PREDICTOR-CORRECTOR ALGORITHMS FOR SOLVING GENERALIZED MIXED IMPLICIT QUASI-EQUILIBRIUM PROBLEMS

A new class of generalized mixed implicit quasi-equilibrium problems （GMIQEP） with four-functions is introduced and studied. The new class of equilibrium problems includes many known generalized equilibrium problems and generalized mixed implicit quasi-variational inequality problems as many special cases. By employing the auxiliary principle technique, some predictor-corrector iterative algorithms for solving the GMIQEP are suggested and analyzed. The convergence of the suggested algorithm only requires the continuity and the partially relaxed implicit strong monotonicity of the mappings

A New Eighth Order Implicit Block Algorithms for the Direct Solution of Second Order Ordinary Differential Equations

This paper focuses on derivation of a uniform order 8 implicit block method for the direct solution of general second order differential equations through continuous coefficients of Linear Multi-step Method (LMM). The continuous formulation and its first derivatives were evaluated at some selected grid and off grid points to obtain our proposed method. The superiority of the method over the existing methods is established numerically.

CHARACTERISTIC GALERKIN METHOD FOR CONVECTION-DIFFUSION EQUATIONS AND IMPLICIT ALGORITHM USING PRECISE INTEGRATION

This paper presents a finite element procedure for solving transient, multidimensional convection-diffusion equations. The procedure is based on the characteristic Galerkin method with an implicit algorithm using precise integration method. With the operator splitting procedure, the precise integration method is introduced to determine the material derivative in the convection-diffusion equation, consequently, the physical quantities of material points. An implicit algorithm with a combination of both the precise and the traditional numerical integration procedures in time domain in the Lagrange coordinates for the characteristic Galerkin method is formulated. The stability analysis of the algorithm shows that the unconditional stability of present implicit algorithm is enhanced as compared with that of the traditional implicit numerical integration procedure. The numerical results validate the presented method in solving convection-diffusion equations. As compared with SUPG method and explicit characteristic Galerkin method, the present method gives the results with higher accuracy and better stability.

EXISTENCE AND ALGORITHM OF SOLUTIONS FOR GENERAL MULTIVALUED MIXED IMPLICIT QUASI-VARIATIONAL INEQUALITIES

A new class of general multivalued mixed implicit quasi-variational inequalities in a real Hilbert space was introduced, which includes the known class of generalized mixed implicit quasi-variational inequalities as a special case , introduced and studied by Ding Xie-ping . The auxiliary variational principle technique was applied to solve this class of general multivalued mixed implicit quasi-variational inequalities. Firstly, a new auxiliary variational inequality with a proper convex , lower semicontinuous , binary functional was defined and a suitable functional was chosen so that its unique minimum point is equivalent to the solution of such an auxiliary variational inequality . Secondly , this auxiliary variational inequality was utilized to construct a new iterative algorithm for computing approximate solutions to general multivalued mixed implicit quasi-variational inequalities . Here , the equivalence guarantees that the algorithm can generate a sequence of approximate solutions. Finally, the existence of solutions and convergence of approximate solutions for general multivalued mixed implicit quasi-variational inequalities are proved. Moreover, the new convergerce criteria for the algorithm were provided. Therefore, the results give an affirmative answer to the open question raised by M. A . Noor, and extend and improve the earlier and recent results for various variational inequalities and complementarity problems including the corresponding results for mixed variational inequalities, mixed quasi-variational inequalities and quasi-complementarity problems involving the single-valued and set- valued mappings in the recent literature .

Existence and algorithm of solutions for a system of generalized mixed implicit equilibrium problems in Banach spaces

A new system of generalized mixed implicit equilibrium problems is introduced and studied in Banach spaces. First, the notion of the Yosida proximal mapping for generalized mixed implicit equilibrium problems is introduced. By using the notion, a system of generalized equation problems is considered, and its equivalence with the system of generalized mixed implicit equilibrium problems is also proved. Next, by applying the system of generalized equation problems, we suggest and analyze an iterative algorithm to compute the approximate solutions of the system of generalized mixed implicit equilibrium problems. The strong convergence of the iterative sequences generated by the algorithm is proved under quite mild conditions. The results are new and unify and generalize some recent results in this field.

