Complex Problems Solution as a Service Based on Predictive Optimization and Tasks Orchestration in Smart Cities

Smart cities have different contradicting goals having no apparent solution.The selection of the appropriate solution,which is considered the best compromise among the candidates,is known as complex problem-solving.Smart city administrators face different problems of complex nature,such as optimal energy trading in microgrids and optimal comfort index in smart homes,to mention a few.This paper proposes a novel architecture to offer complex problem solutions as a service(CPSaaS)based on predictive model optimization and optimal task orchestration to offer solutions to different problems in a smart city.Predictive model optimization uses a machine learning module and optimization objective to compute the given problem’s solutions.The task orchestration module helps decompose the complex problem in small tasks and deploy them on real-world physical sensors and actuators.The proposed architecture is hierarchical and modular,making it robust against faults and easy to maintain.The proposed architecture’s evaluation results highlight its strengths in fault tolerance,accuracy,and processing speed.

Kolmogorov entropy changes and cortical lateralization during complex problem solving task measured with EEG

The objective is to study changes in EEG time-domain Kolmogorov entropy and cortical lateralization of brain function areas during complex problem solving mental task in healthy human subjects. EEG data for healthy subjects are acquired during complex problem solving mental task using a net of 6 electrodes. The subject was given a nontrivial multiplication problem to solve and the signals were recorded for 10s during the task. Kolmogorov entropy values during the task were calculated. It was found that Kolmogorov entropy values were obviously greater in P4 channel (right) than ones in P3 channel (left) during complex problem solving task. It indicated that all subjects presented significant left parietal lateralization for the total frequency spectrum. These results suggest that it may be possible to noninvasively lateralize, and even eventually localize, cerebral regions essential for particular mental tasks from scalp EEG data.

The Similar Structures and Control Problems of Complex Systems

In this paper, the naturally evolving complex systems, such as biotic and social ones, are considered. Focusing on their structures, a feature is noteworthy, i.e., the similarity in structures. The relations between the functions and behaviors of these systems and their similar structures will be studied. Owing to the management of social systems and the course of evolution of biotic systems may be regarded as control processes, the researches will be within the scope of control problems. Moreover, since it is difficult to model for biotic and social systems, it will start with the control problems of complex systems, possessing similar structures, in engineering. The obtained results show that for either linear or nonlinear systems and for a lot of control problems similar structures lead to a series of simplifications. In general, the original system may be decomposed into reduced amount of subsystems with lower dimensions and simpler structures. By virtue of such subsystems, the control problems of original system can be solved more simply. At last, it turns round to observe the biotic and social systems and some analyses are given.

NUMERICAL SOLUTIONS OF DISCONTINUOUS BOUNDARY VALUE PROBLEMS FOR GENERAL ELLIPTIC COMPLEX EQUATIONS OF FIRST ORDER

In this paper, authors discuss the numerical methods of general discontinuous boundary value problems for elliptic complex equations of first order, They first give the well posedness of general discontinuous boundary value problems, reduce the discontinuous boundary value problems to a variation problem, and then find the numerical solutions of above problem by the finite element method. Finally authors give some error-estimates of the foregoing numerical solutions.

The Riemann Hilbert Problem for General Elliptic Complex Equations of Fourth Order

This paper deals with the existence theorem and Riemann Hilbert boundary value problem for general nonlinear elliptic complex equations of fourth order. Firstly we give the representation and existence theorem of solutions for the complex equations. Moreover,we propose the Riemann Hilbert problem and its well posedness,and then we give the representation of solutions for the modified boundary value problem and prove its solvsbility,and finally derive solvability conditions of the original Riemann Hilbert problem.

EQUATION IN COMPLEX VARIABLE OF AXISYMMETRICAL DEFORMATION PROBLEMS FOR A GENERAL SHELL OF REVOLUTION

In this paper, the equation of axisymmetrical deformation problems for a general shell of revolution is derived in one complex variable under the usual Love-Kirchhoff assumption. In the case of circular ring shells, this equation may be simplified into the equation given by F.Tdlke(1938)[3]. R.A. Clark(1950 )[4] and V. V.Novozhilov(1951)[5]. When the horizontal radius of the shell of revolution is much larger than the average radius of curvature of meridian curve, this equation in complex variable may be simplified into the equation for slander ring shells. If the ring shell is circular in shape, then this equation can be reduced into the equation in complex variable for slander circular ring shells given by this author (1979)[6]. If the form of elliptic cross-section is near a circle, then the equation of slander ring shell with near-circle ellipitic cross-section may be reduced to the complex variable equation similar in form for circular slander ring shells.

