This paper studies an initial-boundary-value problem (IBVP) of the Korteweg-de Vries equation posed on a finite interval with general nonhomogeneous boundary conditions. Using the strong Kato smoothing property of the associated linear problem, the IBVP is shown to be locally well-posed in the space $H^s (0,1)$ for any $s\geq0$ via the contraction mapping principle.

Concepts revolving around "displaced cones" are used to extend the ideas of nondominated solutions in multiobjective programming. Necessary and sufficient conditions are formed around the additive models of DEA to idelltify nondominated solutions. This provdes a basis for effecting contacts with other disciplines and other parts of DEA.

The skewness of the return distribution is one of the important features of the security price. In this paper, the authors try to explore the relationship between the skewness and the coefficient of risk premium. The coefficient of the risk premium is estimated by a GARCH-$M$ model, and the robust measurement of skewness is calculated by Groeneveld-Meeden method. The empirical evidences for the composite indexes from 33 securities markets in the world indicate that the risk compensation requirement in the market where the return distribution is positively skewed is virtually zero, and the risk compensation requirement is positive in a significant level in the market where the return distribution is negative skewed. Moreover, the skewness is negatively correlated with the coefficient of the risk premium.

Wireless sensor networks promise a new paradigm for gathering data via collaboration among sensors spreading over a large geometrical region. Many applications impose delay requirements for data gathering and ask for time-efficient schedules for aggregating sensed data and sending to the data sink. In this paper, the authors study the minimum data aggregation time problem under collision-free transmission model. In each time round, data sent by a sensor reaches all sensors within its transmission range, but a sensor can receive data only when it is the only data that reaches the sensor. The goal is to find the method that schedules data transmission and aggregation at sensors so that the time for all requested data to be sent to the data sink is minimal. The authors propose a new approximation algorithm for this NP-hard problem with guaranteed performance ratio $\frac{7\Delta}{\log_2{|\mathsf S|}}+c$, which significantly reduces the current best ratio of $\Delta-1$, where $\mathsf S$ is the set of sensors containing source data, $\Delta$ is the maximal number of sensors within the transmission range of any sensor, and $c$ is a constant. The authors also conduct extensive simulation, the obtained results justify the improvement of proposed algorithm over the existing one.

In this paper, we use the solutions of forward-backward stochastic differential equations to get the explicit form of the optimal control for linear quadratic stochastic optimal control problem and the open-loop Nash equilibrium point for nonzero sum differential games problem. We also discuss the solvability of the generalized Riccati equation system and give the linear feedback regulator for the optimal control problem using the solution of this kind of Riccati equation system.

By handling the travel cost function artfully, the authors formulate the transportation mixed network design problem (MNDP) as a mixed-integer, nonlinear bilevel programming problem, in which the lower-level problem, comparing with that of conventional bilevel DNDP models, is not a side constrained user equilibrium
assignment problem, but a standard user equilibrium assignment problem. Then, the bilevel programming model for MNDP is reformulated as a continuous version of bilevel programming problem by the continuation method. By virtue of the optimal-value
function, the lower-level assignment problem can be expressed as a nonlinear equality constraint. Therefore, the bilevel programming model for MNDP can be transformed into an equivalent single-level optimization problem. By exploring the inherent nature of the MNDP, the optimal-value function for the lower-level equilibrium assignment problem is proved to be continuously differentiable and its functional value and gradient can be obtained efficiently. Thus, a continuously differentiable but still nonconvex optimization formulation of the MNDP is created, and then a locally convergent algorithm is proposed by applying penalty function method. The inner loop of solving the subproblem is mainly to implement an all-or-nothing assignment. Finally, a small-scale transportation network and a large-scale network are presented to verify the proposed model and algorithm.

The main purpose of this paper is to overview some recent methods and results on controllability/observability problems for systems governed by partial differential equations. First, the authors review the theory for linear partial differential equations, including the iteration method for the null controllability of the
time-invariant heat equation and the Rellich-type multiplier method for the exact controllability of the time-invariant wave equation, and especially a unified controllability/observability theory for parabolic and hyperbolic equations based on a global Carleman estimate. Then, the authors present sharp global controllability
results for both semi-linear parabolic and hyperbolic equations, based on linearization approach, sharp observability estimates for the corresponding linearized systems and the fixed point argument. Finally, the authors survey the local null controllability result for a class of quasilinear parabolic equations based on the global Carleman estimate, and the local exact controllability result for
general hyperbolic equations based on a new unbounded perturbation technique.

