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71.
Luen-fai Tam 《Proceedings of the American Mathematical Society》1998,126(10):3097-3108
In this note, we will prove that under certain conditions, the space of polynomial growth harmonic functions and harmonic forms with a fixed growth rate on manifolds which are asymptotically nonnegatively curved is finite dimensional. This is a partial generalization of the works of Li and Colding-Minicozzi. We will also give an explicit estimate for the dimension in case the manifold is a complete surface of finite total curvature. This is a generalization to harmonic forms of the work of Li and the author.
72.
73.
S.W. Tam 《Tetrahedron letters》1974,15(27):2385-2388
74.
Tamás Hausel 《Central European Journal of Mathematics》2005,3(1):26-38
Building on a recent paper [8], here we argue that the combinatorics of matroids are intimately related to the geometry and topology of toric hyperkähler varieties. We show that just like toric varieties occupy a central role in Stanley’s proof for the necessity of McMullen’s conjecture (or g-inequalities) about the classification of face vectors of simplicial polytopes, the topology of toric hyperkähler varieties leads to new restrictions on face vectors of matroid complexes. Namely in this paper we will give two proofs that the injectivity part of the Hard Lefschetz theorem survives for toric hyperkähler varieties. We explain how this implies the g-inequalities for rationally representable matroids. We show how the geometrical intuition in the first proof, coupled with results of Chari [3], leads to a proof of the g-inequalities for general matroid complexes, which is a recent result of Swartz [20]. The geometrical idea in the second proof will show that a pure O-sequence should satisfy the g-inequalities, thus showing that our result is in fact a consequence of a long-standing conjecture of Stanley. 相似文献
75.
Synthesis of novel 6,11-O-bridged bicyclic ketolides via a palladium-catalyzed bis-allylation 总被引:2,自引:0,他引:2
A bridging chemistry process was developed to form an ether bridge between 6-O and 11-O of erythromycin A via a tandem or stepwise palladium-catalyzed bis-pi-allylation. By applying this bridging process, new 6,11-O-bridged bicyclic ketolides (BBKs) were synthesized. These BBKs showed good antibacterial activities against the macrolide-susceptible strains as well as mef-resistant strains and served as a good core for further modifications to study the structure-activity relationship (SAR) and to overcome bacterial resistance. [reaction: see text] 相似文献
76.
We show, within the context of Miyadera–Voigt perturbations on
Lp spaces, that for partial differential equations with delay arising from an
immediately compact undelayed equation the delay semigroup is eventually
compact. We also indicate how this result can be applied to the spectral
analysis and numerical treatment of these equations. 相似文献
77.
Itharat A Plubrukarn A Kongsaeree P Bui T Keawpradub N Houghton PJ 《Organic letters》2003,5(16):2879-2882
[structure: see text] Commonly used among ingredients in Thai traditional anticancer preparations, the rhizome of Dioscorea membranacea Pierre was found potently cytotoxic and possibly contributed to such a therapeutic effect. Bioassay-guided isolation resulted in two novel cytotoxic naphthofuranoxepins, dioscorealides A (1) and B (2), and a new 1,4-phenanthraquinone, dioscoreanone (3). The structure determination, achieved mainly by means of NMR and CD spectral and X-ray crystallographic analyses, and cytotoxicity are discussed here. 相似文献
78.
Denote by span {f 1,f 2, …} the collection of all finite linear combinations of the functionsf 1,f 2, … over ?. The principal result of the paper is the following. Theorem (Full Müntz Theorem in Lp(A) for p ∈ (0, ∞) and for compact sets A ? [0, 1] with positive lower density at 0). Let A ? [0, 1] be a compact set with positive lower density at 0. Let p ∈ (0, ∞). Suppose (λ j ) j=1 ∞ is a sequence of distinct real numbers greater than ?(1/p). Then span {x λ1,x λ2,…} is dense in Lp(A) if and only if $\sum\limits_{j = 1}^\infty {\frac{{\lambda _j + \left( {1/p} \right)}}{{\left( {\lambda _j + \left( {1/p} \right)} \right)^2 + 1}} = \infty } $ . Moreover, if $\sum\limits_{j = 1}^\infty {\frac{{\lambda _j + \left( {1/p} \right)}}{{\left( {\lambda _j + \left( {1/p} \right)} \right)^2 + 1}} = \infty } $ , then every function from the Lp(A) closure of {x λ1,x λ2,…} can be represented as an analytic function on {z ∈ ? \ (?∞,0] : |z| < rA} restricted to A ∩ (0, rA) where $r_A : = \sup \left\{ {y \in \mathbb{R}:\backslash ( - \infty ,0]:\left| z \right|< r_A } \right\}$ (m(·) denotes the one-dimensional Lebesgue measure). This improves and extends earlier results of Müntz, Szász, Clarkson, Erdös, P. Borwein, Erdélyi, and Operstein. Related issues about the denseness of {x λ1,x λ2,…} are also considered. 相似文献
79.
Zhang WY Lei XY Wang ZL Zheng DG Tam WY Chan CT Sheng P 《Physical review letters》2000,84(13):2853-2856
We show theoretically and experimentally that photonic band gaps can be realized using metal or metal-coated spheres as building blocks. Robust photonic gaps exist in any periodic structure built from such spheres when the filling ratio of the spheres exceeds a threshold. The frequency and the size of the gaps depend on the local order rather than on the symmetry or the global long range order. Good agreement between theory and experiment is obtained in the microwave regime. Calculations show that the approach can be scaled up to optical frequencies even in the presence of absorption. 相似文献
80.
Tam T Ohata D Wu M 《Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics》2000,61(1):R9-R12
The structure and dynamics of a penta-hepta defect in a hexagonal pattern are studied experimentally. The hexagonal pattern is formed by placing a layer of soap bubbles (diameter approximately 1 mm) on a flat glass plate. We find that an isolated penta-hepta defect in a bubble raft with free boundary always moves along the direction perpendicular to the wave vector of the nonsingular mode and towards the nearest boundary. The structure of the penta-hepta defect is found to be similar to that found in nonequilibrium pattern forming systems. 相似文献