This paper presents a theoretical analysis for laminar boundary layer flow in a power law non-Newtonian fluids. The Adomian analytical decomposition technique is presented and an approximate analytical solution is obt...This paper presents a theoretical analysis for laminar boundary layer flow in a power law non-Newtonian fluids. The Adomian analytical decomposition technique is presented and an approximate analytical solution is obtained. The approximate analytical solution can be expressed in terms of a rapid convergent power series with easily computable terms. Reliability and efficiency of the approximate solution are verified by comparing with numerical solutions in the literature. Moreover, the approximate solution can be successfully applied to provide values for the skin friction coefficient of the laminar boundary layer flow in power law non-Newtonian fluids.展开更多
This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t&l...This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t<0), u (j) (0)=u(1)=0,(1≤j≤n-2).Effort is devoted to give some sufficient conditions for which the equation has at least two positive solutions.An example to illustrate the application of this theorem is given. [FQ(6*2。39,X-W]展开更多
Cyber losses in terms of number of records breached under cyber incidents commonly feature a significant portion of zeros, specific characteristics of mid-range losses and large losses, which make it hard to model the...Cyber losses in terms of number of records breached under cyber incidents commonly feature a significant portion of zeros, specific characteristics of mid-range losses and large losses, which make it hard to model the whole range of the losses using a standard loss distribution. We tackle this modeling problem by proposing a three-component spliced regression model that can simultaneously model zeros, moderate and large losses and consider heterogeneous effects in mixture components. To apply our proposed model to Privacy Right Clearinghouse (PRC) data breach chronology, we segment geographical groups using unsupervised cluster analysis, and utilize a covariate-dependent probability to model zero losses, finite mixture distributions for moderate body and an extreme value distribution for large losses capturing the heavy-tailed nature of the loss data. Parameters and coefficients are estimated using the Expectation-Maximization (EM) algorithm. Combining with our frequency model (generalized linear mixed model) for data breaches, aggregate loss distributions are investigated and applications on cyber insurance pricing and risk management are discussed.展开更多
软件规模和复杂程度的不断提高,为软件质量保障带来了严峻的挑战.软件缺陷定位是一种重要的软件质量保障技术,其中基于频谱的缺陷定位(Spectrum-based Fault Localization,SFL)是应用最为广泛的软件缺陷定位技术,其通过分析语句覆盖信...软件规模和复杂程度的不断提高,为软件质量保障带来了严峻的挑战.软件缺陷定位是一种重要的软件质量保障技术,其中基于频谱的缺陷定位(Spectrum-based Fault Localization,SFL)是应用最为广泛的软件缺陷定位技术,其通过分析语句覆盖信息矩阵计算代码语句的可疑度值,并根据可疑度值定位缺陷所在语句.然而,语句覆盖信息矩阵中存在着严重的数据冗余问题,冗余的数据极大地影响了SFL的缺陷定位性能.以Defects4J数据集中395个程序的语句覆盖信息矩阵为例,在超过一半的语句覆盖信息矩阵中有90%的语句存在与其具有相同覆盖信息的语句.特征选择是常用的数据预处理技术,通过去除冗余和不相关特征来获取原始特征集中有价值的特征子集.因此,我们将语句覆盖信息矩阵作为原始特征集,将冗余覆盖信息约简建模为特征选择问题,提出了一种基于冗余覆盖信息约简的软件缺陷定位方法(Fault Localization based on Redundant coverage information Reduction,FLRR).首先,使用特征选择技术对语句覆盖信息和测试用例执行结果组成的语句覆盖信息矩阵进行约简,得到语句覆盖信息矩阵子集;然后,使用SFL计算语句覆盖信息矩阵子集中语句的可疑度值,并根据可疑度值对语句进行降序排列,以定位缺陷语句.本文使用六种常用的特征选择技术对语句覆盖信息矩阵进行特征选择和约简,以得到语句覆盖信息矩阵子集,并使用四种典型的SFL技术对语句覆盖信息矩阵子集中的语句进行缺陷定位.为评估FLRR的缺陷定位性能,本文使用E_(inspect)@n和MRR(Mean Reciprocal Rank)评价指标在基于Defects4J的数据集上与四种典型的SFL技术进行了对比实验.实验结果表明,FLRR能够有效提升SFL的缺陷定位性能.对于E_(inspect)@n指标,当n=1时,FLRR相比DStar、Ochiai、Barinel和OP2分别多定位到23条、26条、14条和13条缺陷语句,分别增加了69.70%、76.47%、45.16%和38.24%;对于MRR指标,FLRR相比DStar、Ochiai、Barinel和OP2分别提升了20.08%、24.94%、17.45%和19.15%.展开更多
Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some prop...Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some properties of meromorphic solutions, and we ob- tain some results, which are the improvements and extensions of some results in references. Examples show that our results are precise.展开更多
In this article, we study the initial boundary value problem of generalized Pochhammer-Chree equation utt-uxx-uxxt-uxxtt=f(u)xx,x∈Ω,t〉0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω,u(0,t)=u(1,t)=0,t≥0, where Ω...In this article, we study the initial boundary value problem of generalized Pochhammer-Chree equation utt-uxx-uxxt-uxxtt=f(u)xx,x∈Ω,t〉0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω,u(0,t)=u(1,t)=0,t≥0, where Ω = (0, 1). First, we obtain the existence of local Wkp solutions. Then, we prove that, if f(s) ∈ Ck+1(R) is nondecreasing, f(0) = 0 and |f(u)| ≤ C1|u|∫0uf(s)ds + C2, u0(x),u1(x) ∈ WkP(Ω) ∩ W01,P(Ω), k≥ 1, 1 〈 p≤ ∞, then for any T 〉 0 the problem admits a unique solution u(x, t) ∈ W2,∞(0, T; WkP(Ω) ∩ W01,P(Ω)). Finally, the finite time blow-up of solutions and global Wkp solution of generalized IMBo equations are discussed.展开更多
This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singula...This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations (ODEs) are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.展开更多
基金the Science Foundation of North China Electric Power University(No.93210706)
文摘This paper presents a theoretical analysis for laminar boundary layer flow in a power law non-Newtonian fluids. The Adomian analytical decomposition technique is presented and an approximate analytical solution is obtained. The approximate analytical solution can be expressed in terms of a rapid convergent power series with easily computable terms. Reliability and efficiency of the approximate solution are verified by comparing with numerical solutions in the literature. Moreover, the approximate solution can be successfully applied to provide values for the skin friction coefficient of the laminar boundary layer flow in power law non-Newtonian fluids.
基金Supported by the NSF of Guangdong Province!( 980 0 1 8) Higher Education Bureau!( 1 99873)
文摘This paper discusses the singular ( n\|1,1 ) conjugate boundary value problem as follows by using a fixed point index theorem in cones[HL(2:1,Z;2,Z]u (n) (t)+a(t)f(u(w(t)))=0,(0<t<1), u(t)=φ(t),(-τ≤t<0), u (j) (0)=u(1)=0,(1≤j≤n-2).Effort is devoted to give some sufficient conditions for which the equation has at least two positive solutions.An example to illustrate the application of this theorem is given. [FQ(6*2。39,X-W]
文摘Cyber losses in terms of number of records breached under cyber incidents commonly feature a significant portion of zeros, specific characteristics of mid-range losses and large losses, which make it hard to model the whole range of the losses using a standard loss distribution. We tackle this modeling problem by proposing a three-component spliced regression model that can simultaneously model zeros, moderate and large losses and consider heterogeneous effects in mixture components. To apply our proposed model to Privacy Right Clearinghouse (PRC) data breach chronology, we segment geographical groups using unsupervised cluster analysis, and utilize a covariate-dependent probability to model zero losses, finite mixture distributions for moderate body and an extreme value distribution for large losses capturing the heavy-tailed nature of the loss data. Parameters and coefficients are estimated using the Expectation-Maximization (EM) algorithm. Combining with our frequency model (generalized linear mixed model) for data breaches, aggregate loss distributions are investigated and applications on cyber insurance pricing and risk management are discussed.
