Some remarks on pseudo-umbilical totally real submanifolds in a complex projective space

This paper studies the relationship between the pseudo-umbilical totally real submanifolds and the minimal totally real submanifolds in a complex projective space. Two theo- rems which claim that some types of pseudo-umbilical totally real submanifolds must be minimal submanifolds are proved.

Safety Risk Analysis of Large⁃scale Complex Project based on WBS⁃RBS and Interval Numbers

Safety risks are essential to the success or failure of the large⁃scale complex projects.In order to assess and evaluate the safety risks of the large⁃scale complex projects scientifically,a risk assessment method of work breakdown structure and risk breakdown structure(WBS⁃RBS)is proposed to identify the project risks.In this paper,interval numbers are used to evaluate the risk levels,weights are assigned automatically based on the complexity and risk degree of WBS to distinguish three types of nodes in WBS,and a risk assessment algorithm is designed to assess safety risk at all layers of the project.A case study is conducted to demonstrate how to apply the method.The results show the practicality,robustness and efficiency of our new method,which can be applied to different kinds of large⁃scale complex projects in reality.

Discrete decision model and multi-agent simulation of the Liang Zong two-chain hierarchical organization in a complex project

Different from the organization structure of complex projects in Western countries, the Liang Zong hierarchical organization structure of complex projects in China has two different chains, the chief-engineer chain and the general-director chain,to handle the trade-off between technical and management decisions. However, previous works on organization search have mainly focused on the single-chain hierarchical organization in which all decisions are regarded as homogeneous. The heterogeneity and the interdependency between technical decisions and management decisions have been neglected. A two-chain hierarchical organization structure mapped from a real complex project is constructed. Then, a discrete decision model for a Liang Zong two-chain hierarchical organization in an NK model framework is proposed. This model proves that this kind of organization structure can reduce the search space by a large amount and that the search process should reach a final stable state more quickly. For a more complicated decision mechanism, a multi-agent simulation based on the above NK model is used to explore the effect of the two-chain organization structure on the speed, stability, and performance of the search process. The results provide three insights into how, compared with the single-chain hierarchical organization, the two-chain organization can improve the search process: it can reduce the number of iterations efficiently; the search is more stable because the search space is a smoother hill-like fitness landscape; in general, the search performance can be improved.However, when the organization structure is very complicated, the performance of a two-chain organization is inferior to that of a single-chain organization. These findings about the efficiency of the unique Chinese-style organization structure can be used to guide organization design for complex projects.

Finite-time complex projective synchronization of fractional-order complex-valued uncertain multi-link network and its image encryption application

Multi-link networks are universal in the real world such as relationship networks,transportation networks,and communication networks.It is significant to investigate the synchronization of the network with multi-link.In this paper,considering the complex network with uncertain parameters,new adaptive controller and update laws are proposed to ensure that complex-valued multilink network realizes finite-time complex projective synchronization(FTCPS).In addition,based on fractional-order Lyapunov functional method and finite-time stability theory,the criteria of FTCPS are derived and synchronization time is given which is associated with fractional order and control parameters.Meanwhile,numerical example is given to verify the validity of proposed finite-time complex projection strategy and analyze the relationship between synchronization time and fractional order and control parameters.Finally,the network is applied to image encryption,and the security analysis is carried out to verify the correctness of this method.

A Note on Totally Real Riemannian Foliations with Parallelized Mean Curvature Vectors in a Complex Projective Space

我们讨论了有平行的生叶意味着的完全真实的 Riemannian 在一个复杂射影的空格的弯曲。我们在它上执行了一块向量地的分叉并且获得了西蒙的类型的一个公式。

Volume Difference Inequalities for the Polars of Mixed Complex Projection Bodies

In this paper, based on the notion of mixed complex projection and generalized the recent works of other authors, we obtain some volume difference inequalities containing Brunn-Minkowski type inequality, Minkowski type inequality and Aleksandrov-Fenchel inequality for the polars of mixed complex projection bodies.

2-Harmonic Totally Real Submanifolds in a Complex Projective Space

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A Characterization of Complex Projective Spaces by Sections of Line Bundles

Let M be a n-dimensional compact irreducible complex space with a line bundle L. It is shown that if M is completely intersected with respect to L and dimH0(M, L) = n + 1, then M is biholomorphic to a complex projective space Pn of dimension n.

Mean Curvature Flow of Arbitrary Codimension in Complex Projective Spaces

Recently,Pipoli and Sinestrari[Pipoli,G.and Sinestrari,C.,Mean curvature flow of pinched submanifolds of CPn,Comm.Anal.Geom.,25,2017,799-846]initiated the study of convergence problem for the mean curvature flow of small codimension in the complex projective space CPm.The purpose of this paper is to develop the work due to Pipoli and Sinestrari,and verify a new convergence theorem for the mean curvature flow of arbitrary codimension in the complex projective space.Namely,the authors prove that if the initial submanifold in CPm satisfies a suitable pinching condition,then the mean curvature flow converges to a round point in finite time,or converges to a totally geodesic submanifold as t→∞.Consequently,they obtain a differentiable sphere theorem for submanifolds in the complex projective space.

On Complete Totally Real Pseudo-Umbilical Submanifolds in a Complex Projective Space

Let Mn be a totally real pseudo-umbilical submanifold in a complex projective space CPn＋p. In this paper, we study the position of completeness of Mn. By choosing a suitable frame field, we obtain a rigidity theorem such that Mn becomes totally umbilical submanifold and improve the related results.

Orlicz-Brunn-Minkowski Inequalities for Complex Projection Bodies

Abardia and Bernig introduced the complex projection body and established the Brunn-Minkowski inequality for complex projection bodies.In this paper,we generalize their result and establish the Orlicz-Brunn-Minkowski inequality for complex projection bodies.And the Orlicz-Brunn-Minkowski inequality for polars of complex projection bodies is also obtained.

