New Multiple Soliton-like Solutions to （3＋1）-Dimensional Burgers Equation with Variable Coefficients

A new generalized tanh function method is used for constructing exact travelling wave solutions of nonlinear partial differential equations in a unified way. The main idea of this method is to take full advantage of the Riccati equation, which has more new solutions. More new multiple soliton-like solutions are obtained for the (3+ 1 )-dimensional Burgers equation with variable coefficients.

Some New Exact Solutions to the Dispersive Long－Wave Equation in（2＋1）－Dimensional Spaces

In this paper, by using a further extended tanh method- and symbolic computation system, some new soliton-like and period form solutions of the dispersive long-wave equation in (2+l )-dimensional spaces are obtained.

Symbolic Computation and Construction of Soliton－Like Solutions to the（2＋l）－Dimensional Breaking Soliton Equation

Based on the computerized symbolic system Mapte, a new generalized expansion method of Riccati equation for constructing non-travelling wave and coefficient functions' soliton-like solutions is presented by a new general ansatz. Making use of the method, we consider the (2+1)-dimensional breaking soliton equation, ut + buxxy + 4buvx+4buxv = O,uv=vx, and obtain rich new families of the exact solutions of the breaking sofiton equation, including then on-traveilin~ wave and constant function sofiton-like solutions, singular soliton-like solutions, and triangular function solutions.

A New Generalization of Extended Tanh—Function Method for Solving Nonlinear Evolution Equations

Making use of a new generalized ans?tze and a proper transformation, we generalized the extended tanh-function method. Applying the generalized method with the aid of Maple, we consider some nonlinear evolution equations. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods. More importantly, for some equations, we also obtain other new and more general solutions at the same time. The results include kink-profile solitary-wave solutions, bell-profile solitary-wave solutions, periodic wave solutions, rational solutions, singular solutions and new formal solutions.

Positive Periodic Solutions of Nonlinear Second Order Ordinary Differential Equations

This paper discusses the problem of positive periodic solutions for a class of nonlinearsecond order ordinary differential equations. By utilizing a fixed point theorem on cone, some exist-ence and multiplicity results of positive periodic solutions are derived. Our results improve theoremsin the literature.

New Exact Travelling Wave Solutions for Generalized Zakharov-Kuzentsov EquationsUsing General Projective Riccati Equation Method

Applying the generalized method, which is a direct and unified algebraic method for constructing multipletravelling wave solutions of nonlinear partial differential equations (PDEs), and implementing in a computer algebraicsystem, we consider the generalized Zakharov-Kuzentsov equation with nonlinear terms of any order. As a result, wecan not only successfully recover the previously known travelling wave solutions found by existing various tanh methodsand other sophisticated methods, but also obtain some new formal solutions. The solutions obtained include kink-shapedsolitons, bell-shaped solitons, singular solitons, and periodic solutions.

Baecklund Transformation and Exact Solutions for a New Generalized Zakharov—Kuzentsov Equation with Nonlinear Terms of Any Order

In this paper,with the help of symbolic computation,a new Backlund transformation(BT)for a new generalized Zakharov-Kuznetsov equation with nonlinear term of any order,ut+aupux+bu2pux+γuxy+δuxxx+ρuxyy=0,is obtained by using the homogeneous balance method.Based on the BT,some exact solutions are presented.

A flower image retrieval method based on ROI feature

Flower image retrieval is a very important step for computer-aided plant species recognition. In this paper, we propose an efficient segmentation method based on color clustering and domain knowledge to extract flower regions from flower images. For flower retrieval, we use the color histogram of a flower region to characterize the color features of flower and two shape-based features sets, Centroid-Contour Distance (CCD) and Angle Code Histogram (ACH), to characterize the shape features of a flower contour. Experimental results showed that our flower region extraction method based on color clustering and domain knowledge can produce accurate flower regions. Flower retrieval results on a database of 885 flower images collected from 14 plant species showed that our Region-of-Interest (ROI) based retrieval approach using both color and shape features can perform better than a method based on the global color histogram proposed by Swain and Ballard (1991) and a method based on domain knowledge-driven segmentation and color names proposed by Das et al.(1999).

On a New Modified Extended Tanh—Function Method

In this paper, a new modified extended tanh-function method is presented for constructing multiple soliton-like, periodic form and rational solutions of nonlinear evolution equations (NLEEs). This method is more powerful thanthe extended tanh-function method [Phys. Lett. A277 (2000) 212] and the modified extended tanh-function method[Phys. Lett. A299 (2002) 179] Abundant new solutions of two physically important NLEEs are obtained by using thismethod and symbolic computation system Maple.

