12162530
A new general algebraic method with symbolic computation to construct new doubly-periodic solutions of the (2 + 1)-dimensional dispersive long wave equation
For constructing more new exact doubly-periodic solutions in terms of rational form Jacobi elliptic function of nonlinear evolution equations, a new direct and unified algebraic method, named Jacobi elliptic function rational expansion method, is presented and implemented in a computer algebraic system. Compared with most of the existing Jacobi elliptic function expansion methods, the proposed method can be expected to obtain new and more general formal solutions. We choose a (2+1)-dimensional dispersive long wave equation to illustrate the method.
9624275
Exact analytical solutions to the nonlinear Schrödinger equation model
A method is developed for constructing a series of exact analytical solutions of the nonlinear Schrödinger equation model (NLSE) with varying dispersion, nonlinearity, and gain or absorption. With the help of symbolic computation, a broad class of analytical solutions of NLSE are obtained. From our results, many previous known results of NLSE obtained by some authors can be recovered by means of some suitable selections of the arbitrary functions and arbitrary constants. Further, the formation, interaction and stability of solitons have been investigated.
41322043
New exact travelling wave solutions for the shallow long wave approximate equations
Based upon a generally projective Riccati equation method, which is a direct and unified algebraic method for constructing more general form travelling wave solutions of nonlinear partial differential equations and implemented in a computer algebraic system, we consider the shallow long wave approximate equations. New and more general form solutions are obtained, including kink-shaped solitons, bell-shaped solitons, singular solitons and periodic solutions. The properties of the new formal solitary wave solutions are shown by some figures.
20461063
The function cascade synchronization approach with uncertain parameters or not for hyperchaotic systems
The function cascade synchronization scheme for the hyperchaotic systems is proposed to make the states of two identical the hyperchaotic systems both with and without uncertain parameters asymptotically synchronized. Based on Lyapunov stability theory and the proposed scheme, the Lu system and Chen hyperchaotic system with and without uncertain parameters are chosen to achieve the function cascade synchronization simultaneously. Numerical simulations are used to verify the effectiveness and feasibility of the presented control scheme.
27234161
Two-dimensional symmetry reduction of (2 + 1)-dimensional nonlinear Klein-Gordon equation
In this paper, one-dimensional optimal system of group invariant solutions of (2+1)-dimensional Klein-Gordon system is constructed. Then the classification of group invariant solutions is given out and the corresponding two-dimensional symmetry reduced equations are obtained. At last some symmetry transformations are gained in detail. Especially, we obtain the most general solution from a given solution by use of six variable one-parameter subgroups transformations.
18967560
Generalized Cascade Synchronization of Discrete-time Henon-like Map
This Letter addresses the generalized cascade synchronization problem of discrete-time hyperchaotic systems. By choosing a general kind of proportional scaling error functions and based on rigorous control theory, we take the discrete-time Henon-like map as a example to achieve the generalized cascade synchronization. Numerical simulations are used to show the effectiveness of the proposed technique.
43007315
The impact of smart disks and spatial reuse property on RAID-5 storage systems
RAID storage systems using SCSI and traditional disk drives cannot meet the growing demand of new I/O intensive applications. New technologies such as smart disks and SSA are being proposed to improve the performance, scalability, and reliability of RAID systems. The objective of this work is to investigate the impact of smart disks and SSA's spatial reuse property on the performance of RAID-5 storage systems. In order to perform this work, we have enhanced CMU's RAIDframe simulator so that it accurately models the overhead of current SCSI and SSA protocols, and we have created smart disk models which include on-drive XOR logic and on-drive caches. We observe that neither smart disks alone nor spatial reuse property alone has much impact on RAID system performance. However, if smart disks and spatial reuse property are properly used in combination, RAID-5 system performance and scalability can be further enhanced. In particular, we propose a parity caching approach to improve the performance of small writes.
40372820
Mining circumstance-oriented association rules using singular value decomposition technique
Association rule has evolved from the primitive form of single dimension intratransaction to the form of multi-dimension intertransaction. The challenge for mining multi-dimension intertransaction rules is the formidable search space. Researchers have proposed various methods to handle this problem, such as restricting the number of dimensions, confining search space in a small window, etc. These methods unavoidably have negative impact on mining result and they are less effective when the number of dimensions and the length of rule are really large. Moreover, all these methods are derived from the a priori algorithm and have common weaknesses: time consuming and redundancy caused by the iterative nature of the a priori algorithm. To approach this problem from a different angle, we propose to use the singular value decomposition technique (SVD). With SVD, the multi-dimension intertransaction rules can be easily identified.
12297104
CoStore: a reliable and highly available storage system using clusters
The CoStore cluster architecture is proposed to construct a reliable and highly available storage system. A prototype CoStore was implemented and its performance was measured with the cluster being mirrored in various network environments. The preliminary results demonstrate that there is little impact on performance if the cluster is mirrored in efficient campus network environments with high bandwidth and low latency. As a result the CoStore architecture considerably reinforces a storage system's preparedness for disaster recovery without sacrificing performance.
16724396
Weighted Rough Graph and Its Application
Rough graph is the graph that can be used to research uncertainty problems, and it is a new research tool to analyze the rough characteristic of the system according to Tong He and Kaiquan Shi. This paper makes further research on rough graph, and gives the definitions of class connection of rough graph and some subgraphs of rough graph. Furthermore, this paper presents the definition of weighted rough graph by enduing the edges of rough graph with weight attribute, and gives the algorithm of exploring the class optimal tree in weighted rough graph, which generalizes the classical Kruskal algorithm of exploring the optimal tree. Finally, the application in relationship analysis shows the effectiveness of the algorithm
206370432
An accurate sampling-based method for approximating geometry
We present a sampling-based method for approximating the boundary of a geometry defined by various geometric operations. Based on a novel adaptive sampling condition, we first construct volumetric grids such that an error-minimizing point can be found in each cell to capture all the geometric objects inside the cell. We then construct a polygonal model from the grid. We guarantee the boundary approximation has the same topology as the exact surfaces, and the maximum approximation error from the exact surfaces is bounded by a user specified tolerance. Our method is robust and easy to implement. We have applied it in various applications such as remeshing of polygonal models, Boolean operations, and offsetting operations. We report experimental results on a variety of CAD models.