Search results for: Weibull bi-parameter probability function

Authors: Christian Lavault

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In this paper, the generalized fractional integral operators of two generalized Mittag-Leffler type functions are investigated. The special cases of interest involve the generalized M-series and K-function, both introduced by Sharma. The two pairs of theorems established herein generalize recent results about left- and right-sided generalized fractional integration operators applied here to the M-series and the K-function. The note also results in important applications in physics and mathematical engineering.

Keywords: Fox–Wright Psi function, generalized hypergeometric function, generalized Riemann– Liouville and Erdélyi–Kober fractional integral operators, Saigo's generalized fractional calculus, Sharma's M-series and K-function

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Authors: Diogo Silva, Fadul Rodor, Carlos Moraes

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This work compares the results of multidimensional function approximation using two algorithms: the classical Particle Swarm Optimization (PSO) and the Quantum Particle Swarm Optimization (QPSO). These algorithms were both tested on three functions - The Rosenbrock, the Rastrigin, and the sphere functions - with different characteristics by increasing their number of dimensions. As a result, this study shows that the higher the function space, i.e. the larger the function dimension, the more evident the advantages of using the QPSO method compared to the PSO method in terms of performance and number of necessary iterations to reach the stop criterion.

Keywords: PSO, QPSO, function approximation, AI, optimization, multidimensional functions

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Authors: Dheyaa W. Abbood, Rafa H. AL-Suhaili, May S. Saleh

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A model using the artificial neural networks and genetic algorithm technique is developed for obtaining optimum dimensions of the foundation length and protections of small hydraulic structures. The procedure involves optimizing an objective function comprising a weighted summation of the state variables. The decision variables considered in the optimization are the upstream and downstream cutoffs length sand their angles of inclination, the foundation length, and the length of the downstream soil protection. These were obtained for a given maximum difference in head, depth of impervious layer and degree of anisotropy.The optimization carried out subjected to constraints that ensure a safe structure against the uplift pressure force and sufficient protection length at the downstream side of the structure to overcome an excessive exit gradient. The Geo-studios oft ware, was used to analyze 1200 different cases. For each case the length of protection and volume of structure required to satisfy the safety factors mentioned previously were estimated. An ANN model was developed and verified using these cases input-output sets as its data base. A MatLAB code was written to perform a genetic algorithm optimization modeling coupled with this ANN model using a formulated optimization model. A sensitivity analysis was done for selecting the cross-over probability, the mutation probability and level ,the number of population, the position of the crossover and the weights distribution for all the terms of the objective function. Results indicate that the most factor that affects the optimum solution is the number of population required. The minimum value that gives stable global optimum solution of this parameters is (30000) while other variables have little effect on the optimum solution.

Keywords: inclined cutoff, optimization, genetic algorithm, artificial neural networks, geo-studio, uplift pressure, exit gradient, factor of safety

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Authors: Ali S. Gargoum

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Graphical modeling plays an important role in providing efficient probability calculations in high dimensional problems (computational efficiency). In this paper, we address one of such problems where we discuss fragmenting puff models and some distributional assumptions concerning models for the instantaneous, emission readings and for the fragmenting process. A graphical representation in terms of a junction tree of the conditional probability breakdown of puffs and puff fragments is proposed.

Keywords: graphical models, influence diagrams, junction trees, Bayesian nets

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Authors: Arefeh Arabaninezhad, Ali Fakher

