Bcklund Transformation and Multisoliton Solutions in Terms of Wronskian Determinant for (2+1)-Dimensional Breaking Soliton Equations with Symbolic Computation

In this paper, two types of the (2+1)-dimensional breaking soliton equations are investigated, whichdescribe the interactions of the Riemann waves with the long waves.With symbolic computation, the Hirota bilinearforms and Bcklund transformations are derived for those two systems.Furthermore, multisoliton solutions in termsof the Wronskian determinant are constructed, which are verified through the direct substitution of the solutions intothe bilinear equations.Via the Wronskian technique, it is proved that the Bcklund transformations obtained are theones between the (N-1)-and N-soliton solutions.Propagations and interactions of the kink-/bell-shaped solitonsare presented.It is shown that the Riemann waves possess the solitonic properties, and maintain the amplitudes andvelocities in the collisions only with some phase shifts.

The Baicklund Transformation and Explicit Solution of Volterra Lattice Equation

The Bcklund transformation and the generalized Miura transformation for the Volterra lattice equation are constructed by using point symmetry method.As an application,the explicit solution to the lattice equation is obtained.

Bcklund Transformation and Localized Coherent Structure for the (2+1)-Dimensional Asymmetric Nizhnik-Novikov-Veselov Equation

This article is concerned with the extended homogeneous balance method for studying the abundant localized solution structure of the (2+1) dimensional asymmetric Nizhnik Novikov Veselov equation. A B a¨ cklund transformation was first obtained, and then the richness of the localized coherent structures was found, which was caused by the entrance of two variable separated arbitrary functions, in the model. For some special choices of the arbitrary functions, it is shown that the localized structures of the model may be dromions, lumps, and ring solitons.

Bcklund Transformations and Solutions of a Generalized Kadomtsev-Petviashvili Equation

In this paper,the bilinear form of a generalized Kadomtsev-Petviashvili equation is obtained by applying the binary Bell polynomials.The N-soliton solution and one periodic wave solution are presented by use of the Hirota direct method and the Riemann theta function,respectively.And then the asymptotic analysis demonstrates one periodic wave solution can be reduced to one soliton solution.In the end,the bilinear Bcklund transformations are derived.

Generating a New Higher-Dimensional Coupled Integrable Dispersionless System:Algebraic Structures,Bcklund Transformation and Hidden Structural Symmetries

The prolongation structure methodologies of Wahlquist-Estabrook [H.D.Wahlquist and F.B.Estabrook,J.Math.Phys.16 (1975) 1] for nonlinear differential equations are applied to a more general set of coupled integrable dispersionless system.Based on the obtained prolongation structure,a Lie-Algebra valued connection of a closed ideal of exterior differential forms related to the above system is constructed.A Lie-Algebra representation of some hidden structural symmetries of the previous system,its Bcklund transformation using the Riccati form of the linear eigenvalue problem and their general corresponding Lax-representation are derived.In the wake of the previous results,we extend the above prolongation scheme to higher-dimensional systems from which a new (2 + 1)-dimensional coupled integrable dispersionless system is unveiled along with its inverse scattering formulation,which applications are straightforward in nonlinear optics where additional propagating dimension deserves some attention.

In the Atmosphere and Oceanic Fluids:Scaling Transformations,Bilinear Forms,Bäcklund Transformations and Solitons for A Generalized Variable-Coefficient Korteweg-de Vries-Modified Korteweg-de Vries Equation

The atmosphere is an evolutionary agent essential to the shaping of a planet,while in oceanic science and daily life,liquids are commonly seen.In this paper,we investigate a generalized variable-coefficient Korteweg-de Vriesmodified Korteweg-de Vries equation for the atmosphere,oceanic fluids and plasmas.With symbolic computation,beginning with a presumption,we work out certain scaling transformations,bilinear forms through the binary Bell polynomials and our scaling transformations,N solitons(with N being a positive integer)via the aforementioned bilinear forms and bilinear auto-Bäcklund transformations through the Hirota method with some solitons.In addition,Painlevé-type auto-Bäcklund transformations with some solitons are symbolically computed out.Respective dependences and constraints on the variable/constant coefficients are discussed,while those coefficients correspond to the quadratic-nonlinear,cubic-nonlinear,dispersive,dissipative and line-damping effects in the atmosphere,oceanic fluids and plasmas.

