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.

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.

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.

An Amorphous 2-Dimensional Barcode

Most existing 2-dimensional barcodes are designed with a fixed shape and clear area.Having a fixed shape and clear area makes the barcode difficult to lay out with other text and pictures.To solve this problem,an amorphous 2-dimensional barcode is presented in this paper.The barcode uses encoding graph units to encode data.There are two key points in a 2-dimensional barcode:One is the encoding graph unit,the other is its encoding rules.Because encoding graph units of a 2-dimensional barcode are surrounded by other graphics,the units should be self-positioned and distinguished from other units.This paper presents an encoding graph unit generation algorithm,which is based on genetic algorithms.Encoding rules of the barcode are also given in this paper.Those rules include data encoding rules and encoding graph unit sequence arrangement rules.Data encoding rules are used to encode data to an encoding graph unit sequence.Encoding graph unit sequence arrangement rules are used to embed the unit sequence in the target picture.In addition to those rules,it also discussed the steps to restore encoding graph unit sequence from a picture.In the experiments section of this paper,an example is provided to encode a string and embed it in a car ad picture by the barcode.According to encoding rules of the barcode,those encoding graphic units can be scattered and embedded in a picture with other graphics,so amorphous 2-dimensional barcode has no fixed shape.Take advantage of this,designer can present a more elegant design to lay out barcodes with other graphic elements.

基于恒定梯度编码一维选层T_(2)谱的胶结砂岩层析成像方法

核磁共振成像是探究岩心尺度非均质性的先进技术,受岩石复杂性和编码技术影响,现有方法效果不佳。基于梯度场的二维/三维核磁共振技术成像容易但信噪比低,无梯度场的传统选层T_(2)谱(频率编码/相位编码)方法效率低。该研究提出恒定梯度编码一维选层T_(2)谱层析成像方法,做到了成像数据体量小、信噪比高且信号更完整。层析T_(2)谱图像及其热度分布,能够有效表征毛细管压力和成岩作用对流体非均匀分布的影响。饱和油状态时,T_(2)谱层间差异性反映成岩作用影响。高饱和油阶段,轴向热度图反映了低毛细管压力游离油的脱出规律。完全驱替后毛细管压力进入稳定状态,轴向热度图反映了微孔中吸附油赋存状态的差异。该技术在胶结砂岩气驱油实验中取得了良好效果,并对解析强非均质岩石渗流规律有重要作用。

