广义地球物理KdV方程的Lump波与扭结波相互作用解初值扰动行为

针对一类广义地球物理KdV方程进行研究,利用Painleve分析思想构造了一个包含初始常数解的双线性变换,并应用拟设函数法得到两类与初值有关的Lump波与周期波、扭结波相互作用的显式精确解.此外,根据包含初始常数解u 0扰动的解的结构得到u 0的两个分叉点.最后,在一定参数条件下,利用数学软件对所得Lump波与周期波相互作用模式、Lump波与扭结波相互作用模式进行了绘图展示.结果表明:方程初始常数解对广义地球物理KdV方程的发展性态具有明显的扰动特征.

(3+1)维Hirota双线性方程的lump解

非线性发展方程是现代数学的一重要分支,其精确解的计算一直都是非线性科学领域的主流与焦点问题.lump解是精确解析解的一种特殊形式,以(3+1)维Hirota双线性方程为例对此展开研究.首先,利用Hirota双线性方法研究其经典lump解.其次,以双线性神经网络方法为基础,借助符号计算方法,得到方程的高阶lump解,主要是4阶lump解的计算.最后,通过对参数赋予一些特殊值,借助Maple软件,绘制出相关的三维图、密度图、相图以及传播图等,得到一些新的现象,同时展示了所求出的解的动力学行为.

New Lump Solution and Their Interactions with N-Solitons for a Shallow Water Wave Equation

By employing the Hirota’s bilinear method and different test functions, the breather solutions of HSI equation with different structures are obtained based on symbolic calculation with perturbation parameters. Some new lump solitons are found in the process of studying the degradation behavior of breather solutions. The interaction between lump solution and soliton solution is constructed in the form of lump solution, and the motion trajectory of lump is obtained. In addition, the theorem of lump solitons and N-solitons superposition is given and proved. The superposition formula of lump is derived from the theorem, and its spatial evolution behavior is given.

(2+1)-维Boussinesq方程的lump解与lump-stripe混合解

通过利用Hirota双线性形式,并借助符号计算Maple,得到了(2+1)-维Boussinesq方程的lump解、lump-stripe混合解、周期解与孤子解。通过选取不同的参数,并结合图像研究了这些解的动力学性质,特别是讨论了lump孤子和stripe孤子之间的相互作用现象,这些解及相关的性质将有利于理解(2+1)-维Boussinesq方程所描述的物理现象。

A more general form of lump solution,lumpoff,and instanton/rogue wave solutions of a reduced (3+1)-dimensional nonlinear evolution equation

In this manuscript,a reduced(3+1)-dimensional nonlinear evolution equation is studied.We first construct the bilinear formalism of the equation by using the binary Bell polynomials theory,then explore a lump solution to the special case for z=x.Furthermore,a more general form of lump solution of the equation is found which possesses seven arbitrary parameters and four constraint conditions.By cutting the lump by the induced soliton(s),lumpoff and instanton/rogue wave solutions are also constructed by the more general form of lump solution.

Lump,lumpoff and predictable rogue wave solutions to a dimensionally reduced Hirota bilinear equation

We study a simplified(3+1)-dimensional model equation and construct a lump solution for the special case of z=y using the Hirota bilinear method.Then,a more general form of lump solution is constructed,which contains more arbitrary autocephalous parameters.In addition,a lumpoff solution is also derived based on the general lump solutions and a stripe soliton.Furthermore,we figure out instanton/rogue wave solutions via introducing two stripe solitons.Finally,one can better illustrate these propagation phenomena of these solutions by analyzing images.

(3+1)维广义BKP方程的N-孤子解、lump解和lump-kink解

基于简化的Hirota双线性方法,研究了(3+1)维广义BKP方程的N-孤子解.其次通过一类代数直接方法即所谓的正定二次函数法,研究了约化的广义BKP方程的lump解.然后将指数函数与正定二次函数结合,代入方程,求得约化的广义BKP方程的lump-kink解.最后通过选取不同的自由参数,画图加以说明条纹孤子与lump孤子的碰撞规律,并进行动力学分析.

