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.

广义(3+1)维KdV方程的lump解、相互作用解和呼吸子解

基于广义(3+1)维KdV方程的双线性形式,得到了方程的lump解、相互作用解及呼吸子解.证明了lump解在空间各个方向上都是有理局域的,并在lump波与线孤子的相互作用过程中观察到了“聚变”和“裂变”现象,最后得到了方程的呼吸子解.

Dynamics of lump chains for the BKP equation describing propagation of nonlinear waves

A large member of lump chain solutions of the(2+1)-dimensional Bogoyavlenskii-Kadomtsev-Petviashvili(BKP)equation are constructed by means of theτ-function in the form of Grammian.The lump chains are formed by periodic arrangement of individual lumps and travel with distinct group and velocities.An analytical method related dominant regions of polygon is developed to analyze the interaction dynamics of the multiple lump chains.The degenerate structures of parallel,superimposed,and molecular lump chains are presented.The interaction solutions between lump chains and kink-solitons are investigated,where the kink-solitons lie on the boundaries of dominant region determined by the constant term in theτ-function.Furthermore,the hybrid solutions consisting of lump chains and individual lumps controlled by the parameter with high rank and depth are investigated.The analytical method presented in this paper can be further extended to other integrable systems to explore complex wave structures.

From breather solutions to lump solutions:A construction method for the Zakharov equation

Periodic solutions of the Zakharov equation are investigated.By performing the limit operationλ_(2l-1)→λ_(1)on the eigenvalues of the Lax pair obtained from the n-fold Darboux transformation,an order-n breather-positon solution is first obtained from a plane wave seed.It is then proven that an order-n lump solution can be further constructed by taking the limitλ_(1)→λ_(0)on the breather-positon solution,because the unique eigenvalueλ_(0)associated with the Lax pair eigenfunctionΨ(λ_(0))=0 corresponds to the limit of the infinite-periodic solutions.A convenient procedure of generating higher-order lump solutions of the Zakharov equation is also investigated based on the idea of the degeneration of double eigenvalues in multi-breather solutions.

Rheological and Morphological Characterization of Modified Bitumen with Cup Lump Rubber

Pure bitumen is not suitable for heavy traffic loads;hence modifiers are used to improve the bitumen performance.Recently,cup lump rubber(CLR)has become a preferred modifier due to its outstanding performance and less cost.However,little is known about the interactions between CLR and bitumen.Thus,this study investigates the behavior of bitumen with CLR.Four percentages of CLR(2.5%,5.0%,7.5%,and 10.0%by weight of bitumen)were used to modify conventional 60/70 penetration grade bitumen.The modified bitumen was evaluated through different laboratory testing such as dynamic shear rheometer,rotational viscosity,softening point,bending beam rheometer,ductility,and elastic recovery.The testing results show that the addition of CLR increased the bitumen’s rutting resistance by 3 PG grades at high temperatures.At low pavement temperatures,the cup lump rubber modified bitumen(CMB)can withstand up to−34℃.Fourier Transform Infrared(FTIR)analysis shows that the Aromaticity index at 1600 cm^(−1) rose as the CLR percentage increased,indicating the formation of a binder with a compact structure.This is expected to improve the elasticity of bitumen throughπ-πinteractions.Atomic Force Microscopy(AFM)results showed the Catana phase increased in size and quantity at 5.0%and 7.5%CLR content.While contact angle measurement revealed that the binders are hydrophobic and tend to repel the dropped water on the bitumen surface.

Resonant interactions among two-dimensional nonlinear localized waves and lump molecules for the(2+1)-dimensional elliptic Toda equation

The(2+1)-dimensional elliptic Toda equation is a high-dimensional generalization of the Toda lattice and a semidiscrete Kadomtsev–Petviashvili I equation.This paper focuses on investigating the resonant interactions between two breathers,a breather/lump and line solitons as well as lump molecules for the(2+1)-dimensional elliptic Toda equation.Based on the N-soliton solution,we obtain the hybrid solutions consisting of line solitons,breathers and lumps.Through the asymptotic analysis of these hybrid solutions,we derive the phase shifts of the breather,lump and line solitons before and after the interaction between a breather/lump and line solitons.By making the phase shifts infinite,we obtain the resonant solution of two breathers and the resonant solutions of a breather/lump and line solitons.Through the asymptotic analysis of these resonant solutions,we demonstrate that the resonant interactions exhibit the fusion,fission,time-localized breather and rogue lump phenomena.Utilizing the velocity resonance method,we obtain lump–soliton,lump–breather,lump–soliton–breather and lump–breather–breather molecules.The above works have not been reported in the(2+1)-dimensional discrete nonlinear wave equations.

Simulation of anchor chain based on lumped mass method

In order to develop a anchoring operation simulation system and improve safety during anchoring operations,a relatively accurate mathematical model of anchoring operations needs to be established.In this paper,the stress condition of anchor chain under environmental and subsea geological conditions is further studied and the stress condition of anchor chain is analyzed based on the previous research.In this paper,a quasi-static model based on catenary method is used as the basis of dynamic analysis,and the dynamic model of anchor chain is established based on the concentrated mass method,which fully considers the influence of anchor chain weight,hydrodynamic force,ocean current and interaction with the seabed.The fourth-order Runge Kutta method was used to solve the model numerically,and a calculation procedure was developed.The accuracy of the model was verified by comparing the calculated results with the experimental results,indicating that the constructed anchor chain dynamics model has a high accuracy.

