20-relative neighborhood graphs are hamiltonian

For any two points p and q in the Euclidean plane, define LUN_pq = { v | v ∈ R², d_pv < d_pq and d_qv < d_pq}, where d_uv is the Euclidean distance between two points u and v . Given a set of points V in the plane, let LUN_pq(V) = V ∩ LUN_pq. 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 LUN_pq (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 | LUN_pq(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 E_c = {e_pq| p ∈ V and q ∈ V}. Then G_c = (V,E_c) is a complete graph. For any subset F of E_c, define the maximum distance of F as max_epq∈Fd_pq. A Euclidean bottleneck Hamiltonian cycle is a Hamiltonian cycle in graph G_c whose maximum distance is the minimum among all Hamiltonian cycles in graph G_c. We shall prove that there exists a Euclidean bottleneck Hamiltonian cycle which is a subgraph of 20RNG(V). Hence, 20RNGs are Hamiltonian.     

Rankin-Cohen brackets on pseudodifferential operators

Pseudodifferential operators that are invariant under the action of a discrete subgroup Γ of SL(2,R) correspond to certain sequences of modular forms for Γ. Rankin-Cohen brackets are noncommutative products of modular forms expressed in terms of derivatives of modular forms. We introduce an analog of the heat operator on the space of pseudodifferential operators and use this to construct bilinear operators on that space which may be considered as Rankin-Cohen brackets. We also discuss generalized Rankin-Cohen brackets on modular forms and use these to construct certain types of modular forms.     

Identification of dislocations and their influence on the recombination of charge carriers in gallium nitride

The relation between the density of etch pits revealed in GaN by etching in a KOH/NaOH eutectic and the density of dislocations determined by transmission electron microscopy (TEM) is studied along with the relation between the density of dislocations and the density of dark spot defects observed in GaN by microcathodoluminescence (MCL) and electron-beam-induced current (EBIC). It is demonstrated that selective etching is a reliable rapid method for the determination of the type and density of dislocations in GaN in the range 10⁶–10⁸ cm^?2, while MCL and EBIC can be used for the rapid nondestructive determination of the density of dislocations in the range 10⁶–10⁸ cm^?2. It is also found that some deep electron and hole traps are related to dislocations.     

The effect of olefinic terminal chains on the mesomorphic properties of 4,4'-disubstituted diphenyldiacetylenes

New diphenyldiacetylenes of the type with A, B = H and/or F; m = 0, 1; n = 1-4; and X = C n H 2n + 1 , F, CF 3 or CN were synthesized and their mesomorphic properties determined by hot stage polarizing microscopy and DSC. When m = 0, all of these compounds showed only a nematic phase except when X = CF 3 when both nematic and smectic A phases were seen. Both clearing and melting temperatures were higher than those reported for substitution with the corresponding alkyl chains but the much larger increase in clearing temperatures produced considerably wider nematic phases. Eutectic mixtures of a few of these olefins yielded nematic materials also having much wider temperature ranges and higher clearing temperatures than the eutectic mixtures of the alkyl compounds, while retaining their high birefringence and low viscosities. Such materials are of interest for beam-steering devices.

Four of the diacetylenes with m = 1 ( A, B = H) were also prepared ( X = C 6 H 13 , F, n = 2, 3). When X was C 6 H 13 ( n = 2), the nematic range was smaller in the 2- than in the 1-olefin but wider than in the alkyl series. When X = F, either no nematic phase or a monotropic one was observed, whereas the 1-olefins gave a much wider nematic phase. Both transition temperatures were lower than those for the corresponding 1-olefin and alkyl analogues. The compound with X = C 6 H 13 and n = 2 had a melting temperature below room temperature.     

金属表面生成氧化膜在电解质中的电位

测量金属表面生成氧化膜在电解质中的电位时,金属/氧化膜/电解质/参比电极构成了多电极体系,其中包括3个电池,由3个电池之间的关系、电池过程中所有的电化学反应、电荷传输步骤和化学反应步骤,导出电位的普遍适用的公式: E=E_a⁰+sum from s=1 to 3|η_t,s|-1/(ne)v₇ΔG₇, E=E_c⁰-sum from s=4 to 6|η_t,s|+1/(ne)v₈ΔG₈.当金属/氧化膜/电解质电池受到不同的步骤控制时,可以得到不同的简化公式.     

不可微泛函拟极小问题解的Hlder连续性

不可微泛函拟极小问题解的Ｈｏｌｄｅｒ连续性于鸣岐，闵泰山（山西大学数学系，太原０３０００６）（北京轻工业学院，１０００３７）金霁（河北工学院，天津３００１３０）１９９２年１１月２７日收到．设Ｇ是ｎ维欧氏空间Ｅｎ中的有界区域，在上定义，对固定的ｘ关于为...     

Memory Effect in Ceramic Superconductors

We measured the time decay of the magnetic moment of high T_c superconductors YBa₂Cu₃O_7-δ ceramic samples and found the memory effect which has hitherto been reported only in single crystals. The temperature and field ranges, especially the memory phenomenon in ceramic samples at liquid nitrogen temperature can only be understood in a combined picture of both flux creep and glass behaviour     

平台石墨炉原子吸收测磷的方法研究

研究了平台石墨炉原子吸收测定磷的方法,表明以氯化钯和硝酸钙的混合液作为基体改进剂测定生物样品中的磷效果最好,方法特征量为8×10~(-9)g,工作曲线线性范围为0～0.400吸光度,精密度好,抗干扰能力强,方法简单,利用标准曲线即可测定生物样品中磷。     

Emission and sputtering characteristics of Ne-Ar mixed gas glow discharge plasmas.

The emission characteristics of several Cu lines emitted from a Ne-Ar mixed gas glow discharge plasma were investigated. The addition of small amounts of Ar to a Ne plasma increases the sputtering rate of a Cu sample because Ar ions, which work as the impinging ions for cathode sputtering, are predominantly produced through Penning ionization collisions between Ne metastables and Ar atoms. Ar addition also elevates the number density of electrons in the plasma. These changes occurring in the Ne-Ar mixed gas plasma result in enhanced emission intensities of the Cu lines. The Cu II 270.10-nm and the Cu II 224.70-nm lines yield different intensity dependence on the Ar partial pressure added. This phenomenon is because these Cu II lines are excited principally through different charge transfer processes: collisions with Ne ions for the Cu II 270.10-nm line and collisions with Ar ions for the Cu II 224.70-nm line. The shape of sputtered craters in the Ne-Ar glow discharge plasma was measured. The depth resolution was improved when Ar was added to a Ne plasma because the crater bottoms were flatter with larger Ar partial pressures.