A Necessary and Sufficient Condition for the Existence of a Heterochromatic Spanning Tree in a Graph

We prove the following theorem. An edge-colored (not necessary to be proper) connected graph G of order n has a heterochromatic spanning tree if and only if for any r colors (1≤r≤n−2), the removal of all the edges colored with these r colors from G results in a graph having at most r+1 components, where a heterochromatic spanning tree is a spanning tree whose edges have distinct colors.     

In-situ X-ray diffraction study on β-CrOOH at high pressure and high-temperature

ABSTRACT

High pressure hydrous phases with distorted rutile-type structure have attracted much interest as potential water reservoirs in the Earth’s mantle. An in-situ X-ray diffraction study of β-CrOOH was performed at high pressures of up to 6.2?GPa and high-temperatures of up to 700?K in order to clarify the temperature effect on compression behaviors of β-CrOOH. The P-V-T data fitted to a Birch–Murnaghan equation of state yielded the following results: isothermal bulk modulus K_T0?=?191(4)?GPa, temperature derivative (?K_T/?T)_P?=??0.04(2)?GPa?K^?1, and volumetric thermal expansion coefficient α?=?3.3(2)?×?10^?5?K^?1. In this study, at 300?K, the a-axis became less compressible at pressures above 1–2?GPa. We found that the pressure where the slopes of a/b and a/c ratios turned positive increased with temperature. This is the first experimental study indicating the temperature dependence of the change in the axial compressibility in distorted rutile-type M³⁺OOH.     

Sorption and pervaporation properties of crosslinked membranes of poly(ethylene oxide imide) segmented copolymer to aromatic/nonaromatic hydrocarbon mixtures

Poly(ethylene oxide imide) segmented copolymer (PEO‐PI) membranes were crosslinked by the chemical reaction between ethylene glycol diglycidyl ether and benzylalcohol groups of diamine moieties in polyimide segments at high temperatures. Sorption and diffusion of penetrants took place in poly(ethylene oxide) segment microdomains. Sorption and desorption behavior of pure vapors such as benzene (Bz), cyclohexane (Cx) and n‐hexane (Hx) was classified as the Fickian diffusion. Sorption isotherms of binary liquid mixtures could be represented by the Flory–Rehner model, but the model overpredicted the sorption amounts of Cx and Hx, leading to small predictions of sorption selectivity α_S for Bz/Cx and Bz/Hx systems. UNIFAC‐FV model fairly well predicted the sorption amounts of aromatic hydrocarbons, but significantly overestimated those of nonaromatic ones, leading to too small predictions of α_S. Pervaporation (PV) behavior of PEO‐PI membranes was governed by sorption behavior followed by membrane swelling. Diffusion coefficient weakly depended on the minimum cross section of a penetrant. The diffusivity selectivity α_D hardly depended on the feed composition and was about 1.4 and 0.75 for Bz/Cx and Bz/Hx, respectively. PV selectivity α_PV was larger for Bz/Hx than for Bz/Cx because of larger α_S. PEO‐PI membranes displayed high specific permeation flux Ql and reasonably high α_PV for aromatic/nonaromatic hydrocarbons; for example, Ql = 60 Kg μm/(m² h) and α_PV = 8 for a feed mixture containing Bz, Tol, Hx, n‐Ot and i‐Ot of 20 wt % at 353 K. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 38: 1800–1811, 2000     

Sequential pericyclic reaction of ene-diallenes: an efficient approach to the steroid skeleton

[reaction: see text] The one-pot construction of polycyclic aromatic systems from acyclic ene-bis(propargyl alcohols) was achieved through a tandem dual [2,3]-sigmatropic rearrangement/6pi-electrocyclic reaction/intramolecular [4 + 2] cycloaddition sequence. A steroidal compound was conveniently synthesized using the present method.     

Influence of the Coordination of Donor Solvent Molecules to 1,4,7,10-Tetramethyl-1,4,7,10- tetraazacyclododecanenickel(II) and Analogous Nickel(II) Complexes on Their Steric Factors

