(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.

Structure-oriented edge-preserving smoothing based on accurate estimation of orientation and edges

In this paper, we present a new method for reducing seismic noise while preserving structural and stratigraphic discontinuities. Structure-oriented edge-preserving smoothing requires information such as the local orientation and edge of the reflections. The information is usually estimated from seismic data with full frequency bandwidth. When the data has a very low signal to noise ratio （SNR）, the noise usually reduces the estimation accuracy. For seismic data with extremely low SNR, the dominant frequency has higher SNR than other frequencies, so it can provide orientation and edge information more reliably than other frequencies. Orientation and edge are usually described in terms of apparent reflection dips and coherence differences, respectively. When frequency changes, both dip and coherence difference change more slowly than the seismogram itself. For this reason, dip and coherence estimated from dominant frequency data can approximately represent those of other frequency data. Ricker wavelet are widely used in seismic modeling. The Marr wavelet has the same shape as Ricker wavelets in both time and frequency domains, so the Marr wavelet transform is selected to divide seismic data into several frequency bands. Reflection apparent dip as well as the edge information can be obtained by scanning the dominant frequency data. This information can be used to selectively smooth the frequency bands （dominant, low, and high frequencies） separately by structure-oriented edge-preserving smoothing technology. The ultimate noise-suppressed seismic data is the combination of the smoothed frequency band data. Application to synthetic and real data shows the method can effectively reduce noise, preserve edges, improve trackable reflection continuity, and maintain useful information in seismic data.

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.

Application of Bayesian Approach in the Parameter Estimation of Continuous Lumping Kinetic Model of Hydrocracking Process

Hydrocracking is a catalytic reaction process in the petroleum refineries for converting the higher boiling temperature residue of crude oil into a lighter fraction of hydrocarbons such as gasoline and diesel. In this study, a modified continuous lumping kinetic approach is applied to model the hydro-cracking of vacuum gas oil. The model is modified to take into consideration the reactor temperature on the reaction yield distribution. The model is calibrated by maximizing the likelihood function between the modeled and measured data at four different reactor temperatures. Bayesian approach parameter estimation is also applied to obtain the confidence interval of model parameters by considering the uncertainty associated with the measured errors and the model structural errors. Then Monte Carlo simulation is applied to the posterior range of the model parameters to obtain the 95% confidence interval of the model outputs for each individual fraction of the hydrocracking products. A good agreement is observed between the output of the calibrated model and the measured data points. The Bayesian approach based on the Markov Chain Monte Carlo simulation is shown to be efficient to quantify the uncertainty associated with the parameter values of the continuous lumping model.

A Lumping Kinetic Model for Catalytic Reforming

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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.

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.

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.

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.

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.

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.

(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。

基于磁热耦合法的非对称混合磁极永磁电机热分析

针对传统内置永磁电机损耗高、发热量大的问题,提出非对称混合磁极永磁电机拓扑结构.介绍非对称混合磁极永磁电机的拓扑结构,对比分析两者的电磁特性与损耗分布特性.针对非对称混合磁极永磁电机分布式绕组的结构特点,对绕组进行等效处理,确定等效导热系数,建立集中参数热网络模型.建立单向磁热耦合模型,计算电机各部件的温度分布,验证了热网络模型的正确性.考虑到温度对永磁材料的影响,建立双向磁热耦合模型,对比分析不同电流密度对电机温升的影响规律.试制一台样机并搭建温升试验平台进行温升试验,验证了新型拓扑结构的有效性与合理性以及磁热双向耦合法计算结果的准确性.

原油直接催化裂解UPC工艺过程模拟与反应参数多目标优化

原油直接催化裂解技术可以实现从原油到三烯(乙烯、丙烯、丁烯)、三苯(苯、甲苯、二甲苯)的一步跨越,对我国炼化行业的转型升级具有重要意义。以全馏分石蜡基中原原油(159~780℃)为原料,采用混合馏分结构与分子组成集总建模策略,对原油直接催化裂解制烯烃(UPC)反应过程进行建模与工艺参数校准,并基于工业试验数据验证了其准确性。以多产烯烃、控制焦炭生成为目的,利用NSGA-Ⅲ多目标优化算法对模型进行了优化,得到优化后的操作参数。采用优化后的操作参数,即在第一段预热闪蒸温度为194.32℃、第二段预热闪蒸温度为228.16℃、第一段提升管反应器出口温度为615.73℃、第二段提升管反应器出口温度为622.59℃的条件下,UPC工艺得到的乙烯和丙烯收率之和为53.367%,焦炭收率为8.311%。此外,由于现行税费体系燃料型工艺路线税收贡献明显高于化工型工艺路线,UPC工艺参数优化后,烯烃收率大幅度提升,燃料油收率大幅度下降,原油生产总值降低44.30元t。