20937522
Generalized Riccati equation expansion method and its application to the (3 + 1)-dimensional Jumbo-Miwa equation
Based on the computerized symbolic system Maple and a Riccati equation, a generalized Riccati equation expansion method for constructing soliton-like solutions of non-linear evolution equations (NEEs) is presented by a new general ansatz. The proposed method is more powerful than most of the existing tanh methods, the extended tanh-function method, the modified extended tanh-function method and generalized hyperbolic-function method. By use of the method, we not only can successfully recover the previously known formal solutions but also construct new and more general formal solutions for some NEEs. Making use of the method, we study the the (3+1)-dimensional Jumbo-Miwa equation and obtain rich new families of the exact solutions, including the non-travelling wave and coefficient functions' soliton-like solutions, singular soliton-like solutions, periodic form solutions.
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.
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.
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.
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.
135957559
Accelerated Publication: A resist for electric imprint lithography
An electrically curable resist has been developed that can make electric imprint lithography (EIL) a reality. The resist is composed of a diaryliodonium salt photo acid generator and a cycloaliphatic epoxy monomer. Its polymerization takes place when an electric potential is applied between a conductive imprint mold and a substrate which sandwich the resist. A proof-of-concept pattern transfer by EIL with a micron-scale resolution has been demonstrated.
17242205
On the (co)girth of a connected matroid
This article studies the girth and cogirth problems for a connected matroid. The problem of finding the cogirth of a graphic matroid has been intensively studied, but studies on the equivalent problem for a vector matroid or a general matroid have been rarely reported. Based on the duality and connectivity of a matroid, we prove properties associated with the girth and cogirth of a matroid whose contraction or restriction is disconnected. Then, we devise algorithms that find the cogirth of a matroid M from the matroids associated with the direct sum components of the restriction of M. As a result, the problem of finding the (co)girth of a matroid can be decomposed into a set of smaller sub-problems, which helps alleviate the computation. Finally, we implement and demonstrate the application of our algorithms to vector matroids.
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.
38431053
An Optimization Method Based on Chaotic Immune Evolutionary Algorithm
Immune Evolutionary Algorithm (IEA) is proposed on the shortages of evolution algorithm and biological immune mechanism. According to the characteristics of chaos, a novel Chaotic Immune Evolutionary Algorithm (CIEA) is presented which introduces chaos to IEA. The algorithm has the merits of chaos, immunity and evolutionary algorithm. It can ensure the ability of global search and local search and enhance the performances of the algorithm. At last, we analyze the efficiency of the algorithm with two typical optimization problems. The analysis result shows that CIEA converges quickly and effectively avoids the inherent problem that the evolution algorithm traps in immature convergence, so CIEA is an effective way to solve complex optimization problem.