On the Method of Multiplier-enlargement and Approximation of Unbounded Continuous Functions

By combining the classical appropriate functions “1, x, x 2” with the method of multiplier enlargement, this paper establishes a theorem to approximate any unbounded continuous functions with modified positive linear operators. As an example, Hermite Fejér interpolation polynomial operators are analysed and studied, and a general conclusion is obtained.

Ant colony algorithm based on genetic method for continuous optimization problem

A new algorithm is presented by using the ant colony algorithm based on genetic method （ACG） to solve the continuous optimization problem. Each component has a seed set. The seed in the set has the value of component, trail information and fitness. The ant chooses a seed from the seed set with the possibility determined by trail information and fitness of the seed. The genetic method is used to form new solutions from the solutions got by the ants. Best solutions are selected to update the seeds in the sets and trail information of the seeds. In updating the trail information, a diffusion function is used to achieve the diffuseness of trail information. The new algorithm is tested with 8 different benchmark functions.

On Approximation of Nonbounded Continuous Functions

This paper generalizes the basic principle of multiplier-enlargement approach to approximating any nonbounded continuous functions with positive linear operators, and as an example, Bernstein polynomial operators are analysed and studied. This paper gives a certain theorem as a general rule to approximate any nonbounded continuous functions.

High-precision inverse potentials for neutron-proton scattering using piece-wise smooth Morse functions

The aim of this study is to construct inverse potentials for various ℓ-channels of neutron-proton scattering using a piece-wise smooth Morse function as a reference.The phase equations for single-channel states and the coupled equations of multi-channel scattering are solved numerically using the 5^(th) order Runge-kutta method.We employ a piece-wise smooth reference potential comprising three Morse functions as the initial input.Leveraging a machine learning-based genetic algorithm,we optimize the model parameters to minimize the mean-squared error between simulated and anticipated phase shifts.Our approach yields inverse potentials for both single and multichannel scattering,achieving convergence to a mean-squared error≤10^(-3).The resulting scattering lengths"a_(0)"and effective ranges"r"for ^(3)S_(1) and ^(1)S_(0) states,expressed as[a_(0),r],are found to be[5.445(5.424),1.770(1.760)]and[–23.741(–23.749),2.63(2.81)],respectively;these values are in excellent agreement with experimental ones.Furthermore,the calculated total scattering cross-sections are highly consistent with their experimental counterparts,having a percentage error of less than 1%.This computational approach can be easily extended to obtain interaction potentials for charged particle scattering.

EXTENSION OF SMOOTHING FUNCTIONS TO SYMMETRIC CONE COMPLEMENTARITY PROBLEMS

The paper uses Euclidean Jordan algebras as a basic tool to extend smoothing functions, which include the Chen-Mangasarian class and the Fischer-Burmeister smoothing functions, to symmetric cone complementarity problems. Computable formulas for these functions and their Jacobians are derived. In addition, it is shown that these functions are Lipschitz continuous with respect to parameter # and continuously differentiable on J × J for any μ 〉 0.

Global Convergence of a New Restarting Conjugate Gradient Method for Nonlinear Optimizations

Conjugate gradient optimization algorithms depend on the search directions with different choices for the parameters in the search directions. In this note, by combining the nice numerical performance of PR and HS methods with the global convergence property of the class of conjugate gradient methods presented by HU and STOREY(1991), a class of new restarting conjugate gradient methods is presented. Global convergences of the new method with two kinds of common line searches, are proved. Firstly, it is shown that, using reverse modulus of continuity function and forcing function, the new method for solving unconstrained optimization can work for a continously dif ferentiable function with Curry-Altman's step size rule and a bounded level set. Secondly, by using comparing technique, some general convergence properties of the new method with other kind of step size rule are established. Numerical experiments show that the new method is efficient by comparing with FR conjugate gradient method.

Global Convergence of a New Restarting Three Terms Conjugate Gradient Method for Non-linear Optimizations

In this note,by combining the nice numerical performance of PR and HS methods with the global convergence property of FR method,a class of new restarting three terms conjugate gradient methods is presented.Global convergence properties of the new method with two kinds of common line searches are proved.

Existence and Uniqueness of 2π-Periodic Solution About Duffing Equation and Its Numerical Method

A new provement of the existence and uniqueness about periodic boundary value Duffing equation is established by using global inverse function theorem. An algorithm for solving differential equation that has a large convergence domain is given. Finally, a numerical example is given.

