Balanced decomposition of a vertex-colored graph

A balanced vertex-coloring of a graph G is a function c from V(G) to {−1,0,1} such that ∑{c(v):v∈V(G)}=0. A subset U of V(G) is called a balanced set if U induces a connected subgraph and ∑{c(v):v∈U}=0. A decomposition V(G)=V₁∪?∪V_r is called a balanced decomposition if V_i is a balanced set for 1≤i≤r.In this paper, the balanced decomposition number f(G) of G is introduced; f(G) is the smallest integer s such that for any balanced vertex-coloring c of G, there exists a balanced decomposition V(G)=V₁∪?∪V_r with |V_i|≤s for 1≤i≤r. Balanced decomposition numbers of some basic families of graphs such as complete graphs, trees, complete bipartite graphs, cycles, 2-connected graphs are studied.     

Enantioseparation of nicotine alkaloids in cigarettes by CE using sulfated β‐CD as a chiral selector and a capillary coated with amino groups

Nicotine (NC) and its related compounds (cotinine (CN), nornicotine (NN), anatabine (AT) and anabasine (AB)) were simultaneously enantioseparated by CE using a capillary with amino groups and sulfated β‐CD as a chiral selector. The optimum running conditions were found to be 30 mM acetate buffer (pH 5.0) containing 8% sulfated β‐CD with an applied voltage of +15 kV at 30°C using direct detection at 260 nm. Using a capillary coated with amino groups, the EOF migrates toward the positive pole. However, when sulfated β‐CD was added to the BGE, it was found that the EOF migrated toward the negative pole due to ionic adsorption of sulfated β‐CD to amino groups on the capillary inner wall. All the cationic analytes migrated as anions, suggesting that they formed stable anionic complexes with sulfated β‐CD. With this system and a simple pretreatment with mini‐cartridges, NC alkaloids in five cigarette samples were enantioseparated. As a result, each of the compounds except for CN was detected. In the case of NC, only (S)‐NC was detected (more than 99.9%), but in the case of NN, AT and AB, the ratios of (S)‐isomer to total isomers were in the ranges 58–70, 81–85 and 59–65%, respectively. On the other hand, only NC was detected in cigarette smoke and the ratio of (S)‐ and (R)‐NCs was 96:4. The amounts of NC alkaloids in cigarettes suggest that the production of (R)‐NC resulted from racemization due to the high temperature/burning of the cigarette.     

Comparison of Differently Bound Molecules in the Gel and Subgel Phases of a Phospholipid Bilayer System

The thermal behavior associated with the melting of ice was investigated by differential scanning calorimetry (DSC) for the gel and L-subgel phases of dipalmitoylphosphatidylcholine (DPPC)-water system of varying water contents up to a full hydration. By calorimetric analysis previously developed by us, the numbers of differently bound water molecules were estimated, and used to construct water distribution diagrams (i.e., a plot of the cumulative numbers of these water molecules vs. water content) for the two phases. A comparison of the diagrams revealed the critical role of interlamellar water which changes from freezable to non-freezable one in a conversion of the gel to the L-subgel phase by the thermal annealing. This revised version was published online in July 2006 with corrections to the Cover Date.     

On degree sum conditions for long cycles and cycles through specified vertices

Let G be a graph. For S⊂V(G), let Δ_k(S) denote the maximum value of the degree sums of the subsets of S of order k. In this paper, we prove the following two results. (1) Let G be a 2-connected graph. If Δ₂(S)≥d for every independent set S of order κ(G)+1, then G has a cycle of length at least min{d,|V(G)|}. (2) Let G be a 2-connected graph and X a subset of V(G). If Δ₂(S)≥|V(G)| for every independent set S of order κ(X)+1 in G[X], then G has a cycle that includes every vertex of X. This suggests that the degree sum of nonadjacent two vertices is important for guaranteeing the existence of these cycles.     

iVDR business perspective

This paper describes a perspective for information versatile disk for removable usage (iVDR) business. iVDR is the best bridge media for high-resolution image because of high capacity and high reliability. The first iVDR product was delivered with PMR technology hard disk drives and a copyright protection function for high-definition TV programs. The business opportunity and the new business model are discussed.     

Zur Bestimmung des Adrenalins

Ohne Zusammenfassung     

Chemoselective N-acetylation of primary aliphatic amines promoted by pivalic or acetic acid using ethyl acetate as an acetyl donor

The combination of pivalic or acetic acid as a promoter and EtOAc as a solvent and acetyl donor proved to be efficient for the chemoselective N-acetylation of primary aliphatic amines to afford the corresponding acetamides. We developed a simple and convenient approach, which requires mild reaction conditions. Competitive inter- and intramolecular reactions between aliphatic amines, alcohols, and aromatic amines were examined, and chemoselectivity was achieved by adjusting the conditions of the reaction.