Study on Seed Plant Flora of Yunfeng Mountain,an Offshoot of Gaoligong Mountain Range

In this paper, the flora in an area of 35 km2 of Yunfeng Mountain, an off- shoot of Gaoligong mountain range, were sampled and analyzed. The results showed that Yunfeng Mountain had a high diversity in seed plants, which covered 92 families, 247 genera and 431 species. Among the seed plants, the gymnosperms covered 4 families, 5 genera and 7 species, while the angiosperms covered 88 families, 242 genera and 424 species. The seed plants in Yunfeng Mountain had rich distribution types, and they formed a flora dominated by tropical and subtropical plants.

Fault Detection Observer Design for LSFDJ:A Factorization Approach

Based on a new special co-inner-outer factorization, a factorization approach for design fault detection observer for LSFDJ was proposed. It is a simple state-space method and can deal with time-varying LSFDJ with sensor noise and sensor faults. The performance of the fault detection observer is optimized in an H ∞ setting, where the ratio between the gains from disturbance and fault to residual respectively is minimized. The design parameters of the detection observer were given in terms of the solution to the Riccati differential equation with jumps.

Totally Real Minimal Submanifolds in a Quaternion Projective Space

Some curvature pinching theorems for compact or complete totally real minimal submanifolds in a quaternion projective space are given,so that the corresponding results due to B. Y.Chen and C. S. Houh as well as Y. B. Shen are improved and generalized.

Compact Space-like Submanifolds in Pseudo-Riemann Manifold

We first establish a integral inequality for compact maximal space-like subman ifolds in pseudo-Riemannian manifolds Np(n+p). Then, we investigate compact space-like sub manifolds and hupersurfaces with parallel second fundamental form in Np(n+p) and some other ambient spaces. We obtain some distribution theorems for the square norm of the second fundamental form.

Reductions to Korteweg-de Vries Soliton Hierarchy

Based on the nonlinearization of Lax pairs, the Korteweg-de Vries （KdV） soliton hierarchy is decomposed into a family of finite-dimensional Hamiltonian systems, whose Liouville integrability is proved by means of the elliptic coordinates. By applying the Abel-Jacobi coordinates on a Riemann surface of hyperelliptic curve, the resulting Hamiltonian flows as well as the KdV soliton hierarchy are ultimately reduced into linear superpositions, expressed by the Abel-Jacobi variables.

Direct Approach to Construct the Periodic Wave Solutions for Two Nonlinear Evolution Equations

With symbolic computation, the Hirota method and Riemann theta function are employed to directly construct the periodic wave solutions for the Hirota-Satsuma equation for shallow water waves and Boiti-Leon-Manna- Pempinelli equation. Then, the corresponding figures of the periodic wave solutions are given. Fhrthermore, it is shown that the known soliton solutions can be reduced from the periodic wave solutions.

On Two Conjectures Concerning the Veronese Generating submanifolds

The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper the conjectures on scalar curvature of Veronese generating submanifolds in E~σ and the minimal conjecture on Veronese space-like submanifold Σ and Veronese pseudo-Riemannian submanifold in E_1~σ are proved. We have Σ is minimal in H^5. is minimal in S_1~5, Σ and are of 1-type in E_1~σ.

Lower Bound of the First Eigenvalue for the Laplace Operator on Compact Riemannian Manifold

Let M be a compact m-dimensional Riemannian manifold, let d denote, its diameter, -R(R>O) the lower bound of the Ricci curvature, and λ_1 the first eigerivalue for the Laplacian on M. Then there exists a constant C_m=max{2^(1/m-1),2^(1/2)}, Such that λ_1≥π~2/d^2·1/(2-(11)/(2π~2))+11/2π~2e^cm、

2-Harmonic Totally Real Submanifolds in a Complex Projective Space

In this paper, we discuss the relations between the 2-harmornic totally real submsnifold and the minimal totall real submanifold in the complex protective spsace, and obtain the pinching conductions for the second fundamental form and the Rieci curature of the 2-harmornic totally real submanifold in the complex projective space.

A Scheme for Generating Cluster States via Raman Interaction

A scheme for generating cluster states via Raman interaction is proposed. In the scheme, we firstly prepare cluster states of multi-cavities with information encoded in the coherent states and then generate cluster states of multiatoms, which encode the information in the ground states of A-type atoms. The advantages of our scheme are that the atomic spontaneous radiation can be efficiently reduced since the cavity frequency is largely detuned from the atomic transition frequency and the Hadamard gate operation of the coherent states is replaced by measuring the coherent states.

