New cavitand derivatives bearing four coumarin groups as fluorescent chemosensors for Cu and recognition of dicarboxylates utilizing Cu complex

New cavitand derivatives (1, 2) bearing four coumarin groups were synthesized, and the binding properties of these cavitands towards metal ions were examined through their fluorescent changes. Cavitand 1 effectively recognized the Cu²⁺ ions among the metal ions examined. The recognition of cavitand 1-Cu²⁺ with dicarboxlyates is also described.     

The number of pancyclic arcs in a k‐strong tournament

A tournament is a digraph, where there is precisely one arc between every pair of distinct vertices. An arc is pancyclic in a digraph D, if it belongs to a cycle of length l, for all 3 ≤ l ≤ |V (D) |. Let p(D) denote the number of pancyclic arcs in a digraph D and let h(D) denote the maximum number of pancyclic arcs belonging to the same Hamilton cycle of D. Note that p(D) ≥ h(D). Moon showed that h(T) ≥ 3 for all strong non‐trivial tournaments, T, and Havet showed that h(T) ≥ 5 for all 2‐strong tournaments T. We will show that if T is a k‐strong tournament, with k ≥ 2, then p(T) ≥ 1/2, nk and h(T) ≥ (k + 5)/2. This solves a conjecture by Havet, stating that there exists a constant α_k, such that p(T) ≥ α_k n, for all k‐strong tournaments, T, with k ≥ 2. Furthermore, the second results gives support for the conjecture h(T) ≥ 2k + 1, which was also stated by Havet. The previously best‐known bounds when k ≥ 2 were p(T) ≥ 2k + 3 and h(T) ≥ 5. © 2005 Wiley Periodicals, Inc. J Graph Theory     

Finding cheapest cycles in vertex-weighted quasi-transitive and extended semicomplete digraphs

We consider the problem of finding a minimum cost cycle in a digraph with real-valued costs on the vertices. This problem generalizes the problem of finding a longest cycle and hence is NP-hard for general digraphs. We prove that the problem is solvable in polynomial time for extended semicomplete digraphs and for quasi-transitive digraphs, thereby generalizing a number of previous results on these classes. As a byproduct of our method we develop polynomial algorithms for the following problem: Given a quasi-transitive digraph D with real-valued vertex costs, find, for each j=1,2,…,|V(D)|, j disjoint paths P₁,P₂,…,P_j such that the total cost of these paths is minimum among all collections of j disjoint paths in D.     

When the greedy algorithm fails

We provide a characterization of the cases when the greedy algorithm may produce the unique worst possible solution for the problem of finding a minimum weight base in an independence system when the weights are taken from a finite range. We apply this theorem to TSP and the minimum bisection problem. The practical message of this paper is that the greedy algorithm should be used with great care, since for many optimization problems its usage seems impractical even for generating a starting solution (that will be improved by a local search or another heuristic).     

Nanomechanical Property and Nanowear Measurements for Sub-10-nm Thick Films in Magnetic Storage

In the magnetic storage industry, thin film carbon overcoats play a critical role in reducing magnetic and physical spacing between the recording slider and the rotating disk so that the information stored per unit area is maximized. Thin film carbon overcoats have been improved such that they exhibit higher hardness with lower thickness of few nanometers and still being able to perform reliably. In this paper, nanoindentation and nanoscratch techniques to measure nanomechanical properties, namely hardness, elastic modulus and shear strength of thin solid films were presented along with a recently developed high resolution force transducer. Nanowear behavior characterization techniques were also examined and were applied to commercially available magnetic disks to characterize their wear behavior. It was shown that the properties and wear behavior of sub-10-nm thick film carbon overcoats were reliably measured. These techniques could be applied to different thin solid films on substrates, and they are not restricted to magnetic storage systems.     

