Vertices of Degree 5 in a Contraction Critically 5-connected Graph

An edge of a k-connected graph is said to be k-contractible if the contraction of the edge results in a k-connected graph. A k-connected graph with no k-contractible edge is said to be contraction critically k-connected. We prove that a contraction critically 5-connected graph on n vertices has at least n/5 vertices of degree 5. We also show that, for a graph G and an integer k greater than 4, there exists a contraction critically k-connected graph which has G as its induced subgraph.     

Spectrophotometric determination of arsenic in water samples based on micro particle formation of ethyl violet-molybdoarsenate.

In this study, a simple and sensitive method for the determination of arsenic in water samples was developed. The method is based on the formation of micro particles of Ethyl Violet and molybdoarsenate, which gives an apparently homogeneous blue color to the solution. The absorption of the excess dye gradually decreases due to its conversion to a colorless carbinol species under strongly acidic conditions. Consequently, the sufficiently low reagent blank enables the spectrophotometric determination of arsenic with the detection limit of 4 microg l(-1). The coefficient of variation for the spectrophotometry at 50 microg l(-1) was 3.5% (n = 5). Furthermore, it is possible to detect concentrations as low as 10 microg l(-1) of arsenic visually. Our method will be useful as a simple, rapid, and cost-effective field test of arsenic, requiring no complex apparatus or skilled laboratory support.     

Separation of V(V)-4-(2-pyridylazo)resorcinolato complex from a large excess reagent using an ODS cartridge for high-performance liquid chromatography.

A selective off-line preconcentration technique for the V(V) complex with 4-(2-pyridylazo)resorcinol has been developed and successfully applied to the determination of V(V) in an air-borne sample. The target complex was separated from excess reagent using an ODS cartridge and water as the eluent. The complex was then concentrated on another ODS cartridge using tetrabutylammonium bromide and eluted with methanol; the eluate was applied to a one-drop concentration/HPLC. A detection limit as low as (6.05 +/- 0.82)x 10(-11) M (5 ppt) was achieved.     

Preparation of flexible and transparent polylactic acids films by crystallization manipulation

Highly flexible and transparent polylactic acids (PLAs) films were successfully prepared by manipulating their crystallization. The semicrystalline poly(L ‐lactic acid) (L) was blended with a noncrystalline poly(DL ‐lactic acid) (DL) together with diglycerol tetraacetate (DGTA). Optimal DGTA content to plasticize PLAs was about 17%. Addition of DL hindered the crystallization of the films. Tensile strengths of the films having DL content more than 5% were about 10 MPa while the elongations at break were boosted as DL content increased. Films having L/DL ratio of 50/50 showed elongations at break of 270%. Stretch ability and clarity of films containing 15–50% DL were fair although they were subjected to annealing at 60 °C for 1 h. © 2008 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 46: 6489–6495, 2008     

Convenient synthesis of 2-(2-pyridyl)-1, 3-diaminopropane,and its copper(II), nickel(II), and cobalt(III) complexes

Summary 2-(2-Pyridyl)-1, 3-propanediol was converted into the diacetate, which was then condensed with phthalimide. The product was hydrolyzed with hydrochloric acid to give 2-(2-pyridyl)-1, 3-diaminopropane. The free amine gave 12 complexes with copper(II), nickel(II), and cobalt(III), which were characterized spectroscopically and magnetically. Features of the amine as a ligand are discussed. A few related complexes were also studied.     

A reduction theorem for the linear complementarity problem with a certain patterned matrix

Matrices with a certain pattern are defined and their properties are studied. A reduction theorem is stated and proved which can be used to reduce the size of the linear complementarity problem defined by a matrix with the pattern. The identification of the pattern and the reduction theorem provide a mathematical model for a problem in structural mechanics when a certain symmetry prevails in the structural problem to be analyzed.     

Note on transferable utility

We provide a condition for an individual preference ordering to be represented by a function measured in terms of a commodity, i.e., for the commodity to be transferable utility. We also consider the relationships between conditions of the preference ordering and the utility function.     

Properties of titanium solid solutions prepared by reactive sputtering

Films of titanium solid solutions Ti-X_x (X = C, N, or O) of the hexagonal phase were prepared on glass substrates heated at 350°C in a mixture of argon and the reactive gas with controlled partial pressures from 2×10^?6 to 8×10^?3 Torr. The maximum solubilities of C, N, and O in Ti were estimated to be 0.05, 0.46, and 0.28, respectively. The observed values of the maximum solubilities are discussed in connection with the structural and electrical properties.