The Brownian coagulation of nanoparticles with initial bimodal size distribution, i.e., mode i and j, is numerically studied using the moment method. Evolutions of particle number concentration, geometric average diam...The Brownian coagulation of nanoparticles with initial bimodal size distribution, i.e., mode i and j, is numerically studied using the moment method. Evolutions of particle number concentration, geometric average diameter and geometric standard deviation are given in the free molecular regime, the continuum regime, the free molecular regime and transition regime, the free molecular regime and continuum regime, respectively. The results show that, both in the free molecular regime and the continuum regime, the num- ber concentration of mode i and j decreases with increasing time. The evolutions of particle geometric average diameter with different initial size distribution are quite different. Both intra-modal and inter-modal coagulation finally make the polydispersed size distribution become monodispersed. As time goes by, the size distribution with initial bimodal turns to be unimoda/and shifts to a larger particle size range. In the free molecular regime and transition regime, the inter- modal coagulation becomes dominant when the number concentrations of mode i and j are of the same order. The effects of the number concentration of mode i and mode j on the evolution of geometric average diameter of mode j are negligible, while the effects of the number concentration of mode j on the evolution of geometric average diameter of mode j is distinct. In the free molecular regime and continuum regime, the higher the initial number concentration of mode j, the more obvious the variation of the number concentration of mode i.展开更多
The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of...The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of fields,including reliability,economics,engineering,biomedical science,biological research,environmental studies,and finance.For modeling real data,several expanded classes of distributions have been established.The modified alpha power transformed approach is used to implement the new model.The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models.It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters.Precise expressions for quantiles,moments,incomplete moments,moment generating function,characteristic generating function,and entropy expression are among the determined attributes of the new distribution.The point and interval estimates are studied using the maximum likelihood method.Simulation research is conducted to illustrate the correctness of the theoretical results.Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.展开更多
Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and b...Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and bridges,given the HSR’s extended operational duration.Therefore,ensuring the running safety of train-bridge coupled(TBC)system,primarily composed of simply supported beam bridges,is paramount.Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently.Instead,efficient algorithm like the new point estimate method combined with moment expansion approximation(NPEM-MEA)is applied to study random responses of numerical simulation TBC systems.Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method.Comparative analysis confirms the accuracy and efficiency of the method,with a recommended truncation order of four to six for the NPEM-MEA.Additionally,the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system.This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions.展开更多
The paper considers the theoretical basics and the specific mathematical techniques having been developed for solving the tasks of the stochastic data analysis within the Rice statistical model in which the output sig...The paper considers the theoretical basics and the specific mathematical techniques having been developed for solving the tasks of the stochastic data analysis within the Rice statistical model in which the output signal’s amplitude is composed as a sum of the sought-for initial value and a random Gaussian noise. The Rician signal’s characteristics such as the average value and the noise dispersion have been shown to depend upon the Rice distribution’s parameters nonlinearly what has become a prerequisite for the development of a new approach to the stochastic Rician data analysis implying the joint signal and noise accurate evaluation. The joint computing of the Rice distribution’s parameters allows efficient reconstruction of the signal’s in-formative component against the noise background. A meaningful advantage of the proposed approach consists in the absence of restrictions connected with any a priori suppositions inherent to the traditional techniques. The results of the numerical experiments are provided confirming the efficiency of the elaborated approach to stochastic data analysis within the Rice statistical model.展开更多
The g-factor hence the magnetic moment,of the isomeric state <sup>43</sup>Sc（|9/2<sup>-</sup>,3.1232 MeV）has been measured by the time differential perturbed angular distributionmethod.The me...The g-factor hence the magnetic moment,of the isomeric state <sup>43</sup>Sc（|9/2<sup>-</sup>,3.1232 MeV）has been measured by the time differential perturbed angular distributionmethod.The measured values are g=0.3279（19）and μ=3.108（18）nm.展开更多
In this paper, the estimation of parameters based on a progressively type-I interval censored sample from a Rayleigh distribution is studied. Different methods of estimation are discussed. They include mid-point appro...In this paper, the estimation of parameters based on a progressively type-I interval censored sample from a Rayleigh distribution is studied. Different methods of estimation are discussed. They include mid-point approximation estima- tor, the maximum likelihood estimator, moment estimator, Bayes estimator, sampling adjustment moment estimator, sampling adjustment maximum likelihood estimator and estimator based on percentile. The estimation procedures are discussed in details and compared via Monte Carlo simulations in terms of their biases.展开更多
