Independence number,connectivity, and r-factors

We show that if r ? 1 is an odd integer and G is a graph with |V(G)| even such that k(G) ? (r + 1)²/2 and (r + 1)²α(G) ? 4rk(G), then G has an r-factor; if r ? 2 is even and G is a graph with k(G) ? r(r + 2)/2 and (r + 2)α(G) ? 4k(G), then G has an r-factor (where k(G) and α(G) denote the connectivity and the independence number of G, respectively).     

Assembly of a Benzo-Fused Bridged Ketone Scaffold from 1,5,10-Enediynes through One-Pot Ruthenium-Catalyzed Cyclization/Iodine-Mediated Oxidative Ring Expansion

In the presence of a cationic Ru catalyst, 1,6-diynes bearing a terminal styryl moiety underwent [2+2+2] cyclization to produce dehydrobiphenylenes fused with a five-membered ring. Although the cycloadducts were unstable toward purification, their one-pot iodine-mediated ring expansion successfully afforded unprecedented bridged ketone products containing a benzo-fused bicyclo[3.2.1] framework.     

Synthesis of 2-azabicyclo[2.1.0]pentanes by the intramolecular nucleophilic substitution of cyclopropylmagnesium carbenoids with magnesium anilide

A variety of 2-azabicyclo[2.1.0]pentanes were synthesized by the intramolecular nucleophilic substitution of cyclopropylmagnesium carbenoids with magnesium anilide. The 1-chlorocyclopropyl p-tolyl sulfoxides possessing an N-aryl-substituted aminomethyl group were prepared from dichloromethyl p-tolyl sulfoxide, α,β-unsaturated carboxylic acid esters, and anilines in four steps. The deprotonation of the amine with t-BuMgCl followed by sulfoxide/magnesium exchange of the sulfoxides with i-PrMgCl led to the generation of the cyclopropylmagnesium carbenoids possessing a magnesium anilide moiety. Subsequent intramolecular nucleophilic substitution of the cyclopropylmagnesium carbenoids occurred in a 4-exo-tet manner to give the 2-azabicyclo[2.1.0]pentanes. The optically active 2-azabicyclo[2.1.0]pentane was synthesized using a p-tolylsulfinyl group as a chiral auxiliary.     

Formation of Metal‐Assisted Stable Double Helices in Dimers of Cyclic Bis‐Tetrapyrroles that Exhibit Spring‐Like Motion

Bidipyrrin‐bridged macrocycles, prepared from Ni^II‐bridged dipyrrin‐based nanorings by intramolecular oxidative biaryl coupling reactions, yielded [2+4]‐type Zn^II‐assisted stable twisted‐ring dimers comprising two double helices. These [2+4]‐type metal complexes can be optically resolved by chiral HPLC and exhibit tunable electronic and optical properties as a result of spring‐like motions. The double helices behave as glue to connect two macrocycles and as the screws of hinges to form thermally responsive synchronized spring systems.     

High field magnetization of Pr1-xGdxNi single crystals

Magnetization measurements were carried out on Pr_1−xGd_xNi single crystals for x=0.1, 0.2, 0.3 and 0.4 using pulsed magnetic fields up to 55 T and at 4.2 K. For the data observed along the c-axis there are clear indications of transitions, of the combined system of Pr and Gd moments, from a ferrimagnetic to a ferromagnetic state. The observed saturation magnetizations at 55 T and intermediate magnetizations at 1 T were well modeled assuming ferro- and ferri-magnetic structures, respectively.     

Experimental observation of the bifurcation dynamics of an intrinsic localized mode in a driven 1D nonlinear lattice

Linear response spectra of a driven intrinsic localized mode in a micromechanical array are measured as it approaches two fundamentally different kinds of bifurcation points. A linear phase mode associated with this autoresonant state softens in frequency and its amplitude grows as the upper frequency bifurcation point is approached, similar to the soft-mode kinetic transition for a single driven Duffing resonator. A lower frequency bifurcation point occurs when the four-wave-mixing partner of this same phase mode intercepts the top of the extended wave branch, initiating a second kinetic transition process.     

Study of Proton Resonances in ~(22)Mg by Resonant Elastic Scattering of ~(21)Na+p and Its Astrophysical Implication in ~(18)Ne(α,p)~(21)Na Reaction Rate

Proton resonant states in ~(22)Mg have been investigated by the resonant elastic scattering of ~(21)Na+p.The ~(21)Na beam with a mean energy of 4.00 MeV/u was separated by the CNS radioactive ion beam separator(CRIB) and bombarded a thick(CH_2)_n target.The energy spectra of recoiled protons were measured at scattering angles of θ_(cm)～172° and 146°,respectively.A new state at 7.06 MeV has been observed clearly and another new one at 7.28 MeV is tentatively identified due to its low statistics.The proton resonant parameters were deduced from an R-matrix analysis of the differential cross section data.The astrophysical resonant reaction rate for the ~(18)Ne(α,p) ~(21)Na reaction has been estimated,and it is about five times larger than that assumed before.     

EPMA line analysis of chemical states of chromium

A novel technique for determining the chemical states of elements with a heterogeneous distribution in samples involving EPMA line analysis is proposed. LLS (linear least squares) calculation was applied to a set of reduced spectra measured in the line analysis. The reduced spectra which have several energy points (including two points for backgrounds) were measured in order to save measuring time. The LLS calculation gives the mole fraction of each chemical state. We applied this method to the analysis of corrosion products formed on Cr-containing steel after corrosion tests. EPMA mapping revealed that Cr is enriched only in the inner layer of the corrosion products. From the results of the LLS calculation, it was determined that Cr in the corrosion products exists in the trivalent Cr state whereas in the steel Cr is in the metallic state. This result corresponds to the spectra of characteristic x-rays from the corroded steel. Copyright © 2001 John Wiley & Sons, Ltd.