SOME PROPERTIES OF THE INTEGRATION OPERATORS ON THE SPACES F(p,q,s)

We study the closed range property and the strict singularity of integration operators acting on the spaces F(p,pα-2,s).We completely characterize the closed range property of the Volterra companion operator I_(g)on F(p,pα-2,s),which generalizes the existing results and answers a question raised in[A.Anderson,Integral Equations Operator Theory,69(2011),no.1,87-99].For the Volterra operator J_(g),we show that,for 0<α≤1,J_(g)never has a closed range on F(p,pα-2,s).We then prove that the notions of compactness,weak compactness and strict singularity coincide in the case of J_(g)acting on F(p,p-2,s).

Painlevé Property and Integrability of Polynomial Dynamical Systems

The main purpose of this paper is to investigate the connection between the Painlev′e property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has Painlev′e property, then it admits certain class of first integrals. We also present some relationships between the Painlev′e property and the structure of the differential Galois group of the corresponding variational equations along some complex integral curve.

Painleve Integrability, Consistent Riccati Expansion Solvability and Interaction Solution for the Coupled mKdV-BLMP System

The integrability of the coupled, modified KdV equation and the potential Boiti-Leon-Manna-Pempinelli (mKdV-BLMP) system is investigated using the Painlevé analysis approach. It is shown that this coupled system possesses the Painlevé property in both the principal and secondary branches. Then, the consistent Riccati expansion (CRE) method is applied to the coupled mKdV-BLMP system. As a result, it is CRE solvable for the principal branch while non-CRE solvable for the secondary branch. Finally, starting from the last consistent differential equation in the CRE solvable case, soliton, multiple resonant soliton solutions and soliton-cnoidal wave interaction solutions are constructed explicitly.

High-chromium vanadium-titanium magnetite all-pellet integrated burden optimization and softening-melting behavior based on flux pellets

High-chromium vanadium-titanium magnetite(HVTM)is a crucial polymetallic-associated resource to be developed.The allpellet operation is a blast furnace trend that aims to reduce carbon dioxide emissions in the future.By referencing the production data of vanadium-titanium magnetite blast furnaces,this study explored the softening-melting behavior of high-chromium vanadium-titanium magnetite and obtained the optimal integrated burden based on flux pellets.The results show that the burden with a composition of 70wt%flux pellets and 30wt%acid pellets exhibits the best softening-melting properties.In comparison to that of the single burden,the softening-melting characteristic temperature of this burden composition was higher.The melting interval first increased from 307 to 362℃and then decreased to 282℃.The maximum pressure drop(ΔPmax)decreased from 26.76 to 19.01 kPa.The permeability index(S)dropped from 4643.5 to 2446.8 kPa·℃.The softening-melting properties of the integrated burden were apparently improved.The acid pellets played a role in withstanding load during the softening process.The flux pellets in the integrated burden exhibited a higher slag melting point,which increased the melting temperature during the melting process.The slag homogeneity and the TiC produced by over-reduction led to the gas permeability deterioration of the single burden.The segregation of the flux and acid pellets in the HVTM proportion and basicity mainly led to the better softening-melting properties of the integrated burden.

Painlevé integrability of a generalized fifth-order KdV equation with variable coefficients: Exact solutions and their interactions

By means of singularity structure analysis, the integrability of a generalized fifth-order KdV equation is investigated. It is proven that this equation passes the Painleve test for integrability only for three distinct cases. Moreover, the multi- soliton solutions are presented for this equation under three sets of integrable conditions. Finally, by selecting appropriate parameters, we analyze the evolution of two solitons, which is especially interesting as it may describe the overtaking and the head-on collisions of solitary waves of different shapes and different types.

Painlevé integrability of the supersymmetric Ito equation

A supersymmetric version of the Ito equation is proposed by extending the independent and dependent variables for the classic Ito equation.To investigate the integrability of the N = 1 supersymmetric Ito(sIto) equation, a singularity structure analysis for this system is carried out.Through a detailed analysis in two cases by using Kruskal’s simplified method, the sIto system is found to pass the Painlevé test, and thus is Painlevé integrable.