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Since the deterministic analysis methods fail to take system uncertainties into account, probabilistic and non-probabilistic methods are suggested. Geotechnical analyses are used to determine the stress and deformation caused by construction; accordingly, many input variables which depend on ground behavior are required for geotechnical analyses. The Random Set approach is an applicable reliability analysis method when comprehensive sources of information are not available. Using Random Set method, with relatively small number of simulations compared to fully probabilistic methods, smooth extremes on system responses are obtained. Therefore random set approach has been proposed for reliability analysis in geotechnical problems. In the present study, the application of random set method in reliability analysis of deep excavations is investigated through three deep excavation projects which were monitored during the excavating process. A finite element code is utilized for numerical modeling. Two expected ranges, from different sources of information, are established for each input variable, and a specific probability assignment is defined for each range. To determine the most influential input variables and subsequently reducing the number of required finite element calculations, sensitivity analysis is carried out. Input data for finite element model are obtained by combining the upper and lower bounds of the input variables. The relevant probability share of each finite element calculation is determined considering the probability assigned to input variables present in these combinations. Horizontal displacement of the top point of excavation is considered as the main response of the system. The result of reliability analysis for each intended deep excavation is presented by constructing the Belief and Plausibility distribution function (i.e. lower and upper bounds) of system response obtained from deterministic finite element calculations. To evaluate the quality of input variables as well as applied reliability analysis method, the range of displacements extracted from models has been compared to the in situ measurements and good agreement is observed. The comparison also showed that Random Set Finite Element Method applies to estimate the horizontal displacement of the top point of deep excavation. Finally, the probability of failure or unsatisfactory performance of the system is evaluated by comparing the threshold displacement with reliability analysis results.

Keywords: deep excavation, random set finite element method, reliability analysis, uncertainty

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Authors: Bohli Afef

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The fifth-generation (5G) wireless systems is featured by extreme densities of cell stations to overcome the higher future demand. Hence, interference management is a crucial challenge in 5G ultra-dense cellular networks. In contrast to the classical inter-cell interference coordination approach, which is no longer fit for the high density of cell-tiers, this paper proposes a novel virtual coordination based on the dynamic common cognitive monitor channel protocol to deal with the inter-cell interference issue. A tractable and flexible model for the coverage probability of a typical user is developed through the use of the stochastic geometry model. The analyses of the performance of the suggested protocol are illustrated both analytically and numerically in terms of coverage probability.

Keywords: ultra dense heterogeneous networks, dynamic common channel protocol, cognitive radio, stochastic geometry, coverage probability

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Authors: Rakiya Abba

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This paper investigates the effect of the money supply, exchange and interest rate on economic growth in Nigeria through the application of Augmented Dickey-Fuller technique in testing the unit root property of the series and Granger causality test of causation between GDP, money supply, the exchange, and interest rate. The results of unit root suggest that all the variables in the model are stationary at 1, 5 and 10 percent level of significance, and the results of Causality suggest that money supply and exchange granger cause IR, the result further reveals two – way causation existed between M2 and EXR while IR granger cause GDP the null hypothesis is rejected and GDP does not granger cause IR as indicated by their probability values of 0.4805 and confirmed by F-statistics values of 0.75483. The results revealed that M2 and EXR do not granger causes GDP, the null hypothesis is accepted at 75percent 18percent respectively as indicated by their probability values of 0.7472 and 0.1830 respectively; also, GDP does not granger cause M2 and EXR. The Johansen cointegration result indicates that despite GDP does not granger cause M2, IR, and EXR, but there existed 1 cointegrating equation, implying the existence of long-run relationship between GDP, M2 IR, and EXR. A major policy implication of this result is that economic growth is function of and money supply and exchange rate, effective monetary policies should direct on manipulating instruments and importance should be placed on justification for adopting a particular policy be rationalized in order to increase growth in economy

Keywords: economic growth, money supply, interest rate, exchange rate, causality

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Authors: Mario Perez-Won, Roberto Lemus-Mondaca, Fernanda Marin, Constanza Olivares

