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91.
Spectral and Pseudospectral Approximations Using Hermite Functions: Application to the Dirac Equation 总被引:1,自引:0,他引:1
We consider in this paper spectral and pseudospectral approximations using Hermite functions for PDEs on the whole line. We first develop some basic approximation results associated with the projections and interpolations in the spaces spanned by Hermite functions. These results play important roles in the analysis of the related spectral and pseudospectral methods. We then consider, as an example of applications, spectral and pseudospectral approximations of the Dirac equation using Hermite functions. In particular, these schemes preserve the essential conservation property of the Dirac equation. We also present some numerical results which illustrate the effectiveness of these methods. 相似文献
92.
A convenient and large-scale preparation of retinoic acid 1 from β-ionone in five steps with 38% overall yield is described.The key steps are the epoxidization of 2 with a new methylated agent and the condensation 4 with tetraethyl methylenediphophonate in one-pot procedure to prepare 6. 相似文献
93.
在超高真空分子束外延(MBE)生长技术中,反射式高能电子衍射仪(RHEED)能实时显示半导体和金属外延生长过程,给出薄膜表面结构和平整度的信息,成为MBE必备的原位表面分 析仪.为了研究氧化物薄膜如高温超导(YBa2Cu3O7) 、铁电薄膜(Sr1-xBax TiO3)及它们的同质和异质外延结构的生长机理,获得高质量的符合各种应用 需要的氧化 物多层薄膜结构,在常规的制备氧化
关键词:
高温超导薄膜
RHEED 相似文献
94.
Hong‐Qing Wang Zhao‐Jie Liu Li‐Min Yang Ming‐Wu Ding 《Journal of heterocyclic chemistry》2004,41(3):393-397
A series of new 1H‐pyrazolo[3,4‐d]pyrimidin‐4(5H)‐one Derivatives 5 has been designed and regio‐selectively synthesized via a tandem aza‐Wittig reaction. The structures of all compounds prepared have been confirmed by 1H NMR, IR, EI‐MS spectroscopy and elemental analyses. The results of preliminary bioassay indicate that most compounds 5 possess an inhibition effect against Botrytis cinereapers and Pyricularia oryzae at the concentration of 50 mg/L. 相似文献
95.
完全Rees矩阵半群的分解及性质 总被引:1,自引:0,他引:1
用等价关系Q^~出了完全Rees矩阵半群的一种分解.而且得到了它的每个Q^~一类的表示. 相似文献
96.
97.
For any two points p and q in the Euclidean plane, define LUNpq = { v | v ∈ R2, dpv < dpq and dqv < dpq}, where duv is the Euclidean distance between two points u and v . Given a set of points V in the plane, let LUNpq(V) = V ∩ LUNpq. Toussaint defined the relative neighborhood graph of V, denoted by RNG(V) or simply RNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of RNG(V) if and only if LUNpq (V) = ?. The relative neighborhood graph has several applications in pattern recognition that have been studied by Toussaint. We shall generalize the idea of RNG to define the k-relative neighborhood graph of V, denoted by kRNG(V) or simply kRNG, to be the undirected graph with vertices V such that for each pair p,q ∈ V, (p,q) is an edge of kRNG(V) if and only if | LUNpq(V) | < k, for some fixed positive number k. It can be shown that the number of edges of a kRNG is less than O(kn). Also, a kRNG can be constructed in O(kn2) time. Let Ec = {epq| p ∈ V and q ∈ V}. Then Gc = (V,Ec) is a complete graph. For any subset F of Ec, define the maximum distance of F as maxepq∈Fdpq. A Euclidean bottleneck Hamiltonian cycle is a Hamiltonian cycle in graph Gc whose maximum distance is the minimum among all Hamiltonian cycles in graph Gc. We shall prove that there exists a Euclidean bottleneck Hamiltonian cycle which is a subgraph of 20RNG(V). Hence, 20RNGs are Hamiltonian. 相似文献
98.
由“从正则分布出发,在小涨落近似下得出的能量涨落分布公式”求得的能量涨落的二次矩与直接由正则分布求得的二次矩完全相同,但分别由二求得的高次矩并不完全相同。 相似文献
99.
KunHuaLIN MaoPingSONG ChenXiaDU QiaoHongZHANG YangJieWU 《中国化学快报》2003,14(7):673-676
The cyclomercurated ferrocenylimines containing heterocyclic ring were prepared by the condensation of cyclomercuration of acylferrocene with the appropriate heterocyclic amine.This procedure provides an efficient method for the synthesis of cyclomerucurated ferrocenylimines containing heterocyclic ring which are difficultly synthesized by the conventional method.The reaction mechanism is proposed. 相似文献
100.
Keith Vaughan Ronald J. LaFrance York Tang Donald L. Hooper 《Journal of heterocyclic chemistry》1991,28(7):1709-1713
3-Alkyl-4-arylazomethylene-3,4-dihydro-1,2,3-benzotriazines 5a and 5b undergo facile 1,4-addition of methanol or ethanol to afford stable crystalline hydrazones, 6 and 8 which have been characterised by spectroscopic analysis. In particular, the nmr spectrum of 8 shows novel features due to the diastereotopic nature of the CH2 protons in the two O-ethyl groups. Compound 5b shows a property unique to the compounds in this series; refluxing this arylazomethylenetriazine in ethanol affords a rearranged product, characterised as the 1-aryl-2-cinnolinylhydrazine ( 9 ). The formation of 9 is rationalised as a ring opening-ring closure process analogous to the Dimroth rearrangement. The cinnoline 9 displays some novel chemistry arising from the facility of the arylhydrazino substituent to react with acid to give a fragmentation product, 3-methylindazole ( 7 ). 相似文献