A Series of Soliton-like and Double-like Periodic Solutions of a （2＋1）-Dimensional Asymmetric Nizhnik-Novikov-Vesselov Equation

We generalize the algebraic method presented by Fan [J. Phys. A: Math. Gen. 36 (2003) 7009)] to uniformly construct a series of soliton-like solutions and double-like periodic solutions for nonlinear partial differential equations(NPDE). As an application of the method, we choose a (2+1)-dimensional asymmetric Nizhnik-Novikov-Vesselov equation and successfully construct new and more general solutions including a series of nontraveling wave and coefficient functions' soliton-like solutions, double-like periodic and trigonometric-like function solutions.

Exact Solutions of the （3＋1）—Dimensional KP and KdV—Type Equations

Abundant new soliton-like and period form solutions for certain (3+1)-dimensional physically important nonlinear evolution equations are obtained by using a further extended tanh method and symbolic computation system, Maple.

EXACT BOUNDS OF THE MODIFIED LPT ALGORITHMS APPLYING TO PARALLEL MACHINES SCHEDULING WITH NONSILMULTANEOUS MACHINE AVAILABLE TIMES

In this paper, we consider Parallel Machines Scheduling with nonsimultaneous machine available time. We give the exact worst case performance bound of MLPT proposed by Lee. Furthermore, two other modified LPT algorithms are discussed. The paper is ended by numerical ex-periments of these algorithms.

Genetic Searching Algorithm for Optimal Runlength-Limited Codes with Error Control

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Solving Integrable Broer-Kaup Equations in （2＋1）-Dimensional Spaces via an Improved Variable Separation Approach

Starting from Backlund transformation and using Cole-Hopf transformation, we reduce the integrable Broer-Kaup equations in (2+1)-dimensional spaces to a simple linear evolution equation with two arbitrary functions of {x,t} and {y,t} in this paper. And we can obtain some new solutions of the original equations by investigating the simple nonlinear evolution equation, which include the solutions obtained by the variable separation approach.

On the Spectral Radius of Trees with the Given Diameter d

Let T denote a tree with the diameter d(d≥2) and order n. Let Pd,r,n-d-1 denote the tree obtained by identifying the rth vertex of path Pd+1 and the center of star K1,n-d-1, where r = r(d) is the integer part about d+2/2. Then p(T) ≤p(Pd,r,n-d-1),and equality holds if and only if T≌ Pd,r,n-d-1

New Explicit and Exact Travelling Wave Solutions for Burgers-Kolmogorov-Petrovskii-Piscounov Equations

In this paper, many new explicit and exact travelling wave solutions for Burgers-Kolmogorov-Petrovskii-Piscounov(Burgers-KPP) equations are obtained by using hyperbola function method and Wu-elimination method, which include new singular solitary wave solutions and periodic solutions. Particular important cases of the equation, such as the generalized Burgers-Fisher equation, Burgers-Chaffee infante equation and KPP equation, the corresponding solutions can be obtained also. The method can also solve other nonlinear partial differential equations.

STABILITY OF MAJORLY EFFICIENT POINTS AND SOLUTIONS IN MULTIOBJECTIVE PROGRAMMING

In this paper, we obtain some other properties of the majorly efficient points and solutions of the multiobjective optimization presellted in two previous papers of Hu. By decomposing the major cone, which is non-pointed, non-convex and non-closed into a finite union of disjoint strictly supported pointed convex cones, we discuss the continuous perturbations of the decision space. Several sufficient conditions for the continuity of the sets of majorly efficiellt points and solutions are given.

New Symmetry Reductions,Dromions—Like and Compacton Solutions for a 2D BS（m,n） Equations Hierarchy with Fully Nonlinear Dispersion

We have found two types of important exact solutions, compacton solutions, which are solitary waves with the property that after colliding with their own kind, they re-emerge with the same coherent shape very much as the solitons do during a completely elastic interaction, in the and even models, and dromion solutions (exponentially decaying solutions in all direction) in many and models. In this paper, symmetry reductions in are considered for the break soliton-type equation with fully nonlinear dispersion (called equation) , which is a generalized model of break soliton equation , by using the extended direct reduction method. As a result, six types of symmetry reductions are obtained. Starting from the reduction equations and some simple transformations, we obtain the solitary wave solutions of equations, compacton solutions of equations and the compacton-like solution of the potential form (called ) . In addition, we show that the variable admits dromion solutions rather than the field itself in equation.

New Exact Solutions of the Integrable Broer-Kaup Equations in （2＋ 1）-DimensionalSpaces

In this paper,by improving some procedure of extended tanh-function method,some new exact solutions to the integrable Broer-Kaup equations in(2 + 1)-dimensional spaces are obtained,which include soliton-like solutions,solitary wave solutions,trigonometric function solutions,and rational solutions.

Exact Travelling Wave Solutions to a Coupled Nonlinear Evolution Equation[

By using an improved hyperbola function method, several types of exact travelling wave solutions to a coupled nonlinear evolution equation are obtained, which include kink-shaped soliton solutions, bell-shaped soliton solutions, envelop solitary wave solutions, and new solitary waves. The method can be applied to other nonlinear evolution equations in mathematical physics.