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This study presents the simultaneous application of high hydrostatic pressure (HHP) and osmotic dehydration of jumbo squid (Dosidicus gigas) slice. Diffusion coefficients for both components water and solids were improved by the process pressure, being influenced by pressure level. The working conditions were different pressures such as 100, 250, 400 MPa and pressure atmospheric (0.1 MPa) for time intervals from 30 to 300 seconds and a 15% NaCl concentration. The mathematical expressions used for mass transfer simulations both water and salt were those corresponding to Newton, Henderson and Pabis, Page and Weibull models, where the Weibull and Henderson-Pabis models presented the best fitted to the water and salt experimental data, respectively. The values for water diffusivity coefficients varied from 1.62 to 8.10x10⁻⁹ m²/s whereas that for salt varied among 14.18 to 36.07x10⁻⁹ m²/s for selected conditions. Finally, as to quality parameters studied under the range of experimental conditions studied, the treatment at 250 MPa yielded on the samples a minimum hardness, whereas springiness, cohesiveness and chewiness at 100, 250 and 400 MPa treatments presented statistical differences regarding to unpressurized samples. The colour parameters L* (lightness) increased, however, but b* (yellowish) and a* (reddish) parameters decreased when increasing pressure level. This way, samples presented a brighter aspect and a mildly cooked appearance. The results presented in this study can support the enormous potential of hydrostatic pressure application as a technique important for compounds impregnation under high pressure.

Keywords: colour, diffusivity, high pressure, jumbo squid, modelling, texture

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Authors: A. T. Kassem

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Fires areconsidered a common hazardous action that any building may face. Most buildings’ structural elements are designed, taking into consideration precautions for fire safety, using deterministic design approaches. Public and highly important buildings are commonly designed considering standard fire rating and, in many cases, contain large compartments with central domes. Real fire scenarios are not commonly brought into action in structural design of buildings because of complexities in both scenarios and analysis tools. This paper presents a modern approach towards analysis of spherical domes in real fire condition via implementation of building information modelling, and adopting a probabilistic approach. BIMhas been implemented to bridge the gap between various software packages enabling them to function interactively to model both real fire and corresponding structural response. Ventilation controlled fires scenarios have been modeled using both “Revit” and “Pyrosim”. Monte Carlo simulation has been adopted to engage the probabilistic analysis approach in dealing with various parameters. Conclusions regarding failure probability and fire endurance, in addition to the effects of various parameters, have been extracted.

Keywords: concrete, spherical domes, ventilation controlled fires, BIM, monte carlo simulation, pyrosim, revit

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Authors: Hao Chen, Bo Guo, Ping Jiang

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Residual life (RL) estimation based on multi-phase nonlinear Wiener process was studied in this paper, which is significant for complicated products with small samples. Firstly, nonlinear Wiener model with random parameter was introduced and multi-phase nonlinear Wiener model was proposed to model degradation process of products that were nonlinear and separated into different phases. Then the multi-phase RL probability density function based on the presented model was derived approximately in a closed form and parameters estimation was achieved with the method of maximum likelihood estimation (MLE). Finally, the method was applied to estimate the RL of high voltage plus capacitor. Compared with the other three different models by log-likelihood function (Log-LF) and Akaike information criterion (AIC), the results show that the proposed degradation model can capture degradation process of high voltage plus capacitors in a better way and provide a more reliable result.

Keywords: multi-phase nonlinear wiener process, residual life estimation, maximum likelihood estimation, high voltage plus capacitor

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Authors: Viriyavudh Sim, Woo Young Jung

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The failure of roof cladding mostly occurs due to the failing of the connection between claddings and purlins, which is the pull-out of the screw connecting the two parts when the pull-out load, i.e. typhoon, is higher than the resistance of the connection screw. As typhoon disasters in Korea are constantly on the rise, probability risk assessment (PRA) has become a vital tool to evaluate the performance of civil structures. In this study, we attempted to determine the fragility of roof cladding with the screw connection. Experimental study was performed to evaluate the pull-out resistance of screw joints between honeycomb panels and back frames. Subsequently, by means of Monte Carlo Simulation method, probability of failure for these types of roof cladding was determined. The results that the failure of roof cladding was depends on their location on the roof, for example, the edge most panel has the highest probability of failure.