乳腺癌组织lncRNA CASC2、miR-532-3p表达水平与患者术后5年内生存的相关性

目的探究乳腺癌(BC)组织长链非编码RNA癌易感性候选基因2(lncRNA CASC2)、微小RNA-532-3p(miR-532-3p)表达与患者术后5年内生存的相关性。方法选择2015年1月—2018年6月大同市第五人民医院普通外科收治BC患者127例,术中收集BC组织及癌旁正常组织,荧光定量PCR法检测BC组织和癌旁正常组织中lncRNA CASC2、miR-532-3p表达;对BC患者术后进行为期5年的随访,记录患者5年内生存和死亡情况。比较癌旁正常组织和BC组织lncRNA CASC2及miR-532-3p表达,BC组织中lncRNA CASC2和miR-532-3p表达在不同临床病理特征中的差异,生存组和死亡组临床病理特征和BC组织中lncRNA CASC2及miR-532-3p表达的差异。分析BC组织lncRNA CASC2、miR-532-3p表达的相关性;BC组织中lncRNA CASC2和miR-532-3p表达与术后5年内生存的关系;影响BC患者术后5年内生存的因素;lncRNA CASC2、miR-532-3p对BC患者术后5年内生存的预测价值。结果BC组织中lncRNA CASC2表达水平低于癌旁正常组织,miR-532-3p表达水平高于癌旁正常组织(t/P=38.239/<0.001,49.406/<0.001);肿瘤直径≥2 cm、TNM分期Ⅲ期、肿瘤低分化、淋巴结转移者比例lncRNA CASC2低表达组高于高表达组,而miR-532-3p低表达组低于高表达组(lncRNA CASC2:χ^(2)/P=17.361/<0.001、17.052/<0.001、14.694/<0.001、13.173/<0.001;miR-532-3p:χ^(2)/P=10.733/0.001、9.813/0.002、10.134/0.001、7.444/0.006);127例BC患者术后随访5年,生存99例(生存组),死亡28例(死亡组),肿瘤直径≥2 cm、TNM分期Ⅲ期、肿瘤低分化、淋巴结转移者比例及miR-532-3p表达水平死亡组高于生存组,而lncRNA CASC2表达水平死亡组低于生存组[χ^(2)(t)/P=5.211/0.022、27.149/<0.001、27.990/<0.001、4.590/0.032、19.155/<0.001、10.818/<0.001];BC组织中lncRNA CASC2与miR-532-3p表达呈负相关(r/P=-0.561/<0.001);lncRNA CASC2高表达组BC患者术后5年内总生存率为89.23%(58/65),高于lncRNA CASC2低表达组66.13%(41/62)(χ^(2)/P=9.854/0.002);miR-532-3p高表达组BC患者术后5年内总生存率为65.57%(40/61),低于miR-532-3p低表达组89.39%(59/66)(χ^(2)/P=10.466/0.001);肿瘤直径≥2 cm、TNM分期Ⅲ期、肿瘤低分化、有淋巴结转移、lncRNA CASC2低表达、miR-532-3p高表达均是影响BC患者术后5年内生存的独立危险因素[HR(95%CI)=2.255(1.192~4.263)、2.143(1.252~3.666)、3.089(1.386~6.887)、2.219(1.223~4.026)、2.606(1.174~5.788)、2.855(1.592~5.120)];lncRNA CASC2、miR-532-3p及二者联合预测BC患者术后5年内生存的AUC分别为0.840、0.852、0.908,二者联合预测的AUC大于lncRNA CASC2、miR-532-3p各自单独预测的AUC(Z/P=2.246/0.025、2.033/0.042)。结论BC组织中lncRNA CASC2表达下调,miR-532-3p表达上调,且术后5年内死亡的BC患者较存活患者变化更显著,二者表达与临床病理特征相关,对预测BC患者术后5年内生存情况价值较高。

lncRNA H19和IGF2基因在乳腺癌组织中的表达水平及印记状态

目的:研究长链非编码RNA(lncRNA)H19和胰岛素样生长因子2(IGF2)基因在乳腺癌组织中的表达水平,分析其印记状态。方法:采用实时荧光定量PCR(RT-qPCR)法检测乳腺癌组织及癌旁组织中H19和IGF2 mRNA表达水平,分析H19和IGF2 mRNA在乳腺癌组织及癌旁组织中的表达差异,利用单核苷酸多态性(SNP)区分等位基因表达情况(纯合或杂合),基因组DNA中IGF2(ApaⅠ位点)或H19(AluⅠ位点)为杂合则进行印记分析,确定H19和IGF2在乳腺癌组织中的印记状态,即印记保持(MOI)或印记丢失(LOI)。分析乳腺癌组织中H19和IGF2表达与分子分型的关系。结果:RT-qPCR法检测,乳腺癌组织中H19和IGF2 mRNA表达水平高于癌旁组织(P<0.01),H19 mRNA表达水平与IGF2 mRNA表达水平呈正相关关系(r=0.567,P<0.01)。不同分子分型乳腺癌患者癌组织中H19 mRNA表达水平均高于癌旁组织(P<0.05或P<0.01)。H19和IGF2在乳腺癌组织中均存在LOI,IGF2的LOI发生率为36.7%,高于H19的LOI发生率(4.3%)。RT-qPCR法检测,IGF2 LOI组乳腺癌组织中IGF2 mRNA表达水平明显高于IGF2 MOI组(P<0.01)。结论:乳腺癌组织中H19和IGF2 mRNA表达水平明显高于癌旁组织,IGF2的LOI发生率高于H19的LOI发生率,IGF2的LOI可能是乳腺癌发病的关键因素之一。

