State-Based Opacity Verification of Networked Discrete Event Systems Using Labeled Petri Nets

The opaque property plays an important role in the operation of a security-critical system,implying that pre-defined secret information of the system is not able to be inferred through partially observing its behavior.This paper addresses the verification of current-state,initial-state,infinite-step,and K-step opacity of networked discrete event systems modeled by labeled Petri nets,where communication losses and delays are considered.Based on the symbolic technique for the representation of states in Petri nets,an observer and an estimator are designed for the verification of current-state and initial-state opacity,respectively.Then,we propose a structure called an I-observer that is combined with secret states to verify whether a networked discrete event system is infinite-step opaque or K-step opaque.Due to the utilization of symbolic approaches for the state-based opacity verification,the computation of the reachability graphs of labeled Petri nets is avoided,which dramatically reduces the computational overheads stemming from networked discrete event systems.

Finite Words,Infinite Wisdom

As picture books gain popularity,they create a bridge between China and the rest of the world.

Infinitely Many Solutions and a Ground-State Solution for Klein-Gordon Equation Coupled with Born-Infeld Theory

In this paper, we intend to consider a kind of nonlinear Klein-Gordon equation coupled with Born-Infeld theory. By using critical point theory and the method of Nehari manifold, we obtain two existing results of infinitely many high-energy radial solutions and a ground-state solution for this kind of system, which improve and generalize some related results in the literature.

STATIONARY DISTRIBUTIONS OF INFINITE PARTICLE SYSTEMS WITH NONCOMPACT STATE SPACE.

This paper deals with the preblem of existence and uniqueness of the stationary distributions (abbr., s. d.'s) for the processes constructed in [4] .The main results are stated in § 1. For the reader's convenience we first restate the existence theorems (Theorem 1 and 2) of the processes given in [4]. Then two existence theorems (Theorem 3 and 4) and a uniqueness theorem (Theorem 5) for the s. d.'s of the processes are presented. The last result (Theorem 6), as an application of the previous ones, is about the Schlgl model which comes from nonequilibrium statisticali physics. The details of the proofs of Theorem 3—6 are given in § 2—4.

POSITIVE SOLUTIONS AND INFINITELY MANY SOLUTIONS FOR A WEAKLY COUPLED SYSTEM

We study a Schrodinger system with the sum of linear and nonlinear couplings.Applying index theory,we obtain infinitely many solutions for the system with periodic potent ials.Moreover,by using the concentration compactness met hod,we prove the exis tence and nonexistence of ground state solutions for the system with close-to-periodic potentials.

Boundary Control Problem of Infinite Order Distributed Hyperbolic Systems Involving Time Lags

Various optimal boundary control problems for linear infinite order distributed hyperbolic systems involving constant time lags are considered. Constraints on controls are imposed. Necessary and sufficient optimality conditions for the Neumann problem with the quadratic performance functional are derived.

AN INFINITE SYSTEM OF ALGEBRAICALLY INDEPENDENT NUMBERS

In this note we prove the followingTheorem. Let a_n(n=1, 2, 3,…) be an infinite sequence of positive integers withe the following

PLANE INFINITE ANALYTICAL ELEMENT AND HAMILTONIAN SYSTEM

It is not convenient to solve those engineering problems defined in an infinite field by using FEM. An infinite area can be divided into a regular infinite external area and a finite internal area. The finite internal area was dealt with by the FEM and the regular infinite external area was settled in a polar coordinate. All governing equations were transformed into the Hamiltonian system. The methods of variable separation and eigenfunction expansion were used to derive the stiffness matrix of a new infinite analytical element.This new element, like a super finite element, can be combined with commonly used finite elements. The proposed method was verified by numerical case studies. The results show that the preparation work is very simple, the infinite analytical element has a high precision, and it can be used conveniently. The method can also be easily extended to a three-dimensional problem.