广义变系数BKP方程的lump解

广义变系数BKP方程可以用来描述弱色散准介质中的波传播与流体力学。本文利用Hirota双线性方法获得了广义变系数BKP方程新的lump解,并结合指数函数和三角函数讨论了lump解和不同类型孤子解之间的交互作用,获得了许多重要的结果。

Frozen Section Analysis of Breast Lumpectomy Margins

Objectives: To evaluate breast lumpectomy margins by frozen section in breast conservation surgery. Methods: A retrospective study of frozen section of lumpectomy margins of one hundred ten patients was done at King Abdulaziz University Hospital from June 2007 to June 2013. All patients underwent lumpectomy + Sentinel lymph node biopsy. Patient records were studied for location of mass in breast, size of mass, site of breast, pre or postmenopausal, frozen section margins, new frozen section margins, permanent margins, reoperation. Complications like skin necrosis, numbness, and wound infection were studied. Result: Majority were Saudis (64.5%). Left breast was involved in 60%. Upper outer quadrant was involved in majority (51.9%). Size of mass was less than 1 cm in 14.8% cases, 1 - 2.9 cm in 43.5%, 3 - 4 cm in 13%, more than 4 cm in 10.2%. Lumpectomy plus sentinel lymph node biopsy was done in 96.4% and lumpectomy and axillary lymph node dissection was done in 1.8% cases. Gross margins were positive in 17.3% and frozen margins were positive in 28.2%. New margin on frozen section were positive in 3.6% and negative in 79.1%. Permanent section histology showed positive margins in 5.5% and negative in 94.5% cases. Re-operation was done in 7.3%. Lympho-vascular margins were positive in 20.9%. Skin necrosis was found in 2.2%, numbness was found in 4.4%, wound infection was in 2.2%. Conclusion: Lumpectomy margins with frozen section reduce re-operation and recurrence.

Antidiastole Value of Three-dimensional Ultrasonography and Power Doppler between Uterine Parenchyma Lumps and Endometrial Cancer:A Retrospective Study

Sometimes endometrial polyps,submucosal myomas,and endometrial cancer show similar findings under ultrasonography.The aim of this study was to assess the antidiastole value of blood flow parameters using three-dimensional(3D)power Doppler ultrasonography angiography(PDA)between endometrial cancer and uterine parenchyma lumps.The data of the blood flow indices in 3D-PDA including the vascularization index(VI),flow index(FI),and vascularization flow index(VFI)in 40 patients with endometrial cancer and 41 patients with uterine parenchyma lumps(endometrial polyps and submucosal myomas)were retrospectively analysed and compared utilizing Virtual Organ Computer-aided AnaLysis(VOCAL)software.The results showed that all the blood flow parameters(VI,FI,VFI)were significantly higher in women with endometrial cancer than in those with uterine parenchyma lumps(P<0.001).The area under the curve of ROC of VI,FI,and VFI was 0.98,0.84,and 0.97,respectively.Thus,the best predictor of endometrial carcinoma was VI with a sensitivity of 97.0% and a specificity of 91.0%.The optimal cutoff value of VI was 4.06%.Our data demonstrated that all of the blood flow signal parameters(including VI,FI,and VFI)in 3D power Doppler ultrasonography had significant antidiastole values between endometrial cancer and uterine parenchyma lumps to assist clinicians in properly diagnosing patients.

LUMP AND INTERACTION SOLUTIONS TO LINEAR (4+1)-DIMENSIONAL PDES

Taking a class of linear(4+1)-dimensional partial differential equations as examples, we would like to show that there exist lump solutions and interaction solutions in(4+1)-dimensions. We will compute abundant lump solutions and interaction solutions to the considered linear(4+1)-dimensional partial differential equations via symbolic computations,and plot three specific solutions with Maple plot tools, which supplements the existing literature on lump, rogue wave and breather solutions and their interaction solutions in soliton theory.

A lumped mass nonconforming finite element method for nonlinear parabolic integro-differential equations on anisotropic meshes

A lumped mass approximation scheme of a low order Crouzeix-Raviart type noncon- forming triangular finite element is proposed to a kind of nonlinear parabolic integro-differential equations. The L2 error estimate is derived on anisotropic meshes without referring to the traditional nonclassical elliptic projection.

尘埃等离子体中的分数阶模型及其Lump解

近年来,尘埃等离子体的研究在太空、工业和实验室等领域中有着重要的作用.该文从双温尘埃等离子体的控制方程组出发,通过运用多尺度分析与约化摄动方法,推导了(2+1)维的Kadomtsev-Petviashvili(KP)方程来描述双温尘埃等离子体声波的传播.接下来,利用半逆方法和分数变分原理,将(2+1)维KP方程推广到时空分数阶KP方程;分数阶KP方程对于描述实际问题中的物理现象具有潜在的应用价值.进一步,基于李对称分析方法,讨论了时间分数阶KP方程的守恒律,得到了双温尘埃等离子体声波的守恒量.最后,基于双线性方法,获得了分数阶KP方程的Lump解.该解的存在说明双温尘埃等离子体中存在怪波,特别地,分析了分数阶阶数对怪波的影响.