AN IMPLICIT ALGORITHM OF THIN LAYER EQUATIONS IN VISCOUS，TRANSONIC，TWO－PHASE NOZZLE FLOW

Omitting viscosity along flow direction, we have simplified the dimensionless N-Sequations in arbitrary curved coordinate system as the thin layer equations. Using theimplicit approximate-factorization algorithm to solve the gas-phase governing equ-ations and the characteristic method to follow the tracks of particles, we then obtainedthe full coupled numerical method of two-phase.transonic, turbulent flow. Here, par- ticle size may be grouped, the subsonic boundary condition at entry of nozzle is ireatedby quasi-characteristic method in reference plane and the algebraic model is used forturbulent flow. These methods are applied in viscous two-phase flow. calculation of ro-cket nozzle and in the prediciton of thrust and specific impulse for solid propellant ro-cket motor. The calculation results are in good agreement with the measurerment va-lues. Moreover, the influences of different particle radius, different particle mass frac-tion and particle size grouped on flow field have been discussed, and the influences of particle two-dimensional radial velosity component and viscosity on specific impulse ofrocket motor have been analysed.The method of this paper possesses the advantage of saving computer time. More important, the effect is more obvious for the calculation of particle size being grouped.

Existence and Algorithm of Solutions for Generalized Mixed Implicit Quasi-Variational-Like Inequalities

By applying the auxiliary variational principle technique, the existence of solutions for a new class of generalized mixed implicit quasi-variational-like inequalities and the convergence criteria of a new iterative algorithm to compute approximate solutions are proved in Hilbert spaces. The obtained result is a improvement over and generalization of the main theorem proposed by Ding.

Iterative algorithm for solutions to new system of generalized mixed implicit equilibrium

A new system of generalized mixed implicit equilibrium problems （SGMIEP） involving nonmonotone set-valued mappings is introduced and studied in real reflexive Banach spaces. First, an auxiliary mixed equilibrium problem （AMEP） is introduced. The existence and the uniqueness of the solutions to the AMEP are proved under quite mild assumptions without any coercive conditions. Next, by using the solution mapping of the AMEP, a system of generalized equation problems （SGEP） is considered, and its equivalence with the SGMIEP is shown. By using the SGEP, a new iterative algorithm for solving the SGMIEP is proposed and analyzed. The strong convergence of the iterative sequences generated by the algorithm is proved under suitable conditions. These results are new, which unify and generalize some recent results in this field.

考虑小应变刚度特性的软土边界面模型与应用

基坑开挖导致周边土体经历复杂的加卸载应力路径,传统的本构模型难以同时反映此过程中土体的超固结和小应变刚度特性。在现有的边界面模型中,引入土体小应变刚度特性,提出软土边界面模型小应变刚度修正方法。基于一种高效的半隐式应力更新算法,将改进后的边界面模型采用UMAT子程序二次开发嵌入有限元软件ABAQUS中,并应用于某地铁车站深基坑开挖工程的数值模拟。分析结果表明,采用改进模型准确地反映了上海地区典型土层的小应变状态本构关系和土体的应变刚度相关性;由于改进的边界面模型能够同时反映土体超固结和小应变刚度特性,计算的围护结构变形与现场监测数据吻合较好。

不锈钢板式热沉传热特性的实验与模拟研究

目的 研究流量、胀高及焊点排布方式对不锈钢板式热沉传热特性的影响。方法 搭建实验平台,加工出结构参数不同的板式热沉实验件,同时采用静力隐式算法建立相应的几何模型,通过实验与数值模拟相结合的方法,研究流量、胀高和焊点排布方式的变化对板式热沉热阻的影响规律,并分析热沉流道内部流场状态。结果 首先计算了6个工况下的热阻,发现实际换热量为540 W时,数值模拟与实验结果的最大相对误差不大于25%。然后分析了误差来源,最后得到了热沉全流道速度场与温度场的分布情况。结论 实验与模拟结果有较好的符合程度,证明了数值模拟方法的可靠性。在换热量相同时,板式热沉的热阻随流量与胀高的增大而减小,焊点为菱形排布的热沉传热性能相对更好。板式热沉内部的流场具有周期性,焊点使流体扰动增强,并形成射流和旋涡,起到了强化传热的效果。

