Identification of variable coefficients for vibrating systems by boundary control and observation

We consider the identification problem of coefficients for vibrating systems described by a Euler-Bernoulli beam eq~. ation Or a string equation, with one end clamped and with an input exerted on the other end. For the beam equation, the observations are the velocity and the angle velocity at the free end, while for the string equation, the observation is the velocity at the free end. In the framework of well-posed linear system theory, we show that both the density and the flexural rigidity of the beam, and the tension of the string, can be uniquely determined by the observations for all positive times. Moreover, a general constructive method is developed to show that the mass density and the elastic modulus of the string are not determined by the observation.

Estimation, Intervention and Interaction of Multi-agent Systems

在这篇论文，我们在关于多代理人系统的最近的研究上提供简短调查。也就是，我们在研究的三个区域集中于结果评价并且过滤，由外部工具的干预，和交互控制。

Dynamic Control and Optimization of Capital-Constrained Stochastic Inventory Systems

For most firms,especially the small-and medium-sized ones,the operational decisions are affected by their internal capital and ability to obtain external capital.However,the majority of the current studies on dynamic inventory control ignore the firm’s financial status and financing issues completely.An important question that arises is:what are the dynamic optimal inventory and financing policies for firms with limited capital and limited access to external capital?In this paper,we review some of the latest developments in this area.After a brief review of single period models,we focus on multi-period dynamic control of the firm who aims to optimize its xpected terminal wealth.Two cases are discussed in detail:self-finance and short term finance.In the first case,the firm has to rely on its own capital for all ordering decisions,while in the second,the firm can borrow short term loan from lenders.A detailed characterization of the optimal policy is presented and its managerial insights are discussed.Several possible extensions are suggested.

Frontiers in biomolecular mesh generation and molecular visualization systems

With the development of biomolecular modeling and simulation,especially implicit solvent modeling,higher requirements are set for the stability,efficiency and mesh quality of molecular mesh generation software.In this review,we summarize the recent works in biomolecular mesh generation and molecular visualization.First,we introduce various definitions of molecular surface and corresponding meshing software.Second,as the mesh quality significantly influences biomolecular simulation,we investigate some remeshing methods in the fields of computer graphics and molecular modeling.Then,we show the application of biomolecular mesh in the boundary element method(BEM)and the finite element method(FEM).Finally,to conveniently visualize the numerical results based on the mesh,we present two types of molecular visualization systems.

Robust Set Stabilization and Its Instances for Open Quantum Systems

We propose and discuss a novel concept of robust set stabilization by permissible controls; this concept is helpful when dealing with both a priori information of model parameters and different permissible controls including quantum measurements. Both controllability and stabilization can be regarded as the special case of the novel concept. An instance is presented for a kind of uncertain open quantum systems to further justify this gen- eralized concept. It is underlined that a new type of hybrid control based on periodically perturbed projective measurements can be the permissible control of uncertain open quantum systems when perturbed projective measurements are available. The sufficient conditions are given for the robust set stabilization of uncertain quantum open systems by the hybrid control, and the design of the hybrid control is reduced to selecting the period of measurements.

Failure-Informed Adaptive Sampling for PINNs,Part Ⅱ:Combining with Re-sampling and Subset Simulation

This is the second part of our series works on failure-informed adaptive sampling for physic-informed neural networks(PINNs).In our previous work(SIAM J.Sci.Comput.45:A1971–A1994),we have presented an adaptive sampling framework by using the failure probability as the posterior error indicator,where the truncated Gaussian model has been adopted for estimating the indicator.Here,we present two extensions of that work.The first extension consists in combining with a re-sampling technique,so that the new algorithm can maintain a constant training size.This is achieved through a cosine-annealing,which gradually transforms the sampling of collocation points from uniform to adaptive via the training progress.The second extension is to present the subset simulation(SS)algorithm as the posterior model(instead of the truncated Gaussian model)for estimating the error indicator,which can more effectively estimate the failure probability and generate new effective training points in the failure region.We investigate the performance of the new approach using several challenging problems,and numerical experiments demonstrate a significant improvement over the original algorithm.