Regularization Methods to Approximate Solutions of Variational Inequalities

In this paper, we study the regularization methods to approximate the solutions of the variational inequalities with monotone hemi-continuous operator having perturbed operators arbitrary. Detail, we shall study regularization methods to approximate solutions of following variational inequalities: and with operator A being monotone hemi-continuous form real Banach reflexive X into its dual space X*, but instead of knowing the exact data (y0, A), we only know its approximate data satisfying certain specified conditions and D is a nonempty convex closed subset of X;the real function f defined on X is assumed to be lower semi-continuous, convex and is not identical to infinity. At the same time, we will evaluate the convergence rate of the approximate solution. The regularization methods here are different from the previous ones.

The non-interior continuation methods for solving the function nonlinear complementarity problem

In this paper, we propose a new smooth function that possesses a property not satisfied by the existing smooth functions. Based on this smooth function, we discuss the existence and continuity of the smoothing path for solving the P0 function nonlinear complementarity problem (NCP). Using the characteristics of the new smooth function, we investigate the boundedness of the iteration sequence generated by the non-interior continuation methods for solving the P0 function NCP under the assumption that the solution set of the NCP is nonempty and bounded. We show that the assumption that the solution set of the NCP is nonempty and bounded is weaker than those required by a few existing continuation methods for solving the NCP.

混凝土徐变柔度函数的高效逼近方法

混凝土徐变是引起安全壳预应力损失的主要因素之一,采用指数算法求解混凝土徐变效应时需要将混凝土徐变柔度函数采用Dirichlet级数表达,如何获得精确表征柔度函数的Dirichlet级数是实现指数算法的关键。基于连续延迟谱法,本文提出一种求解拉普拉斯逆变换的Weeks方法来逼近Dirichlet级数。对工程中常用的CEB MC90徐变模型,构建了基于Weeks方法的Dirichlet级数逼近算法,并给出了提高方法效率的相关参数取值范围。结果表明,提出的方法仅需对原混凝土徐变柔度函数求1阶导数,即可返回时域函数的显示表达式,避免了高阶求导存在计算复杂和计算效率低的问题。将本文方法计算结果与原柔度函数解析解进行对比,验证了方法的有效性。

Real-Time Pricing of Smart Grid Based on Piece-Wise Linear Functions

In a power grid system, utility is a measure of the satisfaction of users’ electricity consumption;cost is a monetary value of electricity generated by the supplier. The utility and cost functions represent the satisfaction of different users and the supplier. Quadratic utility, logarithmic utility,and quadratic cost functions are widely used in social welfare maximization models of real-time pricing. These functions are not universal;they have to be discussed in detail for individual models. To overcome this problem, a piece-wise linear utility function and a piece-wise linear cost function with general properties are proposed in this paper. By smoothing the piece-wise linear utility and cost functions, a social welfare maximization model can be transformed into a differentiable convex optimization problem. A dual optimization method is used to solve the smoothed model. Through mathematical deduction and numerical simulations, the rationality of the model and the validity of the algorithm are verified as long as the elastic and cost coefficients take appropriate values. Thus, different user types and the supplier can be determined by selecting different elastic and cost coefficients.

不同管饲方法对脑卒中后吞咽障碍患者营养状况、吞咽功能及并发症的影响

目的:探讨间歇口-胃管管饲法(IOE)和持续鼻-胃管管饲法(NGT)对脑卒中后吞咽障碍患者营养状况、吞咽功能及并发症的影响。方法:按照治疗方法不同将120例脑卒中后吞咽障碍患者分为IOE组和NGT组,每组各60例。两组采取相应管饲法,均连续干预14 d。比较两组营养状况[体质量指数(BMI)、血红蛋白(Hb)、白蛋白(ALB)、总蛋白(TP)]、吞咽功能[功能性经口摄食量表(FOIS)]、管饲舒适度及并发症发生情况。结果:干预后,IOE组BMI、Hb、ALB、TP水平及FOIS评分均高于NGT组(P<0.05)。IOE组鼻腔不适、口腔干燥、吞咽不适发生率均低于NGT组(P<0.05)。IOE组并发症总发生率低于NGT组(8.33%vs.26.67%,P<0.05)。结论:相比于NGT,IOE可以更好地改善对脑卒中后吞咽障碍患者营养状况、吞咽功能,且IOE的管饲舒适度更高、并发症发生率更低。

Spectral collocation method for solving continuous population models for single and interacting species by means of exponential Chebyshev approximation

In this paper, an efficient and accurate method is presented to solve continuous population models for single and interacting species using spectral collocation method with exponential Chebyshev (EC) functions. The first problem is a logistic growth model in a population, while the second problem is a prey-predator model: Lotka-Volterra system, the tbird is a simple 2-species Lotka-Volterra competition model, and the final one is a prey-predator model with limit cycle periodic behavior. The high accuracy of this method is verified through some numerical examples. The obtained numerical results are compared with other methods, showing that the proposed method gives higher accuracy.

