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.

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.

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.

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.

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.

Noether conserved quantities and Lie point symmetries of difference Lagrange-Maxwell equations and lattices

This paper presents a method to find Noether-type conserved quantities and Lie point symmetries for discrete mechanico-electrical dynamical systems,which leave invuriant the set of solutions of the corresponding difference scheme. This approach makes it possible to devise techniques for solving the Lagrange Maxwell equations in differences which correspond to mechanico-electrical systems,by adapting existing differential equations.In particular,it obtains a new systematic method to determine both the one-parameter Lie groups and the discrete Noether conserved quantities of Lie point symmetries for mechanico-electrical systems.As an application,it obtains the Lie point symmetries and the conserved quantities for the difference equation of a model that represents a capacitor microphone.

A KERNEL-TYPE ESTIMATOR OF A QUANTILE FUNCTION UNDER RANDOMLY TRUNCATED DATA

A kernel-type estimator of the quantile function Q（p） = inf{t：F（t） ≥ p}, 0 ≤ p ≤ 1, is proposed based on the kernel smoother when the data are subjected to random truncation. The Bahadur-type representations of the kernel smooth estimator are established, and from Bahadur representations the authors can show that this estimator is strongly consistent, asymptotically normal, and weakly convergent.

Geometric Structures and Field Equations of Dirac-Lu Space

In this paper,a■-invariant Lorentz metric on the Dirac-Lu space is given,and then the geodesic equationis investigated.Finally,we discuss the field equations and find their solutions by the method of separating variables.

On Study of Solutions of Kac-van Moerbeke Lattice and Self-dual Network Equations

The closed form of solutions of Kac-van Moerbeke lattice and self-dual network equations are considered by proposing transformations based on Riccati equation, using symbolic computation. In contrast to the numerical computation of travelling wave solutions for differential difference equations, our method obtains exact solutions which have physical relevance.

The Role of Japanese Candlestick in DVAR Model

The decomposition-based vector autoregressive model （DVAR） provides a new framework for scrutinizing the efficiency of technical analysis in forecasting stock returns. However, its relation- ships with other technical indicators still remain unknown. This paper investigates the relationships of DVAR model with the Japanese Candlestick indicators using simulations, theoretical explanations and empirical studies. The main finding of this paper is that both lower and upper shadows in Japanese Candlestick Granger contribute to the DVAR model explanation power, and thus, providing useful information for improving the DVAR forecasts. This finding makes sense as it means that the infor- mation contained in the lower and upper shadows should be used when modeling the stock returns with DVAR. Empirical studies performed on China SSEC stock index demonstrate that DVAR model with upper and lower shadows as exogenous variables does have informative and valuable out-of-sample forecasts.

Control of random Boolean networks via average sensitivity of Boolean functions

In this paper, we discuss how to transform the disordered phase into an ordered phase in random Boolean networks. To increase the effectiveness, a control scheme is proposed, which periodically freezes a fraction of the network based on the average sensitivity of Boolean functions of the nodes. Theoretical analysis is carried out to estimate the expected critical value of the fraction, and shows that the critical value is reduced using this scheme compared to that of randomly freezing a fraction of the nodes. Finally, the simulation is given for illustrating the effectiveness of the proposed method.

NONTRIVIAL SOLUTIONS OF HARDY-HENON TYPE ELLIPTIC SYSTEMS

In this article, the authors investigate the existence problem for Hardy Henon type strongly indefinite elliptic systems. Existence results are obtained for such systems with superlinear subcritical nonlinearities.

The Homogeneity of Distributional Patterns of the Global Terrestrial Animal,Plant and Microorganism under the Influence of Ecological Conditions

The world animal geographical regionalization scheme and the plant geographical regionalization scheme have been formulated by zoologists and botanists respectively since the biogeography has been established.This research team initially confirmed the homogeneity of Chinese animal and plant geography.To explore the relationship between the distribution pattern of global animals,plants,and microorganisms,global 141,814 genera of terrestrial animals,17,526 genera of plants,21,321 genera of microorganisms,and their major taxa were analyzed using their proposed SGF(Similarity General Formula)and a new multivariate similarity clustering analysis method.Almost identical analytical results were obtained,meeting the requirements of statistics,geography,ecology and biology respectively.The expected consistency of their distribution pattern was achieved for the first time.We prove that the earth’s ecological conditions affect the homogeneity and accumulation of the distribution of animals,plants and microorganisms.Homogeneity determines the distribution pattern of global kinds of biological consistency,accumulation determines the impact of the evolutionary period on the breadth of distribution,microorganisms appear earliest,plants second,animals later,and their average distribution domain decreases in turn,reflecting these differences.Therefore,this study not only provides a theoretical basis and quantitative basis for the establishment of geographical regionalization scheme but also advances the development of biogeography to a new stage and raises the theory of biogeographic analysis to a new height.

Fisher Information of Wavefunctions： Classical and Quantum

A parametric quantum mechanical wavefunction naturally induces parametric probability distributions by taking absolute square, and we can consider its classical Fisher information. On the other hand, it also induces parametric rank-one projections which may be viewed as density operators, and we can talk about its quantum Fisher information. Among many versions of quantum Fisher information, there are two prominent ones. The first, defined via a quantum score function, was introduced by Helstrom in 1967 and is well known. The second, defined via the square root of the density operator, has its origin in the skew information introduced by Wigner and Yanase in 1963 and remains relatively unnoticed. This study is devoted to investigating the relationships between the classical Fisher information and these two versions of quantum Fisher information for wavefunctions. It is shown that the two versions of quantum Fisher information differ by a factor 2 and that they dominate the classical Fisher information. The non-coincidence of these two versions of quantum Fisher information may be interpreted as a manifestation of quantum discord. We further calculate the difference between the Helstrom quantum Fisher information and the classical Fisher information, and show that it is precisely the instantaneous phase fluctuation of the wavefunctions.