Keywords: Monte Carlo Simulation, roof cladding, screw pull-out strength, wind fragility

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Authors: Naser Kazemi Eilaki, Carolyn Ahmer, Ilona Heldal, Bjarne Christian Hagen

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Older people and people with disabilities are recognized as at-risk groups when it comes to egress and travel from hazard zone to safe places. One's disability can negatively influence her or his escape time, and this becomes even more important when people from this target group live alone. This research deals with the fire safety of mentioned people's buildings by means of probabilistic methods. For this purpose, fire safety is addressed by modeling the egress of our target group from a hazardous zone to a safe zone. A common type of detached house with a prevalent plan has been chosen for safety analysis, and a limit state function has been developed according to the time-line evacuation model, which is based on a two-zone and smoke development model. An analytical computer model (B-Risk) is used to consider smoke development. Since most of the involved parameters in the fire development model pose uncertainty, an appropriate probability distribution function has been considered for each one of the variables with indeterministic nature. To achieve safety and reliability for the at-risk groups, the fire safety index method has been chosen to define the probability of failure (causalities) and safety index (beta index). An improved harmony search meta-heuristic optimization algorithm has been used to define the beta index. Sensitivity analysis has been done to define the most important and effective parameters for the fire safety of the at-risk group. Results showed an area of openings and intervals to egress exits are more important in buildings, and the safety of people would improve with increasing dimensions of occupant space (building). Fire growth is more critical compared to other parameters in the home without a detector and fire distinguishing system, but in a home equipped with these facilities, it is less important. Type of disabilities has a great effect on the safety level of people who live in the same home layout, and people with visual impairment encounter more risk of capturing compared to visual and movement disabilities.

Keywords: fire safety, at-risk groups, zone model, egress time, uncertainty

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Authors: Yungtai Lo

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Two-part random effects models have been used to fit semi-continuous longitudinal data where the response variable has a point mass at 0 and a continuous right-skewed distribution for positive values. We review methods proposed in the literature for analyzing data with excess zeros. A two-part logit-log-normal random effects model, a two-part logit-truncated normal random effects model, a two-part logit-gamma random effects model, and a two-part logit-skew normal random effects model were used to examine effects of a bottle-weaning intervention on reducing bottle use and daily milk intake from bottles in toddlers aged 11 to 13 months in a randomized controlled trial. We show in all four two-part models that the intervention promoted bottle-weaning and reduced daily milk intake from bottles in toddlers drinking from a bottle. We also show that there are no differences in model fit using either the logit link function or the probit link function for modeling the probability of bottle-weaning in all four models. Furthermore, prediction accuracy of the logit or probit link function is not sensitive to the distribution assumption on daily milk intake from bottles in toddlers not off bottles.

Keywords: two-part model, semi-continuous variable, truncated normal, gamma regression, skew normal, Pearson residual, receiver operating characteristic curve

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Authors: Rogelio Luck, Yucheng Liu

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This paper proposes the continuous-time singular value decomposition (SVD) for the impulse response function, a special kind of Green’s functions e⁻⁽ᵗ⁻ ᵀ⁾, in order to find a set of singular functions and singular values so that the convolutions of such function with the set of singular functions on a specified domain are the solutions to the inhomogeneous differential equations for those singular functions. A numerical example was illustrated to verify the proposed method. Besides the continuous-time SVD, a discrete-time SVD is also presented for the impulse response function, which is modeled using a Toeplitz matrix in the discrete system. The proposed method has broad applications in signal processing, dynamic system analysis, acoustic analysis, thermal analysis, as well as macroeconomic modeling.