On 2‐Colorings of Hypergraphs

In this article, we continue the study of 2‐colorings in hypergraphs. A hypergraph is 2‐colorable if there is a 2‐coloring of the vertices with no monochromatic hyperedge. Let denote the class of all k‐uniform k‐regular hypergraphs. It is known (see Alon and Bregman [Graphs Combin. 4 (1988) 303–306] and Thomassen [J. Amer. Math. Soc. 5 (1992), 217–229] that every hypergraph is 2‐colorable, provided . As remarked by Alon and Bregman the result is not true when , as may be seen by considering the Fano plane. Indeed there are several constructions for building infinite families of hypergraphs in that are not 2‐colorable. Our main result in this paper is a strengthening of the above results. For this purpose, we define a set X of vertices in a hypergraph H to be a free set in H if we can 2‐color such that every edge in H receives at least one vertex of each color. We conjecture that for , every hypergraph has a free set of size in H. We show that the bound cannot be improved for any and we prove our conjecture when . Our proofs use results from areas such as transversal in hypergraphs, cycles in digraphs, and probabilistic arguments.     

Development of new reference materials for the determination of cadmium,chromium, mercury and lead in polycarbonate

Reference materials for quantitative determination of Cd, Cr, Hg and Pb in polycarbonate were developed. Reference materials with two concentration level of elements were prepared by adding appropriate amounts of chemicals to a blank polycarbonate base material. It was shown that ten bottles with triplicate analysis are enough to demonstrate the homogeneity of these candidate reference materials. The statistical results also showed no significant trends in both short-term stability test for four weeks and long-term stability test for twelve months. The certification of the four elements was carried out by isotope-dilution-inductively coupled plasma mass spectrometry (ID-ICP-MS) with microwave-assisted digestion. Certification of candidate reference materials in a single laboratory was confirmed with interlaboratory comparison participated by a certain number of well-recognized testing laboratories in Korea. The certified values and expanded uncertainties (k = 2) for the candidate reference material with low level and the one with high level were (51.7 ± 2.1) mg kg⁻¹ Cd, (103.8 ± 2.9) mg kg⁻¹ Cd, (98.8 ± 4.5) mg kg⁻¹ Cr, (1004 ± 49.8) mg kg⁻¹ Cr, (107.4 ± 4.6) mg kg⁻¹ Hg, (1133 ± 50.7) mg kg⁻¹ Hg, (94.8 ± 3.7) mg kg⁻¹ Pb and (988.4 ± 53.6) mg kg⁻¹ Pb, respectively. The reference materials developed in this study demonstrated their suitability for the quality assurance in Cd, Cr, Hg and Pb analysis for the implementation of RoHS Directive.     

Enhancement of Long-Chain Fatty Acid Production in Escherichia coli by Coexpressing Genes, Including fabF, Involved in the Elongation Cycle of Fatty Acid Biosynthesis

The goal of this study was to increase the production of long-chain fatty acids and to change the composition of fatty acids through the overexpression of genes involved in the fatty acid synthase (FAS) pathway and utilizing characteristics of a specific gene, namely, fabF. The four genes, fabB, fabG, fabZ, and fabI, are Escherichia coli homologues and function in the elongation cycle of fatty acid biosynthesis. FabB (fabB), an activator of FAS, is a β-oxoacyl-ACP synthase, which catalyzes the addition of acyl-ACP to malonyl-ACP to generate β-oxoacyl-ACP. FabF (fabF) participates at the same step as FabB in the elongation cycle and is structurally and functionally similar to FabB. Hence, we attempted to see if FabF was an activator of FAS, like FabB, with the rationale that these two enzymes have striking similarities. FabF exhibits thermal regulation in that enzyme activity increases at lower temperatures. To confirm its role as an activator of FAS, fabF was overexpressed solely or with other genes in the elongation cycle through biochemical engineering. The fabF recombinants were cultured at different temperatures, resulting in increased total and unsaturated fatty acid accumulation in all the recombinants, compared to wild type, at lower temperatures.