The relationship between attribute performance and customer satisfaction: an interpretable machine learning approach

Understanding the relationship between attribute performance(AP)and customer satisfaction(CS)is crucial for the hospitality industry.However,accurately modeling this relationship remains challenging.To address this issue,we propose an interpretable machine learning-based dynamic asymmetric analysis(IML-DAA)approach that leverages interpretable machine learning(IML)to improve traditional relationship analysis methods.The IML-DAA employs extreme gradient boosting(XGBoost)and SHapley Additive exPlanations(SHAP)to construct relationships and explain the significance of each attribute.Following this,an improved version of penalty-reward contrast analysis(PRCA)is used to classify attributes,whereas asymmetric impact-performance analysis(AIPA)is employed to determine the attribute improvement priority order.A total of 29,724 user ratings in New York City collected from TripAdvisor were investigated.The results suggest that IML-DAA can effectively capture non-linear relationships and that there is a dynamic asymmetric effect between AP and CS,as identified by the dynamic AIPA model.This study enhances our understanding of the relationship between AP and CS and contributes to the literature on the hotel service industry.

Output Feedback Based Admissible Control of Switched Linear Singular Systems

The admissibility analysis and robust admissible control problem of the uncertain discrete-time switched linear singular (SLS) systems for arbitrary switching laws are investigated. Based on linear matrix inequalities, some sufficient conditions are given for: A) the existence of generalized common Lyapunov solution and the admissibility of the SLS systems for arbitrary switching laws, B) the existence of static output feedback control laws ensuring the admissibility of the closed-loop SLS systems for arbitrary switching laws and norm-bounded uncertainties.

Reliability Analysis of a Cold Standby Repairable System with Repairman Extra Work

This paper deals with a cold standby repairman who can do extra work in idle time. The repairable system with two identical units and one authors are devoted to studying the unique existence and exponential stability of the system solution. C0-semigroup theory is used to prove the existence of a unique nonnegative time-dependent solution of the system. Then by using the theory of resolvent positive operator, the authors derive that dynamic solution of the system exponentially converges to its steady-state one which is the eigenfunction corresponding to eigenvalue 0 of the system operator. Some reliability indices of the system are discussed with a different method from traditional one. The authors also make a profit analysis to determine the optimal service time outside the system to maximize the system profit.

An optimized industry processing technology of peanut tofu and the novel prediction model for suitable peanut varieties

Peanut protein is easily digested and absorbed by the human body,and peanut tofu does not contain flatulence factors and beany flour.However,at present,there is no industrial preparation process of peanut tofu,whereas the quality of tofu prepared by different peanut varieties is quite different.This study established an industrial feasible production process of peanut tofu and optimized the key process that regulates its quality.Compared with the existing method,the production time is reduced by 53.80%,therefore the daily production output is increased by 183.33%.The chemical properties of 26 peanut varieties and the quality characteristics of tofu prepared from these 26 varieties were determined.The peanut varieties were classified based on the quality characteristics of tofu using the hierarchical cluster analysis(HCA)method,out of which 7 varieties were screened out which were suitable for preparing peanut tofu.An evaluation standard was founded based on peanut tofu qualities.Six chemical trait indexes were correlated with peanut tofu qualities(P<0.05).A logistic regressive model was developed to predict suitable peanut varieties and this prediction model was verified.This study may help broaden the peanut protein utilization,and provide guidance for breeding experts to select certain varieties for product specific cultivation of peanut.

Consensus Control With a Constant Gain for Discrete-time Binary-valued Multi-agent Systems Based on a Projected Empirical Measure Method

This paper studies the consensus control of multiagent systems with binary-valued observations.An algorithm alternating estimation and control is proposed.Each agent estimates the states of its neighbors based on a projected empirical measure method for a holding time.Based on the estimates,each agent designs the consensus control with a constant gain at some skipping time.The states of the system are updated by the designed control,and the estimation and control design will be repeated.For the estimation,the projected empirical measure method is proposed for the binary-valued observations.The algorithm can ensure the uniform boundedness of the estimates and the mean square error of the estimation is proved to be at the order of the reciprocal of the holding time(the same order as that in the case of accurate outputs).For the consensus control,a constant gain is designed instead of the stochastic approximation based gain in the existing literature for binary-valued observations.And,there is no need to make modification for control since the uniform boundedness of the estimates ensures the uniform boundedness of the agents’states.Finally,the systems updated by the designed control are proved to achieve consensus and the consensus speed is faster than that in the existing literature.Simulations are given to demonstrate the theoretical results.