Keywords: singular value decomposition, impulse response function, Green’s function , Toeplitz matrix , Hankel matrix

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Authors: Ramin Rostamkhani, Thurasamy Ramayah

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One of the most important topics of today’s industrial organizations is the challenging issue of supply chain management. In this field, scientists and researchers have published numerous practical articles and models, especially in the last decade. In this research, to our best knowledge, the discussion of data modeling of supply chain management components using well-known statistical distribution functions has been considered. The world of science owns mathematics, and showing the behavior of supply chain data based on the characteristics of statistical distribution functions is innovative research that has not been published anywhere until the moment of doing this research. In an analytical process, describing different aspects of functions including probability density, cumulative distribution, reliability, and failure function can reach the suitable statistical distribution function for each of the components of the supply chain management. It can be applied to predict the behavior data of the relevant component in the future. Providing a model to adapt the best statistical distribution function in the supply chain management components will be a big revolution in the field of the behavior of the supply chain management elements in today's industrial organizations. Demonstrating the final results of the proposed model by introducing the process capability indices before and after implementing it alongside verifying the approach through the relevant assessment as an acceptable verification is a final step. The introduced approach can save the required time and cost to achieve the organizational goals. Moreover, it can increase added value in the organization.

Keywords: analyzing, process capability indices, statistical distribution functions, supply chain management components

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Authors: Deepa S N, Srinivasan a D, Veeramanju K T

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The power transformer is a critical equipment in the transmission and distribution network that must be managed to ensure uninterrupted power service. The liquid insulation is essential for the proper functioning of the transformer, as it serves as both coolant and insulating medium, which influences the transformer’s durability. Further, the insulating state of a power transformer has a significant impact on its reliability. Mineral oil derived from petroleum crude oil has been employed as liquid dielectrics for decades due to its superior functional characteristics, however as a resource for the same are getting depleted over the years. Research is undertaken across the globe to identify a viable substitute for mineral oil. Further, alternate insulating oils are being investigated for better environmental impact, biodegradability and economics. Several combinations of vegetable oil derived natural esters are being inspected by researchers across the globe in these domains. In this work, mineral oil is blended with soyabean oil with various proportions and dielectric properties such as dielectric breakdown voltage, relative permittivity, dissipation factor, viscosity, flash and fire point have been investigated according to international standards. A quantitative comparison is made among various samples and is observed that the blended oil sample of equal proportion of mineral oil and soyabean oil, MO50+SO50 exhibits superior dielectric properties such as breakdown voltage of 65kV, dissipation factor of 0.0044, relative permittivity of 3.1680 that are closer to the range of values recommended for power transformer applications. Also, Breakdown voltage values of all the investigated oil samples obeyed the Weibull and Normal probability distribution.

Keywords: blended oil, dielectric breakdown, liquid insulation, power transformer

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Authors: Pyung Soo Kim, Eung Hyuk Lee, Mun Suck Jang

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A packet loss probability (PLP) estimation filter with finite memory structure is proposed to estimate the packet rate mean and variance of the input traffic process in real-time while removing undesired system and measurement noises. The proposed PLP estimation filter is developed under a weighted least square criterion using only the finite traffic measurements on the most recent window. The proposed PLP estimation filter is shown to have several inherent properties such as unbiasedness, deadbeat, robustness. A guideline for choosing appropriate window length is described since it can affect significantly the estimation performance. Using computer simulations, the proposed PLP estimation filter is shown to be superior to the Kalman filter for the temporarily uncertain system. One possible explanation for this is that the proposed PLP estimation filter can have greater convergence time of a filtered estimate as the window length M decreases.

Keywords: packet loss probability estimation, finite memory filter, infinite memory filter, Kalman filter

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Authors: Vernie C. Convicto, Henry P. Aringa, Wilson I. Barredo

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This study presents a conformational model of the helical structures of globular protein particularly ferritin in the framework of white noise path integral formulation by using Associated Legendre functions, Bessel and convolution of Bessel and trigonometric functions as modulating functions. The model incorporates chirality features of proteins and their helix-turn-helix sequence structural motif.