<strong>Background:</strong> Acute Myeloid leukemia (AML) is the most prominent acute leukemia in adults. In the United States, we experience over 20,000 cases per year. Over the past decade, improvements ...<strong>Background:</strong> Acute Myeloid leukemia (AML) is the most prominent acute leukemia in adults. In the United States, we experience over 20,000 cases per year. Over the past decade, improvements in the diagnosis of subtypes of AML and advances in therapeutic approaches have improved the outlook for patients with AML. However, despite these advancements, the survival rate among patients who are less than 65 years of age is only 40 percent. <strong>Purpose:</strong> The purpose of the paper is to study if there exists any significant difference in the survival probabilities of male and female AML patients. Also, we want to investigate if there is any parametric probability distribution that best fits the male and female patient survival and compare the survival probabilities with the non-parametric Kaplan-Meier (KM) method. <strong>Methods:</strong> We used both parametric and non-parametric statistical methods to perform the survival analysis to assess the survival probabilities of 2015 patients diagnosed with AML.<strong> Results:</strong> We found evidence of a statistically significant difference between the mean survival time of male and female patients diagnosed with AML. We performed parametric survival analysis and found a Generalized Extreme Value (GEV) distribution best fitting the data of the survival time for male and female patients. We then estimated the survival probabilities and compared them with the frequently used non-parametric Kaplan-Meier (KM) survival method. <strong>Conclusion:</strong> The comparison between the survival probability estimates of the two methods revealed a better survival probability estimate by the parametric method than the Kaplan-Meier. We also compared the median survival time of male and female patients individually with descriptive, parametric, and non-parametric methods of analysis. The parametric survival analysis is more robust and efficient because it is based on a well-defined parametric probabilistic distribution, hence preferred over the non-parametric Kaplan-Meier estimate. This study offers therapeutic significance for further enhancement to treat patients with Acute Myeloid Leukemia.展开更多
Numerical analysis is presented for the characteristic parameters of centered-inclined coupling slot in rectangular waveguides, taking into account the transverse distribution of the electric field across the slot ape...Numerical analysis is presented for the characteristic parameters of centered-inclined coupling slot in rectangular waveguides, taking into account the transverse distribution of the electric field across the slot aperture. Integral equations are formulated based on dyadic Green's function theories and solved using the method of moments. Trigonometric basis functions are adopted. It is found that the method will converge with up to ten basis functions. The characteristic parameters can be easily obtained for different slot sizes. Resonant length and resonant resistance of the coupling slots are calculated. It is shown that the calculated results have very high accuracy, compared with simulated results obtained from commercial software. Therefore, it can be effectively applied in the synthesis of antenna arrays. Effects of the transverse distribution on calculating resonant parameters of the coupling slot are also analyzed. The results show that if the transverse distribution of the electric field is neglected, the calculated error tends to become larger when the slot gets wider or thinner.展开更多
In this paper, a three-parameter lifetime distribution named power Hamza distribution (PH) is proposed. The PH distribution is a useful generalization of the Hamza distribution which accommodates heavy-tailed, upside-...In this paper, a three-parameter lifetime distribution named power Hamza distribution (PH) is proposed. The PH distribution is a useful generalization of the Hamza distribution which accommodates heavy-tailed, upside-down bathtub and J-shaped hazard rates making it more flexible than the Hamza distribution for modelling various kinds of lifetime data. A comprehensive account of the properties of this distribution is presented. The maximum likelihood estimators of the unknown model parameters are discussed. Finally, a real-life data is analyzed for illustrative purpose proving that the PH outperforms the Hamza distribution and several other lifetime distributions.展开更多
基金supported by the Major Program of National Natural Science Foundation of China (11132008)
文摘The Brownian coagulation of nanoparticles with initial bimodal size distribution, i.e., mode i and j, is numerically studied using the moment method. Evolutions of particle number concentration, geometric average diameter and geometric standard deviation are given in the free molecular regime, the continuum regime, the free molecular regime and transition regime, the free molecular regime and continuum regime, respectively. The results show that, both in the free molecular regime and the continuum regime, the num- ber concentration of mode i and j decreases with increasing time. The evolutions of particle geometric average diameter with different initial size distribution are quite different. Both intra-modal and inter-modal coagulation finally make the polydispersed size distribution become monodispersed. As time goes by, the size distribution with initial bimodal turns to be unimoda/and shifts to a larger particle size range. In the free molecular regime and transition regime, the inter- modal coagulation becomes dominant when the number concentrations of mode i and j are of the same order. The effects of the number concentration of mode i and mode j on the evolution of geometric average diameter of mode j are negligible, while the effects of the number concentration of mode j on the evolution of geometric average diameter of mode j is distinct. In the free molecular regime and continuum regime, the higher the initial number concentration of mode j, the more obvious the variation of the number concentration of mode i.
