• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.709-723
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• 2024

We study the distributions of waiting times in variations of the geometric distribution of order k. Variation imposes length on the runs of successes and failures. We study two types of waiting time random variables. First, we consider the waiting time for a run of k consecutive successes the first time no sequence of consecutive k failures occurs prior, denoted by T^(k). Next, we consider the waiting time for a run of k consecutive failures the first time no sequence of k consecutive successes occurred prior, denoted by J^(k). In addition, we study the distribution of the weighted average. The exact formulae of the probability mass function, mean, and variance of distributions are also obtained.

• Communications for Statistical Applications and Methods
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• v.21 no.2
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• pp.147-160
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• 2014

In this paper, we introduce the exponentiated Weibull-geometric (EWG) distribution which generalizes two-parameter exponentiated Weibull (EW) distribution introduced by Mudholkar et al. (1995). This proposed distribution is obtained by compounding the exponentiated Weibull with geometric distribution. We derive its cumulative distribution function (CDF), hazard function and the density of the order statistics and calculate expressions for its moments and the moments of the order statistics. The hazard function of the EWG distribution can be decreasing, increasing or bathtub-shaped among others. Also, we give expressions for the Renyi and Shannon entropies. The maximum likelihood estimation is obtained by using EM-algorithm (Dempster et al., 1977; McLachlan and Krishnan, 1997). We can obtain the Bayesian estimation by using Gibbs sampler with Metropolis-Hastings algorithm. Also, we give application with real data set to show the flexibility of the EWG distribution. Finally, summary and discussion are mentioned.

• Journal of the Semiconductor & Display Technology
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• v.5 no.4 s.17
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• pp.29-34
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• 2006

In order to design an OLED(Organic Luminescent Emitting Device) evaporation system, geometric simulation of film thickness distribution profile is required. For the OLED evaporation process, thin film thickness uniformity is of great practical importance. In this paper, a geometric modeling algorithm is introduced for process simulation of the OLED evaporating process. The physical fact of the evaporating process is modeled mathematically. Based on the developed method, the thickness of the thin-film layer can be successfully controlled.

• The KSFM Journal of Fluid Machinery
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• v.12 no.6
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• pp.7-12
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• 2009

This paper presents a numerical study on the design of side-suction inlet geometry which is used for multi stage centrifugal pumps or inline centrifugal pumps. In order to achieve an optimum inlet geometry and to explain the interactions between the different geometric configurations, the three dimensional computational fluid dynamics and the design of experiment methods have been applied. Geometric design variables describing the cross sectional area distribution through the inlet were selected. The objective functions are defined as the non-uniformity of the velocity distribution at the passage exit which is just in front of the impeller eyes. From the 2k factorial design results, the most important design variable was found and the performance of the side suction inlet was improved compared to the base line shape.

• Communications for Statistical Applications and Methods
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• v.21 no.3
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• pp.201-212
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• 2014

We provide a simple basic method to find bounds for higher order moments of unimodal distributions in terms of lower order moments when the random variable takes value in a given finite real interval. The bounds for moments in terms of the geometric mean of the distribution are also derived. Both continuous and discrete cases are considered. The bounds for the ratio and difference of moments are obtained. The special cases provide refinements of several well-known inequalities, such as Kantorovich inequality and Krasnosel'skii and Krein inequality.

• Steel and Composite Structures
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• v.29 no.3
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• pp.319-332
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• 2018

This paper investigates the free vibration of geometrically imperfect functionally graded car-bon nanotube-reinforced composite (FG-CNTRC) beams that are integrated with two sur-face-bonded piezoelectric layers and subjected to a combined action of a uniform temperature rise, a constant actuator voltage and an in-plane force. The material properties of FG-CNTRCs are assumed to be temperature-dependent and vary continuously across the thick-ness. A generic imperfection function is employed to simulate various possible imperfections with different shapes and locations in the beam. The governing equations that account for the influence of initial geometric imperfection are derived based on the first-order shear deformation theory. The postbuckling configurations of FG-CNTRC hybrid beams are determined by the differential quadrature method combined with the modified Newton-Raphson technique, after which the fundamental frequencies of hybrid beams in the postbuckled state are obtained by a standard eigenvalue algorithm. The effects of CNT distribution pattern and volume fraction, geometric imperfection, thermo-electro-mechanical load, as well as boundary condition are examined in detail through parametric studies. The results show that the fundamental frequency of an imperfect beam is higher than that of its perfect counterpart. The influence of geometric imperfection tends to be much more pronounced around the critical buckling temperature.

