INTEGRABILITY AND LINEARIZABILITY FOR A CLASS OF CUBIC KOLMOGOROV SYSTEMS

The integrability and linearizability for a class of cubic Kolmogorov systems are studied. A recursive formula to compute the saddle quantities of the systems is deduced firstly, and integrable conditions for the systems are obtained. Then a recursive formula to compute the coefficients of the normal form for saddle points of the systems is also applied. Finally linearizable conditions of the origin for the systems are given. Both formulas to find necessary conditions are all linear and readily done using computer algebra system such as Mathematica or Maple, and some good methods are given to obtain the sufficient conditions.

THE FOKAS-LENELLS EQUATION ON THE FINITE INTERVAL

Using the Fokas unified method, we consider the initial boundary value problem for the Fokas-Lenells equation on the finite interval. We present that the Neumann boundary data can be explicitly expressed by Dirichlet boundary conditions prescribed, and extend the idea of the linearizable boundary conditions for equations on the half line to Pokas-Lenells equation on the finite interval.

Fault-tolerant precise data access on distributed log-structured merge-tree

Log-structured merge tree has been adopted by many distributed storage systems. It decomposes a large database into multiple parts: an in?writing part and several read-only ones. Records are firstly written into a memoryoptimized structure and then compacted into in-disk struc? tures periodically. It achieves high write throughput. However, it brings side effect that read requests have to go through multiple structures to find the required record. In a distributed database system, different parts of the LSM-tree are stored in distributed fashion. To this end, a server in the query layer has to issues multiple network communications to pull data items from the underlying storage layer. Coming to its rescue, this work proposes a precise data access strategy which includes: an efficient structure with low maintaining overhead designed to test whether a record exists in the in?writing part of the LSM-tree;a lease-based synchronization strategy proposed to maintain consistent copies of the structure on remote query servers. We further prove the technique is capable of working robustly when the LSM-Tree is re?organizing multiple structures in the backend. It is also fault-tolerant, which is able to recover the structures used in data access after node failures happen. Experiments using the YCSB benchmark show that the solution has 6x throughput improvement over existing methods.

Classification of discrete equations linearizable by point transformation on a square lattice

We provide a complete set of linearizability conditions for nonlinear partial difference equations defined on four points and, using them, we classify all linearizable multilinear partial difference equations defined on four points up to a MSbious transformation.