Senior Recital, Binyan Xu, piano

VCU DEPARTMENT OF MUSIC SENIOR RECITAL Binyan Xu, piano Tuesday, November 24 at 4:00 p.m. Sonia Vlahcevic Concert Hall W. E. Singleton Center for the Performing Art

State control can result in good performance for firms

State firms are now hybrid organisations, say Ciprian Stan, David Ahlstrom, Mike W. Peng, Kehan Xu and Garry D. Bruto

Properties for Allocation Rules for Cooperative Games and Revenue Sharing Problems

Brink, J.R. van den [Promotor]Sun, H. [Promotor]Xu, G. [Copromotor

On fuzzy non-discrimination

We show that the incompatibility between the Pareto principle and the notion of non-discrimination as presented in Xu (2000) continues to hold when the individuals have exact preferences and the social preference relation is allowed to be a reflexive and transitive fuzzy binary relation. Our result can be seen as a strengthening of the result of Xu in two directions: (1) the range of the aggregation rule is enlarged and (2) a weaker condition on non-discrimination is used.fuzzy preferences

Approximation algorithms for Capacitated Facility Location Problem with Penalties

In this paper, we address the problem of capacitated facility location problem with penalties (CapFLPP) paid per unit of unserved demand. In case of uncapacitated FLP with penalties demands of a client are either entirely met or are entirely rejected and penalty is paid. In the uncapacitated case, there is no reason to serve a client partially. Whereas, in case of CapFLPP, it may be beneficial to serve a client partially instead of not serving at all and, pay the penalty for the unmet demand. Charikar et. al. \cite{charikar2001algorithms}, Jain et. al. \cite{jain2003greedy} and Xu- Xu \cite{xu2009improved} gave $3$, $2$ and $1.8526$ approximation, respectively, for the uncapacitated case . We present $(5.83 + \epsilon)$ factor for the case of uniform capacities and $(8.532 + \epsilon)$ factor for non-uniform capacities

The split decomposition of a tridiagonal pair

Let $K$ denote a field and let $V$ denote a vector space over $K$ with finite positive dimension. We consider a pair of linear transformations $A:V \to V$ and $A^*:V \to V$ that satisfy (i)--(iv) below: (i) Each of $A$, $A^*$ is diagonalizable. (ii) There exists an ordering $V_{0},V_{1},...,V_{d}$ of the eigenspaces of $A$ such that $A^* V_i \subseteq V_{i-1} + V_{i} + V_{i+1}$ for $0 \leq i \leq d$, where $V_{-1}=0$, $V_{d+1}=0$. (iii) There exists an ordering $V^*_{0},V^*_{1},...,V^*_{\delta}$ of the eigenspaces of $A^*$ such that $A V^*_i \subseteq V^*_{i-1} + V^*_{i} + V^*_{i+1}$ for $0 \leq i \leq \delta$, where $V^*_{-1}=0$, $V^*_{\delta+1}=0$. (iv) There is no subspace $W$ of $V$ such that both $AW \subseteq W$, $A^* W \subseteq W$, other than W=0 and $W=V$. We call such a pair a tridiagonal pair on $V$. In this note we obtain two results. First, we show that each of $A,A^*$ is determined up to affine transformation by the $V_i$ and $V^*_i$. Secondly, we characterize the case in which the $V_i$ and $V^*_i$ all have dimension one. We prove both results using a certain decomposition of $V$ called the split decomposition.Comment: 7 page