A Priori and A Posteriori Error Estimates of Streamline Diffusion Finite Element Method for Optimal Control Problem Governed by Convection Dominated Diffusion Equation

In this paper,we investigate a streamline diffusion finite element approxi- mation scheme for the constrained optimal control problem governed by linear con- vection dominated diffusion equations.We prove the existence and uniqueness of the discretized scheme.Then a priori and a posteriori error estimates are derived for the state,the co-state and the control.Three numerical examples are presented to illustrate our theoretical results.

HILBERT PROBLEM 15 AND NONSTANDARD ANALYSIS(Ⅰ)

Hilbert problem 15 required understanding Schubert's book.In this book,reducing to degenerate cases was one of the main methods for enumeration.We found that nonstandard analysis is a suitable tool for making rigorous of Schubert's proofs of some results,which used degeneration method,but are obviously not rigorous.In this paper,we give a rigorous proof for Example 4 in Schubert's book,Chapter 1.§4 according to his idea.This shows that Schubert's intuitive idea is correct,but to make it rigorous a lot of work should be done.

UNDERSTANDING SCHUBERT’S BOOK(Ⅱ)

In this paper,we give rigorous justification of the ideas put forward in§20,Chapter 4 of Schubert’s book;a section that deals with the enumeration of conics in space.In that section,Schubert introduced two degenerate conditions about conics,i.e.,the double line and the two intersection lines.Using these two degenerate conditions,he obtained all relations regarding the following three conditions:conics whose planes pass through a given point,conics intersecting with a given line,and conics which are tangent to a given plane.We use the language of blow-ups to rigorously treat the two degenerate conditions and prove all formulas about degenerate conditions stemming from Schubert’s idea.

A Compound Algorithm of Denoising Using Second-Order and Fourth-Order Partial Differential Equations

In this paper, we propose a compound algorithm for the image restoration. The algorithm is a convex combination of the ROF model and the LLT model with a parameter function 0. The numerical experiments demonstrate that our compound algorithm is efficient and preserves the main advantages of the two models. In particular, the errors of the compound algorithm in L2 norm between the exact images and corresponding restored images are the smallest among the three models. For images with strong noises, the restored images of the compound algorithm are the best in the corresponding restored images. The proposed algorithm combines the fixed point method, an improved AMG method and the Krylov acceleration. It is found that the combination of these methods is efficient and robust in the image restoration.

Analysis of Conditional Value-at-Risk for Newsvendor with Holding and Backorder Cost under Market Search

We consider a distribution system with one supplier and two retailers. For the two retailers, they face different demand and are both risk averse. We study a single period model which the supplier has ample goods and the retailers order goods separately. Market search is measured as the fraction of customers who unsatisfied with their ＂local＂ retailer due to stock-out, and search for the goods at the other retailer before leaving the system. We investigate how the retailers game for order quantity in a Conditional Value-at-Risk framework and study how risk averse degree, market search level, holding cost and backorder cost influence the optimal order strategies. Furthermore, we use uniform distribution to illustrate these results and obtain Nash equilibrium of order strategies.

EXISTENCE AND UNIQUENESS OF ENTROPY SOLUTION TO PRESSURELESS EULER SYSTEM WITH A FLOCKING DISSIPATION

We study the existence and uniqueness problem for the nonhomogeneous pressureless Euler system with the initial density being a Radon measure. Our uniqueness result is obtained in the same space as the existence theorem. Besides, by counterexample we prove that Huang-Wang’s energy condition is also necessary for our nonhomogeneous system.

Networked Knowledge and Complex Networks:An Engineering View

Along with the development of information technologies such as mobile Internet,information acquisition technology,cloud computing and big data technology,the traditional knowledge engineering and knowledge-based software engineering have undergone fundamental changes where the network plays an increasingly important role.Within this context,it is required to develop new methodologies as well as technical tools for network-based knowledge representation,knowledge services and knowledge engineering.Obviously,the term“network”has different meanings in different scenarios.Meanwhile,some breakthroughs in several bottleneck problems of complex networks promote the developments of the new methodologies and technical tools for network-based knowledge representation,knowledge services and knowledge engineering.This paper first reviews some recent advances on complex networks,and then,in conjunction with knowledge graph,proposes a framework of networked knowledge which models knowledge and its relationships with the perspective of complex networks.For the unique advantages of deep learning in acquiring and processing knowledge,this paper reviews its development and emphasizes the role that it played in the development of knowledge engineering.Finally,some challenges and further trends are discussed.

Reachability analysis of switched linear discrete singular systems

This paper studies the reachability problem of the switched linear discrete singular （SLDS） systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.