A boundary Schwarz lemma on the classical domain of type I

Let R_I(m,n) be the classical domain of type I in C^(m×n)with 1≤m≤n.We obtain the optimal estimates of the eigenvalues of the Fréchet derivative Df(Z) at a smooth boundary fixed point Z of R_I(m,n)for a holomorphic self-mapping f of R_L(m,n).We provide a necessary and sufficient condition such that the boundary points of R_I(m,n) are smooth,and give some properties of the smooth boundary points of R_L(m,n).Our results extend the classical Schwarz lemma at the boundary of the unit disk △ to R_I(m,n),which may be applied to get some optimal estimates in several complex variables.

Schwarz Lemma at the Boundary on the Classical Domain of Type Ⅲ

Let R_Ⅲ(n) be the classical domain of type Ⅲ with n≥2. This article is devoted to a deep study of the Schwarz lemma on R_Ⅲ(n) via not only exploring the smooth boundary points of R_Ⅲ(n) but also proving the Schwarz lemma at the smooth boundary point for holomorphic self-mappings of R_Ⅲ(n).

ON THE COMPLETE INTEGRABILITY OF NONLINEARIZED LAX SYSTEMS FOR THE CLASSICAL BOUSSINESQ HIERARCHY

The N involutive integrals of motion with linearly independent gradients for the nonlin earized eigenvalue problem corresponding to the classical Boussinesq (CB) hierarchy are given. It is shown that when n=1,2,3, the nonlinearized time parts of Lax systems for the CB hierarchy are transformed into three finite-dimensional integrable Hamiltonian systems under the constraint of the nonlinearized spatial part.

EVOLUTION OF THE SCATTERING DATA UNDER THE CLASSICAL DARBOUX TRANSFORM FOR su(2) SOLITON SYSTEMS

The changing of the scattering data for the solutions of su (2) soliton systems which are relatedby a classical Darboux transformation (CDT) is obtained. It is shown that how a CDT creates anderases a soliton.

Classic mechanisms and experimental models for the anti-inflammatory effect of traditional Chinese medicine

Inflammation is a common disease involved in the pathogenesis,complications,and sequelae of a large number of related diseases,and therefore considerable research has been directed toward developing anti-inflammatory drugs for the prevention and treatment of these diseases.Traditional Chinese medicine(TCM)has been used to treat inflammatory and related diseases since ancient times.According to the re-view of abundant modern scientific researches,it is suggested that TCM exhibit anti-inflammatory effects at different levels,and via multiple pathways with various targets,and recently a series of in vitro and in vivo anti-inflammatory models have been developed for anti-inflammation research in TCM.Currently,the reported classic mechanisms of TCM and experimental models of its anti-inflammatory effects pro-vide reference points and guidance for further research and development of TCM.Importantly,the research clearly confirms that TCM is now and will continue to be an effective form of treatment for many types of inflammation and inflammation-related diseases.

On the Mean Value of High-Powers of a Special Character Sum Modulo a Prime

In this paper,we use the elementary methods,the properties of Dirichlet character sums and the classical Gauss sums to study the estimation of the mean value of high-powers for a special character sum modulo a prime,and derive an exact computational formula.It can be conveniently programmed by the“Mathematica”software,by which we can get the exact results easily.

Several inequalities for L_2-projection body

In this paper, by using the Lp-Brunn-Minkowski theory and its dual theory, L2-version on the conjectured projection inequality is investigated, the （reverse） inclusive relationship between L2-projection body and the classical projection body are established, and a constrained minimization problem is solved.

The Hybrid Power Mean Involving the Character Sum of Polynomials and a Sum Analogous to Kloosterman Sum

The main purpose of this paper is using the properties of the classical Gauss sum and the analytic methods to study the computational problem of one kind of hybrid power mean involving the character sum of polynomials and a sum analogous to Kloosterman sum mod p,an odd prime,and give two sharp asymptotic formulae for them.

A Generalized （G＇/G）-Expansion Method to Find the Traveling Wave Solutions of Nonlinear Evolution Equations

In this article, we construct the exact traveling wave solutions for nonlinear evolution equations in the mathematical physics via the modified Kawahara equation, the nonlinear coupled KdV equations and the classical Boussinesq equations, by using a generalized （G＇/G）-expansion method, where G satisfies the Jacobi elliptic equation. Many exact solutions in terms of Jacobi elliptic functions are obtained.

In Search of“Voices”:Linguistic Choice and Construction of Subjectivity in Lu Xun’s Early Translations and Writings

Unlike Hu Shih and Chen Duxiu,among other leading intellectuals in the May Fourth New Literature Movement,Lu Xun had no experience of writing in vernacular Chinese(baihua)in his early years.Except Jules Verne’s two novels translated by Lu Xun in the 1900s,all his translations and writings before 1918 were produced in classical Chinese(wenyan),until“Diary of a Madman”(Kuangren riji)was published in May 1918.Despite the well-known fact that Lu Xun wrote his first vernacular fiction at the quest of Qian Xuantong,the sudden and seemingly effortless change in Lu Xun's linguistic choice remains a mystery.This article attempts to shed new light on the problem by focusing on Lu Xun’s understanding and practice of voices(sheng)in his early works.First,I explore the meaning of the term"voices of the heart"(xinsheng)in Lu Xun's thoughts and connect it to the rendering of subjectivity in his writings and translations in the late Qing dynasty.The archaic style he chose implies,paradoxically,both his effort to deliver inner"voices of the heart"and his self-awareness of the difficulty in conveying it.Then along this line,I try to grasp Lu Xun;s intrinsic motivation for the change in his linguistic choice.Vernacular Chinese provided Lu Xun with a channel of constructing inter-subjectivity by appealing to a broad public,thus emancipating him from the dilemma of expressing“voices of the heart.”Throughout the first two decades of the twentieth century,Lu Xun's perception and application of written language were closely interwoven with his concern for subjectivity.