Complex variable solution for boundary value problem with X-shaped cavity in plane elasticity and its application*

A new type of displacement pile, the X-section cast-in-place concrete （XCC） pile, has recently been developed in China. Extensive field tests and laboratory experi- ments are undertaken to evaluate its performance and quantify the non-uniform deforma- tion effect （NUDE） of the X-shaped cross section during installation. This paper develops a simplified theoretical model that attempts to capture the NUDE. Based on the theory of complex variable plane elasticity, closed-form solutions of the stress and displacement for the X-shaped cavity boundary value problem are given. Subsequently, the analytical solution is used to evaluate the NUDE, the concrete filling index （CFI）, and the perimeter reduction coefficient of the XCC pile cross section. The computed results are compared with field test results, showing reasonable agreement. The present simplified theoretical model reveals the deformation mechanism of the X-shaped cavity and facilitates applica- tion of the newly developed XCC pile technique in geotechnical engineering.

Riemann-Hilbert problem for first order complex equations of mixed type with degenerate curve

This paper considers the Riemann-Hilbert problem for linear mixed（elliptichyperbolic） complex equations of first order with degenerate curve in a simply connected domain. We first give the representation theorem and uniqueness of solutions for such boundary value problem. Then by using the methods of successive iteration and parameter extension, the existence of solutions for this problem is proved.

A NEW MATRIX PERTURBATION METHOD FOR ANALYTICAL SOLUTION OF THE COMPLEX MODAL EIGENVALUE PROBLEM OF VISCOUSLY DAMPED LINEAR VIBRATION SYSTEMS

A new matrix perturbation analysis method is presented for efficient approximate solution of the complex modal quadratic generalized eigenvalue problem of viscously damped linear vibration systems. First, the damping matrix is decomposed into the sum of a proportional-and a nonproportional-damping parts, and the solutions of the real modal eigenproblem with the proportional dampings are determined, which are a set of initial approximate solutions of the complex modal eigenproblem. Second, by taking the nonproportional-damping part as a small modification to the proportional one and using the matrix perturbation analysis method, a set of approximate solutions of the complex modal eigenvalue problem can be obtained analytically. The result is quite simple. The new method is applicable to the systems with viscous dampings-which do not deviate far away from the proportional-damping case. It is particularly important that the solution technique be also effective to the systems with heavy, but not over, dampings. The solution formulas of complex modal eigenvlaues and eigenvectors are derived up to second-order perturbation terms. The effectiveness of the perturbation algorithm is illustrated by an exemplar numerical problem with heavy dampings. In addition, the practicability of approximately estimating the complex modal eigenvalues, under the proportional-damping hypothesis, of damped vibration systems is discussed by several numerical examples.

THE AVERAGE CASE COMPLEXITY OF THE SHIFT-INVARIANT PROBLEM

The present paper deals with the average case complexity of the shift—invariant problem. The main aim is to give a new proof of the upper bound of average error of finite element method. Our method is based on the techniques proposed by Heinrich (1990). We also point out an essential error regarding the proof of the upper bound in A. G. Werschulz (1991).

The oblique derivative problem for nonlinear elliptic complex equations of second order in multiply connected unbounded domains

In this article,we discuss that an oblique derivative boundary value problem for nonlinear uniformly elliptic complex equation of second order with the boundary conditions in a multiply connected unbounded domain D.The above boundary value problem will be called Problem P.Under certain conditions,by using the priori estimates of solutions and Leray-Schauder fixed point theorem,we can obtain some results of the solvability for the above boundary value problem（0.1） and（0.2）.

New complex variable meshless method for advection-diffusion problems

In this paper,an improved complex variable meshless method（ICVMM） for two-dimensional advection-diffusion problems is developed based on improved complex variable moving least-square（ICVMLS） approximation.The equivalent functional of two-dimensional advection-diffusion problems is formed,the variation method is used to obtain the equation system,and the penalty method is employed to impose the essential boundary conditions.The difference method for twopoint boundary value problems is used to obtain the discrete equations.Then the corresponding formulas of the ICVMM for advection-diffusion problems are presented.Two numerical examples with different node distributions are used to validate and investigate the accuracy and efficiency of the new method in this paper.It is shown that ICVMM is very effective for advection-diffusion problems,and has a good convergent character,accuracy,and computational efficiency.

