Pattern and feature designed growth of ZnO nanowire arrays for vertical devices

An approach is demonstrated for growing aligned ZnO nanowire/nanorod arrays following a predesigned pattern and feature with controlled site, shape, distribution, and orientation. The technique relies on an integration of atomic force microscopy (AFM) nanomachining with catalytically activated vapor-liquid-solid (VLS) growth. The pattern and growth locations are defined by the catalyst distribution created by AFM, and the orientation is determined by the epitaxial growth on a single-crystal substrate. The technique opens a variety of possibilities of using nanowire arrays as sensor arrays, piezoelectric antenna arrays, nanolasers, photonic band gap crystal, biosensors, and field emitters with controlled density, location, shape, and distribution according to a designed pattern and feature.     

Coumarinolignans from the Root of Formosan Antidesma pentandrum var. barbatum

Four new coumarinolignans, antidesmanin A (=7‐(1,1‐dimethylallyl)‐2,3‐dihydro‐3‐(4‐hydroxy‐3,5‐dimethoxyphenyl)‐10‐methoxy‐2‐methyl‐6H‐1,4,5‐trioxaphenanthren‐6‐one; 1 ), antidesmanin B (=3,7‐bis(1,1‐dimethylallyl)‐2,3‐dihydro‐2‐(4‐hydroxy‐3‐methoxyphenyl)‐10‐methoxy‐6H‐1,4,5‐trioxaphenanthren‐6‐one; 2 ), antidesmanin C (=2,7‐bis‐(1,1‐dimethylallyl)‐2,3‐dihydro‐3‐(4‐hydroxy‐3‐methoxyphenyl)‐10‐methoxy‐6H‐1,4,5‐trioxaphenanthren‐6‐one; 3 ) and antidesmanin D (=2‐(3,4‐dihydroxyphenyl)‐3,7‐bis(1,1‐dimethylallyl)‐2,3‐dihydroxy‐10‐methoxy‐6H‐1,4,5‐trioxaphenanthren‐6‐one or 3‐(3,4‐dihydroxyphenyl)‐2,7‐bis(1,1‐dimethylallyl)‐2,3‐dihydro‐10‐methoxy‐6H‐1,4,5‐trioxaphenanthren‐6‐one; 4 ) have been isolated from the root of the Formosan Antidesma pentandrum var. barbatum. The structures of these new compounds were elucidated by spectroscopic data. Compounds 1 – 3 exhibited marginal cytotoxicity against MCF‐7 (breast) and SF‐268 (CNS) cancer cell lines in vitro.     

On Cycle Sequences

. For each vertex v in a graph G, the maximum length of a cycle which passes through v is called the cycle number of v, denoted by c(v). A sequence a ₁,a ₂,…,a _n of nonnegative integers is called a cycle sequence of a graph G if the vertices of G can be labeled as v ₁,v ₂,…,v _n such that a _i =c(v _i ) for 1≤i≤n. We give some sufficient and necessary conditions for a sequence to be a cycle sequence. We can thereby derive a polynomial time procedure for recognizing cycle sequences. Received: July 14, 1997 Final version received: June 15, 1998     

Non-cover generalized Mycielski, Kneser, and Schrijver graphs

A graph is said to be a cover graph if it is the underlying graph of the Hasse diagram of a finite partially ordered set. We prove that the generalized Mycielski graphs M_m(C_2t+1) of an odd cycle, Kneser graphs KG(n,k), and Schrijver graphs SG(n,k) are not cover graphs when m?0,t?1, k?1, and n?2k+2. These results have consequences in circular chromatic number.     

Edge‐partitions of planar graphs and their game coloring numbers

Let G be a planar graph and let g(G) and Δ(G) be its girth and maximum degree, respectively. We show that G has an edge‐partition into a forest and a subgraph H so that (i) Δ(H) ≤ 4 if g(G) ≥ 5; (ii) Δ(H) ≤ 2 if g(G) ≥ 7; (iii) Δ(H)≤ 1 if g(G) ≥ 11; (iv) Δ(H) ≤ 7 if G does not contain 4‐cycles (though it may contain 3‐cycles). These results are applied to find the following upper bounds for the game coloring number col_g(G) of a planar graph G: (i) col_g(G) ≤ 8 if g(G) ≥ 5; (ii) col_g(G)≤ 6 if g(G) ≥ 7; (iii) col_g(G) ≤ 5 if g(G) ≥ 11; (iv) col_g(G) ≤ 11 if G does not contain 4‐cycles (though it may contain 3‐cycles). © 2002 Wiley Periodicals, Inc. J Graph Theory 41: 307–317, 2002     

Comparison of cross-talk effects between colloidal quantum dot and conventional waveguides

We present cross-talk calculations for a subdiffraction nanophotonic waveguide that consists of a colloidal quantum dot (QD) array 10 nm in diameter and compare the results with conventional continuous dielectric waveguides, assuming the same 10 nm size as well as a 200 nm cutoff diameter for guided mode. We find that the QD cascade has much lower cross talk than 10 nm dielectric waveguides at an identical separation >30 nm. Moreover, results for 200 nm dielectric waveguides at a 280 nm gap are comparable with those of QD structures spaced 110 nm apart. Hence the proposed QD device is potentially superior to conventional waveguides in achieving lower cross talk in the subdiffraction regime and provides a new route to achieving high-density photonic integrated circuits.