基于隐式偏好的多目标推荐算法研究

推荐的准确性(accuracy)和多样性(diversity)是推荐算法研究的二个重要指标,能够最大程度地满足用户的喜好.然而,基于准确性的推荐将导致推荐结果过于聚焦集中在某类特征上,使得多样性降低,导致用户选择的广度不足而整体效果不佳.针对推荐算法的两个指标之间的平衡以满足用户的需求,本文采用最大预测评分和最大内部相似度差异的两目标模型,选取极值点和膝点为隐式偏好,利用隐式偏好改进推荐方案搜索优化策略,提出了一种基于隐式偏好的多目标推荐算法.该算法利用切比雪夫距离在迭代过程中对偏好点动态标定,以引导个体收敛于隐式偏好区域,得到具有不同偏好的推荐方案.在Movielens和Netflix数据集上实验结果表明,与Item-based协同过滤推荐算法相比,该算法的推荐结果在确保准确率性能情况下多样性平均提升了38%和33.4%,新颖度平均提升了58.6%和125.4%,降低了多目标推荐算法的复杂度,有效解决了实际应用问题.

基于因素空间理论的扫类连环多分类算法

为解决多分类问题,基于因素空间理论中因素显隐的思想,在扫类连环分类算法基础上,定义类别的合并,提出因素显隐的合并扫类连环分类方法,给出算法步骤,并用数值算例进行分析;定义类别的两两组合,提出因素显隐的两两扫类连环分类方法,给出算法步骤,并用数值算例进行分析。提出采用因素显隐的差额绝对值方法解决两个算法执行过程中出现的决策类别分不开的问题;对UCI数据集中3个实例与支持向量机作了算法对比分析,研究结果表明:提出的合并扫类连环分类方法、两两扫类连环分类方法实现了因素显隐,分类算法的精确度优于支持向量机。多分类学习的因素显隐研究结论拓展了因素空间的理论及应用研究。

基于隐式反馈和加权用户偏好的推荐算法

针对现有隐式反馈算法中正负样本划分不合理、忽略用户操作频次、无法准确建模用户偏好等问题,提出一种基于隐式反馈和加权用户偏好的推荐算法(IFW-LFM)。该算法考虑了用户操作频次与正负样本划分间的关系,学习并改进wALS算法,根据用户操作频次从缺失值中重新挖掘潜在正负样本,将用户操作频次大于1时的样本设置为正样本,用户操作频次为1或0时的样本为正样本或负样本,不再需要人为引入负样本;根据用户操作频次对用户偏好程度的影响,定义了置信度,明确用户偏好,并将其应用在隐因子模型的框架中;利用用户收听歌曲起止时间、收听时长等隐式反馈数据,提高隐式反馈样本利用度。在两个音乐数据集上的对比实验结果说明,该算法在准确率、召回率与NDCG值上与5个经典隐式反馈算法(UserCF、ItemCF、LFM、BPR、SVD)相比最大平均提升了45.81%,83.83%和60.33%,具有更优的推荐效果。

融合电影属性和交互信息的电影推荐算法研究

作为一种信息过滤系统,电影推荐系统通过分析目标用户的历史数据,向用户推荐他们可能会喜欢的电影。为了提高电影推荐系统的推荐质量,提出一种融合电影属性和交互信息的电影推荐算法U-LFM。该算法首先针对用户评分矩阵的稀疏性问题,使用传统的LFM算法进行矩阵填充;其次针对推荐影响因素的单一性问题,通过融合电影属性以及用户交互信息来增加电影推荐系统的多样性;最后通过实验对比其他几种电影推荐算法在同等条件下的查准率和召回率,验证了U-LFM具有较高的推荐质量。

Higher-dimensional Chen-Lee-Liu equation and asymmetric peakon soliton

Integrable systems play a crucial role in physics and mathematics.In particular,the traditional(1+1)-dimensional and(2+1)-dimensional integrable systems have received significant attention due to the rarity of integrable systems in higher dimensions.Recent studies have shown that abundant higher-dimensional integrable systems can be constructed from(1+1)-dimensional integrable systems by using a deformation algorithm.Here we establish a new(2+1)-dimensional Chen-Lee-Liu(C-L-L)equation using the deformation algorithm from the(1+1)-dimensional C-L-L equation.The new system is integrable with its Lax pair obtained by applying the deformation algorithm to that of the(1+1)-dimension.It is challenging to obtain the exact solutions for the new integrable system because the new system combines both the original C-L-L equation and its reciprocal transformation.The traveling wave solutions are derived in implicit function expression,and some asymmetry peakon solutions are found.

