Localized wave solutions and interactions of the (2+1)-dimensional Hirota-Satsuma-Ito equation

This paper studies the(2+1)-dimensional Hirota-Satsuma-Ito equation.Based on an associated Hirota bilinear form,lump-type solution,two types of interaction solutions,and breather wave solution of the(2+1)-dimensional Hirota-Satsuma-Ito equation are obtained,which are all related to the seed solution of the equation.It is interesting that the rogue wave is aroused by the interaction between one-lump soliton and a pair of resonance stripe solitons,and the fusion and fission phenomena are also found in the interaction between lump solitons and one-stripe soliton.Furthermore,the breather wave solution is also obtained by reducing the two-soliton solutions.The trajectory and period of the one-order breather wave are analyzed.The corresponding dynamical characteristics are demonstrated by the graphs.

Dynamics of Nonlinear Waves in(2+1)-Dimensional Extended Boiti-Leon-Manna-Pempinelli Equation

Based on the Hirota bilinear method,this study derived N-soliton solutions,breather solutions,lump solutions and interaction solutions for the(2+1)-dimensional extended Boiti-Leon-Manna-Pempinelli equation.The dynamical characteristics of these solutions were displayed through graphical,particularly revealing fusion and ssion phenomena in the interaction of lump and the one-stripe soliton.

Bifurcations, Analytical and Non-Analytical Traveling Wave Solutions of (2 + 1)-Dimensional Nonlinear Dispersive Boussinesq Equation

For the (2 + 1)-dimensional nonlinear dispersive Boussinesq equation, by using the bifurcation theory of planar dynamical systems to study its corresponding traveling wave system, the bifurcations and phase portraits of the regular system are obtained. Under different parametric conditions, various sufficient conditions to guarantee the existence of analytical and non-analytical solutions of the singular system are given by using singular traveling wave theory. For certain special cases, some explicit and exact parametric representations of traveling wave solutions are derived such as analytical periodic waves and non-analytical periodic cusp waves. Further, two-dimensional wave plots of analytical periodic solutions and non-analytical periodic cusp wave solutions are drawn to visualize the dynamics of the equation.

Correlation of tumor-associated macrophage density and proportion of M2 subtypes with the pathological stage of colorectal cancer

BACKGROUND Colorectal cancer(CRC)is a prevalent global malignancy with complex prognostic factors.Tumor-associated macrophages(TAMs)have shown paradoxical associations with CRC survival,particularly concerning the M2 subset.AIM We aimed to establish a simplified protocol for quantifying M2-like TAMs and explore their correlation with clinicopathological factors.METHODS A cross-sectional study included histopathological assessment of paraffinembedded tissue blocks obtained from 43 CRC patients.Using CD68 and CD163 immunohistochemistry,we quantified TAMs in tumor stroma and front,focusing on M2 proportion.Demographic,histopathological,and clinical parameters were collected.RESULTS TAM density was significantly higher at the tumor front,with the M2 proportion three times greater in both zones.The tumor front had a higher M2 proportion,which correlated significantly with advanced tumor stage(P=0.04),pathological nodal involvement(P=0.04),and lymphovascular invasion(LVI,P=0.01).However,no significant association was found between the M2 proportion in the tumor stroma and clinicopathological factors.CONCLUSION Our study introduces a simplified protocol for quantifying M2-like TAMs in CRC tissue samples.We demonstrated a significant correlation between an increased M2 proportion at the tumor front and advanced tumor stage,nodal involvement,and LVI.This suggests that M2-like TAMs might serve as potential indicators of disease progression in CRC,warranting further investigation and potential clinical application.

MOLECULES AND NEW INTERACTIONAL STRUCTURES FOR A(2+1)-DIMENSIONAL GENERALIZED KONOPELCHENKO-DUBROVSKY-KAUP-KUPERSHMIDT EQUATION

Soliton molecules(SMs)of the(2+1)-dimensional generalized KonopelchenkoDubrovsky-Kaup-Kupershmidt(gKDKK)equation are found by utilizing a velocity resonance ansatz to N-soliton solutions,which can transform to asymmetric solitons upon assigning appropriate values to some parameters.Furthermore,a double-peaked lump solution can be constructed with breather degeneration approach.By applying a mixed technique of a resonance ansatz and conjugate complexes of partial parameters to multisoliton solutions,various kinds of interactional structures are constructed;There include the soliton molecule(SM),the breather molecule(BM)and the soliton-breather molecule(SBM).Graphical investigation and theoretical analysis show that the interactions composed of SM,BM and SBM are inelastic.

