Exact Internal Controllability and Synchronization for a Coupled System of Wave Equations

In this paper the exact internal controllability for a coupled system of wave equations with arbitrarily given coupling matrix is established.Based on this result,the exact internal synchronization and the exact internal synchronization by p-groups are successfully considered.

Strong (Weak) Exact Controllability and Strong (Weak) Exact Observability for Quasilinear Hyperbolic Systems

In this paper,the authors define the strong (weak) exact boundary controllability and the strong (weak) exact boundary observability for first order quasilinear hyperbolic systems,and study their properties and the relationship between them.

On the polynomiality and asymptotics of moments of sizes for random(n,dn ± 1)-core partitions with distinct parts

Amdeberhan’s conjectures on the enumeration,the average size,and the largest size of(n,n+1)-core partitions with distinct parts have motivated many research on this topic.Recently,Straub(2016)and Nath and Sellers(2017)obtained formulas for the numbers of(n,dn-1)-and(n,dn+1)-core partitions with distinct parts,respectively.Let X_(s,t) be the size of a uniform random(s,t)-core partition with distinct parts when s and t are coprime to each other.Some explicit formulas for the k-th moments E[X_(n,n+1)^(k)]and E[X_(2 n+1,2 n+3)^(k)]were given by Zaleski and Zeilberger(2017)when k is small.Zaleski(2017)also studied the expectation and higher moments of X_(n,dn-1) and conjectured some polynomiality properties concerning them in ar Xiv:1702.05634.Motivated by the above works,we derive several polynomiality results and asymptotic formulas for the k-th moments of X_(n,dn+1) and X_(n,dn-1) in this paper,by studying theβ-sets of core partitions.In particular,we show that these k-th moments are asymptotically some polynomials of n with degrees at most 2 k,when d is given and n tends to infinity.Moreover,when d=1,we derive that the k-th moment E[X_(n,n+1)^(k)]of X_(n,n+1) is asymptotically equal to(n^(2)/10)^(k)when n tends to infinity.The explicit formulas for the expectations E[X_(n,dn+1)]and E[X_(n,dn-1)]are also given.The(n,dn-1)-core case in our results proves several conjectures of Zaleski(2017)on the polynomiality of the expectation and higher moments of X_(n,dn-1).

On the Synchronizable System

In this paper,the synchronizable system is defined and studied for a coupled system of wave equations with the same wave speed or with different wave speeds.

Uniqueness of Solution to Systems of Elliptic Operators and Application to Asymptotic Synchronization of Linear Dissipative Systems Ⅱ: Case of Multiple Feedback Dampings

In this paper,the authors consider the asymptotic synchronization of a linear dissipative system with multiple feedback dampings.They first show that under the observability of a scalar equation,Kalman’s rank condition is sufficient for the uniqueness of solution to a complex system of elliptic equations with mixedobservations.The authors then establish a general theory on the asymptotic stability and the asymptotic synchronization for the corresponding evolutional system subjected to mixed dampings of various natures.Some classic models are presented to illustrate the field of applications of the abstract theory.

Multilevel Preconditioners for the Interior Penalty Discontinuous Galerkin Method II-Quantitative Studies

This paper is concerned with preconditioners for interior penalty discontinuous Galerkin discretizations of second-order elliptic boundary value problems.We extend earlier related results in[7]in the following sense.Several concrete realizations of splitting the nonconforming trial spaces into a conforming and(remaining)nonconforming part are identified and shown to give rise to uniformly bounded condition numbers.These asymptotic results are complemented by numerical tests that shed some light on their respective quantitative behavior.