This paper investigates the structures and properties of one-Lee weight codes and two-Lee weight projective codes over Z4. The authors first give the Pless identities on the Lee weight of linear codes over Z4. Then the authors study the necessary conditions for linear codes to have one-Lee weight and two-Lee projective weight respectively, the construction methods of one-Lee weight and two-Lee weight projective codes over Z4 are also given. Finally, the authors recall the weight-preserving Gray map from (Zn4 , Lee weight) to (F2n 2 , Hamming weight), and produce a family of binary optimal oneweight linear codes and a family of optimal binary two-weight projective linear codes, which reach the Plotkin bound and the Griesmer bound.

A method of verifying the viability criterion at a given point for a region with nonsmooth boundary, which is expressed by a quasidifferentiabl function, under a differential inclusion which is a convex hull of finitely many functions, is proposed. By this method, determining the viability is transformed into solving
a number of systems of linear inequalities, or equivalently solving a number of linear programming problems. For the other differential inclusion, called the generalized convex process, it is shown that viability condition holds for a polytope if and only if it holds at all of its vertices. This result is an extension of
corresponding one for a linear control system.

This paper presents a general solution procedure and an interactive fuzzy satisfying method for a kind of fuzzy multi-objective linear programming-problems based on interval valued fuzzy sets. Firstly, a fuzzy set of the fuzzy solutions, which can be focused on providing complete information for the final decision,can be obtained by the proposed tolerance analysis of a non-dominated set.

An $M/G/1$ retrial queue with a first-come-first-served (FCFS) orbit, general retrial time, two-phase service and server breakdown is investigated in this paper. Customers are allowed to balk and renege at particular times. Assume that the customers who find the server busy are queued in the orbit in accordance with an
FCFS discipline. All customers demand the first ``essential" service, whereas only some of them demand the second ``optional" service, and the second service is multi-optional. During the service, the server is subject to breakdown and repair. Assume
that the retrial time, the service time, and the repair time of the server are all arbitrarily distributed. By using the supplementary variables method, the authors obtain the steady-state solutions for both queueing and reliability measures
of interest.

The type of problem under consideration is $$ \left\{ \begin{array}{ll} u_{t}=\nabla(a(u)b(x)\nabla u)+g(x,q,t)f(u)&$in$ \ D\!\times\!(0,T),\\[1mm] \displaystyle u=0 \ $on$ \ {\it \Gamma}_1\!\times\!(0,T),~ \ \displaystyle \frac{\partial u}{\partial n}+\sigma(x,t)u=0 \ $on$ \ {\it\Gamma}_2\!\times\!(0,T), &{\it \Gamma}_1\!\cup\!{\it \Gamma}_2\!=\!\partial\!D,\\[2mm] u(x,0)=u_0(x)\geq0, \ \not\equiv0&$in$ \ {\overline D}, \end{array} \right. $$ where $D$ is a smooth bounded domain of $R^N, \ q\!=\!|\nabla\!u|^2.$ By constructing an auxiliary function and using Hopf's maximum principles on it, existence theorems of blow-up solutions, upper bound of ``blow-up time" and upper estimates of ``blow-up rate" are given under suitable assumptions on $a, b, f, g, \sigma$ and initial date $u_0(x).$ The obtained results are applied to some examples in which $a, b, f, g$ and $\sigma$ are power functions or exponential functions.

In this paper, a new approach is successfully addressed to design the state-feedback adaptive stabilizing control law for a class of high-order nonlinear systems in triangular form and with unknown and nonidentical control coefficients, whose stabilizing control has been investigated recently under the knowledge that the lower bounds of the control coefficients are exactly known. In the present paper, without any knowledge of the lower bounds of the control coefficients, based on the adaptive technique and appropriately choosing design parameters, we give the recursive design procedure of the stabilizing control law by utilizing the approach of adding a power integrator together with tuning functions. The state-feedback adaptive control law designed not only preserves the equilibrium at the origin, but also guarantees the global asymptotic stability of the closed-loop states and the uniform boundedness of all the other closed-loop signals.

We study a class of discounted models of singular stochastic control. In this kind of models, not only the structure of cost function has been extended to some general type, but also the state can be represented as the solution of a class of stochastic differential equations with nonlinear drift and diffusion term. By the various methods of stochastic analysis, we derive the sufficient and necessary conditions of the existence of optimal control.

In this paper, we investigate the global controllability of a class of $n$-dimensional affine nonlinear systems with $n-1$ controls and constant control matrix. A necessary and sufficient condition for its global controllability has been obtained by
using the methods recently developed. Furthermore, we generalize the above result to a class of affine nonlinear systems with a block-triangular-like structure. Finally, we will give three examples to show the applications of our results.