BCKLUND TRANSFORMATIONS FOR THE EQUATION~2u/x^1x^1+~2u/x^2x^2=f(u)

Backlund transformations for the equation is an arbitrary function) is studied in this paper, using the procedure of Wahlquist and Estabrook (WEP). We conclude that the condition is sufficient for the existence of Backlund transformations for the equation of our interest. A special case of our results leads to the conclusion of Leibbrandt[1,2]

Soliton Solutions, Bcklund Transformations and Lax Pair for a(3 + 1)-Dimensional Variable-Coefficient Kadomtsev–Petviashvili Equation in Fluids

Under investigation in this paper is a(3 + 1)-dimensional variable-coefficient Kadomtsev–Petviashvili equation, which describes the propagation of surface and internal water waves. By virtue of the binary Bell polynomials,symbolic computation and auxiliary independent variable, the bilinear forms, soliton solutions, B¨acklund transformations and Lax pair are obtained. Variable coefficients of the equation can affect the solitonic structure, when they are specially chosen, while curved and linear solitons are illustrated. Elastic collisions between/among two and three solitons are discussed, through which the solitons keep their original shapes invariant except for some phase shifts.

Lie Symmetry Analysis,Bcklund Transformations and Exact Solutions to (2+1)-Dimensional Burgers' Types of Equations

This paper is concerned with the (2+1)-dimensional Burgers' and heat types of equations.All of the geometic vector fields of the equations are obtained,an optimal system of the equation is presented.Especially,the Bcklund transformations (BTs) for the Burgers' equations are constructed based on the symmetry.Then,all of the symmetry reductions are provided in terms of the optimal system method,and the exact explicit solutions are investigated by the symmetry reductions and Bcklund transformations.

Bcklund transformations for the Burgers equation via localization of residual symmetries

We obtain the non-local residual symmetry related to truncated Painlev~ expansion of Burgers equation. In order to localize the residual symmetry, we introduce new variables to prolong the original Burgers equation into a new system. By using Lie＇s first theorem, we obtain the finite transformation for the localized residual symmetry. More importantly, we also Iocalize the linear superposition of multiple residual symmetries to find the corresponding finite transformations. It is interesting to find that the n-th B^icklund transformation for Burgers equation can be expressed by determinants in a compact way.

Painlev Property, Bcklund Transformations and Rouge Wave Solutions of (3+1)-Dimensional Burgers Equation

Burgers equation is the simplest one in soliton theory, which has been widely applied in almost all the physical branches. In this paper, we discuss the Painlev′e property of the(3+1)-dimensional Burgers equation, and then B¨acklund transformation is derived according to the truncated expansion of the obtained Painlev′e analysis. Using the B¨acklund transformation, we find the rouge wave solutions to the equation via the multilinear variable separation approach. And we also give an exact solution obtained by general variable separation approach, which is proved to possess abundant structures.

Generating Solutions to Discrete sine-Gordon Equation from Modified B(a|¨)cklund Transformation

We modify the bilinear Backlund transformation for the discrete sine-Gordon equation and derive varietyof solutions by freely choosing parameters from the modified Backlund transformation.Dynamics of solutions andcontinuum limits are also discussed.