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.

Interaction solutions and localized waves to the(2+1)-dimensional Hirota-Satsuma-Ito equation with variable coefficient

This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method.The equation is proved to be Painlevé integrable by Painlevé analysis.On the basis of the bilinear form,the forms of two-soliton solutions,three-soliton solutions,and four-soliton solutions are studied specifically.The appropriate parameter values are chosen and the corresponding figures are presented.The breather waves solutions,lump solutions,periodic solutions and the interaction of breather waves solutions and soliton solutions,etc.are given.In addition,we also analyze the different effects of the parameters on the figures.The figures of the same set of parameters in different planes are presented to describe the dynamical behavior of solutions.These are important for describing water waves in nature.

保护动机理论的分阶段访谈联合运动指导改善中青年2型糖尿病患者心理痛苦、疲劳和遵医行为的价值

目的:基于保护动机理论(PMT)的分阶段访谈联合运动指导改善中青年2型糖尿病(T2DM)患者心理痛苦、疲劳和遵医行为的价值。方法:选取2021年5月至2024年5月某院收治的中青年T2DM患者78例,以计算机随机数字生成表法分为常规组、观察组,各39例。常规组行常规干预方式,观察组行基于PMT的分阶段访谈联合运动指导干预。比较两组心理痛苦、疲劳、遵医行为及生活质量。结果:干预后观察组中文版糖尿病痛苦量表(DDS)各维度评分均低于常规组(t=3.376,2.676,8.222,4.540;P<0.05);干预后观察组中文版多维疲劳量表(MFI-20)评分低于常规组(t=3.441,P<0.05);干预后观察组遵医依从性评定量表(MARS)评分高于常规组(t=2.281,P<0.05);干预后观察组2型糖尿病患者生存质量量表(DMQLS)评分高于常规组(t=5.321,P<0.001)。结论:基于PMT的分阶段访谈联合运动指导可减轻中青年T2DM患者心理痛苦、疲劳状态,改善遵医行为及生活质量。

Exotic Localized Coherent Structures of New (2+1)-Dimensional Soliton Equation

The variable separation approach is used to obtain localized coherent structures of the new (2+1)-dimensional nonlinear partialdifferential equation. Applying the Backlund transformation and introducing the arbitraryfunctions of the seed solutions, the abundance of the localized structures of this model are derived. Some special types ofsolutions solitoff, dromions, dromion lattice, breathers and instantons are discussed by selecting the arbitrary functionsappropriately. The breathers may breath in their amplititudes, shapes, distances among the peaks and even the numberof the peaks.

A Variable Separation Approach to Solve the Integrable and Nonintegrable Models:Coherent Structures of the (2 + 1)-Dimensional KdV Eqnation

We study the localized coherent structures ofa generally nonintegrable (2+ 1 )-dimensional KdV equation via a variable separation approach. In a special integrable case, the entrance of some arbitrary functions leads to abundant coherent structures. However, in the general nonintegrable case, an additional condition has to be introduced for these arbitrary functions. Although the additional condition has been introduced into the solutions of the nonintegrable KdV equation, there still exist many interesting solitary wave structures. Especially, the nonintegrable KdV equation possesses the breather-like localized excitations, and the similar static ring soliton solutions as in the integrable case. Furthermor,in the integrable case, the interaction between two travelling ring solitons is elastic, while in the nonintegrable case we cannot find even the single travelling ring soliton solution.