基于隐式表达的服装三维重建

随着近年来互联网购物的快速发展,在各大平台上出现了越来越多的服装商品。通过三维重建技术生成服装的三维模型可以帮助消费者更好地了解服装的姿态信息。针对服装的三维重建技术进行研究,提出基于隐式表达的服装三维重建模型。使用神经网络学习获得的占用函数作为服装三维模型的隐式表达,从而建立三维坐标和模型形状的映射。目前已有的三维重建算法需要拟合复杂的曲面模型,但资源消耗量大,而基于隐式表达的三维重建算法不需要进行参数化和网格化,能够提高算法的运行速度。为了进一步提高三维重建效果,采用目前性能最好的Point MetaBase-L网络模型和偏移注意力模块作为模型的特征提取网络。其中Point MetaBase-L网络模型基于现有的点云特征提取网络提出Set Abstraction层的元架构Point Meta,并通过分析选择Point Meta元架构中4个模块的最佳实践构成Point MetaBase-L网络模型的Set Abstraction层,同时引入平面特征投影模块加强特征的局部信息。在特征解码阶段,利用特征权重网络通过加权平均算法获取三维空间中采样点的占用概率。根据这些采样点的占用概率,通过基于区域增长的Marching Cubes算法提取高精度网格重建模型。实验结果表明,与占用网络相比,改进模型在交并比、倒角距离、法线一致性和F1值上分别提升了48.83%,55.17%、4.27%和79.10%。

Full-vectorial finite-difference beam propagation method based on the modified alternating direction implicit method

A modified alternating direction implicit algorithm is proposed to solve the full-vectorial finite-difference beam propagation method formulation based on H fields. The cross-coupling terms are neglected in the first sub-step, but evaluated and doubly used in the second sub-step. The order of two sub-steps is reversed for each transverse magnetic field component so that the cross-coupling terms are always expressed in implicit form, thus the calculation is very efficient and stable. Moreover, an improved six-point finite-difference scheme with high accuracy independent of specific structures of waveguide is also constructed to approximate the cross-coupling terms along the transverse directions. The imaginary-distance procedure is used to assess the validity and utility of the present method. The field patterns and the normalized propagation constants of the fundamental mode for a buried rectangular waveguide and a rib waveguide are presented. Solutions are in excellent agreement with the benchmark results from the modal transverse resonance method.

ON A CLASS OF GENERALIZED NONLINEAR IMPLICIT QUASIVARIATIONAL INCLUSIONS

In this paper, a new class of generalized nonlinear implicit quasivariational inclusions involving a set-valued maximal monotone wrapping are studied. A existence theorem of solutions for this class of generalized nonlinear implicit quasivariational inclusions is Proved without compactness assumptions. A new iterative algorithm for finding approximate solutions of the generalized nonlinear implicit quasivariational inclusions is suggested and analysed and the convergence of iterative sequence generated by the new algorithm is also given, As special cases, some known results in this field are also discussed.

High-order fully implicit SIMPLE-based model for fully implicit simulation of upward two-phase flow

The drift-flux model has a practical importance in two-phase flow analysis.In this study,a finite volume solution is developed for a transient four-equation drift-flux model through the staggered mesh,leading to the development of a fully implicit discretization method.The main advantage of the fully implicit method is its unconditional stability.Newton's scheme is a popular method of choice for the solution of a nonlinear system of equations arising from fully implicit discretization of field equations.However,the lack of convergence robustness and the construction of Jacobian matrix have created several difficulties for the researchers.In this paper,a fully implicit model is developed based on the SIMPLE algorithm for two-phase flow simulations.The drawbacks of Newton's method are avoided in the developed model.Different limiter functions are considered,and the stabilized method is developed under steady and transient conditions.The results obtained by the numerical modeling are in good agreement with the experimental data.As expected,the results prove that the developed model is not restricted by any stability limit.

g-η-Monotone mapping and resolvent operator technique for solving generalized implicit variational-like inclusions

A new class of g-η-monotone mappings and a class of generalized implicit variational-like inclusions involving g-η-monotone mappings are introduced. The resolvent operator of g-η-monotone mappings is defined and its Lipschitz continuity is presented, An iterative algorithm for approximating the solutions of generalized implicit wriational- like inclusions is suggested and analyzed. The convergence of iterative sequences generated by the algorithm is also proved,