基金funded by Princess Nourah bint Abdulrahman University Researchers Supporting Project No. (PNURSP2022R50),Princess Nourah bint Abdulrahman University,Riyadh,Saudi Arabia.
文摘The objective of this article is to provide a novel extension of the conventional inverse Weibull distribution that adds an extra shape parameter to increase its flexibility.This addition is beneficial in a variety of fields,including reliability,economics,engineering,biomedical science,biological research,environmental studies,and finance.For modeling real data,several expanded classes of distributions have been established.The modified alpha power transformed approach is used to implement the new model.The datamatches the new inverseWeibull distribution better than the inverse Weibull distribution and several other competing models.It appears to be a distribution designed to support decreasing or unimodal shaped distributions based on its parameters.Precise expressions for quantiles,moments,incomplete moments,moment generating function,characteristic generating function,and entropy expression are among the determined attributes of the new distribution.The point and interval estimates are studied using the maximum likelihood method.Simulation research is conducted to illustrate the correctness of the theoretical results.Three applications to medical and engineering data are utilized to illustrate the model’s flexibility.
基金National Natural Science Foundation of China under Grant Nos.11972379 and 42377184,Hunan 100-Talent PlanNatural Science Foundation of Hunan Province under Grant No.2022JJ10079+1 种基金Hunan High-Level Talent Plan under Grant No.420030004Central South University Research Project under Grant Nos.202045006(Innovation-Driven Project)and 502390001。
文摘Extensive high-speed railway(HSR)network resembled the intricate vascular system of the human body,crisscrossing mainlands.Seismic events,known for their unpredictability,pose a significant threat to both trains and bridges,given the HSR’s extended operational duration.Therefore,ensuring the running safety of train-bridge coupled(TBC)system,primarily composed of simply supported beam bridges,is paramount.Traditional methods like the Monte Carlo method fall short in analyzing this intricate system efficiently.Instead,efficient algorithm like the new point estimate method combined with moment expansion approximation(NPEM-MEA)is applied to study random responses of numerical simulation TBC systems.Validation of the NPEM-MEA’s feasibility is conducted using the Monte Carlo method.Comparative analysis confirms the accuracy and efficiency of the method,with a recommended truncation order of four to six for the NPEM-MEA.Additionally,the influences of seismic magnitude and epicentral distance are discussed based on the random dynamic responses in the TBC system.This methodology not only facilitates seismic safety assessments for TBC systems but also contributes to standard-setting for these systems under earthquake conditions.
文摘The paper considers the theoretical basics and the specific mathematical techniques having been developed for solving the tasks of the stochastic data analysis within the Rice statistical model in which the output signal’s amplitude is composed as a sum of the sought-for initial value and a random Gaussian noise. The Rician signal’s characteristics such as the average value and the noise dispersion have been shown to depend upon the Rice distribution’s parameters nonlinearly what has become a prerequisite for the development of a new approach to the stochastic Rician data analysis implying the joint signal and noise accurate evaluation. The joint computing of the Rice distribution’s parameters allows efficient reconstruction of the signal’s in-formative component against the noise background. A meaningful advantage of the proposed approach consists in the absence of restrictions connected with any a priori suppositions inherent to the traditional techniques. The results of the numerical experiments are provided confirming the efficiency of the elaborated approach to stochastic data analysis within the Rice statistical model.
