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.     

Spectral characteristics of vertical-cavity surface-emitting lasers with external optical feedback

The measurement of the effects of external optical feedback on the spectra of VCSELs (vertical-cavity surface-emitting lasers) is reported. It is surprising that VCSELs have a sensitivity to optical feedback comparable to that of conventional edge-emitting lasers such as DFBs despite their significantly different structures. This is because the extremely short cavity length of VCSELs negates the effects of their highly reflective output mirrors. As in edge-emitting lasers, VCSELs exhibit well-defined regimes of feedback effects in their spectra. Since optical isolators cannot be easily applied to VCSELs due to their array structure, these lasers may be most useful in applications which are not sensitive to the spectral qualities of the light source.<>     

89-GHz fT room-temperature silicon MOSFETs

The authors report the implementation of deep-submicrometer Si MOSFETs that at room temperature have a unity-current-gain cutoff frequency (f_T) of 89 GHz, for a drain-to-source bias of 1.5 V, a gate-to-source bias of 1 V, a gate oxide thickness of 40 Å, and a channel length of 0.15 μm. The fabrication procedure is mostly conventional, except for the e-beam defined gates. The speed performance is achieved through an intrinsic transit time of only 1.8 ps across the active device region     

Queueing analyses of traffic access control strategies withpreemptive and nonpreemptive disciplines in wideband integrated networks

A multiserver queueing model of access control strategies for a wideband integrated services digital network (ISDN) is considered. There are two types of service requests (SRs): Type 1 SR requires b servers (basic bandwidth units, BBUs) of the c available servers, while Type 2 SR requires a single server. Both types of SRs are queuable in two separate infinite-size buffers. A Type 1 SR is allowed to seize d(⩽b) servers at first and then acquire additional servers as they become available to meet the original requirement of b servers. The arrival processes of both types of SRs are Poisson and the service times are exponentially distributed with mean b/dμ₁ and 1/μ₂ for Type 1 SR and Type 2 SR, respectively. Preemptive and nonpreemptive priority disciplines with movable boundary are analyzed using the Neuts' matrix-analytic approach. Numerical examples of the queue length distribution and the mean waiting time of the SRs are presented     

Analysis and design-optimization of LCC resonant inverter forhigh-frequency AC distributed power system

The analysis and design of an LCC resonant inverter for a 20 kHz AC distributed power system are presented. Several resonant converter topologies are assessed to determine their suitability for high efficiency power conversion, under resistive and reactive loads. Two LCC-resonant inverter designs were implemented. One with all switches operating with zero voltage switching (ZVS), and another with two switches operating with ZVS and two switches with zero current switching (ZCS). The experimental results are presented along with a performance comparison of the two versions     

Tri-band frequency selective surface with circular ring elements

Theoretical analysis, physical reasonings, and experimental verifications are presented for a frequency selective surface with circular ring elements. Both double-screen and single-screen designs are generated for a tri-band system that reflects the X-band signal while transmitting through the S- and Ku-band signals. In these designs, the dielectric loading effect is used to reduce ring size and element spacing and thus avoid the grating lobe problem. The circular ring element is very insensitive to a large variation of the RF incident angle