Abundant invariant solutions of extended(3+1)-dimensional KP-Boussinesq equation

Lie group analysis method is applied to the extended(3+1)-dimensional Kadomtsev–Petviashvili–Boussinesq equation and the corresponding similarity reduction equations are obtained with various infinitesimal generators.By selecting suitable arbitrary functions in the similarity reduction solutions,we obtain abundant invariant solutions,including the trigonometric solution,the kink-lump interaction solution,the interaction solution between lump wave and triangular periodic wave,the two-kink solution,the lump solution,the interaction between a lump and two-kink and the periodic lump solution in different planes.These exact solutions are also given graphically to show the detailed structures of this high dimensional integrable system.

NOVEL 6-SPS PARALLEL 3-DIMENSIONAL PLATFORM MANIPULATOR AND ITS FORCE/MOTION TRANSMISSION ANALYSIS

The unique design for a novel 6-SPS parallel 3-dimensional platformmanipulator with an orthogonal configuration is investigated. The layout feature of the parallelmanipulator is described. Its force/motion transmission capability, evaluation criteria arepresented. At the orthogonal configuration, the criteria and the relationships between the criteriaand the link lengths are analyzed, which is important since it can provide designer a piece ofvaluable information about how to choose the linear actuators. From the analysis of the results itis shown that the force/motion transmission capabilities of the parallel manipulator arecharacterized by isotropy at the orthogonal configuration. The manipulator is particularly suitablefor certain applications in 6-DOF micromanipulators and 6-axis force/moment transducers.

A 3-DIMENSIONAL DATA MODEL FOR VISUALIZING CLOVERLEAF JUNCTION IN A CITY MODEL

The research work has been seldom done about cloverleaf junction expression in a 3-dimensional city model (3DCM). The main reason is that the cloverleaf junction is often in a complex and enormous construction. Its main body is bestraddle in air,and has aerial intersections between its parts. This complex feature made cloverleaf junction quite different from buildings and terrain, therefore, it is difficult to express this kind of spatial objects in the same way as for buildings and terrain. In this paper,authors analyze spatial characteristics of cloverleaf junction, propose an all-constraint points TIN algorithm to partition cloverleaf junction road surface, and develop a method to visualize cloverleaf junction road surface using TIN. In order to manage cloverleaf junction data efficiently, the authors also analyzed the mechanism of 3DCM data management, extended BLOB type in relational database, and combined R-tree index to manage 3D spatial data. Based on this extension, an appropriate data

All Single Traveling Wave Solutions to （3＋1）-Dimensional Nizhnok-Novikov-Veselov Equation

Using elementary integral method, a complete classification of all possible exact traveling wave solutions to （3＋1）-dimensional Nizhnok-Novikov-Veselov equation is given. Some solutions are new.

New Exact Solutions and Conservation Laws to （3＋1）-Dimensional Potential-YTSF Equation

Using the modified find some new exact solutions to Lie point symmetry groups and also get conservation laws, of the CK＇s direct method, we build the relationship between new solutions and old ones and the （3＋1）-dimensional potentiaial-YTSF equation. Baaed on the invariant group theory, Lie symmetries of the （3＋1）-dimensional potential-YTSF equation are obtained. We equation with the given Lie symmetry.

Evaluation of Airway Obstruction at Soft Palate Level in Male Patients with Obstructive Sleep Apnea/Hypopnea Syndrome:Dynamic 3-Dimensional CT Imaging of Upper Airway

This study examined the dynamic characteristics of upper airway collapse at soft palate level in patients with obstructive sleep apnea/hypopnea syndrome（OSAHS） by using dynamic 3-Dimensional（3-D） CT imaging.A total of 41 male patients who presented with 2 of the following symptoms,i.e.,daytime sleepiness and fatigue,frequent snoring,and apnea with witness,were diagnosed as having OSAHS.They underwent full-night polysomnography and then dynamic 3-D CT imaging of the upper airway during quiet breathing and in Muller＇s maneuver.The soft palate length（SPL）,the minimal cross-sectional area of the retropalatal region（mXSA-RP）,and the vertical distance from the hard palate to the upper posterior part of the hyoid（hhL） were compared between the two breathing states.These parameters,together with hard palate length（HPL）,were also compared between mild/moderate and severe OSAHS groups.Association of these parameters with the severity of OSAHS [as reflected by apnea hypopnea index（AHI） and the lowest saturation of blood oxygen（LSaO2）] was examined.The results showed that 31 patients had severe OSAHS,and 10 mild/moderate OSAHS.All the patients had airway obstruction at soft palate level.mXSA-RP was significantly decreased and SPL remarkably increased during Muller＇s maneuver as compared with the quiet breathing state.There were no significant differences in these airway parameters（except the position of the hyoid bone） between severe and mild/moderate OSAHS groups.And no significant correlation between these airway parameters and the severity of OSAHS was found.The position of hyoid was lower in the severe OSAHS group than in the mild/moderate OSAHS group.The patients in group with body mass index（BMI）≥26 had higher collapse ratio of mXSA-RP,greater neck circumference and smaller mXSA-RP in the Muller＇s maneuver than those in group with BMI26（P0.05 for all）.It was concluded that dynamic 3-D CT imaging could dynamically show the upper airway changes at soft palate level in OSAHS patients.All the OSAHS patients had airway obstruction of various degrees at soft palate level.But no correlation was observed between the airway change at soft palate level and the severity of OSAHS.The patients in group with BMI≥26 were more likely to develop airway obstruction at soft palate level than those with BMI26.

