Fixed points of commuting holomorphic mappings other than the Wolff point

Let be the unit disc of and let be such that . For 1$">, let . We study the behavior of on . In particular, we prove that . As a consequence, besides conditions for , we prove a conjecture of C. Cowen in case and are univalent mappings.

     

球面函数的Cesαro平均的收敛性与强求和及其逼近阶的研究

本文研究了球面上的函数用其Fourier—Laplace级数的一种重要的线性求和法-Cesαro平均来求和与强求和及其相应的逼近与强逼近的阶的研究状况、发展态势和前景展望等．     

Involvement of nitric oxide in the signal transduction of salicylic acid regulating stomatal movement

The effects and the relationship between sali-cylic acid(SA)and nitric oxide(NO) on Vicia faba L.stomatal movement were studied.The results here showed that exogenous SA and NO induced stomatal closure,100μmol/L SA induced a rapid and striking NO increase in the cytosol of guard cells.This phenomenon was largely prevented by 2000μmol/L 2-phenyl-4,4,5,5-tetramethylimidazoline-l-oxyl-3-oxide(PTIO),a specific NO scavenger,and 25μmol/L N^G-nitro-L-Arg-methyl eater (L-NAME),an inhibitor of NO synthase(NOS) in mammalian cells that also inhibits plant NOS.In addition,SA-induced stomatal closure was largely prevented by PTIO and L-NAME.These results provide evidence that guard cells generate NO in response to SA via NOS-like activity,and that such NO production is required for full stomatal closure in response to SA.H-(1,2,4)-oxadiazole-[4,3-α]quinoxalin-l-one(ODQ),an inhibitor of guanylate cyclase,and nicotinamide,an antagonist of cADPR production,inhibited the effects of SA-and NO-induced stomatal closure.It suggests that both cGMP and cADPR might mediate the signal transduction of SA and NO-induced stomatal closure.     

Cloning and expressional analyses of a cinnamoyl CoA reductase cDNA from rice seedlings

Cinnamoyl CoA reductase (CCR: EC 1.2.1.44),the entry-point enzyme of the llgnin specific biosynthetic pathway, catalyzes the conversion of cinnamoyl CoA esters to their corresponding dnnamaldehydes. Multiple sequence alignment showed that the deduced polypeptide shared 70% similarity and 30% sequence identity at the amino acid level with defined CCR genes from other plant species and they all contain the common signature sequences thought to be the catalytic site as well as the putative NADP binding domain.Using a conserved OsCCR cDNA fragment as the probe for library screening, we isolated the genomic DNA that covered the whole coding region of OsCCR with total length of 3045bp including 4 introns and 5 exons. The open reading frame for our OsCCR gene coBtAin~ 337 amino adds. Northern blot indicated that OsCCR was expressed in different organs with the highest level found in stems. In situ hybridization results showed that OsCCR mRNA was localized mainly along the vascular bundles in stems and leaves, and also in lateral roots that was differentiating from the tiilering node. We conclude that the vascular-localized expression of OsCCR gene may suggest its possible involvement in llgnin biosynthesis. Cloning and characterization of OsCCR will help to clarify how llgniflcations in plants are regulated and will provide a physical basis for creating genetically engineered rice plants with optimal lignin contents.     

Whitney's extension problem for multivariate -functions

We prove that the trace of the space to an arbitrary closed subset is characterized by the following ``finiteness' property. A function belongs to the trace space if and only if the restriction to an arbitrary subset consisting of at most can be extended to a function such that

The constant is sharp.

The proof is based on a Lipschitz selection result which is interesting in its own right.

     

非齐次守恒律方程分片光滑解的粘性方法

1　引　　言考虑非齐次守恒律方程ut+f(u) x =g(u) ,　　 -∞ 0 ,(1 .1 )u(x,0 ) =u0 (x) ,　　 -∞ 0 , (1 .5)g∈ C3且 g是 Lipschitz连续的 ,Lipschitz系数为 L . (1 .6 )对于一般守恒律齐次方程 ,粘性解逼近熵解的收敛阶为 O(ε ) [1 ] .在 f严格凸的条件下 ,其收敛速度可以提高到 O(ε|lnε|+ε) [2 ] ,[3] .本文考虑具有条件 (1 .5) (1 .6 )的非齐次方程(1 .1 ) ,在较广泛的一类初值条件下…     

Generalized Variation of Mappings with Applications to Composition Operators and Multifunctions

We study (set-valued) mappings of bounded -variation defined on the compact interval I and taking values in metric or normed linear spaces X. We prove a new structural theorem for these mappings and extend Medvedev's criterion from real valued functions onto mappings with values in a reflexive Banach space, which permits us to establish an explicit integral formula for the -variation of a metric space valued mapping. We show that the linear span GV (I;X) of the set of all mappings of bounded -variation is automatically a Banach algebra provided X is a Banach algebra. If h:I× X Y is a given mapping and the composition operator is defined by (f)(t)=h(t,f(t)), where tI and f:I X, we show that :GV (I;X) GV (I;Y) is Lipschitzian if and only if h(t,x)=h₀(t)+h₁(t)x, tI, xX. This result is further extended to multivalued composition operators with values compact convex sets. We prove that any (not necessarily convex valued) multifunction of bounded -variation with respect to the Hausdorff metric, whose graph is compact, admits regular selections of bounded -variation.     

Positivity and Negativity of Solutions to a Schrödinger Equation in ℝ N

Weak L ² -solutions u of the Schrödinger equation, –u + q(x) u – u = f(x) in L ² , are represented by a Fourier series using spherical harmonics in order to prove the following strong maximum and anti-maximum principles in (N 2): Let ₁ denote the positive eigenfunction associated with the principal eigenvalue ₁ of the Schrödinger operator . Assume that the potential q(x) is radially symmetric and grows fast enough near infinity, and f is a `sufficiently smooth' perturbation of a radially symmetric function, f 0 and 0 f / C const a.e. in . Then u is ₁-positive for - < < ₁ (i.e., u c ₁ with c const > 0) and ₁-negative for ₁ < < ₁ + (i.e., u –c₁ with c const > 0), where > 0 is a number depending on f. The constant c > 0 depends on both and f.     

A Note on the KAM Theorem for Symplectic Mappings

The mapping version of Pöschel's theory on differentiable foliation structures of invariant tori is presented and the relevant estimates explicitly in terms of the diophantine constant and the nondegeneracy parameters of frequency maps are given. As a direct application of the main result, a generalization of Moser's small twist theorem to high dimensions is given.