Role of 2-dimensional Doppler echo-cardiography in screening portopulmonary hypertension in portal hypertension patients

BACKGROUND: Portopulmonary hypertension (PPH) is difficult to recognize in the early and middle stages because it is frequently asymptomatic. As right ventricular function is impaired in patients with moderate and severe PPH, any dramatic hemodynamic changes in liver transplantation or other procedures may result in death from pulmonary and cardiac events. In this study, we investigated the prevalence of PPH in patients with portal hypertension (PHT) mainly caused by hepatitis B virus, and evaluated the effect of 2-dimensional Doppler echocardiography (2D-ECHO) in screening for PPH. METHODS: One hundred and five PHT patients received transthoracic 2D-ECHO preoperatively, systolic pulmonary arterial pressure (SPAP, normal range <30 mmHg) and pulmonary acceleration time (PAT, normal range >= 120 msec) were measured to screen for PPH (positive result: SPAP >= 30 mmHg and/or PAT <100 msec). Subsequently, pulmonary hemodynamic parameters were measured by right heart catheterization (RHC) for definitive diagnosis of PPH. The results of the two methods were compared to assess the screening effect of 2D-ECHO. RESULTS: The prevalence of PPH in this study was 3.8% (4/105). About 90% (95/105) of patients had a detectable tricuspid regurgitation by 2D-ECHO and the mean SPAP was 27.7 +/- 5.9 mmHg. Twenty-two of these 95 patients had an SPAP >30 mmHg. The mean PAT of all patients was 140 23 msec and 5 were <100 msec. Twenty-two patients were screened out by 2D-ECHO and 4 were diagnosed by RHC. A positive significant correlation (r=0.55, P<0.01) was found between SPAP measured by 2D-ECHO and mean pulmonary artery pressure (MPAP) measured by RHC, and a weak but significant negative correlation (r=-0.27, P=0.005) existed between PAT and pulmonary vascular resistance (PVR). The sensitivity, specificity, agreement rate, positive predictive value and negative predictive value of the screening test were 100%, 82%, 83%, 18% and 100%, respectively. CONCLUSIONS: The prevalence of PPH in this study is lower than in Western countries. As a screening test, 2D-ECHO has very high sensitivity and negative predictive value. A negative test result can directly be used to exclude PPH, while a positive result should be confirmed by RHC.

Study of （2＋1）-Dimensional Higher-Order Broer-Kaup System

Painleve property and infinite symmetries of the （2＋1）-dimensional higher-order Broer-Kaup （HBK） system are studied in this paper. Using the modified direct method, we derive the theorem of general symmetry gro.ups to （2＋1）-dimensional HBK system. Based on our theorem, some new forms of solutions are obtained. We also find infinite number of conservation laws of the （2＋1）-dimensional HBK system.

3.0T HR-MRI联合血清MMP9、AGR2对宫颈癌FIGO分期诊断价值

目的:探讨3.0T高分辨磁共振成像(HR-MRI)联合血清基质金属蛋白9(MMP9)、前梯度蛋白2(AGR2)诊断宫颈癌FIGO分期价值。方法:选取2016年3月-2022年10月本院诊疗的122例宫颈癌患者临床资料,依据FIGO分期系统分为Ⅰ~Ⅱ期64例、Ⅲ~Ⅳ期58例,均行3.0T HR-MRI检查,并采用酶联免疫吸附法检测血清MMP9、AGR2水平。采用一致性Kappa检验分析HR-MRI单独及联合血清MMP9、AGR2与术后病理结果的一致性,并绘制受试者工作特征(ROC)曲线分析各指标诊断宫颈癌FIGO分期效能;结果:FIGO分期Ⅲ~Ⅳ期宫颈癌患者血清MMP9、AGR2水平高于Ⅰ~Ⅱ期患者(P<0.05)。血清MMP9、AGR2诊断宫颈癌Ⅰ~Ⅱ期与Ⅲ~Ⅳ期的曲线下面积(AUC)分别为0.789(95%CI0.708-0.869)、0.836(95%CI0.765-0.906),特异度分别为76.6%、73.4%,敏感度分别为72.4%、81.3%,截断值分别为178.83ng/ml、13.18ng/ml。HR-MRI检查与术后病理结果一致性较高,Kappa值为0.739,HR-MRI联合血清MMP9、AGR2检查与术后病理结果一致性极高,Kappa值为0.868(均P<0.05)。HR-MRI联合血清MMP9、AGR2诊断宫颈癌患者FIGO分期的特异度(95.3%)、阳性预测值(94.6%)显著高于各单独指标诊断,敏感度(91.4%)、阴性预测值(92.4%)高于血清MMP9,准确度(93.4%)高于血清MMP9、AGR2(P<0.05)。结论:3.0T HR-MRI联合血清MMP9、AGR2对宫颈癌FIGO分期的诊断价值较高。