文摘软件规模和复杂程度的不断提高,为软件质量保障带来了严峻的挑战.软件缺陷定位是一种重要的软件质量保障技术,其中基于频谱的缺陷定位(Spectrum-based Fault Localization,SFL)是应用最为广泛的软件缺陷定位技术,其通过分析语句覆盖信息矩阵计算代码语句的可疑度值,并根据可疑度值定位缺陷所在语句.然而,语句覆盖信息矩阵中存在着严重的数据冗余问题,冗余的数据极大地影响了SFL的缺陷定位性能.以Defects4J数据集中395个程序的语句覆盖信息矩阵为例,在超过一半的语句覆盖信息矩阵中有90%的语句存在与其具有相同覆盖信息的语句.特征选择是常用的数据预处理技术,通过去除冗余和不相关特征来获取原始特征集中有价值的特征子集.因此,我们将语句覆盖信息矩阵作为原始特征集,将冗余覆盖信息约简建模为特征选择问题,提出了一种基于冗余覆盖信息约简的软件缺陷定位方法(Fault Localization based on Redundant coverage information Reduction,FLRR).首先,使用特征选择技术对语句覆盖信息和测试用例执行结果组成的语句覆盖信息矩阵进行约简,得到语句覆盖信息矩阵子集;然后,使用SFL计算语句覆盖信息矩阵子集中语句的可疑度值,并根据可疑度值对语句进行降序排列,以定位缺陷语句.本文使用六种常用的特征选择技术对语句覆盖信息矩阵进行特征选择和约简,以得到语句覆盖信息矩阵子集,并使用四种典型的SFL技术对语句覆盖信息矩阵子集中的语句进行缺陷定位.为评估FLRR的缺陷定位性能,本文使用E_(inspect)@n和MRR(Mean Reciprocal Rank)评价指标在基于Defects4J的数据集上与四种典型的SFL技术进行了对比实验.实验结果表明,FLRR能够有效提升SFL的缺陷定位性能.对于E_(inspect)@n指标,当n=1时,FLRR相比DStar、Ochiai、Barinel和OP2分别多定位到23条、26条、14条和13条缺陷语句,分别增加了69.70%、76.47%、45.16%和38.24%;对于MRR指标,FLRR相比DStar、Ochiai、Barinel和OP2分别提升了20.08%、24.94%、17.45%和19.15%.
基金supported by the National Natural Science Foundation of China(11171013)supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(16XNH117)
文摘Using Nevanlinna theory of the value distribution of meromorphic functions, we investigate the problem of the existence of meromorphic solutions of some types of complex differential-difference equations and some properties of meromorphic solutions, and we ob- tain some results, which are the improvements and extensions of some results in references. Examples show that our results are precise.
基金supported by National Natural Science Foundation of China(10871055,10926149)Natural Science Foundation of Heilongjiang Province (A2007-02+2 种基金A200810)Science and Technology Foundation of Education Office of Heilongjiang Province(11541276)Foundational Science Founda-tion of Harbin Engineering University
文摘In this article, we study the initial boundary value problem of generalized Pochhammer-Chree equation utt-uxx-uxxt-uxxtt=f(u)xx,x∈Ω,t〉0,u(x,0)=u0(x),ut(x,0)=u1(x),x∈Ω,u(0,t)=u(1,t)=0,t≥0, where Ω = (0, 1). First, we obtain the existence of local Wkp solutions. Then, we prove that, if f(s) ∈ Ck+1(R) is nondecreasing, f(0) = 0 and |f(u)| ≤ C1|u|∫0uf(s)ds + C2, u0(x),u1(x) ∈ WkP(Ω) ∩ W01,P(Ω), k≥ 1, 1 〈 p≤ ∞, then for any T 〉 0 the problem admits a unique solution u(x, t) ∈ W2,∞(0, T; WkP(Ω) ∩ W01,P(Ω)). Finally, the finite time blow-up of solutions and global Wkp solution of generalized IMBo equations are discussed.
基金supported by the National Natural Science Foundation of China(Key Program)(Nos.11132004 and 51078145)
文摘This paper presents a high order multiplication perturbation method for sin- gularly perturbed two-point boundary value problems with the boundary layer at one end. By the theory of singular perturbations, the singularly perturbed two-point boundary value problems are first transformed into the singularly perturbed initial value problems. With the variable coefficient dimensional expanding, the non-homogeneous ordinary dif- ferential equations (ODEs) are transformed into the homogeneous ODEs, which are then solved by the high order multiplication perturbation method. Some linear and nonlinear numerical examples show that the proposed method has high precision.