Exact Controllability and Exact Observability of Descriptor Infinite Dimensional Systems

Necessary and sufficient conditions for the exact controllability and exact observability of a descriptor infinite dimensional system are obtained in the sense of distributional solution.These general results are used to examine the exact controllability and exact observability of the Dzektser equation in the theory of seepage and the exact controllability of wave equation.

A nonlinear discrete integrable coupling system and its infinite conservation laws

We construct a nonlinear integrable coupling of discrete soliton hierarchy, and establish the infinite conservation laws （CLs） for the nonlinear integrable coupling of the lattice hierarchy. As an explicit application of the method proposed in the paper, the infinite conservation laws of the nonlinear integrable coupling of the Volterra lattice hierarchy are presented.

Optimality of Distributed Control for <i>n ×n</i>Hyperbolic Systems with an Infinite Number of Variables

In this paper, we study the existence of solutions for 2l order (n × n) cooperative systems governed by Dirichlet and Neumann problems involving hyperbolic operators with an infinite number of variables and with variable coefficients. The necessary and sufficient conditions for optimality of the distributed control with constraints are obtained and the set of inequalities that defining the optimal control of these systems are also obtained.

The Dynamics of an Impulsive Competitive System with Infinite Delay and Diffusion

In this paper, we consider an impulsive competitive system with infinite delay and diffusion. Firstly, on basis of inequality estimation techniques and comparison theorem of impulsive differential equations, we obtain some sufficient conditions for the permanence and extinction of the system. Then, we establish sufficient conditions for the globally attractive of the system by constructing appropriate Lyapunov function. Besides, under different impulsive conditions, we discuss the effect of time delay and diffusion on dynamic behavior of the competitive system.

Boundary Control Problems for 2 ×2 Cooperative Hyperbolic Systems with Infinite Order Operators

In this study, boundary control problems with Neumann conditions for 2 × 2 cooperative hyperbolic systems involving infinite order operators are considered. The existence and uniqueness of the states of these systems are proved, and the formulation of the control problem for different observation functions is discussed.

Distributed Control for <i>n</i>×<i>n</i>Cooperative Systems Governed by Hyperbolic Operator of Infinite Order

In this study, a distributed optimal control problem for n × n cooperative hyperbolic systems with infinite order operators and Dirichlet conditions are considered. The existence and uniqueness of the state of these systems are proved. The necessary and sufficient conditions for optimality of distributed control with constraints are found, and the set of equations and inequalities that defining the optimal control of these systems is also obtained. Finally, some examples for the control problem without constraints are given.

On the Total Dynamic Response of Soil-Structure Interaction System in Time Domain Using Elastodynamic Infinite Elements with Scaling Modified Bessel Shape Functions

This paper is devoted to a new approach—the dynamic response of Soil-Structure System (SSS), the far field of which is discretized by decay or mapped elastodynamic infinite elements, based on scaling modified Bessel shape functions are to be calculated. These elements are appropriate for Soil-Structure Interaction problems, solved in time or frequency domain and can be treated as a new form of the recently proposed elastodynamic infinite elements with united shape functions (EIEUSF) infinite elements. Here the time domain form of the equations of motion is demonstrated and used in the numerical example. In the paper only the formulation of 2D horizontal type infinite elements (HIE) is used, but by similar techniques 2D vertical (VIE) and 2D corner (CIE) infinite elements can also be added. Continuity along the artificial boundary (the line between finite and infinite elements) is discussed as well and the application of the proposed elastodynamical infinite elements in the Finite element method is explained in brief. A numerical example shows the computational efficiency and accuracy of the proposed infinite elements, based on scaling Bessel shape functions.

An Entanglement Criterion for States in Infinite Dimensional Bipartite Quantum Systems

In this paper, an entanglement criterion for states in infinite dimensional bipartite quantum systems is presented. We generalize some of separability criterion that was recently introduced by Wu and Anandan in (Phys. Lett. A, 2002, 297, 4-8) to infinite dimensional bipartite quantum systems. In addition, we give an example aimed to illustrate the application of the theorem.