Approximate Method of Riemann-Hilbert Problem for Elliptic Complex Equations of First Order in Multiply Connected Unbounded Domains

In this article, we discuss the approximate method of solving the Riemann-Hilbert boundary value problem for nonlinear uniformly elliptic complex equation of first order (0.1) with the boundary conditions (0.2) in a multiply connected unbounded domain D, the above boundary value problem will be called Problem A. If the complex Equation (0.1) satisfies the conditions similar to Condition C of (1.1), and the boundary condition (0.2) satisfies the conditions similar to (1.5), then we can obtain approximate solutions of the boundary value problems (0.1) and (0.2). Moreover the error estimates of approximate solutions for the boundary value problem is also given. The boundary value problem possesses many applications in mechanics and physics etc., for instance from (5.114) and (5.115), Chapter VI, [1], we see that Problem A of (0.1) possesses the important application to the shell and elasticity.

A new complex variable element-free Galerkin method for two-dimensional potential problems

In this paper, based on the element-free Galerkin （EFG） method and the improved complex variable moving least- square （ICVMLS） approximation, a new meshless method, which is the improved complex variable element-free Galerkin （ICVEFG） method for two-dimensional potential problems, is presented. In the method, the integral weak form of control equations is employed, and the Lagrange multiplier is used to apply the essential boundary conditions. Then the corresponding formulas of the ICVEFG method for two-dimensional potential problems are obtained. Compared with the complex variable moving least-square （CVMLS） approximation proposed by Cheng, the functional in the ICVMLS approximation has an explicit physical meaning. Furthermore, the ICVEFG method has greater computational precision and efficiency. Three numerical examples are given to show the validity of the proposed method.

Equivalence of three kinds of well-posed-ness of discontinuous Riemann-Hilbert problem for elliptic complex equation in multiply connected domains

In this article, we first introduce the general linear elliptic complex equation of first order with certain conditions, and then propose discontinuous Riemann-Hilbert problem and some kinds of modified well-posed-ness for the complex equation. Then we verify the equivalence of three kinds of well-posed-ness. The discontinuous boundary value problem possesses many applications in mechanics and physics etc.

核心素养导向的学科实践:内在逻辑与学习进程

学科实践是核心素养导向下的学科学习新形态,指向学生应对复杂问题情境的胜任力与协作交往的道德力的培育。学科实践包含人类实践、专业实践和个体实践,其紧紧围绕着学科知识与学科实践、学科观念与学科实践的互通关系而展开,知识在人类实践中产生又在指导和规约实践中得以发展,个体观念则在经历学科知识生产和发展的思维过程和实践过程中得以建构,再应用于实际问题解决以发展学生的学科理解力与学科实践力。学科实践以感性实践为起点,在复杂问题解决学习中通过理性实践与协作探究深化知识理解,并在知行循环中实现知识迁移与知识应用。让学科实践在学校教育中得以真正落实,需明确“学用合一”的学习理念,以“学科心理”来融通系列学习活动,厘清进阶性学科问题与问题链的现实路径,并致力构建意义协商的学习共同体。

A Hybrid Genetic Algorithm for Vehicle Routing Problem with Complex Constraints

Most research on the Vehicle Routing Problem （VRP） is focused on standard conditions, which is not suitable for specific cases. A Hybrid Genetic Algorithm is proposed to solve a Vehicle Routing Problem （VRP） with complex side constraints. A novel coding method is designed especially for side constraints. A greedy algorithm combined with a random algorithm is introduced to enable the diversity of the initial population, as well as a local optimization algorithm employed to improve the searching efficiency. In order to evaluate the performance, this mechanism has been implemented in an oil distribution center, the experimental and executing results show that the near global optimal solution can be easily and quickly obtained by this method, and the solution is definitely satisfactory in the VRP application.

智慧城市科学与工程新兴交叉学科建设的探索与思考

智慧城市科学与工程新兴交叉学科面向建筑智能化发展需求,以创新型人才培养为核心,探索解决复杂工程问题能力培养途径。采用多元化实践教学方式,通过优化课程与实践教学体系、强化教学团队建设、构建协同育人平台和实施立体化评价体系,逐步提高教师跨学科教学、科研能力,提升学生的工程实践能力、交叉融合意识、协作精神,促进学生全面发展。而该学科在建设过程中也面临诸多困难与挑战,通过深化交流合作、扩大师资队伍规模、提升学生交叉融合意识和注重评价体系反馈等措施,推动智慧城市科学与工程交叉学科建设的快速进展,为城市智慧化、绿色化提供人才保障。