Keywords: globular protein, modulating function, white noise, winding probability

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Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

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The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f^-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: analytic functions, bi-univalent functions, Hohlov operator, subordination

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Authors: Ping Jiang, Yunyan Xing, Dian Zhang, Bo Guo

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The reliability qualification test (RQT) is widely used in product development to qualify whether the product meets predetermined reliability requirements, which are mainly described in terms of reliability indices, for example, MTBF (Mean Time Between Failures). It is widely exercised in product development. In engineering practices, RQT plans are mandatorily referred to standards, such as MIL-STD-781 or GJB899A-2009. But these conventional RQT plans in standards are not preferred, as the test plans often require long test times or have high risks for both producer and consumer due to the fact that the methods in the standards only use the test data of the product itself. And the standards usually assume that the product is exponentially distributed, which is not suitable for a complex product other than electronics. So it is desirable to develop an RQT plan derivation method that safely shortens test time while keeping the two risks under control. To meet this end, for the product whose lifetime follows Weibull distribution, an RQT plan derivation method is developed. The merit of the method is that expert judgment is taken into account. This is implemented by applying the Bayesian method, which translates the expert judgment into prior information on product reliability. Then producer’s risk and the consumer’s risk are calculated accordingly. The procedures to derive RQT plans are also proposed in this paper. As extra information and expert judgment are added to the derivation, the derived test plans have the potential to shorten the required test time and have satisfactory low risks for both producer and consumer, compared with conventional test plans. A case study is provided to prove that when using expert judgment in deriving product test plans, the proposed method is capable of finding ideal test plans that not only reduce the two risks but also shorten the required test time as well.

Keywords: expert judgment, reliability qualification test, test plan derivation, producer’s risk, consumer’s risk

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Authors: Lanyan Peng, Ling Chen

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Leishan Miao New-Year is one of the grandest festivals in the southeastern of Guizhou Province in China. It was officially listed in the National Intangible Cultural Heritage List in 2008, as a traditional folk cultural activity organized by the local Miao people. With the rise of cultural tourism, after 19 years of exploration, the local government has successfully built Miao New-Year into a cultural card that is well-known at home and abroad. During the Miao New-Year period, it has attracted 3.8 million tourists and achieves a win-win situation in the economy and culture. However, tourism development has changed the living environment and living state of the local people. And it is accompanied by changes in the form of the festival, the content of the festival, and the local people’s needs and attitudes to the festival. This paper uses the field investigation method to achieve 410 questionnaires and 35 interviews, exploring the process and the reasons for changes of Leishan Miao New-Year’s cultural function. Among all the functions, the economic function, identity function, and entertainment function have been enhanced, and the marriage and love function has been extended. In the meanwhile, sacrificial function has been weakened. There are some trends in functions. The function of commemorating ancestor and self-entertainment has been changed to entertaining people and economic pursuit.

Keywords: Miao New-Year, Miao nationality, festival function, changes

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Authors: Irina Peterburgsky

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Let T be a unit circumference of a complex plane, E be a Banach space, E* and E** be its conjugate and second conjugate, respectively. In general, a Hardy space Hp(E), p ≥1, where functions act from the open unit disk to E, could contain a function for which even weak nontangential (angular) boundary value in the space E** does not exist at any point of the unit circumference T (C. Grossetete.) The situation is "better" when certain restrictions to the Banach space of values are applied (more or less resembling a classical case of scalar-valued functions depending on constrains, as shown by R. Ryan.) This paper shows that, nevertheless, in the case of a Banach space of a general type, the following positive statement is true: Proposition. For any function f(z) from Hp(E), p ≥ 1, there exists a function F(eiθ) on the unit circumference T to E** whose Poisson (in the Pettis sense) is integral regains the function f(z) on the open unit disk. Some characteristics of the function F(eiθ) are demonstrated.