The limit inguages of cellular automata are defined and their complexity are discussed. New tools, which include skew evolution, skew periodic string, trace string, some algebraic calculation method, and restricted membership problem, are developed through a discussion focusing on the limit language of an elementary cellular automata of rule 94.

In this paper, a new modified BFGS method without line searches is proposed. Unlike traditional BFGS method, this modified BFGS method is proposed based on the so-called fixed steplength strategy introduced by Sun and Zhang. Under some suitable assumptions, the global convergence and the superlinear convergence of the new algorithm are established, respectively. And some preliminary numerical experiments, which shows that the new Algorithm is feasible, is also reported.

In this paper we discuss the logarithmic Sobolev inequalities in Besov spaces, and show their applications to the blow-up criterion of smooth solutions to the incompressible magneto-hydrodynamics equations.

In this paper, we study the periodic boundary value problems for a class ofnonlinear integro-differential equations of Volterra type with Caratheodory condition. Weobtain an existence result of generalized solutions between generalized upper and lowersolutions, and develop the monotone iterative technique to find generalized extremal solutions as limits of monotone sequences.

In this paper, control design is investigated for hard disk
drives in mobile applications with unknown external arbitrarily
fast time-varying disturbances. The disturbances can be estimated
with exponential accuracy using the proposed disturbance observer
based on a series of integral filters. The position error signal
will converge to zero with the proposed control technique for
systems subjected to the unknown disturbances. The effectiveness
of the proposed method is demonstrated by extensive simulation
studies.

To control continuous-time uncertain dynamical systems with sampled data-feedback is prevalent today, but the sampling rate is usually not allowed to be arbitrarily fast due to various physical nd/or computational constrains. In this paper, the authors examine the limitations of sampled-data feedback control for a class of uncertain systems in continuous-time, with sampling rate not necessary fast enough and with the unknown system structure confined to a set of functions with both linear and onlinear growth. The limitations of the sampled-data feedback control for the uncertain systems are established quantitatively, which extends the existing related results in the literature.

In the past there were a lot of researches on the topic of economic growth. Nevertheless, the environment has been a. hit abstracted by standard economics. Scarce natural resources and our choices to protect them or exploit them jointly determine the economic and environmental systems. In this paper we describe a model with a particular focus on the relationship among income, pollution, and non-renewable resources. We want to combine both economic and environmental sectors. The system dynamics approach is used in analyzing these complex relationships. This paper gives an insight, into the possibilities for replacing non-renewable resources with more renewable ones. Next, we present the simulation runs of the model that are conducted with the help of existing system dynamics modeling tools. Only the relationships simulated so far between the variables ought to lie put under yet more cautious examination.

Over the past two decades, structural decomposition analysis (SDA) has developed into a major analytical tool in the field of input-output (IO) techniques, but the method was found to suffer from one or more of the following problems. The decomposition forms, which are used to measure the contribution of a specific determinant, are not unique due to the existence of a multitude of equivalent forms, irrational due to the weights of different determinants not matching, inexact due to the existence of large interaction terms. In this paper, a decomposition method is derived to overcome these deficiencies, and we prove that the result of this approach is equal to the Shapley value in cooperative games, and so some properties of the method are obtained. Beyond that, the two approaches that have been used predominantly in the literature have been proved to be the approximate solutions of the method.

A full characterization is given, in terms of the resolvent R(λ; A) of the infinitesimal generator A of a C0 semigroup T(t) on a Hilbert spaced which assures the continuity for t > t0 (t0 0) of T(t) in the uniform operator topology.

This work is concerned with switching diffusion
processes, also known as
regime-switching diffusions.
Our attention focuses on regularity, recurrence, and positive recurrence
of the underlying stochastic processes. The main effort is devoted to
obtaining easily verifiable conditions for the aforementioned
properties. Continuous-state-dependent jump processes are considered.
First general criteria on regularity and recurrence using Liapunov
functions are obtained. Then we focus on a class of problems, in
which
both the drift and the diffusion
coefficients are ``linearizable" with respect to the continuous
state, and suppose that the generator of the jump part of the
process can be approximated by a generator of an ergodic Markov
chain. Sufficient conditions for regularity, recurrence, and
positive recurrence are derived, which are
linear combination of the averaged coefficients (averaged with
respect to the stationary measure of the Markov chain).

In linear regression model, the influence on the regression coefficients has beed paid great attention and other aspects such as the influence on confidence regions have also been studied. However, influence on F-test in linear regression model received few xonsideration.