Grammian Determinant Solution and Pfaffianization for a (3+1)-Dimensional Soliton Equation

Based on the Pfaffian derivative formulae,a Grammian determinant solution for a(3+1)-dimensionalsoliton equation is obtained.Moreover,the Pfaffianization procedure is applied for the equation to generate a newcoupled system.At last,a Gram-type Pfaffian solution to the new coupled system is given.

Spatiotemporal Similaritons in (3+l)-Dimensional Inhomogeneous Nonlinear Medium with Cubic-Quintic Nonlinearity

We obtain exact spatiotemporal similaritons to a （3＋ l）-dimensional inhomogeneous nonlinear Schrodinger equation, which describes the propagation of optical pulses in a cubic-quintic nonlinearity medium with distributed dispersion and gain. A one-to-one correspondence between such self-similar waves and solutions of the elliptic equation is found when a certain compatibility condition is satisfied. Based on exact solutions, we discuss evolutional behaviors of self-similar cnoidal waves and chirped similaritons in two kind of typicai soliton control systems. Moreover, the comparison between chirped similaritons and chirp-free solitons is given.

Some Special Types of Solitary Wave Solutions for （3＋1）-Dimensional Jimbo-MiwaEquation

Using the extended homogeneous balance method, we find some special types of single solitary wave solution and new types of the multisoliton solutions of the (3+1)-dimensional Jimbo-Miwa equation.

A Generalized Variable-Coefficient Algebraic Method Exactly Solving （3＋1）-Dimensional Kadomtsev-Petviashvilli Equation

A generalized variable-coefficient algebraic method is appfied to construct several new families of exact solutions of physical interest for （3＋1）-dimensional Kadomtsev-Petviashvilli （KP） equation. Among them, the Jacobi elliptic periodic solutions exactly degenerate to the soliton solutions at a certain limit condition. Compared with the existing tanh method, the extended tanh method, the Jacobi elliptic function method, and the algebraic method, the proposed method gives new and more general solutions.

Thermal effect on endurance performance of 3-dimensional RRAM crossbar array

Three-dimensional（3D） crossbar array architecture is one of the leading candidates for future ultra-high density nonvolatile memory applications. To realize the technological potential, understanding the reliability mechanisms of the3 D RRAM array has become a field of intense research. In this work, the endurance performance of the 3D 1D1 R crossbar array under the thermal effect is investigated in terms of numerical simulation. It is revealed that the endurance performance of the 3D 1D1 R array would be seriously deteriorated under thermal effects as the feature size scales down to a relatively small value. A possible method to alleviate the thermal effects is provided and verified by numerical simulation.

Applications of Extended Mapping Deformation Method in Two （3＋1）-Dimensional Nonlinear Models

Based on the extended mapping deformation method and symbolic computation, many exact travelling wave solutions are found for the (3+1)-dimensional JM equation and the (3+1)-dimensional KP equation. The obtained solutions include solitary solution, periodic wave solution, rational travelling wave solution, and Jacobian and Weierstrass function solution, etc.

Painleve Analysis and Determinant Solutions of a (3+1)-Dimensional Variable-Coefficient Kadomtsev-Petviashvili Equation in Wronskian and Grammian Form

In this paper, the investigation is focused on a （3＋1）-dimensional variable-coefficient Kadomtsev- Petviashvili （vcKP） equation, which can describe the realistic nonlinear phenomena in the fluid dynamics and plasma in three spatial dimensions. In order to study the integrability property of such an equation, the Painlevé analysis is performed on it. And then, based on the truncated Painlevé expansion, the bilinear form of the （3＋1）-dimensionaJ vcKP equation is obtained under certain coefficients constraint, and its solution in the Wronskian determinant form is constructed and verified by virtue of the Wronskian technique. Besides the Wronskian determinant solution, it is shown that the （3＋1）-dimensional vcKP equation also possesses a solution in the form of the Grammian determinant.

