Influence of dissipation on solitary wave solution to generalized Boussinesq equation

This paper uses the theory of planar dynamic systems and the knowledge of reaction-diffusion equations,and then studies the bounded traveling wave solution of the generalized Boussinesq equation affected by dissipation and the influence of dissipation on solitary waves.The dynamic system corresponding to the traveling wave solution of the equation is qualitatively analyzed in detail.The influence of the dissipation coefficient on the solution behavior of the bounded traveling wave is studied,and the critical values that can describe the magnitude of the dissipation effect are,respectively,found for the two cases of b_3<0 and b_3>0 in the equation.The results show that,when the dissipation effect is significant(i.e.,r is greater than the critical value in a certain situation),the traveling wave solution to the generalized Boussinesq equation appears as a kink-shaped solitary wave solution;when the dissipation effect is small(i.e.,r is smaller than the critical value in a certain situation),the traveling wave solution to the equation appears as the oscillation attenuation solution.By using the hypothesis undetermined method,all possible solitary wave solutions to the equation when there is no dissipation effect(i.e.,r=0)and the partial kink-shaped solitary wave solution when the dissipation effect is significant are obtained;in particular,when the dissipation effect is small,an approximate solution of the oscillation attenuation solution can be achieved.This paper is further based on the idea of the homogenization principles.By establishing an integral equation reflecting the relationship between the approximate solution of the oscillation attenuation solution and the exact solution obtained in the paper,and by investigating the asymptotic behavior of the solution at infinity,the error estimate between the approximate solution of the oscillation attenuation solution and the exact solution is obtained,which is an infinitesimal amount that decays exponentially.The influence of the dissipation coefficient on the amplitude,frequency,period,and energy of the bounded traveling wave solution of the equation is also discussed.

Analysis of KCSE Performance in Nakuru County: A Generalized Estimating Equations Approach

In Kenya, the Ministry of Education has set the pass mark for university entry examination as C plus and above. Using publicly available data for 2006-2010, differences in KCSE performance amongst the three types of schools in Kenya—boys only, girls only, and mixed schools—was assessed. A generalized estimating equations marginal model was applied in order to account for association between scores within a school in the five year period. To account for the missing data, multiple imputation was performed followed by estimation and inference. Results indicated that there was a significant difference between the three type of schools in their candidates’ odds of attaining the stipulated minimum university entry grade. However, the odds of success in KCSE did not depend on the year under review as was evident in the slope parameters which was not statistically significant. Although it was clear that same-gender schools perform better than mixed gender schools, there is need to weigh the social benefits of mixed-schools against respective performance in KCSE. This should guide the policy makers on the way forward with regards to the education policy in Nakuru County.

Estimating Equations for Estimation of Mcdonald Generalized Beta— Binomial Parameters

There has been a considerable recent attention in modeling over dispersed binomial data occurring in toxicology, biology, clinical medicine, epidemiology and other similar fields using a class of Binomial mixture distribution such as Beta Binomial distribution (BB) and Kumaraswamy-Binomial distribution (KB). A new three-parameter binomial mixture distribution namely, McDonald Generalized Beta Binomial (McGBB) distribution has been developed which is superior to KB and BB since studies have shown that it gives a better fit than the KB and BB distribution on both real life data set and on the extended simulation study in handling over dispersed binomial data. The dispersion parameter will be treated as nuisance in the analysis of proportions since our interest is in the parameters of McGBB distribution. In this paper, we consider estimation of parameters of this MCGBB model using Quasi-likelihood (QL) and Quadratic estimating functions (QEEs) with dispersion. By varying the coefficients of the QEE’s we obtain four sets of estimating equations which in turn yield four sets of estimates. We compare small sample relative efficiencies of the estimates based on QEEs and quasi-likelihood with the maximum likelihood estimates. The comparison is performed using real life data sets arising from alcohol consumption practices and simulated data. These comparisons show that estimates based on optimal QEEs and QL are highly efficient and are the best among all estimates investigated.