入院时血清TGF-β1、Smad2、Smad3、HA、LN、PCⅢ、CⅣ水平与CHB肝纤维化严重程度的相关性及对疾病预后的预测价值

目的探讨入院时血清转化生长因子-β1(TGF-β1)、Smad同源蛋白2(Smad2)、Smad同源蛋白3(Smad3)及透明质酸(HA)、Ⅲ型前胶原(PCⅢ)、层黏连蛋白(LN)、Ⅳ型胶原(CⅣ)水平与慢性乙型肝炎(CHB)肝纤维化严重程度的相关性及联合检测对疾病预后的预测价值。方法选取河南省中医院2021年3月至2022年3月收治的78例CHB肝纤维化患者作为研究组,选择同期78名健康体检者作为对照组。比较研究组和对照组及不同肝纤维化分期、不同炎症活动分级CHB肝纤维化患者入院时血清TGF-β1、Smad2、Smad3、HA、PCⅢ、LN、CⅣ水平;分析入院时血清TGF-β1、Smad2、Smad3、HA、PCⅢ、LN、CⅣ水平与肝纤维化分期、炎症活动分级的相关性。CHB肝纤维化患者治疗3个月后,根据患者预后分为预后良好和预后不良亚组,比较预后良好和预后不良患者入院时血清TGF-β1、Smad2、Smad3、HA、PCⅢ、LN、CⅣ水平;分析入院时血清TGF-β1、Smad2、Smad3、HA、PCⅢ、LN、CⅣ水平联合检测对CHB肝纤维化患者预后不良的预测价值。结果研究组入院时血清TGF-β1、Smad2、Smad3、HA、LN、PCⅢ、CⅣ高于对照组(P<0.05);不同肝纤维化分期、炎症活动分级CHB肝纤维化患者入院时血清TGF-β1、Smad2、Smad3、HA、LN、PCⅢ、CⅣ比较:S1<S2<S3<S4、G1<G2<G3<G4,差异有统计学意义(P<0.05);入院时血清TGF-β1、Smad2、Smad3、HA、LN、PCⅢ、CⅣ水平与肝纤维化分期、炎症活动分级均呈正相关(P<0.05)。预后良好患者入院时血清TGF-β1、Smad2、Smad3、HA、LN、PCⅢ、CⅣ水平均低于预后不良患者(P<0.05);入院时血清TGF-β1、Smad2、Smad3、HA、LN、PCⅢ、CⅣ水平联合预测肝纤维化患者预后不良的曲线下面积(AUC)优于各指标单一检测(P<0.05)。结论CHB肝纤维化患者入院时血清TGF-β1、Smad2、Smad3、HA、PCⅢ、LN、CⅣ水平均呈现高表达,且与肝纤维化分期、炎症活动分级密切相关,其联合检测对CHB肝纤维化患者预后有较高的预测价值,可用于评估CHB肝纤维化患者病情严重程度和预后,为制定针对性治疗措施提供参考。

Jimbo-Miwa-Like方程的Lax可积性研究

基于双Bell多项式方法,将Jimbo-Miwa-Like方程化为双线性形式,运用Bell多项式的相关性质,构造出方程的双Bell多项式B?cklund变换、双线性B?cklund变换、Lax对、无穷守恒律和孤子解。运用试探函数法和符号计算软件Mathematica获得方程的复合型解,并选取适当的参数,绘制一部分精确解的图像来说明性质。

UV-B增强后秸秆还田分解对土壤氮转化微生物及酶活性的影响

为明确UV-B辐射增强对水稻秸秆化学成分的影响,阐释UV-B辐射增强后秸秆还田分解特征及其对稻田土壤氮素转化的间接效应,本研究在元阳梯田(海拔1600 m)开展大田试验,以当地水稻品种白脚老粳为研究对象,研究UV-B辐射增强(5.00kJ·m^(-2))对水稻秸秆化学成分及其还田后秸秆降解、土壤氮素转化的影响。结果表明:UV-B辐射增强显著降低水稻秸秆纤维素含量,增加木质素含量,提高秸秆木质素/氮;并导致秸秆纤维素、木质素、总氮的降解速率总体降低,最大降幅分别达38.7%、18.1%、25.8%。与自然光照秸秆相比,UV-B辐射后的秸秆还田显著降低土壤固氮细菌、氨化细菌、硝化细菌和反硝化细菌数量,增加土壤蛋白酶、氨单加氧酶、硝酸还原酶活性,提高土壤硝化和反硝化速率。相关性分析表明,秸秆木质素/氮与秸秆降解速率呈极显著负相关;秸秆纤维素、木质素、总氮降解速率与硝酸还原酶活性呈显著正相关,后者又与N_(2)O排放通量呈显著正相关;硝化细菌数量与NO_(3)^(-)-N含量呈负相关。研究表明,UV-B辐射增强通过提高秸秆木质素/氮,抑制秸秆纤维素、木质素、总氮降解,减少土壤氨化细菌数量,增加氨单加氧酶和硝酸还原酶活性,从而促进土壤NH_(4)^(+)-N向NO_(3)^(-)-N转化,导致N2O排放通量增加。

Kinetic analysis of austenite transformation for B1500HS high-strength steel during continuous heating