Effect of lump ore ratio on the metallurgical properties of blast furnace charge

We conducted a series of experimental studies on the metallurgical properties of N-lump and F-lump ores used in Baosteel’s blast furnace, including thermal cracking, low-temperature reduction pulverization, reducibility, and droplet properties.The results show that the thermal burst properties of N-lump ore are better than those of F-lump ore.The low-temperature reduction degradation index(RDI) pulverization of the charge is the best when the ratios of N-lump ore and F-lump ore account for 35% each.The reduction performance of the charge is improved when F-lump and N-lump ores are mixed with sinter.In the softening-melting performance experiment, when the proportion of N-lump ore is 40%,the characteristic area value(S) as the charge permeability index is the smallest.When F-lump ore is mixed with sinter, its droplet performance improves compared with that of single F-lump ore.The proportion of F-lump ore should not exceed 15%.

Introduction to Mesh Based Generated Lumped Parameter Models for Electromagnetic Problems using Triangular Elements

This paper is an introduction to mesh based generated reluctance network modeling using triangular elements.Many contributions on mesh based generated reluctance networks using rectangular shaped elements have been published,but very few on those generated from a mesh using triangular elements.The use of triangular elements is aimed at extending the application of the approach to any shape of modeled devices.Basic concepts of the approach are presented in the case of electromagnetic devices.The procedure for coding the approach in the case of a flat linear permanent magnet machine is presented.Codes developed under MATLAB environment are also included.

Histopathological and Ultrasound Correlation in Women Presenting with Breast Lumps in Yaoundé, Cameroon

Context: Breast cancer is very deadly among women with higher rates in the developing world. Imaging tools such as ultrasound, can be used to differentiate between the types of breast lumps. This study aimed to determine the value of ultrasound as a first-line examination in the diagnosis of breast masses. Methods: This was a retrospective cross-sectional study of women presenting with breast lumps from November 2022 to June 2023 at the Yaounde General Hospital, which lasted seven months, from November 2022 to June 2023. The sampling was exhaustive and consecutive. Association between variables was studied using the x2 test and concordance between ultrasound and histopathological findings was assessed using the Kappa correlation coefficient. Results: 234 women were included in the study. Their mean age was 46.3 ± 11.4 years. Overall, 15 (6.4%) lumps were benign while 219 (93.6%) were malignant. Triple negative (5.6%) was the most recurrent genomic classification. The correlation between the ultrasound and histopathological findings was significant, with an observed concordance rate at 85.1%, kappa = 0.322 and a p-value Conclusion: The performance of ultrasound in differentiating benign and malignant lesion was high. However, the discordant cases highlight the need for a diagnosis system which blends histopathological and radiological findings for an improved management of patients with breast lumps.

(2+1)维广义Hietarinta-type方程的呼吸解和高阶lump-type解

为了构造(2+1)维广义Hietarinta-type方程丰富的精确解,基于Hirota双线性方法研究该方程。Hirota双线性方法是一种求非线性发展方程孤子解的简单而直接的代数方法。近年来该方法已经在构造非线性发展方程精确解的研究领域上得到了广泛的应用。基于该方法,构造非线性发展方程的非线性波对数学、物理、力学等学科中的高维非线性问题的研究有非常重要的理论和应用价值。利用Hirota双线性方法给出了(2+1)维广义Hietarinta-type方程的双线性形式,并运用符号计算软件Maple获得了该方程的呼吸解和高阶lump-type解。再通过选择适当的参数,绘制了这些解的三维图、等高线图和密度图,并分析和描述了解的动力学性质。这些结果丰富了目前关于(2+1)维广义Hietarinta-type方程文献中的结果。

Study on the Anti-Inflammatory and Analgesic Mechanisms of Breast Lump Resolution Detergent in a Rat Model of Breast Hyperplasia

Objective: This study aimed to investigate the anti-inflammatory and analgesic mechanisms of a breast lump resolution detergent in a rat model of breast hyperplasia. Methods: A rat model of breast hyperplasia was established using injections of estradiol benzoate combined with progesterone. The effects of the breast lump resolution detergent on nipple height and diameter in the rat model were observed, along with its impact on serum levels of estradiol (E2), prolactin (PRL), and progesterone (P). Additionally, the study examined the morphological changes in breast tissue. The impact of the breast nodule detergent on blood rheology parameters was also observed. Furthermore, the anti-inflammatory effect of the breast nodule detergent was assessed using the cotton ball granuloma experiment, and the analgesic effect was observed using the writhing test. Results: The breast lump resolution detergent reduced nipple height and diameter in the rat model, decreased serum levels of E2, PRL, and P, and alleviated pathological changes in breast tissue. It also lowered hemorheological parameters including whole blood high, medium, and low shear viscosity, plasma viscosity, red blood cell hematocrit, red blood cell aggregation index, red blood cell deformability index, red blood cell electrophoresis time, and erythrocyte sedimentation rate in the acute “blood stasis” rat model. The detergent reduced the weight of cotton ball granulomas in mice and decreased the number of writhing episodes caused by acetic acid. Conclusion: The breast lump resolution detergent demonstrates favorable therapeutic effects in treating breast hyperplasia, promoting blood circulation and removing blood stasis, exerting anti-inflammatory properties, and providing analgesic effects. The downregulation of serum E2 and PRL levels and the upregulation of P levels may be critical mechanisms underlying its efficacy.

约化的扩展(3+1)维Jimbo-Miwa方程的lump解和孤子解

研究两个约化的扩展(3+1)维Jimbo-Miwa(简称JM)方程,借助于方程的双线性表示和一些简单的符号计算,构造出这两个方程的精确解.首先,根据贝尔多项式方法建立方程的双线性形式.其次,利用Hirota双线性方法,将双线性方程的解 作为二次函数,直接得到了方程的明暗lump解.然后,根据双线性导数法和泰勒展开法,通过详细地推导,成功获得两个方程的一孤子解和二孤子解.除此之外,利用数学软件Maple,通过选取合适的参数,用图形生动地展示了所得精确解的动力学性质.

(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。