A wideband metamaterial absorber based on a magnetic resonator loaded with lumped resistors

A wideband metamaterial absorber （MA） based on a magnetic resonator loaded with lumped resistors is presented. It is composed of a one-dimensional periodic array of double U-shaped structured magnetic resonators loaded with lumped resistors, a dielectric substrate, and a metal plate. We simulated, fabricated, measured, and analyzed the MA. The experimental results show that the reflectance （S11） is below -10 dB at normal incidence in the frequency range of 7.7 GHz 18 GHz, and the peak value is about -20 dB. Simulated power loss density distributions indicate that wideband absorption of the MA is mainly attributable to the lumped resistors in the magnetic resonator. Further investigations indicate that the distance between two unit cells along the magnetic field direction significantly influences the performance of the MA.

Molecular reconstruction model based on structure oriented lumping and group contribution methods

Molecular management is a promising technology to face challenges in the refining industry, such as more stringent requirements for product oil and heavier crude oil, and to maximize the value of every molecule in petroleum fractions. To achieve molecular management in refining processes, a novel model that is based on structure oriented lumping(SOL) and group contribution(GC) methods was proposed in this study. SOL method was applied to describe a petroleum fraction with structural increments, and GC method aimed to estimate molecular properties. The latter was achieved by associating rules between SOL structural increments and GC structures. A three-step reconstruction algorithm was developed to build a representative set of molecules from partial analytical data. First, structural distribution parameters were optimized with several properties. Then, a molecular library was created by using the optimized parameters. In the final step, maximum information entropy(MIE) method was applied to obtain a molecular fraction. Two industrial samples were used to validate the method, and the simulation results of the feedstock properties agreed well with the experimental data.

(3+1)维变系数Kadomtsev-Petviashvili方程的lump解

变系数Kadomtsev-Petviashvili方程经常用来描述流体力学中具有弱非线性、弱色散和弱扰动的长波和小振幅面波。本文利用Hirota双线性形式和符号计算软件Mathematica,获得了(3+1)维变系数Kadomtsev-Petviashvili方程一些新的lump解,利用一些三维图形分析了这些解的动力学行为。

Research of Measuring Lump Coal Rate by Diameter Classification Method

The rate of lump coal is one of main factors that affects the price of raw coal. The coal mines always puzzle themselves about how to control rate of lump coal effectively. At present, the rate of lump coal is measured mainly by manual operation. The process is inaccurate and the efficiency is low. In this paper, a diameter classification method is proposed to measure the size of lump coal based on image processing.

广义变系数五阶Korteweg-de Vries方程的lump解

Korteweg-de Vries方程在浅水波、分层内波、离子声波、等离子体物理和晶格动力学等领域都有很重要的应用。本文研究的是广义变系数五阶Korteweg-de Vries方程。在符号计算软件和贝尔多项式的帮助下,获得广义变系数五阶Korteweg-de Vries方程的Hirota双线性形式和一些新的lump解,并通过一些三维图形和等高线图形演示了lump解的传播特点。

Modal analysis on transverse vibration of axially moving roller chain coupled with lumped mass

The modal characteristics of the transverse vibration of an axially moving roller chain coupled with lumped mass were analyzed.The chain system was modeled by using the multi-body dynamics theory and the governing equations were derived by means of Lagrange's equations.The effects of the parameters,such as the axially moving velocity of the chain,the tension force,the weight of lumped mass and its time-variable assign position in chain span,on the modal characteristics of transverse vibration for roller chain were investigated.The numerical examples were given.It is found that the natural frequencies and the corresponding mode shapes of the transverse vibration for roller chain coupled with lumped mass change significantly when the variations of above parameters are considered.With the movement of the chain strand,the natural frequencies present a fluctuating phenomenon,which is different from the uniform chain.The higher the order of mode is,the greater the fluctuating magnitude and frequency are.

非线性发展方程的lump解和多孤子解（英文）

运用Maple计算软件,研究(3+1)维广义浅水波方程,给出该方程的lump解并画图加以说明;运用交换公式,研究(2+1)维破碎孤子方程,推出其Bcklund变换,并利用求得的Bcklund变换得到方程的多孤子解.