This paper investigates the problem of adaptive practical
tracking control by output feedback for a class of nonlinear
systems in which the nonlinearities are restricted to be upper
bounded by a constant plus a polynomial function of the output
multiplied by unmeasured states. To solve the problem, an observer
with a dynamic high-gain is first introduced, and then an adaptive
output feedback tracking controller is successfully designed using
the universal control methodology. It is shown that all the states
of the closed-loop system are bounded, and the tracking error can
be made arbitrarily small by an appropriate choice of the design
parameters after some large enough time. A simulation example is
also provided to illustrate the correctness of the theoretical
results.

In this paper the management model a two-species fishery involving impulses is investigated by using optimal impulsive control theorem. Optimal impulsive harvesting times and the corresponding optimal harvesting population levels in different cases are obtained.

The main purpose of this paper is to study a problem related to Golomb's conjectures, and give an interesting asymptotic formula.

As an research example of the widely existing cooperation-competition systems, the authors present an empirical investigation on a fruit nutritive factor network. It is described by a node-weighted bipartite graph. The fruit nutritive factors are defined as the nodes, and two nodes are connected by an edge if at least one fruit contains
these two nutritive factors. The fruits are defined as the collaboration acts. The node-weight $W_{nt}$, which signifies the ``importance degree'' of each actor node, is defined as the content of a nutritive factor in a fruit. The empirical investigation results show some unique features. The node-weight distributions take so-called ``shifted power law" function forms, but the act-weight distribution takes a normal form. The
degree and act-degree distributions show impulsive-spectrum like forms. These observations may be helpful for the study of fruits. The network description method proposed in this article may be universal for a kind of cooperation-competition systems.

For the discrete dynamical system on the nonnegative orthant generated bya cooperative and concave map T, we present an algebraic criterion of its asymptotic behavior. The global behavior of such a system is completely determined by the sign of all principal minors of the matrix I-DT(0). This criterion applies to the cooperative systemwhich is concave, time-dependent and periodic in t. We give the sufficient conditions that the zero solution of such a system is globally asymptotically stable and that it possesses anonzero periodic solution which attracts all initial conditions in the nonnegative orthant, except at the origin. The results of Smith under weaker conditions and some applications are included.

The concepts of logically constrained overall systems and subsystems of recon-structability analysis are introduced. Then the paper gave an important basis for furtherresearches of the author-the sufficient conditions for their structural representation graphsto become Boolean lattices, and proved it.

This paper presents a new look on emergence from the aspect of locality and globality of evaluation functions for solving traditional computer problems. We first translate the Constraint Satisfaction Problem (CSP) into the multi-agent system, and then show how a global solution emerges from the system in which every agent uses a local evaluation function to decide its action, while comparing to other traditional algorithms, such as Local search and Simulated Annealing which use global evaluation functions. We also give some computer experimental results on large-scale JV-queen problems and k-Coloring problems, and show that emergence only depends on problem instance, not details of agent settings, i.e. in some CSPs, the system can self-organize to a global solution, but can not in some other CSPs no matter what settings of agents have.

The stabilization problem of a nonuniform Timoshenko beam system with controllers at the beam's right tip with rotor inertia is studied. First, with a special kind of linear boundary force feedback and moment control existing simultaneously, the energy corresponding to the closed loop system is proven to be exponentially convergent to zero as time $t\to\infty$. Then in other cases, some conditions for the corresponding closed loop system to be asymptotically stable are also derived.

In this paper, we derive a lattice model for a single species on infinite patches of one-dimensional space with that the maturation could occur at any age. The formulation involves a distribution of possible ages of maturation and a probability density function on which ecological assumptions are made. The following results are obtained: the existence and isotropy of the unique nonnegative solution for initial value problem, the extinction of the species provided with the non-existence of positive equilibria, and the existence of wavefronts with the wave speed $c>c_*$.

The authors study decay properties of solutions for a viscoelastic wave equation with variable coefficients and a nonlinear boundary damping by the differential geometric approach.

In this paper, the linear mixed finite element method is considered for the biharmonic Dirichlet boundary value problem. Almost optimal error estimates, superconvergence estimates and the derivative error expansion are obtained.

In this paper, two new dual models of nonsmooth multiobjective programming are constructed and two duality results are derived.

Based on the notion of maximal absolute observability and its normalforms, a new method for studying the local stabilization for a kind of nonlinearcontrol systems is established. Different from the previous results given by Byrnes-Isitori and others, this new method can deal with more general systems, and has much simpler way to prove the stabilization conditions and to design the feedback laws.

This paper studies identification of systems in which the
system output is quantized, transmitted through a digital
communication channel, and observed afterwards. The concept of the
CR Ratio is introduced to characterize impact of communication
channels on identification. The relationship between the CR Ratio
and Shannon channel capacity is discussed. Identification
algorithms are further developed when the channel error
probability is unknown.