On Boolean elements and derivations in 2-dimension linguistic lattice implication algebras

A 2-dimension linguistic lattice implication algebra(2DL-LIA)can build a bridge between logical algebra and 2-dimension fuzzy linguistic information.In this paper,the notion of a Boolean element is proposed in a 2DL-LIA and some properties of Boolean elements are discussed.Then derivations on 2DL-LIAs are introduced and the related properties of derivations are investigated.Moreover,it proves that the derivations on 2DL-LIAs can be constructed by Boolean elements.

A New Rational Algebraic Approach to Find Exact Analytical Solutions to a （2＋1）-Dimensional System

In this paper, we present a new rational algebraic approach to uniformly construct a series of exact analytical solutions for nonlinear partial differential equations. Compared with most existing tanh methods and other sophisticated methods, the proposed method not only recovers some known solutions, but also finds some new and general solutions. The solutions obtained in this paper include rational form triangular periodic wave solutions, solitary wave solutions, and elliptic doubly periodic wave solutions. The efficiency of the method can be demonstrated on （2＋1）-dimensional dispersive long-wave equation.

New Exact Solutions for （2＋1）-Dimensional Breaking Soliton Equation

New exact solutions in terms of the Jacobi elliptic functions are obtained to the (2+1)-dimensional breakingsoliton equation by means of the modified mapping method. Limit cases are studied, and new solitary wave solutionsand triangular periodic wave solutions are obtained.

A General Mapping Approach and New Travelling Wave Solutions to（2＋1）-Dimensional Boussinesq Equation

A general mapping deformation method is presented and applied to a (2+1)-dimensional Boussinesq system. Many new types of explicit and exact travelling wave solutions, which contain solitary wave solutions, periodic wave solutions, Jacobian and Weierstrass doubly periodic wave solutions, and other exact excitations like polynomial solutions, exponential solutions, and rational solutions, etc., are obtained by a simple algebraic transformation relation between the (2+1)-dimensional Boussinesq equation and a generalized cubic nonlinear Klein-Gordon equation.

New Complexiton Solutions of （2＋1）-Dimensional Nizhnik-Novikov-Veselov Equations

In this paper, we extend the multiple Riccati equations rational expansion method by introducing a new ansatz. Using this method, many complexiton solutions of the （2＋ 1 ）-dimensional Nizhnik-Novikov-Veselov equations are obtained which include various combination of hyperbolic and trigonometric periodic function solutions, various combination of hyperbolic and rational function solutions, various combination of trigonometric periodic and rational function solutions, etc. The method can be also used to solve other nonlinear partial differential equations.

Modified (2+1)-dimensional displacement shallow water wave system and its approximate similarity solutions

Recently, a new （2＋1）-dimensional shallow water wave system, the （2＋1）-dlmenslonal displacement shallow water wave system （2DDSWWS）, was constructed by applying the variational principle of the analytic mechanics in the Lagrange coordinates. The disadvantage is that fluid viscidity is not considered in the 2DDSWWS, which is the same as the famous Kadomtsev-Petviashvili equation and Korteweg-de Vries equation. Applying dimensional analysis, we modify the 2DDSWWS and add the term related to the fluid viscidity to the 2DDSWWS. The approximate similarity solutions of the modified 2DDSWWS （M2DDSWWS） is studied and four similarity solutions are obtained. For the perfect fluids, the coefficient of kinematic viscosity is zero, then the M2DDSWWS will degenerate to the 2DDSWWS.

The Travelling Wave Solutions for （2＋1）-dimensional AKNS Equation

Based on the travelling wave method, a(2 + 1)-dimensional AKNS equation is considered. Elliptic solution and soliton solution are presented and it is shown that the soliton solution can be reduced from the elliptic solution. It also proves that the result is consistent with the soliton solution of simplify Hirota bilinear method by Wazwaz and illustrate the solution are right travelling wave solution.