21872537
A unified rational expansion method to construct a series of explicit exact solutions to nonlinear evolution equations
A unified basic frame of rational expansion methods is presented, which leads to closed-form solutions of nonlinear evolution equations (NLEEs). The new unified algorithms are given to find exact rational formal polynomial solutions of NLEEs in terms of Jacobi elliptic functions, solutions of the Riccati equation and solutions of the generalized Riccati equation. They can be implemented in symbolic computation system Maple. As applications of the methods, we choose some physical significance NLEEs to illustrate the methods. As a consequence, we not only can successfully obtain the solutions found by most existing Jacobi elliptic function methods and tanh methods, but also find other new and more general solutions at the same time.
5576433
New exact solutions for modified nonlinear dispersive equations mK(m, n) in higher dimensions spaces
With the use of some proper transformations and symbolic computation, we present a general and unified method for investigating the general modified nonlinear dispersive equations mK(m,n) in higher dimensions spaces. The work formally shows how to construct the general solutions and some special exact-solutions for mK(m,n) equations in higher dimensional spatial domains. The general solutions not only contain the solutions by Wazwaz [Math. Comput. Simulation 59 (2002) 519] but also contain many new compact and noncompact solutions.
205398011
Weierstrass semi-rational expansion method and new doubly periodic solutions of the generalized Hirota-Satsuma coupled KdV system
In the paper, with the aid of symbolic computation, we investigate the generalized Hirota-Satsuma coupled KdV system via our Weierstrass semi-rational expansion method presented recently using the rational expansion of Weierstrass elliptic function and its first-order derivative. As a consequence, three families of new Weierstrass elliptic function solutions via Weierstrass elliptic function P(Ξ;g2,g3) and its first-order derivative P'(Ξ;g2, g3). Moreover, the corresponding new Jacobi elliptic function solutions and solitary wave solutions are also presented, and when Ξ; → ∞, these solitary wave solutions approach to some constants.
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.
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.
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.
135614560
Gold nanohole arrays for biochemical sensing fabricated by soft UV nanoimprint lithography
We report on results of fabrication and optical characterisation of sub-250nm periodic gold nanohole arrays on glass by using UV nanoimprint lithography (UV-NIL) combined with both reactive ion etching (RIE) and Cr/Au lift-off processes. The transmission spectra of the fabricated nanohole gratings were measured for different hole diameters and periods. We also show preliminary results of chemical sensing after surface modification of the gold hole arrays. In agreement with the theoretical prediction, we found that any change in the dielectric index of the surrounding environment of the metallic array produces a transmission peak red shift.
28565174
Trust Evolution Policies for Security in Collaborative Ad Hoc Applications
The vision of pervasive computing has introduced the notion of a vast, networked infrastructure of heterogeneous entities interact through collaborative applications, e.g., playing a multi-player online game on the way to work. This will require interactions between users who may be marginally known or completely unknown to each other, or in situations where complete information is unavailable. This introduces the problem of assigning access rights to such marginally known or unknown entities. Explicit trust management has emerged as a solution to the problem of dealing with partial information about other users and the context in which the interaction takes place. We have implemented an access control mechanism based on the human notion of trust, where recommendations or initial participation in low risk interactions will allow entities to slowly build trust in each other. As the trust between two entities grows, interactions that entail a higher degree of risk may be allowed to proceed. We have used this mechanism in a simple role-based access control mechanism that uses trust to assign roles to users in a distributed blackjack card game application. This application allows us to experiment with different policies for trust-based admission control and trust evolution. In this paper we present an evaluation of policies specifying trust dynamics, which shows that our prototype reacts appropriately to the behaviour of other users and that the system updates trust values and implements admission policies in a manner similar to what would be expected from human trust assessment. This indicates that trust evolution policies can replace explicit human intervention in application scenarios that are similar to the evaluated prototype.
34540225
A Region-Based Image Enhancement Algorithm with the Grossberg Network
In order to enhance the contrast of an image, histogram equalization is wildly used. With global histogram equalization (GHE), the image is enhanced as a whole, and this may induce some areas to be overenhanced or blurred. Although local histogram equalization (LHE) acts adaptively to overcome this problem, it brings noise and artifacts to image. In this paper, a region-based enhancement algorithm is proposed, in which Grossberg network is employed to generate histogram and extract regions. Simulation results show that the image is obviously improved with the advantage of both GHE and LHE.
19656381
Target Recognition of FLIR Images on Radial Basis Function Neural Network
The study of small target recognition in low SNR (Signal Noise Ratio) is the key problem about processing of forward-looking infrared (FLIR) images information. Eight features of objects based on IR radiation characteristics and wavelet-based are presented. These features are used to a radial basis function (RBF) network as input for learning and classification. The propose recognition algorithm is invariant to the translation, rotation, and scale channel of a shape. Experiments by real infrared images and noisy images are performed, and recognition results show that the method is very effective.
20203347
RBF Kernel Based Support Vector Machine with Universal Approximation and Its Application
The SVM has been used to the nonlinear function mapping successfully, but the universal approximation property of the SVM has never been proved in theory. This paper proves the universal approximation of the SVM with RBF kernel to arbitrary functions on a compact set and deduces it to the approximation of discrete function. From simulation we can see that the RBF kernel based LS-SVM is more effective in nonlinear function estimation and can prevent the system from noise pollution, so it has high generalization ability.