LncRNA LBX2-AS1调节miR-873-5p/G6PD轴对胃癌细胞增殖迁移和侵袭的影响

目的:探讨长链非编码RNA(LncRNA)瓢虫同源盒2反义RNA1(LBX2-AS1)调节微小RNA-873-5p(miR-873-5p)/葡萄糖-6-磷酸脱氢酶(G6PD)轴对胃癌(GC)细胞增殖、迁移和侵袭的影响。方法:以SGC7901细胞为研究对象,将其随机分为Control组、sh-NC组、sh-LBX2-AS1组、sh-LBX2-AS1+inhibitor-NC组、sh-LBX2-AS1+miR-873-5p inhibitor组;qRT-PCR法检测LncRNA LBX2-AS1、miR-873-5p、G6PD的表达;MTT法和平板克隆实验检测SGC7901细胞增殖;划痕实验检测SGC7901细胞迁移;Transwell实验检测SGC7901细胞的侵袭;Western blot检测SGC7901细胞中MMP-2、PCNA、MMP-9、G6PD蛋白表达;荧光素酶报告基因实验检测LncRNA LBX2-AS1与miR-873-5p,miR-873-5p与G6PD之间的相互作用;小鼠荷瘤实验验证敲除LncRNALBX2-AS1对CC肿瘤生长及G6PD表达的影响。结果:sh-LBX2-AS1组SGC7901细胞中A490值、克隆数、划痕愈合率、侵袭数、LncRNA LBX2-AS1、G6PD mRNA和PCNA、MMP-2、MMP-9蛋白表达低于sh-NC组、Control组,miR-873-5p表达高于sh-NC组、Control组(P<0.05);与sh-LBX2-AS1组、sh-LBX2-AS1+inhibitor-NC组相比,sh-LBX2-AS+miR-873-5p inhibitor组miR-873-5p表达降低,A490值、克隆数、划痕愈合率、侵袭数、G6PD mRNA和PCNA、MMP-2、MMP-9蛋白表达升高(P<0.05)。LncRNA LBX2-AS1靶向负调控miR-873-5p,miR-873-5p靶向负调控G6PD。实验组移植瘤质量、体积、Ki-67阳性率、G6PD阳性率低于对照组(P<0.05)。结论:敲除LncRNA LBX2-AS1可能抑制GC细胞的增殖、迁移和侵袭,其机制可能是调节miR-873-5p/G6PD轴实现的。

急性缺血性脑卒中患者血清长链非编码RNA母系表达基因3和Zeste同源物增强子-2表达与神经功能损伤的相关性分析

目的探讨长链非编码RNA(lncRNA)母系表达基因3(MEG3)与Zeste同源物增强子-2(EZH2)在急性缺血性脑卒中(AIS)患者血清中的表达水平及其与神经功能损伤之间的关系。方法选取延安市人民医院2021年1月至2022年11月收治的92例AIS患者为脑卒中组,92例健康体检者为对照组,根据NIHSS评分将脑卒中组患者分为致残性损伤组19例,非致残性损伤组73例。采用实时荧光定量聚合酶链式反应、酶联免疫吸附法分别检测血清lncRNAMEG3、EZH2水平。采用Spearman相关分析法进行AIS患者血清lncRNAMEG3、EZH2表达水平与美国国立卫生研究院卒中量表(NIHSS)评分之间的相关性分析;采用多因素Logistic回归分析AIS患者合并神经功能致残性损伤的影响因素,并绘制受试者工作特征(ROC)曲线分析血清lncRNA MEG3、EZH2水平对AIS患者合并神经功能致残性损伤的诊断价值。结果脑卒中组患者血清lncRNA MEG3、EZH2表达水平均高于对照组(t=11.817、11.542,P<0.05)。Spearman相关分析显示,AIS患者血清lncRNA MEG3、EZH2水平与NIHSS评分均呈正相关(r=0.540、0.603,P<0.01)。致残性损伤组体质量指数、吸烟史占比、甘油三酯、总胆固醇、同型半胱氨酸、发病-到院时间(ODT)、lncRNAMEG3、EZH2水平均高于非致残性损伤组(t/χ2=2.103、5.050、9.121、5.585、2.276、5.448、4.638、4.682,P<0.05)。多因素Logistic回归分析显示,甘油三酯、总胆固醇、lncRNA MEG3、EZH2以及ODT均是AIS患者合并神经功能致残性损伤的影响因素(OR=4.853、4.277、2.674、3.052、3.901,P<0.05)。lncRNA MEG3、EZH2联合诊断AIS患者合并神经功能致残性损伤的曲线下面积(AUC)大于lncRNAMEG3以及EZH2单独诊断的AUC(Z=2.626、2.954,P<0.01),敏感度、特异度分别为94.74%、82.15%。结论AIS患者血清lncRNA MEG3、EZH2水平均上升,与AIS患者神经功能损伤程度均正相关,可用作AIS患者合并神经功能致残性损伤的诊断指标,且联合诊断效果更好。

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.

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.