Rota-Baxter Operators on 3-dimensional Lie Algebras and Solutions of the Classical Yang-Baxter Equation

In this paper,we compute Rota-Baxter operators on the 3-dimensional Lie algebra g whose derived algebra’s dimension is 2.Furthermore,we give the corresponding solutions of the classical Yang-Baxter equation in the 6-dimensional Lie algebras g ■ _(ad~*) g~* and some new structures of left-symmetric algebra induced from g and its Rota-Baxter operators.

Extended symmetry transformation of (3+1)-dimensional generalized nonlinear Schrdinger equation with variable coefficients

In this paper, the extended symmetry transformation of （3＋1）-dimensional （3D） generalized nonlinear Schrodinger （NLS） equations with variable coefficients is investigated by using the extended symmetry approach and symbolic computation. Then based on the extended symmetry, some 3D variable coefficient NLS equations are reduced to other variable coefficient NLS equations or the constant coefficient 3D NLS equation. By using these symmetry transformations, abundant exact solutions of some 3D NLS equations with distributed dispersion, nonlinearity, and gain or loss are obtained from the constant coefficient 3D NLS equation.

A New Auto-Backlund Transformation and Two-Soliton Solution for (3+l)-Dimensional Jimbo-Miwa Equation

Abstract By improving the extended homogeneous balance method, a general method is suggested to derive a new auto-Bgcklund transformation （BT） for （3-k l）-Dimensional Jimbo-Miwa （JM） equation. The auto-BT obtained by using our method only involves one quadratic homogeneity equation written as a bilinear equation. Based on the auto-BT, two-soliton solution of the （3＋1）-Dimensional JM equation is obtained.

Multisymplectic Pseudospectral Discretizations for(3+1)-Dimensional Klein-Gordon Equation

We explore the multisymplectic Fourier pseudospectral discretizations for the (3+1)-dimensional Klein-Gordon equation in this paper.The corresponding multisymplectic conservation laws are derived.Two kinds of explicitsymplectic integrators in time are also presented.

A Generalized Hirota Ansatz to Obtain Soliton-Like Solutions for a (3+l)-Dimensional Nonlinear Evolution Equation

Instead of the usual Hirota ansatz,i.e.,the functions in bilinear equations being chosen as exponentialtypes,a generalized Hirota ansatz is proposed for a (3+1)-dimensional nonlinear evolution equation.Based on theresulting generalized Hirota ansatz,a family of new explicit solutions for the equation are derived.

Interactions among special embed-solitons for the (3+1)-dimensional Burgers equation

With the help of a modified mapping method and a new mapping method, we re-study the （3＋1）-dimensional Burgers equation, and derive two families of variable separation solutions. By selecting appropriate functions in the variable separation solution, we discuss the interaction behaviors among taper-like, plateau-type rings, and rectangle-type embed-solitons in the periodic wave background. All the interaction behaviors are completely elastic, and no phase shift appears after interaction.

An image encryption scheme based on three-dimensional Brownian motion and chaotic system

At present, many chaos-based image encryption algorithms have proved to be unsafe, few encryption schemes permute the plain images as three-dimensional（3D） bit matrices, and thus bits cannot move to any position, the movement range of bits are limited, and based on them, in this paper we present a novel image encryption algorithm based on 3D Brownian motion and chaotic systems. The architecture of confusion and diffusion is adopted. Firstly, the plain image is converted into a 3D bit matrix and split into sub blocks. Secondly, block confusion based on 3D Brownian motion（BCB3DBM）is proposed to permute the position of the bits within the sub blocks, and the direction of particle movement is generated by logistic-tent system（LTS）. Furthermore, block confusion based on position sequence group（BCBPSG） is introduced, a four-order memristive chaotic system is utilized to give random chaotic sequences, and the chaotic sequences are sorted and a position sequence group is chosen based on the plain image, then the sub blocks are confused. The proposed confusion strategy can change the positions of the bits and modify their weights, and effectively improve the statistical performance of the algorithm. Finally, a pixel level confusion is employed to enhance the encryption effect. The initial values and parameters of chaotic systems are produced by the SHA 256 hash function of the plain image. Simulation results and security analyses illustrate that our algorithm has excellent encryption performance in terms of security and speed.