Finite Type Non-Minimal Submanifolds

The notion of finite type submanifolds was introduced by B. Y. Chen. In this paper we consider the characteristics and the classifications of finite type non-minimal submanifolds. The characteristic theorems of 2-type Chen submanifolds,mass-symmetrie hypersurfaces and Dupin hypersurfaces in E_3~m are obtained. The classification theorems of 3-type hypersurfaces and null 2-type curves in E_3~m are also proved.

2-Harmonic Curves Isometrially Immersed in a Surface

In this paper,the author proves the necessary and sufficient condition for the existence of 2-harmonically and isometrically immersed curves in a 2-dimensinonal surface N∪→IE^3.

On Twisted Atiyah-Singer Operators(Ⅰ)

In this paper we show that the de Rham and the Signature operators on a Riemannian manifold are all isomorphic to some twisted Atiyah-Singer operators. Then the local index theorem and local Lefschetz fixed point formulas of these operators can be obtained from the corresponding theorems of twisted Atiyah-Singer operators.

世象拾趣（续一）——掌声

会场，两千多职工挤在里面。男的：看报纸，翻小人书；女的：纳鞋底。打毛衣。

HILBERT-DIRAC OPERATORS IN CLIFFORD ANALYSIS

Around the central theme of 'square root' of the Laplace operator it is shown that the classical Riesz potentials of the first and of the second kind allow for an explicit expression of so-called Hilbert-Dirac convolution operators involving natural and complex powers of the Dirac operator.

η-INVARIANT AND CHERN-SIMONS CURRENT

The author presents an alternate proof of the Bismut-Zhang localization formula of η invariants, when the target manifold is a sphere, by using ideas of mod k index theory instead of the difficult analytic localization techniques of Bismut-Lebeau. As a consequence, it is shown that the R/Z part of the analytically defined η invariant of Atiyah-Patodi-Singer for a Dirac operator on an odd dimensional closed spin manifold can be expressed purely geometrically through a stable Chern-Simons current on a higher dimensional sphere. As a preliminary application, the author discusses the relation with the Atiyah-Patodi-Singer R/Z index theorem for unitary flat vector bundles, and proves an R refinement in the case where the Dirac operator is replaced by the Signature operator.

Regular Submanifolds in Conformal Space Q_p^n

The authors study the regular submanifolds in the conformal space Qp^n and introduce the submanifold theory in the conformal space Qp^n. The first variation formula of the Willmore volume functional of pseudo-Riemannian submanifolds in the conformal space Qp^n is given. Finally, the conformal isotropic submanifolds in the conformal space

Convergence of Yang-Mills-Higgs flow for twist Higgs pairs on Riemann surfaces

We consider the gradient flow of the Yang-Mills-Higgs functional of twist Higgs pairs on a Hermitian vector bundle(E,H)over Riemann surface X.It is already known the gradient flow with initial data(A0,φ0)converges to a critical point(A∞,φ∞).Using a modified Chern-Weil type inequality,we prove that the limiting twist Higgs bundle(E,d′′A∞,φ∞)coincides with the graded twist Higgs bundle defined by the HarderNarasimhan-Seshadri filtration of the initial twist Higgs bundle(E,d′′A0,φ0),generalizing Wilkin’s results for untwist Higgs bundle.

Slowly Increasing Cohomology for Discrete Metric Spaces with Polynomial Growth

The authors introduce a kind of slowly increasing cohomology HS＊（X） for a discrete metric space X with polynomial growth, and construct a character map from the slowly increasing cohomology HS＊ （X） into HC＊ont （S（X））, the continuous cyclic cohomol- ogy of the smooth subalgebra S（X） of the uniform Roe algebra B＊ （X）. As an application, it is shown that the fundamental cocycle, associated with a uniformly contractible complete Riemannian manifold M with polynomial volume growth and polynomial contractibility radius growth, is slowly increasing.

On the elliptic curve y^2=x^3-2r Dx and factoring integers

Let D=pq be the product of two distinct odd primes.Assuming the parity conjecture,we construct infinitely many r≥1 such that E2rD:y2=x3-2rDx has conjectural rank one and vp(x([k]Q))≠vq(x([k]Q))for any odd integer k,where Q is the generator of the free part of E(Q).Furthermore,under the generalized Riemann hypothesis,the minimal value of r is less than c log4 D for some absolute constant c.As a corollary,one can factor D by computing the generator Q.