generalized

摘要： The purpose of this paper is to give the extensions of some identities involving generalized Fibonacci and Lucas numbers with binomial coefficients.These results generalize the identities by Gulec,Taskara and Uslu in Appl.Math.Lett.23(2010)68-72 and Appl.Math.Comput.220(2013)482-486.

摘要： Survival of HIV/AIDS patients is crucially dependent on comprehensive and targeted medical interventions such as supply of antiretroviral therapy and monitoring disease progression with CD4 T-cell counts. Statistical modelling approaches are helpful towards this goal. This study aims at developing Bayesian joint models with assumed generalized error distribution (GED) for the longitudinal CD4 data and two accelerated failure time distributions, Lognormal and loglogistic, for the survival time of HIV/AIDS patients. Data are obtained from patients under antiretroviral therapy follow-up at Shashemene referral hospital during January 2006-January 2012 and at Bale Robe general hospital during January 2008-March 2015. The Bayesian joint models are defined through latent variables and association parameters and with specified non-informative prior distributions for the model parameters. Simulations are conducted using Gibbs sampler algorithm implemented in the WinBUGS software. The results of the analyses of the two different data sets show that distributions of measurement errors of the longitudinal CD4 variable follow the generalized error distribution with fatter tails than the normal distribution. The Bayesian joint GED loglogistic models fit better to the data sets compared to the lognormal cases. Findings reveal that patients’ health can be improved over time. Compared to the males, female patients gain more CD4 counts. Survival time of a patient is negatively affected by TB infection. Moreover, increase in number of opportunistic infection implies decline of CD4 counts. Patients’ age negatively affects the disease marker with no effects on survival time. Improving weight may improve survival time of patients. Bayesian joint models with GED and AFT distributions are found to be useful in modelling the longitudinal and survival processes. Thus we recommend the generalized error distributions for measurement errors of the longitudinal data under the Bayesian joint modelling. Further studies may investigate the models with various types of shared random effects and more covariates with predictions.

摘要： Extreme events are defined as values of the event below or above a certain value called threshold. A well chosen threshold helps to identify the extreme levels. Several methods have been used to determine threshold so as to analyze and model extreme events. One of the most successful methods is the maximum product of spacing (MPS). However, there is a problem encountered while modeling data through this method in that the method breaks down when there is a tie in the exceedances. This study offers a solution to model data even if it contains ties. To do so, an optimal threshold that gives more optimal parameters for extreme events, was determined. The study achieved its main objective by deriving a method that improved MPS method for determining an optimal threshold for extreme values in a data set containing ties, estimated the Generalized Pareto Distribution (GPD) parameters for the optimal threshold derived and compared these GPD parameters with GPD parameters determined through the standard MPS model. The study improved maximum product of spacing method and used Generalized Pareto Distribution (GPD) and Peak over threshold (POT) methods as the basis of identifying extreme values. This study will help the statisticians in different sectors of our economy to model extreme events involving ties. To statisticians, the structure of the extreme levels which exist in the tails of the ordinary distributions is very important in analyzing, predicting and forecasting the likelihood of an occurrence of the extreme event.

摘要： Asymptotic eigenvalues and eigenfunctions for the Orr-Sommerfeld equation in two-dimensional and three-dimensional incompressible flows on an infinite domain and on a semi-infinite domain are obtained. Two configurations are considered, one in which a short-wave limit approximation is used, and another in which a long-wave limit approximation is used. In the short-wave limit, Wentzel-Kramers-Brillouin (WKB) methods are utilized to estimate the eigenvalues, and the eigenfunctions are approximated in terms of Green’s functions. The procedure consists of transforming the Orr-Sommerfeld equation into a system of two second order ordinary differential equations for which the eigenvalues and the eigenfunctions can be approximated. In the long-wave limit approximation, solutions are expressed in terms of generalized hypergeometric functions. Our procedure works regardless of the values of the Reynolds number.

摘要： The purpose of this paper is to present a new iterative scheme for finding a common solution of the generalized mixed equilibrium problems with an infinite family of inverse strongly monotone mappings and the fixed point problems of demimetric mappings under nonlinear transformations in Banach spaces. Applications are also included. The results in this paper are the extension and improvement of the recent results in the literature.

摘要： Presented here are the Generalized BCS Equations incorporating Fermi Energy for the study of the {Δ, Tc, jc(T)} values of both elemental and composite superconductors (SCs) for all T ≤ Tc, where Δ, Tc and jc(T) denote, respectively, one of the gap values, the critical temperature and the T-dependent critical current density. This framework, which extends our earlier study that dealt with the {Δ0, Tc, jc(0)} values of an SC, is also shown to lead to T-dependent values of several other related parameters such as the effective mass of electrons, their number density, critical velocity, Fermi velocity (VF), coherence length and the London penetration depth. The extended framework is applied to the jc(T) data reported by Romijn et al. for superconducting Aluminium strips and is shown not only to provide an alternative to the explanation given by them, but also to some novel features such as the role of the Sommerfeld coefficient γ(T) in the context of jc(T) and the role of VF(T) in the context of a recent finding by Plumb et al. about the superconductivity of Bi-2212.