Wave propagation of a functionally graded plate via integral variables with a hyperbolic arcsine function

Several studies on functionally graded materials(FGMs)have been done by researchers,but few studies have dealt with the impact of the modification of the properties of materials with regard to the functional propagation of the waves in plates.This work aims to explore the effects of changing compositional characteristics and the volume fraction of the constituent of plate materials regarding the wave propagation response of thick plates of FGM.This model is based on a higher-order theory and a new displacement field with four unknowns that introduce indeterminate integral variables with a hyperbolic arcsine function.The FGM plate is assumed to consist of a mixture of metal and ceramic,and its properties change depending on the power functions of the thickness of the plate,such as linear,quadratic,cubic,and inverse quadratic.By utilizing Hamilton’s principle,general formulae of the wave propagation were obtained to establish wave modes and phase velocity curves of the wave propagation in a functionally graded plate,including the effects of changing compositional characteristics of materials.

Painlevé Integrability of Nonlinear Schrdinger Equations with both Space-and Time-Dependent Coefficients

We investigate the Painleve integrabiiity of nonautonomous nonlinear Schr6dinger （NLS） equations with both space-and time-dependent dispersion, nonlinearity, and external potentials. The Painleve analysis is carried out without using the Kruskal＇s simplification, which results in more generalized form of inhomogeneous equations. The obtained equations are shown to be reducible to the standard NLS equation by using a point transformation. We also construct the corresponding Lax pair and carry out its Kundu-type reduction to the standard Lax pair. Special cases of equations from choosing limited form of coefficients coincide with the equations from the previous Painleve analyses and/or become unknown new equations.

Painlevé property, local and nonlocal symmetries, and symmetry reductions for a (2+1)-dimensional integrable KdV equation

The Painlevé property for a(2+1)-dimensional Korteweg–de Vries(KdV) extension, the combined KP3(Kadomtsev–Petviashvili) and KP4(cKP3-4), is proved by using Kruskal’s simplification. The truncated Painlevé expansion is used to find the Schwartz form, the Bäcklund/Levi transformations, and the residual nonlocal symmetry. The residual symmetry is localized to find its finite Bäcklund transformation. The local point symmetries of the model constitute a centerless Kac–Moody–Virasoro algebra. The local point symmetries are used to find the related group-invariant reductions including a new Lax integrable model with a fourth-order spectral problem. The finite transformation theorem or the Lie point symmetry group is obtained by using a direct method.

若干非线性偏微分方程的Painleve性质和Backlund变换

若干非线性偏微分方程的Ｐａｉｎｌｅｖé性质和Ｂａｃｋｌｕｎｄ变换朱佐农（扬州大学农学院，扬州２２５００１）对于一个非线性偏微分方程，判别其可积性是重要的课题．Ｊ．Ｗｅｉｓｓ等人对偏微分方程定义了Ｐａｉｎｌｅｖｅ性质，从Ｐａｉｎｌｅｖｅ性质的分析出发可...

Painleve定理的拓广

R2中的Painleve定理在求解方程的边值问题中有十分重要的作用。此定理对多复变数中的Cauchy型积分的边界行为的研究也起关键作用。将R2中的Painleve定理推广到Cn(n>1)中,得到复的Painleve定理。并简述其在多复变数奇异积分研究中的应用。

Boundary properties for several singular integral operators in real Clifford analysis

On the basis of the Cauchy integral formulas for regular and biregular functions, we define some Cauchy-type singular integral operators. Then we discuss the Holder continuous property of some singular integral operators with one integral variable. Then we divide a singular integral operator with two variables into three parts and prove its Holder continuous property on the boundary.

A class of coupled nonlinear Schrdinger equations:Painlev'e property,exact solutions,and application to atmospheric gravity waves

The Painleve integrability and exact solutions to a coupled nonlinear Schrodinger （CNLS） equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass the Painleve test. Twenty periodic cnoidal wave solutions are obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions to the CNLS equation are used to explain the generation and propagation of atmospheric gravity waves.

带自由参数高阶变系数耦合非线性Schrdinger方程的Painleve可积性

借助于奇异分析的手段判断带自由参数高阶变系数耦合非线性Schrdinger方程的Painleve可积性.得到了在一定参数约束下,仅有两个子系统是Painleve可积的.