Coordination equilibrium constants (K _NiS) of some donor solvent molecules to 1,4,7,10-tetramethyl-1,4,7,10-tetraazacyclododecanenickel(II) ([Ni(Me₄[12]aneN₄)]²⁺) were determined in nitrobenzene (a noncoordinating bulk solvent). The first (K _NiS1) and second stepwise coordination equilibrium constants (K _NiS2) for 1,4,7,10-tetraazacyclododecanenickel(II) ([Ni([12]aneN₄)]²⁺), 1,4,8,11-tetraazac yclotetradecane- nickel(II) ([Ni([14] aneN₄)]²⁺), 1,4,8,11-tetrathiacyclotetra-decanenickel(II) ([Ni([14]aneS₄)]²⁺) were also reinvestigated. The K _NiS values for [Ni(Me₄[12]aneN₄)]²⁺ were compared to those of [Ni([12]aneN₄)]²⁺, (1R,4S, 8R,11S)-1,4,8,11-tetramethyl-1,4,8,11-tetraazacyclotetradecanenickel(II) (R,S,R,S-[Ni(Me₄[14]aneN₄)]²⁺), R,R,S,S-[Ni(Me₄[14]aneN₄)]²⁺, [Ni([14]aneN₄)]²⁺, and [Ni([14]aneS₄)]²⁺. Coordination of pyridine (Py), N,N,N′,N′-tetramethylurea (TMU), and N,N-dimethylacetamide (DMA) to [Ni(Me₄[12]aneN₄)]²⁺ was observed, although these donor solvent molecules did not coordinate to R,S,R,S-[Ni(Me₄[14]aneN₄)]²⁺. The K _NiS values for Py, TMU, and DMA are 7.9, 2.8, and 9.0 dm³⋅mol⁻¹, respectively. Some hydrogen-bonding waters were coordinated to R,S,R,S-[Ni(Me₄[14]aneN₄)]²⁺, but such waters did not coordinate to [Ni(Me₄[12] aneN₄)]²⁺. Also, the K _NiS2 values were larger than the corresponding K _NiS1 values for [Ni([14]aneS₄)]²⁺. Furthermore, the K _NiS1 values for [Ni([12]aneN₄)]²⁺ were the largest among these nickel(II) complex cations. The K _NiS, K _NiS1, and K _NiS2 values are discussed in terms of properties of the donor solvents and steric strains of these nickel(II) complex cations.     

Synthesis and evaluation of fluorogenic reagents for simultaneous detection of peptides and proteins by HPLC in two different samples

To find the pairs of fluorogenic reagents having similar retention times in HPLC but with different fluorescent characteristics, six fluorogenic reagents bearing benzoxadiazole or benzoselenadiazole skeletons were synthesized. The resultant derivatives obtained from the reaction of peptides and proteins with reagents which have a benzoselenadiazole skeleton showed different fluorescence characteristics from those with a benzoxadiazole skeleton. Since each corresponding derivatives of trypsin inhibitor and BSA with DAABD-Cl and 7-fluoro-N-[2-(diethylamino)ethyl]-2,1,3-benzoselenadiazole-4-sulfonamide (DEAEABSeD-F) have similar retention times, the pair of reagents was adopted for the sensitive simultaneous detection of proteins in two different samples. When the soluble fraction of mouse hippocampus was divided into the two samples (A and B), each was reacted with DEAEABSeD-F for A and DAABD-Cl for B, respectively. The two reaction solutions were combined and subjected to HPLC analysis with two fluorescent detectors in series (excitation and emission at different wavelengths for A and B, respectively). The resultant two chromatograms had quite similar patterns for each other. The new pair of fluorogenic reagents (DAABD-Cl and DEAEABSeD-F) would be applicable to proteomics studies using the previously reported FD-LC-MS/MS method.     

Highly efficient total synthesis of the marine natural products (+)-avarone, (+)-avarol, (-)-neoavarone, (-)-neoavarol and (+)-aureol

Biologically important and structurally unique marine natural products avarone (1), avarol (2), neoavarone (3), neoavarol (4) and aureol (5), were efficiently synthesized in a unified manner starting from (+)-5-methyl-Wieland-Miescher ketone 10. The synthesis involved the following crucial steps: i) Sequential BF(3)Et(2)O-induced rearrangement/cyclization reaction of 2 and 4 to produce 5 with complete stereoselectivity in high yield (2 --> 5 and 4 --> 5); ii) strategic salcomine oxidation of the phenolic compounds 6 and 8 to derive the corresponding quinones 1 and 3 (6 --> 1 and 8 --> 3); and iii) Birch reductive alkylation of 10 with bromide 11 to construct the requisite carbon framework 12 (10 + 11 --> 12). An in vitro cytotoxicity assay of compounds 1-5 against human histiocytic lymphoma cells U937 determined the order of cytotoxic potency (3 > 1 > 5 > 2 > 4) and some novel aspects of structure-activity relationships.     

Microfaceting explains complicated structures on rutile TiO2 surfaces

Surface structures on rutile TiO2 (001) have been studied by using scanning tunneling microscopy (STM), X-ray photoelectron spectroscopy (XPS), and density functional calculations. Prior investigations have observed many kinds of complicated surface structures; however, detailed atomic structures and the mechanism of the reconstructions are still unknown. We evaluate the energetical stability of the surface structures. The calculational results suggest that a [111] microfaceting model is energetically stable compared with the unreconstructed (1 x 1) model. We propose microfaceting structural models that are in good agreement with atomically resolved STM images. This structural concept can be extended to other rutile TiO2 surfaces in general.