摘要： We study the generalized Riemann problem of the Chapman-Jouguet model for an ideal combustible Chaplygin gas. By analyzing the wave curves in the phase plane, we construct uniquely the solution of the generalized Riemann problem under the global entropy conditions. We find that although there is no combustion wave of the corresponding Riemann solution, the combustion wave may occur after perturbation which reveals the instability of the unburnt gas.

摘要： In this paper, generalized KdV equations are investigated by using a mathematical technique based on the reduction of order for solving differential equations. The compactons, solitons, solitary patterns and periodic solutions for the equations presented in this paper are obtained. For these generalized KdV equations, it is found that the change of the exponents of the wave function u and the coefficient a, positive or negative, leads to the different physical structures of the solutions.

摘要： To Statisticians, the structure of the extreme levels which exist in the tails of the ordinary distributions is very important in analyzing, predicting and forecasting the likelihood of an occurrence of extreme event. Extreme events are defined as values of the event below or above a certain value called threshold. A well chosen threshold helps to identify the extreme levels. Several methods have been used to determine threshold so as to analyze and model extreme events. One of the most successful methods is the maximum product of spacing (MPS). However, there is a problem encountered while modeling data through this method in that the method breaks down when there is a tie in the exceedances. This study offers a solution to model data even when it contains ties. In the study, a method that improved MPS method for determining an optimal threshold for extreme values in a data set containing ties was derived. The Generalized Pareto Distribution (GPD) parameters for the optimal threshold were derived and compared to GPD parameters determined through the standard MPS model. The study improved the standard MPS methodology by introducing the concept of frequency and used Generalized Pareto Distribution (GPD) and Peak over threshold (POT) methods as the basis of identifying extreme values. The improved MPS models and the standard models were applied to Nairobi Securities Exchange (NSE) trading volume data to determine the GPD parameters for different sectors registered in NSE market and their performance compared. It was realized that the improved MPS model performed better than the standard models. This study will help the Statisticians in different sectors of our economy to model extreme events involving ties.

摘要： The duplicate form of the generalized Gould-Hsu inversions has been obtained by Shi and Zhang. In this paper, we present a simple proof of this duplicate form. With the same method, we construct the duplicate form of the generalized Carlitz inversions. Using this duplicate form, we obtain several terminating basic hypergeometric identities and some limiting cases.

摘要： In this paper, a method of chaotic synchronization is introduced which is obtained from the perspective of passivity{based state observer design in the context of Generalized Hamiltonian systems including dissipation and destabilizing vector ˉelds. Two cases of chaotic synchronization, namely, the synchronization of the dynamical systems with/without time{delay are analyzed. And the synchroniza- tion is simulated employing the nonlinear dynamical software WinPP in this paper.

摘要： In this paper, a method of chaotic synchronization is introduced which is obtained from the perspective of passivity{based state observer design in the context of Generalized Hamiltonian systems including dissipation and destabilizing vector ˉelds. Two cases of chaotic synchronization, namely, the synchronization of the dynamical systems with/without time{delay are analyzed. And the synchroniza- tion is simulated employing the nonlinear dynamical software WinPP in this paper.

摘要： In this paper, a method of chaotic synchronization is introduced which is obtained from the perspective of passivity{based state observer design in the context of Generalized Hamiltonian systems including dissipation and destabilizing vector ˉelds. Two cases of chaotic synchronization, namely, the synchronization of the dynamical systems with/without time{delay are analyzed. And the synchroniza- tion is simulated employing the nonlinear dynamical software WinPP in this paper.

摘要： In this paper, a method of chaotic synchronization is introduced which is obtained from the perspective of passivity{based state observer design in the context of Generalized Hamiltonian systems including dissipation and destabilizing vector ˉelds. Two cases of chaotic synchronization, namely, the synchronization of the dynamical systems with/without time{delay are analyzed. And the synchroniza- tion is simulated employing the nonlinear dynamical software WinPP in this paper.

摘要： In this paper, a method of chaotic synchronization is introduced which is obtained from the perspective of passivity{based state observer design in the context of Generalized Hamiltonian systems including dissipation and destabilizing vector ˉelds. Two cases of chaotic synchronization, namely, the synchronization of the dynamical systems with/without time{delay are analyzed. And the synchroniza- tion is simulated employing the nonlinear dynamical software WinPP in this paper.