Determination of optical properties of normal and adenomatous human colon tissues in vitro using integrating sphere techniques

AIM: The purpose of the present study is to compare the optical properties of normal human colon mucosa/submucosa and muscle layer/chorion, and adenomatous human colon mucosa/submucosa and muscle layer/chorion in vitro at 476.5, 488, 496.5, 514.5 and 532 nm. We believe these differences in optical properties should help differential diagnosis of human colon tissues by using optical methods.METHODS: In vitro optical properties were investigated for four kinds of tissues: normal human colon mucosa/submucosa and muscle layer/chorion, and adenomatous human colon mucosa/submucosa and muscle layer/chorion. Tissue samples were taken from 13 human colons (13 adenomatous, 13 normal). From the normal human colons a total of 26 tissue samples, with a mean thickness of 0.40 mm, were used (13 from mucosa/submucosa and 13 from muscle layer/chorion), and from the adenomatous human bladders a total of 26 tissue samples, with a mean thickness of 0.40 mm, were used (13 from mucosa/submucosa and 13 from muscle layer/chorion). The measurements were performed using a double-integratingsphere setup and the optical properties were assessed from these measurements using the adding-doubling method that was considered reliable.RESULTS: The results of measurement showed that there were significant differences in the absorption coefficients and scattering coefficients between normal and adenomatous human colon mucosa/submucosa at the same wavelength,and there were also significant differences in the two optical parameters between both colon muscle layer/chorion at the same wavelength. And there were large differences in the anisotropy factors between both colon mucosa/submucosa at the same wavelength, there were also large differences in the anisotropy factors between both colon muscle layer/chorion at the same wavelength.There were large differences in the value ranges of the absorption coefficients, scattering coefficients and anisotropy factors between both colon mucosa/submucosa,and there were also large differences in these value ranges between both colon muscle layer/chorion. There are the same orders of magnitude in the absorption coefficients for four kinds of colon tissues. The scattering coefficients of these tissues exceed the absorption coefficients by at least two orders of magnitude.CONCLUSION: There were large differences in the three optical parameters between normal and adenomatous human colon mucosa/submucosa at the same laser wavelength, and there were also large differences in these parameters between both colon muscle layer/chorion at the same laser wavelength. Large differences in optical parameters indicate that there were large differences in compositions and structures between both colon mucosa/submucosa, and between both colon muscle layer/chorion.Optical parameters for four kinds of colon tissues are wavelength dependent, and these differences would be useful and helpful in clinical applications of laser and tumors photodynamic therapy (PDT).

Painlevé Property and Exact Solutions to a (2+1) Dimensional KdV-mKdV Equation

A (2 + 1) dimensional KdV-mKdV equation is proposed and integrability in the sense of Painlevé and some exact solutions are discussed. The B?cklund transformation and bilinear equations are obtained through Painlevé analysis. Some exact solutions are deduced by Hirota method and generalized Wronskian method.

Painlev properties and exact solutions for the high-dimensional Schwartz Boussinesq equation

The usual （1＋1）-dimensional Schwartz Boussinesq equation is extended to the （1＋1）-dimensional space-time symmetric form and the general （n＋1）-dimensional space-time symmetric form. These extensions are Painleve integrable in the sense that they possess the Painleve property. The single soliton solutions and the periodic travelling wave solutions for arbitrary dimensional space-time symmetric form are obtained by the Painleve-Backlund transformation.

Painlev property of the modified C-KdV equation and its exact solutions

In this paper, the Painleve properties of the modified C-KdV equation are verified by using the W-K algorithm. Then some exact soliton solutions are obtained by applying the standard truncated expansion method and the nonstandard truncated expansion method with the help of Maple software, respectively.

Effect of a force-free end on the mechanical property of a biopolymer--A path integral approach

We study the effect of a force-free end on the mechanical property of a stretched biopolymer.The system can be divided into two parts.The first part consists of the segment counted from the fixed point（i.e.,the origin） to the forced point in the biopolymer,with arclength L_f.The second part consists of the segment counted from the forced point to the force-free end with arclength △L.We apply the path integral technique to find the relationship between these two parts.At finite temperature and without any constraint at the end,we show exactly that if we focus on the quantities related to the first part,then we can ignore the second part completely.Monte Carlo simulation confirms this conclusion.In contrast,the effect for the quantities related to the second part is dependent on what we want to observe.A force-free end has little effect on the relative extension,but it affects seriously the value of the end-to-end distance if △L is comparable to L_f.

Painlevé Property and Complexiton Solutions of a Special Coupled KdV Equation

A special coupled KdV equation is proved to be the Painleve property by the Kruskal＇s simplification of WTC method. In order to search new exact solutions of the coupled KdV equation, Hirota＇s bilinear direct method and the conjugate complex number method of exponential functions are applied to this system. As a result, new analytical eomplexiton and soliton solutions are obtained synchronously in a physical field. Then their structures, time evolution and interaction properties are further discussed graphically.