On a Definitizable Analog of the Trigonometric Moment Problem Generating an Indefinite Toeplitz Form

We prove the existence of an integro-polynomial representation for a sequence of numbers such that there exists a difference operator mapping this sequence to a sequence that generates the solvable trigonometric moment problem. A similar result related to the power moment problem was given in [12].     

Invariant ideals of twisted crossed products

We will prove a result concerning the inclusion of non-trivial invariant ideals inside non-trivial ideals of a twisted crossed product. We will also give results concerning the primeness and simplicity of crossed products of twisted actions of locally compact groups on -algebras. Received: 25 January 2002; in final form: 22 May 2002/Published online: 2 December 2002 This work is partially supported by Hong Kong RGC Direct Grant.     

Contact hypersurfaces of Kaehler manifolds

Contact hypersurfaces of a Kaehler manifold have been characterized and classified, assuming the second fundamental form to be Codazzi (in particular, parallel). We have also discussed the special cases when the ambient space is a (i) Calabi-Yau manifold and (ii) a complex space-form.     

白三叶草花蜜腺的发育解剖学研究

白三叶草花蜜腺突起环状，位于花丝基部并延续至花托上，属于环状花托／雄蕊蜜腺，蜜腺由分泌表皮和产蜜组织组成．在花的发育过程中，蜜腺由本身的原始细胞分裂，分化而来．分泌表皮具角质层，其上分布有变态气孔器，蜜汁经产蜜组织合成后，经变态气孔器泌出．     

A note on minimization problems and multistep methods

Summary. We use the qualitative properties of the solution flow of the gradient equation to compute a local minimum of a real-valued function . Under the regularity assumption of all equilibria we show a convergence result for bounded trajectories of a consistent, strictly stable linear multistep method applied to the gradient equation. Moreover, we compare the asymptotic features of the numerical and the exact solutions as done by Humphries, Stuart (1994) and Schropp (1995) for one-step methods. In the case of -stable formulae this leads to an efficient solver for stiff minimization problems. Received July 10, 1995 / Revised version received June 27, 1996     

Berezin transform on¶compact Hermitian symmetric spaces

Let X=G ^* be a compact Hermitian symmetric space. We study the Berezin transform on L ²(X) and calculate its spectrum under the decomposition of L ²(X) into the irreducible representations of G ^*. As applications we find the expansion of powers of the canonical polynomial (Bergman reproducing kernel for the canonical line bundle) in terms of the spherical polynomials on X, and we find the irreducible decomposition of tensor products of Bergman spaces on X. Received: 10 September 1996 / Revised version: 10 September 1997     

Spectral operators generated by damped hyperbolic equations

We announce a series of results on the spectral analysis for a class of nonselfadjoint opeators, which are the dynamics generators for the systems governed by hyperbolic equations containing dissipative terms. Two such equations are considered: the equation of nonhomogeneous damped string and the 3-dimensional damped wave equation with spacially nonhomogeneous spherically symmetric coefficients. Nonselfadjoint boundary conditions are imposed at the ends of a finite interval or on a sphere centered at the origin respectively. Our main result is the fact the aforementioned operators are spectral in the sense of N. Dunford. The result follows from the fact that the systems of root vectors of the above operators form Riesz bases in the corresponding energy spaces. We also give asymptotics of the spectra and state the Riesz basis property results for the nonselfadjoint operator pencils associated with these operators.     

To the spectral theory of Krein systems

We consider the Krein systems. For the set of Stummel class coefficients, we establish the criterion in terms of these coefficients for the system to satisfy the Szegö-type estimate on the spectral measure.