Module Structure on Invariant Jacobians

In this paper we show that a conjecture of Stephen Yau on highest weights of invariant Jacobians is true for arbitrary connected semisimple algebraic groups.Comment: 3 page

Sign changes of Kloosterman sums with almost prime moduli

We prove that the Kloosterman sum $S(1,1;c)$ can change sign infinitely often as $c$ runs over squarefree moduli with at most 10 prime factors, which improves the previous results of E. Fouvry and Ph. Michel, J. Sivak-Fischler and K. Matom\"{a}ki, replacing 10 by 23, 18 and 15, respectively. The method combines the Selberg sieve, equidistribution of Kloosterman sums and spectral theory of automorphic forms.Comment: 18 pages, to appear in Monatshefte f\"ur Mathemati

A New Proof for Classification of Irreducible Modules of a Hecke Algebra of Type An A_n

In this paper we give a new proof for the classification of irreducible modules of an affine Hecke algebra of type $A_n$, which was obtained by G. E. Murphy in 1995.Comment: 9 page

J2EE application for clustered servers : focus on balancing workloads among clustered servers : a thesis presented in partial fulfilment of the requirements for the degree of Master of Information Science in Computer Science at Massey University, Albany, New Zealand

J2EE has become a de facto platform for developing enterprise applications not only by its standard based methodology but also by reducing the cost and complexity of developing multi-tier enterprise applications. J2EE based application servers keep business logic separate from the front-end applications (client-side) and back-end database servers. The standardized components and containers simplify J2EE application design. The containers automatically manage the fundamental system level services for its components, which enable the components design to focus on the business requirement and business logic. This study applies the latest J2EE technologies to configure an online benchmark enterprise application - MG Project. The application focuses on three types of components design including Servlet, entity bean and session bean. Servlets run on the web server Tomcat, EJB components, session beans and entity beans run on the application server JBoss and the database runs on the database server Postgre SQL. This benchmark application is used for testing the performance of clustered JBoss due to various load-balancing policies applied at the EJB level. This research also focuses on studying the various load-balancing policies effect on the performance of clustered JBoss. As well as the four built-in load-balancing policies i.e. First Available, First Available Identical All Proxies, Random Robin and Round Robin, the study also extend the JBoss Load balance Policy interface to design two dynamic load-balancing policies. They are dynamic and dynamic weight-based load-balancing policies. The purpose of dynamic load-balancing policies design is to ensure minimal response time and obtain better performance by dispatching incoming requests to the appropriate server. However, a more accurate policy usually means more communications and calculations, which give an extra burden to a heavily loaded application server that can lead to drops in the performance