Construction of an Early Warning Model for Ischemic Stroke Recurrence Based on Generalized Estimating Equation

Objective:To explore the appropriate modeling method of the early warning model of ischemic stroke recurrence in TCM.Methods:This was a prospective,multi-center and registered study conducted in 7 clinical subcenters from 8 provinces and 10 cities in China between 3rd November 2016 and 27th April,2019.1,741 patients with first-ever ischemic stroke were recruited.Univariate analysis was carried out using distance correlation coefficient,mutual information entropy,and statistical correlation test.Multivariate analysis adopted multi-factor Cox regression model and combined with expert opinions in the field of stroke to determine modeling variables.The generalized estimating equation of longitudinal data and the Cox proportional hazard regression model of cross-sectional data were used to construct and compare in the early warning model of ischemic stroke recalls.The area under the ROC curve(AUC value)was used to evaluate the early warning capability of the model.Results:The follow-up time was 1-3 years,and the median follow-up time was 1.42 years(95%CI:1.37-1.47).Recurrence events occurred in 175 cases,and the cumulative recurrence rate was 10.05%(95%CI:8.64%-11.47%).The AUC values of the TCM syndrome and TCM constitution model were 0.71809 and 0.72668 based on the generalized estimating equation and the AUC values.Conclusion:The generalized estimating equation may be more suitable for the construction of early warning models of stroke recurrence with TCM characteristics,which provides a certain reference for the evaluation of secondary prevention of ischemic stroke.

NONLINEAR STABILITY OF PLANAR SHOCK PROFILES FOR THE GENERALIZED KdV-BURGERS EQUATION IN SEVERAL DIMENSIONS

This paper is concerned with the nonlinear stability of planar shock profiles to the Cauchy problem of the generalized KdV-Burgers equation in two dimensions. Our analysis is based on the energy method developed by Goodman [5] for the nonlinear stability of scalar viscous shock profiles to scalar viscous conservation laws and some new decay estimates on the planar shock profiles of the generalized KdV-Burgers equation.

Global Attractors and Their Dimension Estimates for a Class of Generalized Kirchhoff Equations

In this paper, we studied the long-time properties of solutions of generalized Kirchhoff-type equation with strongly damped terms. Firstly, appropriate assumptions are made for the nonlinear source term g (u) and Kirchhoff stress term M (s) in the equation, and the existence and uniqueness of the solution are proved by using uniform prior estimates of time and Galerkin’s finite element method. Then, abounded absorption set B0k is obtained by prior estimation, and the Rellich-kondrachov’s compact embedding theorem is used to prove that the solution semigroup S (t) generated by the equation has a family of the global attractor Ak in the phase space . Finally, linearize the equation and verify that the semigroups are Frechet diifferentiable on Ek. Then, the upper boundary estimation of the Hausdorff dimension and Fractal dimension of a family of the global attractor Ak was obtained.

A PRIORI ESTIMATE FOR MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF QUASI-LINEAR ELLIPTIC EQUATIONS

Let G he a hounded domain in E Consider the following quasi-linear elliptic equationAlthough the houndedness of generalized solutions of the equation is proved for very general structural conditions, it does not supply a priori estimate for maximum modulus of solutions. In this paper an estimate to the maximum modulus is made firstly for a special case of quasi-linear elliptic equations, i.e. the A and B satisfy the following structural conditions

A PRIORI ESTIMATES TO THE MAXIMUM MODULUS OF GENERALIZED SOLUTIONS OF A CLASS OF QUASILINEAR ELLIPTIC EQUATIONS WITH ANISOTROPIC GROWTH CONDITIONS

In this paper we give a priori estimates for the maximum modulus of generalizedsolulions of the quasilinear elliplic equations irith anisotropic growth condition.