The dilatometric curves of B1500HS high-strength steel at different heating rates were measured by a Gleeble-3800 thermal simulator and analyzed to investigate the effect of heating rate on austenitization.Results show that the value of starting temperature and ending temperature of austenite transformation increase with the rise of heating rates,whereas the temperature interval of austenite formation decreases.The kinetic equation of austenite transformation was solved using the Johnson–Mehl–Avrami model,and the related parameters of the equation were analyzed by the Kissinger method.For those calculations,the activation energy of austenite transformation is 1.01×10^6 J/mol,and the values of kinetic parameters n and ln k0 are 0.63 and 103.03,respectively.The relationship between the volume fraction of austenite and the heating time at different heating rates could be predicted using the kinetic equation.The predicted and experimental results were compared to verify the accuracy of the kinetic equation.The microstructure etched by different corrosive solutions was analyzed,and the reliability of kinetic equation was further verified from the microscopic perspective.

Agrobacterium tumefaciens-mediated genetic transformation of the phytopathogenic fungus Penicillium digitatum

Agrobacterium tumefaciens-mediated transformation (ATMT) system was assessed for conducting insertional mutagenesis in Penicillium digitatum, a major fungal pathogen infecting post-harvest citrus fruits. A transformation efficiency of up to 60 transformants per 106 conidia was achieved by this system. The integration of the hph gene into the fungal genome was verified by polymerase chain reaction (PCR) amplification and sequencing. These transformants tested were also shown to be mitotically stable. Southern blot analysis of 14 randomly selected transformants showed that the hph gene was randomly integrated as single copy into the fungal genome of P. digitatum. Thus, we conclude that ATMT of P. digitatum could be used as an alter-natively practical genetic tool for conducting insertional mutagenesis in P. digitatum to study functional genomics.

Genetic transformation of cry1A(b) gene into teak

Teak (Tectona grandis) provides one of the most highly sought after timber in the world and is a widely recommended species for reforestation. As such teak is widely planted in Malaysia. Though no serious outbreaks have been recorded for teak in Malaysia, but insect attack remains the most important threat to the timber industry. Thus, in efforts to overcome the problem, an integrated pest management system needs to be developed. Spraying of commercial Bt has been a common practice in addressing minor outbreaks. However, one of the main limitations of the spraying technique is poor coverage, especially on plant surfaces. Poor coverage, however, could be overcome by planting insect resistant trees. In addition, the approach of using genetic engineering in addressing the above problem proves to be possible with the advancement made in genetic transformation of trees especially in the last decade. This, together with improved knowledge on gene function following improved DNA recombinant techniques promises the major advancement in pest management of forest species. This report demonstrates the possibility of transferring foreign gene into teak cells. In this study, nodal segments of teak were subjected to particle bombardment. Nodal segments bombarded with gold particles coated with plasmid DNA carrying hygromycin phosphotransferase (hpt), β glucuronidase (gus) and cry1A(b) genes were then transferred onto medium for shoot development. The shoots were than transferred onto the same medium supplemented with 10mg/L hygromycin for selection. Selection was repeated several times with six week subculture intervals on the same Hm containing media. The presence of the transgenes in the Hmr plants was confirmed using PCR.

PD-L1激活NF-κB促进子宫内膜癌细胞上皮间质转化的作用研究

目的探讨程序性死亡蛋白配体-1(programmed death ligand-1,PD-L1)过表达对子宫内膜癌细胞Ishikawa上皮间质转化的影响及可能机制。方法使用实验室构建的PD-L1过表达稳转细胞株Ishikawa/PD-L1及稳转空载对照组Ishikawa/EV,qPCR及Western blot法检测PD-L1过表达效率,Transwell和划痕实验检测细胞迁移能力和侵袭活性,Western blot法检测上皮间质转化相关蛋白表达和核转录因子-κB(nuclear factor kappa-B,NF-κB)磷酸化水平。结果与对照组相比,Ishikawa/PD-L1迁移能力与侵袭活性显著增强,Vimentin、N-cadherin、p-p65蛋白表达明显升高,E-cadherin表达明显下调。结论PD-L1可通过诱导NF-κB信号通路激活,促进上皮间质转化,进而增强子宫内膜癌细胞的迁移、侵袭能力。

Sine Transformation and the Reparametrization of Bézier Curves

A solution to the reparametrization of Bézier curves by sine transformation of Bemstein basis is presented. The new effective reparametrization method is given through the following procedures： educing Sine Bemstein-Bézier Class-SBBC function, defining SBBC curve and discussing the relation between SBBC and Bézier curve.