Keywords: hardy spaces, Banach space-valued function, boundary values, Pettis integral

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Authors: Serdal Pamuk, Irem Cay

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Our model is based on the theory of reinforced random walks coupled with Michealis-Menten mechanisms which view endothelial cell receptors as the catalysts for transforming both tumor and macrophage derived tumor angiogenesis factor (TAF) into proteolytic enzyme which in turn degrade the basal lamina. The model consists of two main parts. First part has seven differential equations (DE’s) in one space dimension over the capillary, whereas the second part has the same number of DE’s in two space dimensions in the extra cellular matrix (ECM). We connect these two parts via some boundary conditions to move the cells into the ECM in order to initiate capillary formation. But, when does this movement begin? To address this question we estimate the thresholds that activate the transport equations in the capillary. We do this by using steady-state analysis of TAF equation under some assumptions. Once these equations are activated endothelial, pericyte and macrophage cells begin to move into the ECM for the initiation of angiogenesis. We do believe that our results play an important role for the mechanisms of cell migration which are crucial for tumor angiogenesis. Furthermore, we estimate the long time tendency of these three cells, and find that they tend to the transition probability functions as time evolves. We provide our numerical solutions which are in good agreement with our theoretical results.

Keywords: angiogenesis, capillary formation, mathematical analysis, steady-state, transition probability function

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Authors: Muhammad Imran Ahmad, Ruzelita Ngadiran, Mohd Nazrin Md Isa, Nor Ashidi Mat Isa, Mohd ZaizuIlyas, Raja Abdullah Raja Ahmad, Said Amirul Anwar Ab Hamid, Muzammil Jusoh

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This paper presents two technique, local feature extraction using image spectrum and low frequency spectrum modelling using GMM to capture the underlying statistical information to improve the performance of face recognition system. Local spectrum features are extracted using overlap sub block window that are mapping on the face image. For each of this block, spatial domain is transformed to frequency domain using DFT. A low frequency coefficient is preserved by discarding high frequency coefficients by applying rectangular mask on the spectrum of the facial image. Low frequency information is non Gaussian in the feature space and by using combination of several Gaussian function that has different statistical properties, the best feature representation can be model using probability density function. The recognition process is performed using maximum likelihood value computed using pre-calculate GMM components. The method is tested using FERET data sets and is able to achieved 92% recognition rates.

Keywords: local features modelling, face recognition system, Gaussian mixture models, Feret

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Authors: Seon Soon Choi

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The principal purpose of this paper is to find the influence of maximum fatigue load on the probabilistic aspect of fatigue crack propagation life at a specified grown crack in magnesium alloys. The experiments of fatigue crack propagation are carried out in laboratory air under different conditions of the maximum fatigue loads to obtain the fatigue crack propagation data for the statistical analysis. In order to analyze the probabilistic aspect of fatigue crack propagation life, the goodness-of fit test for probability distribution of the fatigue crack propagation life at a specified grown crack is implemented through Anderson-Darling test. The good probability distribution of the fatigue crack propagation life is also verified under the conditions of the maximum fatigue loads.

Keywords: fatigue crack propagation life, magnesium alloys, maximum fatigue load, probability

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Authors: Zuhier Altawallbeh

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In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra.by providing certain homotopic function.

Keywords: hochschild homology, homotopic function, free and projective modules, free resolution, exterior algebra, symmetric algebra

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Authors: M. A. Tayfun, M. A. Alkhalidi

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The exact theoretical expression describing the probability distribution of nonlinear sea-surface elevations derived from the second-order narrowband model has a cumbersome form that requires numerical computations, not well-disposed to theoretical or practical applications. Here, the same narrowband model is re-examined to develop a simpler closed-form approximation suitable for theoretical and practical applications. The salient features of the approximate form are explored, and its relative validity is verified with comparisons to other readily available approximations, and oceanic data.

Keywords: ocean waves, probability distributions, second-order nonlinearities, skewness coefficient, wave steepness

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Authors: Yoshiaki Shikata

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A prioritized processor-sharing (PS) system with a maximum permissible sojourn time (MPST) is proposed. In this PS system, a higher-priority request is allocated a larger service ratio than a lower-priority request. Moreover, each request receiving service is guaranteed the maximum permissible sojourn time determined by each priority class, regardless of its service time. Arriving requests that cannot receive service due to this guarantee are rejected. We further propose a guarantee method for implementing such a system, and discuss performance evaluation procedures for the resulting system. Practical performance measures, such as the relationships between the loss probability or mean sojourn time of each class request and the maximum permissible sojourn time are evaluated via simulation. At the arrival of each class request, its acceptance or rejection is judged using extended sojourn times of all requests receiving service in the server. As the MPST increases, the mean sojourn time increases almost linearly. However, the logarithm of the loss probability decreases almost linearly. Moreover with an MPST, the difference in the mean sojourn time for different MPSTs increases with the traffic rate. Conversely, the difference in the loss probability for different MPSTs decreases as the traffic rate increases.