• Structural Engineering and Mechanics
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• v.66 no.5
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• pp.557-568
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• 2018

An investigation is made in the present work on the post-buckling and geometrically nonlinear behaviors of moderately thick perfect and imperfect rectangular plates made-up of functionally graded materials. Spectral collocation approach based on Legendre basis functions is developed to analyze the functionally graded plates while they are subjected to end-shortening strain. The material properties in this study are varied through the thickness according to the simple power law distribution. The fundamental equations for moderately thick rectangular plates are derived using first order shear deformation plate theory and taking into account both geometric nonlinearity and initial geometric imperfections. In the current study, the domain of interest is discretized with Legendre-Gauss-Lobatto nodes. The equilibrium equations will be obtained by discretizing the Von-Karman's equilibrium equations and also boundary conditions with finite Legendre basis functions that are substituted into the displacement fields. Due to effect of geometric nonlinearity, the final set of equilibrium equations is nonlinear and therefore the quadratic extrapolation technique is used to solve them. Since the number of equations in this approach will always be more than the number of unknown coefficients, the least squares technique will be used. Finally, the effects of boundary conditions, initial geometric imperfection and material properties are investigated and discussed to demonstrate the validity and capability of proposed method.

• International Journal of Aeronautical and Space Sciences
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• v.17 no.4
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• pp.622-630
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• 2016

In the operation of a low earth orbit satellite, a series of antenna commands are transmitted from a ground station to the satellite within a visibility window (i.e., the time period for which an antenna of the satellite is visible from the station) and executed to control the antenna. The window is a limited resource where all data transmission is carried out. Therefore, minimizing the transmission time for the antenna commands by reducing the data size is necessary in order to provide more time for the transmission of other data. In this paper, we propose a geometric compression method based on B-spline curve fitting using dominant points in order to compactly represent the antenna commands. We transform the problem of command size reduction into a geometric problem that is relatively easier to deal with. The command data are interpreted as points in a 2D space. The geometric properties of the data distribution are considered to determine the optimal parameters for a curve approximating the data with sufficient accuracy. Experimental results demonstrate that the proposed method is superior to conventional methods currently used in practice.

• Asian Journal of Atmospheric Environment
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• v.6 no.4
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• pp.304-313
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• 2012

In this study, the ${\AA}$ngstrom exponent for polydispersed aerosol during dynamic processes was investigated. Log-normal aerosol size distribution was assumed, and a sensitivity analysis of the ${\AA}$ngstrom exponent with regards the coagulation and condensation process was performed. The ${\AA}$ngstrom exponent is expected to decrease because of the particle growth due to coagulation and condensation. However, it is difficult to quantify the degree of change. In order to understand quantitatively the change in the ${\AA}$ngstrom exponent during coagulation and condensation, different real and imaginary parts of the refractive index were considered. The results show that the ${\AA}$ngstrom exponent is sensitive to changes in size distribution and refractive index. The total number concentration decreases and the geometric mean diameter of aerosols increase during coagulation. On the while, the geometric standard deviation approaches monodispersed size distribution during the condensation process, and this change in size distribution affects the ${\AA}$ngstrom exponent. The degree of change in the ${\AA}$ngstrom exponent depends on the refractive index and initial size distribution, and the size parameter changes with the ${\AA}$ngstrom exponent for a given refractive index or chemical composition; this indicates that the size distribution plays an important role in determining the ${\AA}$ngstrom exponent as well as the chemical composition. Subsequently, this study shows how the ${\AA}$ngstrom exponent changes quantitatively during the aerosol dynamics processes for a log-normal aerosol size distribution for different refractive indices; the results showed good agreement with the results for simple analytic size distribution solutions.

• International Journal of CAD/CAM
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• v.7 no.1
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• pp.1-10
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• 2007

The compression of CAD models is a key technology for realizing Internet-based collaborative product development because big model sizes often prohibit us to achieve a rapid product information transmission. Although there exist some algorithms for compressing discrete CAD models, original precise CAD models are focused on in this paper. Here, the characteristics of hierarchical structures in CAD models and the distribution of their redundant data are exploited for developing a novel data encoding method. In the method, different encoding rules are applied to different types of data. Geometric data is a major concern for reducing model sizes. For geometric data, the control points of B-spline curves and surfaces are compressed with the second-order predictions in a local coordinate system. Based on analysis to the distortion induced by quantization, an efficient method for computation of the distortion is provided. The results indicate that the data size of CAD models can be decreased efficiently after compressed with the proposed method.