ANALYSIS OF CHEBYSHEV PSEUDOSPECTRAL METHOD FOR MULTI-DIMENSIONAL GENERALIZED SRLW EQUATIONS

The Chebyshev pseudospectral approximation of the homogeneous initial boundary value problem for a class of multi-dimensional generalized symmetric regularized long wave (SRLW) equations is considered. The fully discrete Chebyshev pseudospectral scheme is constructed. The convergence of the approximation solution and the optimum error of approximation solution are obtained.

A Local Discontinuous Galerkin Method with Generalized Alternating Fluxes for 2D Nonlinear Schrödinger Equations

In this paper,we consider the local discontinuous Galerkin method with generalized alter-nating numerical fluxes for two-dimensional nonlinear Schrödinger equations on Carte-sian meshes.The generalized fluxes not only lead to a smaller magnitude of the errors,but can guarantee an energy conservative property that is useful for long time simulations in resolving waves.By virtue of generalized skew-symmetry property of the discontinuous Galerkin spatial operators,two energy equations are established and stability results con-taining energy conservation of the prime variable as well as auxiliary variables are shown.To derive optimal error estimates for nonlinear Schrödinger equations,an additional energy equation is constructed and two a priori error assumptions are used.This,together with properties of some generalized Gauss-Radau projections and a suitable numerical initial condition,implies optimal order of k+1.Numerical experiments are given to demonstrate the theoretical results.

Optimal error estimates for Fourier spectral approximation of the generalized KdV equation

A Fourier spectral method for the generalized Korteweg-de Vries equation with periodic boundary conditions is analyzed, and a corresponding optimal error estimate in L^2-norm is obtained. It improves the result presented by Maday and Quarteroni. A modified Fourier pseudospectral method is also presented, with the same convergence properties as the Fourier spectral method.

多元广义线性模型经验似然方法分析

针对多元广义线性模型,基于估计相关阵、广义估计方程和经验似然方法,本文构造出经验似然比统计量,此统计量能克服“工作相关阵”方法的误设定问题.在一定的条件下,本文也获得了经验似然比统计量渐近Wilks性质,该结果可用作未知参数向量置信域的构造.最后,通过数值模拟对所提方法的有效性进行验证.

个别托盘预留空间厚度与牙槽嵴低平无牙颌义齿修复效果的关系

目的探究个别托盘不同预留空间厚度与牙槽嵴低平无牙颌义齿修复的关系。方法选择2020年3月至2023年3月期间于我院就诊的75例牙槽嵴低平无牙颌患者,采用随机数字表法将患者分为A组(n=25)、B组(n=25)和C组(n=25),3组分别按无预留空间(0 mm),预留空间(1.5 mm)和(2 mm)制作个别托盘并行全口义齿修复。对比3组患者的一般资料、修复有效率、VAS评分、TMD及PES评分,并分析3组患者修复后的满意程度评分。采用广义估计方程模型评价3组患者各项指标的改善情况。结果3组在终印与组织面的偏差值、复诊次数以及压痛位点之间存在显著差异,B组<C组<A组(P<0.05)。B组患者的总有效率高于A组和C组(P<0.05)。术后3个月,3组患者的VAS评分无明显差异,B组患者的TMD评分显著低于A组和C组,PES评分显著高于A组和C组(P<0.05)。比较3组患者对固位效果、稳定性、咀嚼功能、舒适度的满意度,B组患者的满意度明显高于A组和C组(P<0.05)。经广义估计方程分析可见:B组在TMD评分、PES评分、固位效果、稳定性、咀嚼功能、舒适度方面的改善情况优于A组和C组,C组在各方面的改善情况优于A组。结论个别托盘预留空间为1.5 mm时制作终义齿组织面与粘膜形态适合性较好、复诊次数和压痛位点较少、修复效果较好、患者的满意度较高。

纵向多分类数据的广义估计方程分析

广义估计方程(GEE)是分析纵向数据的常用方法.如果响应变量的维数是一,XIE和YANG(2003)及WANG(2011)分别研究了协变量维数是固定的和协变量维数趋于无穷时,GEE估计的渐近性质.本文研究纵向多分类数据(multicategorical data)的GEE建模和GEE估计的渐近性质.当数据的分类数大于二时,响应变量的维数大于一,所以推广了文献的相关结果.