Keywords: prioritized processor sharing, priority ratio, permissible sojourn time, loss probability, mean sojourn time, simulation

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Authors: Ariful Islam, Showkat Ahmad Lone

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Statistical distributions have long been employed in the assessment of semiconductor devices and product reliability. The power function-distribution is one of the most important distributions in the modern reliability practice and can be frequently preferred over mathematically more complex distributions, such as the Weibull and the lognormal, because of its simplicity. Moreover, it may exhibit a better fit for failure data and provide more appropriate information about reliability and hazard rates in some circumstances. This study deals with estimating information about failure times of items under step-stress partially accelerated life tests for competing risk based on adoptive type-I progressive hybrid censoring criteria. The life data of the units under test is assumed to follow Mukherjee-Islam distribution. The point and interval maximum-likelihood estimations are obtained for distribution parameters and tampering coefficient. The performances of the resulting estimators of the developed model parameters are evaluated and investigated by using a simulation algorithm.

Keywords: adoptive progressive hybrid censoring, competing risk, mukherjee-islam distribution, partially accelerated life testing, simulation study

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Authors: Alexander K. Guo

Abstract:

PM2.5 poses a large threat to people’s health and the environment and is an issue of large concern in Beijing, brought to the attention of the government by the media. In addition, both the United States Embassy in Beijing and the government of China have increased monitoring of PM2.5 in recent years, and have made real-time data available to the public. This report utilizes hourly historical data (2008-2016) from the U.S. Embassy in Beijing for the first time. The first objective was to attempt to fit probability distributions to the data to better predict a number of days exceeding the standard, and the second was to uncover any yearly, seasonal, monthly, daily, and hourly patterns and trends that may arise to better understand of air control policy. In these data, 66,650 hours and 2687 days provided valid data. Lognormal, gamma, and Weibull distributions were fit to the data through an estimation of parameters. The Chi-squared test was employed to compare the actual data with the fitted distributions. The data were used to uncover trends, patterns, and improvements in PM2.5 concentration over the period of time with valid data in addition to specific periods of time that received large amounts of media attention, analyzed to gain a better understanding of causes of air pollution. The data show a clear indication that Beijing’s air quality is unhealthy, with an average of 94.07µg/m3 across all 66,650 hours with valid data. It was found that no distribution fit the entire dataset of all 2687 days well, but each of the three above distribution types was optimal in at least one of the yearly data sets, with the lognormal distribution found to fit recent years better. An improvement in air quality beginning in 2014 was discovered, with the first five months of 2016 reporting an average PM2.5 concentration that is 23.8% lower than the average of the same period in all years, perhaps the result of various new pollution-control policies. It was also found that the winter and fall months contained more days in both good and extremely polluted categories, leading to a higher average but a comparable median in these months. Additionally, the evening hours, especially in the winter, reported much higher PM2.5 concentrations than the afternoon hours, possibly due to the prohibition of trucks in the city in the daytime and the increased use of coal for heating in the colder months when residents are home in the evening. Lastly, through analysis of special intervals that attracted media attention for either unnaturally good or bad air quality, the government’s temporary pollution control measures, such as more intensive road-space rationing and factory closures, are shown to be effective. In summary, air quality in Beijing is improving steadily and do follow standard probability distributions to an extent, but still needs improvement. Analysis will be updated when new data become available.

Keywords: Beijing, distribution, patterns, pm2.5, trends

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