability of the production process and reduce variation, different tools are used. Control charts are significant tools to monitor a production process. In this article, we design an extended exponentially weighted moving average (EEWMA) chart under the assumption of inverse Maxwell (IM) distribution, an IM EEWMA (IMEEWMA) control chart. We have estimated the performance of the proposed chart in terms of various run-length (RL) properties, including the average RL, standard deviation of the RL and median RL. We have also carried out a comparative analysis of the proposed chart with the existing Shewhart-type chart for IM distribution (VIM chart) and IM exponential weighted moving average (IMEWMA) chart. We observed that the proposed IMEEWMA chart performed better than the VIM chart and IMEWMA chart in terms of the ability to detect small and moderate shifts. To demonstrate its practical application, we have applied the IMEEWMA chart, along with existing control charts, to monitor the lifetime of car brake pad data. This real-world example illustrates the superiority of the IMEEWMA chart over its counterparts in industrial scenarios

Glosarium Matematika

273 p.; 24 cm