Arranging Solid Balls to Represent a Graph

 By solid balls, we mean a set of balls in R ³ no two of which can penetrate each other. Every finite graph G can be represented by arranging solid balls in the following way: Put red balls in R ³, one for each vertex of G, and connect two red balls by a chain when they correspond to a pair of adjacent vertices of G, where a chain means a finite sequence of blue solid balls in which each consecutive balls are tangent. (We may omit the chain if the two red balls are already tangent.) The ball number b(G) of G is the minimum number of balls (red and blue) necessary to represent G. If we put the balls and chains on a table so that all balls sit on the table, then the minimum number of balls for G is denoted by b _T (G). Among other things, we prove that b(K ₆)=8,b(K ₇)=13 and b _T (K ₅)=8,b _T (K ₆)=14. We also prove that c ₁ n ³<b(K _n )<c ₂ n ³ log n, c ₃ n ⁴ log n<b _T (K _n )<c ₄ n ⁴. Received: March 29, 1999 Final version received: January 17, 2000     

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.     

The synthesis of 2-ethoxy-6,11-dimethyl-7,9-bisdehydroaza[14]annulene and its benzannelated derivatives

Title azaannulenes were synthesized starting from annulenones, and the ¹H-NMR spectra are discussed in connection with tropicity of these annulenes.     

A new tomato pregnane glycoside from the overripe fruits

A new pregnane glycoside has been isolated from the overripe fruits of Cherry tomato (Mini tomato), Lycopersicon esculentum var. cerasiforme (DUNAL) ALEF. The structure was determined to be 3-O-beta-lycotetraosyl 3beta-hydroxy-5alpha-pregn-16-en-20-one on the basis of spectroscopic analysis. The seasonal variation of the tomato saponin is discussed.     

Br NQR relaxation and successive phase transitions of CH3NH3HgBr3

The measurement of ⁸¹Br NQR in CH₃NH₃HgBr₃ has been carried out in the temperature range between 80 and 300 K using a pulse NQR method. The temperature dependence of ⁸¹Br NQR frequencies in CH₃NH₃HgBr₃ has revealed that it undergoes three characteristic successive phase transitions at T?=?123, 184 and 239 K. The phase transition temperature at T?=?239 K is the second-order type, whereas those at T?=?184 and 123 K are the first-order nature of the phase transitions. Each phase transition seems to be closely related to the motions of methyl ammonium cation as a partial or whole. The enhancement of 1/T ₁ at T?=?239 K indicates the onset of the molecular motion of the cation as a whole with increasing temperatures.     

Asymptotic analysis for an extended discrete Lotka–Volterra system related to matrix eigenvalues

The integrable discrete hungry Lotka–Volterra (dhLV) system is easily transformed to the qd-type dhLV system, which resembles the recursion formula of the qd algorithm for computing matrix eigenvalues. Some of the qd-type dhLV variables play a role for assisting the time evolution of the others. This property does not appear in the original dhLV system. In this article, we first show the existence of a centre manifold for the qd-type dhLV system. With the help of the centre manifold theory, we next investigate the local convergence of the qd-type dhLV system, and then clarify the monotonicity related to the qd-type dhLV variables at the final phase of the convergence.     

Variational Calculation of 4He Tetramer Ground and Excited States Using Realistic 4He–4He Potentials

We calculated binding energies and wave functions of the ⁴He tetramer ground and excited states employing various realistic ⁴He?⁴He potentials which includes the currently most accurate one with the adiabatic, relativistic, QED and residual retardation corrections. We used our Gaussian expansion method (GEM) for ab initio variational calculations of few-body systems. We found that precisely the same shape of the short-range correlation (r _ij < 4Å) in the dimer appear in the ground and excited states of trimer and tetramer. The four kinds of the binding energies of the trimer and tetramer ground and excited states, ${B_3^{(0)}, B_3^{(1)}, B_4^{(0)}}$ and ${B_4^{(1)}}$ , for the different potentials exhibit perfect linear correlations over the range of binding energies relevant for ⁴He atoms; namely, six types of the generalized atomic Tjon lines were observed.     

DNA Origami Scaffolds as Templates for Functional Tetrameric Kir3 K+ Channels

In native systems, scaffolding proteins play important roles in assembling proteins into complexes to transduce signals. This concept is yet to be applied to the assembly of functional transmembrane protein complexes in artificial systems. To address this issue, DNA origami has the potential to serve as scaffolds that arrange proteins at specific positions in complexes. Herein, we report that Kir3 K⁺ channel proteins are assembled through zinc‐finger protein (ZFP)‐adaptors at specific locations on DNA origami scaffolds. Specific binding of the ZFP‐fused Kir3 channels and ZFP‐based adaptors on DNA origami were confirmed by atomic force microscopy and gel electrophoresis. Furthermore, the DNA origami with ZFP binding sites nearly tripled the K⁺ channel current activity elicited by heterotetrameric Kir3 channels in HEK293T cells. Thus, our method provides a useful template to control the oligomerization states of membrane protein complexes in vitro and in living cells.     

Odd-even effect and metal induced structural convergence in self-assembled monolayers of bipyridine derivatives

Scanning tunneling microscopy (STM) observations reveal that bipyridine derivatives which exhibit various two-dimensional structures due to the odd-even chain length effect are converged into a lamellar structure upon metal coordination.