Establishment of infinite dimensional Hamiltonian system of multilayer quasi-geostrophic flow & study on its linear stability

A multilayer flow is a stratified fluid composed of a finite number of layers with densities homogeneous within one layer but different from each other. It is an intermediate system between the single-layer barotropic model and the continuously stratified baroclinic model. Since this system can simulate the baroclinic effect simply, it is widely used to study the large-scale dynamic process in atmosphere and ocean. The present paper is concerned with the linear stability of the multilayer quasi-geostrophic flow, and the associated linear stability criteria are established. Firstly, the nonlinear model is turned into the form of a Hamiltonian system, and a basic flow is defined. But it cannot be an extreme point of the Hamiltonian function since the system is an infinite-dimensional one. Therefore, it is necessary to reconstruct a new Hamiltonian function so that the basic flow becomes an extreme point of it. Secondly, the linearized equations of disturbances in the multilayer quasi-geostrophic flow are derived by introducing infinitesimal disturbances superposed on the basic flows. Finally, the properties of the linearized system are discussed, and the linear stability criteria in the sense of Liapunov are derived under two different conditions with respect to certain norms.

Theories on the Propulsion System for Lithium-ion Battery Electric Vehicles with Infinite Cruising Range

On-board electric power generation in the absence of external energy may be sufficient to realize tough electric vehicles.The method to charge the Li-ion battery modules in the present investigation differs from the conventional single voltage source scheme in that the power requirement is only 12%of the power required for typical direct voltage applications.This method utilizes the ESI-PSC(electrostatic-induction potential-superposed electrolytic charge).The on-board electric power generation system is an identical twin of battery modules that function in ESI-PSC mode,in which the performance can be explained through consecutive cycles of field-induced charge and discharge between two batteries.When the charge of one battery is terminated,it becomes responsible for both the power to recharge the other battery and the power to drive the motor.This power generation system works with zero energy input,zero matter input and zero emission,without violating the laws of thermodynamics.The commercially available Li-ion battery modules and power control systems enable the realization of this type of EVs(electric vehicles).A simulation based on the official standard cruising mode(JCO08)showed that an electric vehicle with an on-board twin of 13.2 kWh energy capacity modules can travel 132 km before switching from charge to discharge.

Theoretical Propulsion System for Fuel Cell Vehicles with Infinite Cruising Range

The realization of a clean automobile society would require electrically-powered propulsion systems in vehicles.In recent years,electric vehicles have attracted considerable attention from the perspective of utilizing electricity generated from natural sources,such as solar and wind power.The propulsion method considered in the present investigation differs from the conventional off-board energy scheme in a manner such that pure stoichiometric H2/O2 fuels for fuel cells are generated on-board during vehicle operation.In this method,energy conversion occurs by means of ESI-PSE(electrostatic-induction potential-superposed electrolysis).If a quasi-static process is assumed,the theoretical power requirement to produce pure stoichiometric H2/O2 fuels is only 17%of the total energy required owing to a new method for supplying power to the EC(electrolytic cell).If an ESI-PSE EC is combined with a fuel cell(FC)to form an energy cycle,a HREG(hydrogen redox electric power generator)that uses solid PEMs(polymer electrolyte membranes)for the EC as well as the FC can be realized.According to calculations based on data from the operational conditions of commercially available ECs and FCs,more than 70%of the power delivered from the FC can be extracted for driving a motor constantly while a car is in motion.Because of energy self-sustainability on the HREG side,the power control system should not have any power loss.This propulsion system will realize tough vehicles that can continue running at a top speed at long unlimited cruising range.

Darboux transformation,infinite conservation laws,and exact solutions for the nonlocal Hirota equation with variable coefficients

This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation.Using zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation,along with the expression for N-soliton solutions.Influence of coefficients that are taken as a function of time instead of a constant,i.e.,coefficient functionδ(t),on the solutions is investigated by choosing the coefficient functionδ(t),and the dynamics of the solutions are analyzed.This article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations.The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.