广义估计方程GEE1在婴儿生长监测回归分析中的应用

广义估计方程ＧＥＥｓ代表了纵向资料统计方法的一个划时代突破。本文把广义估计方程ＧＥＥ１应用于生长监测资料的分析领域，在进行母乳喂养与婴儿体重发育回归分析的同时，较好地解决了困扰生长监测资料分析的数据相关性问题。

广义估计方程评估调督通脉针灸法治疗不同年龄临床前类风湿关节炎的效果

背景:针灸在类风湿关节炎中的治疗效果尚存在争议。因此,该研究旨在通过广义估计方程评估调督通脉针灸法治疗不同年龄临床前类风湿关节炎患者的效果,为针灸在类风湿关节炎中的应用提供依据。目的:基于广义估计方程探讨调督通脉针灸法对不同年龄临床前类风湿关节炎患者的影响。方法:选取2023年1-9月收治的123例临床前类风湿关节炎患者为研究对象,根据治疗方法不同分为研究组(n=64)和对照组(n=59),研究组给予调督通脉针灸治疗,对照组给予乙酰氨基酚片治疗。采用倾向性评分匹配法调整基线均衡性,比较两组患者临床疗效和治疗前后细胞因子水平,建立广义估计方程模型评估调督通脉针灸法治疗不同年龄临床前类风湿关节炎患者的效果。结果与结论:(1)治疗0 d,研究组和对照组在关节疼痛、C-反应蛋白方面存在显著差异(P<0.05);治疗4周,两组患者在目测类比评分、关节疼痛、C-反应蛋白、红细胞沉降率方面存在显著差异(P<0.05);治疗8周,两组患者在目测类比评分、C-反应蛋白、红细胞沉降率方面存在显著差异(P<0.05);治疗12周,两组患者在目测类比评分、C-反应蛋白、红细胞沉降率方面存在显著差异(P<0.05)。(2)研究组治疗后总有效率为93.75%,对照组为79.17%,研究组患者临床疗效显著优于对照组(P<0.05)。(3)研究组治疗后在白细胞介素6、干扰素γ、巨噬细胞迁移抑制因子、类风湿因子IgA、类风湿因子IgM、基质金属蛋白酶3、基质金属蛋白酶9、抗环状瓜氨酸抗体方面与治疗前相比差异显著(P<0.05);对照组治疗后在白细胞介素6、干扰素γ、类风湿因子IgA、类风湿因子IgM、基质金属蛋白酶3、基质金属蛋白酶9、抗环状瓜氨酸抗体方面与治疗前相比差异显著(P<0.05);研究组治疗后在白细胞介素6、干扰素γ、巨噬细胞迁移抑制因子、类风湿因子IgA、类风湿因子IgM、基质金属蛋白酶3、抗环状瓜氨酸抗体方面与对照组治疗后相比差异显著(P<0.05)。(4)治疗12周,研究组各年龄段患者综合疗效优于对照组(P<0.05);治疗8周,研究组23-35岁、36-50岁、51-60岁患者的综合疗效优于对照组(P<0.05),两组18-22岁患者综合疗效相当;治疗4周,研究组36-50岁、51-60岁患者综合疗效优于对照组(P<0.05),两组18-22岁、23-35岁患者综合疗效相当。结果表明,调督通脉针灸法治疗36-50岁、51-60岁临床前类风湿关节炎患者具有一定优势。

应用SPSS软件实现二分类重复测量资料的GEE及GLMMs分析

目的在SPSS软件上实现分类重复测量资料的广义估计方程(GEE)和广义线性混合效应模型(GLMMs)分析。方法结合二分类重复测量的实例资料,按照SPSS 19.0软件的菜单操作过程,实现GEE与GLMMs模型的统计分析。结果在SPSS19.0软件上实现二分类重复测量资料GEE和GLMMs模型分析的菜单操作不需编程、结果直观清晰。结论 SPSS 19.0软件上可实现二分类重复测量资料的GEE与GLMMs模型分析,无需复杂的编程过程,操作简便。