基金supported by National Natural Science Foundation of ChinaNuclear Industry Science Foundation of China
文摘The g-factor hence the magnetic moment,of the isomeric state <sup>43</sup>Sc（|9/2<sup>-</sup>,3.1232 MeV）has been measured by the time differential perturbed angular distributionmethod.The measured values are g=0.3279（19）and μ=3.108（18）nm.
基金The NSF(11271155,11001105,11071126,10926156,11071269)of Chinathe Specialized Research Fund(20110061110003,20090061120037)for the Doctoral Program of Higher Education+1 种基金the Scientific Research Fund(201100011,200903278)of Jilin Universitythe NSF(20101596,20130101066JC)of Jilin Province
文摘In this paper, the estimation of parameters based on a progressively type-I interval censored sample from a Rayleigh distribution is studied. Different methods of estimation are discussed. They include mid-point approximation estima- tor, the maximum likelihood estimator, moment estimator, Bayes estimator, sampling adjustment moment estimator, sampling adjustment maximum likelihood estimator and estimator based on percentile. The estimation procedures are discussed in details and compared via Monte Carlo simulations in terms of their biases.
文摘<strong>Background:</strong> Acute Myeloid leukemia (AML) is the most prominent acute leukemia in adults. In the United States, we experience over 20,000 cases per year. Over the past decade, improvements in the diagnosis of subtypes of AML and advances in therapeutic approaches have improved the outlook for patients with AML. However, despite these advancements, the survival rate among patients who are less than 65 years of age is only 40 percent. <strong>Purpose:</strong> The purpose of the paper is to study if there exists any significant difference in the survival probabilities of male and female AML patients. Also, we want to investigate if there is any parametric probability distribution that best fits the male and female patient survival and compare the survival probabilities with the non-parametric Kaplan-Meier (KM) method. <strong>Methods:</strong> We used both parametric and non-parametric statistical methods to perform the survival analysis to assess the survival probabilities of 2015 patients diagnosed with AML.<strong> Results:</strong> We found evidence of a statistically significant difference between the mean survival time of male and female patients diagnosed with AML. We performed parametric survival analysis and found a Generalized Extreme Value (GEV) distribution best fitting the data of the survival time for male and female patients. We then estimated the survival probabilities and compared them with the frequently used non-parametric Kaplan-Meier (KM) survival method. <strong>Conclusion:</strong> The comparison between the survival probability estimates of the two methods revealed a better survival probability estimate by the parametric method than the Kaplan-Meier. We also compared the median survival time of male and female patients individually with descriptive, parametric, and non-parametric methods of analysis. The parametric survival analysis is more robust and efficient because it is based on a well-defined parametric probabilistic distribution, hence preferred over the non-parametric Kaplan-Meier estimate. This study offers therapeutic significance for further enhancement to treat patients with Acute Myeloid Leukemia.
文摘Numerical analysis is presented for the characteristic parameters of centered-inclined coupling slot in rectangular waveguides, taking into account the transverse distribution of the electric field across the slot aperture. Integral equations are formulated based on dyadic Green's function theories and solved using the method of moments. Trigonometric basis functions are adopted. It is found that the method will converge with up to ten basis functions. The characteristic parameters can be easily obtained for different slot sizes. Resonant length and resonant resistance of the coupling slots are calculated. It is shown that the calculated results have very high accuracy, compared with simulated results obtained from commercial software. Therefore, it can be effectively applied in the synthesis of antenna arrays. Effects of the transverse distribution on calculating resonant parameters of the coupling slot are also analyzed. The results show that if the transverse distribution of the electric field is neglected, the calculated error tends to become larger when the slot gets wider or thinner.
文摘In this paper, a three-parameter lifetime distribution named power Hamza distribution (PH) is proposed. The PH distribution is a useful generalization of the Hamza distribution which accommodates heavy-tailed, upside-down bathtub and J-shaped hazard rates making it more flexible than the Hamza distribution for modelling various kinds of lifetime data. A comprehensive account of the properties of this distribution is presented. The maximum likelihood estimators of the unknown model parameters are discussed. Finally, a real-life data is analyzed for illustrative purpose proving that the PH outperforms the Hamza distribution and several other lifetime distributions.