基于自收敛同伦延拓法搜索七自由度机械臂零空间解集

针对七自由度机械臂零空间解集的无穷性,传统数值迭代只能求取单一解,解析法通用性较低,微分映射法精度较低的问题,本文在传统同伦延拓法的基础上采用同伦延拓参数自收敛的方式并加入关节限幅环节以优化延拓空间,并在此基础上,采用余弦函数作为同伦延拓辅助函数为方程组加入扰动。首先,根据改进DH参数法得到正运动学变换矩阵;其次,对自收敛同伦延拓法和传统同伦延拓法的求解时效、求解范围、对求解精度的适应性以及迭代限幅对求解的影响进行对比实验;最后,使用球形包围盒法结合加权取解的方式使得机械臂利用搜索到的零空间解集进行避障运动。经实验证明自收敛法的求解时效要优于传统法,加入关节限幅过程后,两种方法的时效性均有提升。

深埋双隧洞开挖的解析延拓法求解

将隧洞所处的地下空间转换为平面应变情况下的弹性半空间,考虑两隧洞开挖次序的影响,利用解析延拓法及Schwarz交替法求解出弹性半空间内2个任意形状任意尺寸的双隧洞在任意相对位置下其半空间内任意一点的应力解和位移解的隐式表达式。将双圆形隧洞作为特例,考虑到隧洞埋深与孔径相比比较大,从而不考虑重力梯度的影响,将重力化为作用在边界上的均布外荷载,考虑2个隧洞衬砌法向反力的影响,求解出弹性半空间内圆形双隧洞任意一点处的应力值和位移值解析解的具体显式表达式。最后利用二维有限元分析对理论推导的两圆形孔洞解析解进行验证,表明解的可靠性。

任意形状隧道围岩应力与位移的解析延拓求解

考虑隧道断面开挖轮廓线为任意不规则形状的情况,基于复变函数方法中的解析延拓法对弹性半无限空间内隧道的围岩应力与位移进行求解,建立了任意形状隧道围岩中任意一点处的应力值和位移值的隐式解析表达式.然后以圆形断面隧道、马蹄形断面隧道作为特例,同时考虑隧道衬砌等内支撑法向反力作用的影响,求解出弹性半空间内任意一点处的应力值和位移值解析解的具体显式表达式,其中假设隧道埋深与隧道直径之比较大,从而不用考虑重力梯度的影响,将重力简化为作用在边界上的均布外荷载.最后与已有的解析解与数值解进行比较,证明了该方法的准确性.该求解方法拓展了解析延拓法的应用,并能快捷地评估任意断面形状隧道开挖中的围岩应力状态及位移变形情况.

独立、连续、映射法刚度过滤函数

为了构造刚度过滤函数,利用均匀化方法计算了单胞挖不同尺寸方孔时对应的等效刚度,再依据计算出的离散刚度值按正则化最小二乘法拟合等效刚度的系数,然后用这些系数再次使用最小二乘法拟合出独立、连续、映射法刚度过滤函数的幂指数．由这种方法得到的刚度过滤函数能够正确地反映挖孔单胞等效刚度随方孔尺寸变化的规律,并且其幂指数值与拓扑优化经验值较吻合．

福建省森林碳储量及碳密度特征分析

【目的】估算福建省森林碳储量及碳密度，进行特征分析，为今后福建省森林的综合经营和管理提供一定的科学依据。【方法】基于第八次全国森林资源清查为数据源，运用转换因子连续函数法，以2012年发布的全国各树种（组）含碳率为基准，进行碳储量和碳密度估算。【结果】福建省森林碳储量约为2．96×10^8t，平均碳密度48．87t／hm2。各森林类型碳储量在36．85×10^4-15664．58×10^4t，其中以阔叶混交林的碳储量最高，占森林碳储量的52．83％。各森林类型碳密度在25．58—99．93t／hm2。【结论】福建省森林碳储量及碳密度高于全国平均水平，可通过提高成熟林和过熟林的比例来提升福建省森林的碳密度和碳储量。

应力约束处理为应变能集成的连续体结构拓扑优化

为克服应力约束下拓扑优化问题约束多、应力敏度计算量大的困难,本文提出了将应力约束处理为应变能集成的结构拓扑优化ICM方法。文中用几个典型算例对该方法进行了检验,结果表明:本方法优化效率较高,而且得到的结构最优拓扑较为合理。