司美格鲁肽和度拉糖肽治疗2型糖尿病的疗效与安全性比较:基于倾向性评分匹配的回顾性队列研究

目的探究司美格鲁肽对比度拉糖肽治疗2型糖尿病的疗效和安全性。方法采用多中心、回顾性队列研究设计,选择2021年4月—2023年7月在3家医院就诊的2型糖尿病患者为研究对象。根据用药情况分为司美格鲁肽组(以下简∶称“SEMA组”)、度拉糖肽组(以下简称“DULA组”),并根据基线性别、年龄、身体质量指数、血糖水平、糖尿病病程及并发症等,采用倾向性评分匹配法对2组患者进行1观察治疗后3、6、9、12个月的空腹血糖、餐后2 h血糖、糖化血红蛋白(HbA1c)、血肌酐、尿素氮、估算肾小球滤过率(eGFR)、尿白蛋白/肌酐比值(UACR)及不良反应的发生情况。结果倾向性评分匹配后,SEMA组和DULA组各纳入98例患者,2组患者的基线特征差异无统计学意义(P>0.05)。2组各随访时点的空腹血糖、餐后2 h血糖、HbA1c均较基线明显降低(P≤0.05)。2组各随访时点空腹血糖、餐后2 h血糖、HbA1c变化(各随访时点与基线差值)差异无统计学意义(P>0.05);第6个月时,SEMA组HbA1c<7%的比例高于DULA组(P<0.05)。相较于基线,SEMA组第6个月时血肌酐和尿素氮下降,第3、6个月时eGFR升高、UACR降低,差异均有统计学意义(P<0.05);DULA组第3、6个月时血肌酐升高、eGFR下降,第9个月时尿素氮下降,差异均有统计学意义(P<0.05)。第3、6个月时,SEMA组血肌酐较基线的降幅大于DULA组,SEMA组eGFR较基线的升幅大于DULA组,差异均有统计学意义(P<0.05);第6个月时,SEMA组UACR较基线的降幅大于DULA组,SEMA组肾功能不全比例低于DULA组,差异均有统计学意义(P<0.05)。2组不良反应发生率差异无统计学意义(P>0.05)。结论司美格鲁肽和度拉糖肽均可显著改善血糖控制效果,总体降糖效果相似,安全性相当,而司美格鲁肽有潜在的肾功能保护作用。

户主职业对农户响应林业科技服务的影响——基于江西纵向数据GEE分析

基于江西农户8年跟踪调查纵向样本数据,运用广义估计方程(GEE)Logistic回归模型,检验户主职业与农户林业科技服务响应之间关系。结果表明:户主职业对农户林业科技服务响应行为产生显著性影响,户主全职务农农户逐步成为技术采纳的弱质性农户,户主长期外出务工的农户林业科技服务响应具有异质性,户主职业的变动对农户林业科技服务响应有正向影响。提出林业科技服务供给以及协同推进发展现代林业与实施乡村振兴战略等方面政策建议。

森林度假活动与人格特质对参与者行为意图的影响

以森林康养为实验组、森林旅游为对照组进行准自然实验,分析了不同森林度假活动与人格特质类别对被试行为意图的影响,结果发现:(1)2组森林度假活动参与者人格特质分为心理弹性型、过度控制型和情绪型3类;(2)不同人格特质类别群体之间的行为意图提升存在显著差异,且整体呈现心理弹性型>过度控制型>情绪型的特征;(3)在2组森林度假活动和3种人格特质的交互作用下,行为意图受人格特质与森林度假活动协同影响。在理论层面拓展了森林康养者行为意图的主体影响因素研究,在实践层面有助于深化森林康养产品开发,为合理安排体验内容提供实证依据。