Meta-synthesis management framework of a complex project： A case study of the deck pavement project of the Hong Kong-Zhuhai-Macao Bridge

Innovative technology and deep uncertainty during the design and construction process of complex projects introduce great challenges to their organization and management.The traditional methods,represented in the project management body of knowledge(PMBOK)guide,can solve systematic problems;however,they cannot solve complex problems.Based on the management practice implemented in the deck pavement project of the Hong Kong-Zhuhai-Macao Bridge(HZMB),in this work,we propose a meta-synthesis management framework for a complex project from the perspective of the science of complexity.The method deems that the complexity of the project has the characteristic of being multi-scale both in the design phase and the construction phase.These problems can be classified into different categories,each of which requires a different strategy.As a result,it is first necessary to adopt the"exploration"strategy to reduce project complexity and to transform the deep uncertainty problems into systematic problems.Then,the"exploitation"strategy should be used to apply the PMBOK and other traditional methods to achieve the design and construction goals of the project and to improve its efficiency.More specifically,in the design phase of a complex project,the"innovative integration"process is used for the exploration of the new engineering technology and knowledge;then,the"functional integration"process is employed to define the system architecture,the interface relationship,the technical index,and other functions.In the construction phase,the"adaptive integration"process is used for the construction of the engineering organization system;next,the"efficient integration"process is employed to improve the actual construction performance.The meta-synthesis management framework proposed in this work reveals the multi-scale principle of solving complex problems in the management practice of a complex project,and develops the methodology of metasynthesis.

The Eigen Functions of the Complex Projective Space

In the complex n-dimensional projective space CP^n. let λ_p(=4p(p+n)) be the eigen vaiue of the Laplace-Beltrami operator and H_p be the space of all eigen functions of eigen value λ_p. The reproducing kernel h_p(z, w) of H_p is constructed explicitly in this paper. and a system of complete orthogohal functions of H_p is construncted from h_p(z, w)(p=1,2…).

On Totally Real Pseudo-Umbilical Submanifolds in a Complex Projective Space

Let M^n be a totally real submanifold in a complex projective space CP^(n+p).In this paper,we study the position of the parallel umbilical normal vector field of M^n in the normal bundle.By choosing a suitable frame field,we obtain a pinching theorem,in the case p>0, for the square of the length of the second fundamental form of a totally real pseudo-umbilical submanifold with parallel mean curvature vector.

Projective synchronization of a complex network with different fractional order chaos nodes

Based on the stability theory of the linear fractional order system, projective synchronization of a complex network is studied in the paper, and the coupling functions of the connected nodes are identified. With this method, the projective synchronization of the network with different fractional order chaos nodes can be achieved, besides, the number of the nodes does not affect the stability of the whole network. In the numerical simulations, the chaotic fractional order Lu system, Liu system and Coullet system are chosen as examples to show the effectiveness of the scheme.

Generalized projective synchronization of two coupled complex networks of different sizes

We investigate a new generalized projective synchronization between two complex dynamical networks of different sizes. To the best of our knowledge, most of the current studies on projective synchronization have dealt with coupled networks of the same size. By generalized projective synchronization, we mean that the states of the nodes in each network can realize complete synchronization, and the states of a pair of nodes from both networks can achieve projective synchronization. Using the stability theory of the dynamical system, several sufficient conditions for guaranteeing the existence of the generalized projective synchronization under feedback control and adaptive control are obtained. As an example, we use Chua’s circuits to demonstrate the effectiveness of our proposed approach.

Adaptive function projective synchronization of uncertain complex dynamical networks with disturbance

We investigate the problem of function projective synchronization （FPS） in drive–response dynamical networks with non-identical nodes. An adaptive controller is proposed for the FPS of complex dynamical networks with uncertain parameters and disturbance. Not only are the unknown parameters of the networks estimated by the adaptive laws obtained from the Lyapunov stability theory and Taylor expansions, but the unknown bounded disturbances are also simultaneously conquered by the proposed control. Finally, a numerical simulation is provided to illustrate the feasibility and effectiveness of the obtained result.

Adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions

The adaptive generalized matrix projective lag synchronization between two different complex networks with non-identical nodes and different dimensions is investigated in this paper. Based on Lyapunov stability theory and Barbalat＇s lemma, generalized matrix projective lag synchronization criteria are derived by using the adaptive control method. Furthermore, each network can be undirected or directed, connected or disconnected, and nodes in either network may have identical or different dynamics. The proposed strategy is applicable to almost all kinds of complex networks. In addition, numerical simulation results are presented to illustrate the effectiveness of this method, showing that the synchronization speed is sensitively influenced by the adaptive law strength, the network size, and the network topological structure.

Software Project’s Complexity Measurement: A Case Study

Project management is a well understood management method, widely adopted today, in order to give predictable results to complex problems. However, quite often projects fail to satisfy their initial objectives. This is why studying the factors that affect the complexity of projects is quite important. In this paper, we will present the complexity factors that are related to project time, cost and quality management and then we will apply them to a number of selected projects, in order to compare the acquired results. The projects have been chosen in a way that results can be easily compared.

Generalized projective synchronization of fractional-order complex networks with nonidentical nodes

This paper investigates the synchronization problem of fractional-order complex networks with nonidentical nodes. The generalized projective synchronization criterion of fractional-order complex networks with order 0 〈 q 〈 1 is obtained based on the stability theory of the fractional-order system. The control method which combines active control with pinning control is then suggested to obtain the controllers. Furthermore, the adaptive strategy is applied to tune the control gains and coupling strength. Corresponding numerical simulations are performed to verify and illustrate the theoretical results.