Normal Bundles to Laufer Rational Curves in Local Calabi–Yau Threefolds

We prove a conjecture by F. Ferrari. Let X be the total space of a nonlinear deformation of a rank two holomorphic vector bundle on a smooth rational curve, such that X has trivial canonical bundle and has sections. Then the normal bundle to such sections is computed in terms of the rank of the Hessian of a suitably defined superpotential at its critical points.     

Algorithms for finding connected separators between antipodal points

A set (or a collection of sets) contained in the Euclidean space Rm is symmetric if it is invariant under the antipodal map. Given a symmetric unicoherent polyhedron X (like an n-dimensional cube or a sphere) and an odd real function f defined on vertices of a certain symmetric triangulation of X, we algorithmically construct a connected symmetric separator of X by choosing a subcollection of the triangulation. Each element of the subcollection contains the vertices v and u such that f(v)f(u)?0.     

Nonminimal sets,their projections and integral representations of stable processes

New criteria are provided for determining whether an integral representation of a stable process is minimal. These criteria are based on various nonminimal sets and their projections, and have several advantages over and shed light on already available criteria. In particular, they naturally lead from a nonminimal representation to the one which is minimal. Several known examples are considered to illustrate the main results. The general approach is also adapted to show that the so-called mixed moving averages have a minimal integral representation of the mixed moving average type.     

Photoelectron spectroscopic study of Li oxides on Li over-deposited V2O5 thin film surfaces

The Li oxides species formed on Li over-deposited V₂O₅ thin film surfaces have been studied by using X-ray and UV induced photoelectron spectroscopy (XPS and UPS). The photoelectron spectroscopic data show that the Li over-deposited V₂O₅ system itself is not stable. Further chemical decomposition reactions are taken place even under UHV conditions and lead to form Li₂O and Li₂O₂ compounds on the surface. The formation of Li₂O₂ causes to arise an emission line at about 11.3 eV in the valence band spectra.     

Association Behavior of 4-Acylpyrazolone Derivative and Tertiary Amine of High Molecular Weight in Antagonistic Synergistic Extraction of Palladium

To find an effective extraction and removal method for palladium(II), which is one of the main fission products from an acidic nuclear spent fuel solution, the extraction behavior of palladium(II) from a nitric acid medium by an acidic chelating extractant, 1-phenyl-3-methyl-4-trifluoroacetylpyrazolone-5-one (HPMTP) and a tertiary amine of high molecular weight, tri-n-octylamine (TOA), has been studied by spectrophotometry. A noticeable antagonistic extraction effect was observed in the extraction system under the given conditions. To understand this phenomenon, a preliminary investigation was performed to explain the mechanism of this reaction. According to the theory of corresponding solutions (TCS), the association reaction between HPMTP and TOA is proposed in the organic phase. An associated species, HPMTP·TOA, formed through hydrogen bonding in a chloroform medium might be the main reason why an antagonistic extraction effect occurred. The association constant between HPMTP and TOA was calculated to be 2.86±0.05.     

Laplacians and the Cheeger Inequality for Directed Graphs

We consider Laplacians for directed graphs and examine their eigenvalues. We introduce a notion of a circulation in a directed graph and its connection with the Rayleigh quotient. We then define a Cheeger constant and establish the Cheeger inequality for directed graphs. These relations can be used to deal with various problems that often arise in the study of non-reversible Markov chains including bounding the rate of convergence and deriving comparison theorems.Received September 8, 2004     

Transition‐metal‐catalyzed reactions of 5‐methylene‐2‐oxazolidinone and 5‐methylene‐1,3‐thiazolidine‐2‐thione with isocyanates

5‐Methylene‐2‐oxazolidinone (1) and 5‐methylene‐1,3‐thiazolidine‐2‐thione (4) react with various isocyanates to give the corresponding urethanes 3 and 5 in high yields in the presence of palladium(0) or palladium(II) catalyst under mild reaction conditions. A mechanism is proposed. Copyright © 2003 John Wiley & Sons, Ltd.     

Crystal Structure of Adduct 2-Phenyl-imidazo [ 4,5-f ] 1,10-phenanthroline Methanol

The structure of the title adduct comprises a phenanthroline derivative 2-phenyl-imidazo[4,5-f]1,10-phenanthroline and a methanol.The composition of the crystalline adduct was characterized as C19H12N4.CH3OH.It belongs to orthorhombic system,space group Pna21 with a=1.3693(4)nm,b=2.2988(7)nm,c=0.51338(15)nm,V=1.6160(8)nm^3.Z=4,and final R1=0.0423.wR2=0.1012 .Crystal structure shows that all the 19 carbon atoms and 4 nitrogen atoms are coplanar.The bond length data indicated that a very extensive conjugation system was formed.This conjugation makes the compound being a potentially excellent energy transformer used for luminescent materials.     

Microwave‐improved polymerization of ϵ‐caprolactone initiated by carboxylic acids

The ring‐opening polymerization of ε‐caprolactone (ε‐CL), initiated by carboxylic acids such as benzoic acid and chlorinated acetic acids under microwave irradiation, was investigated; with this method, no metal catalyst was necessary. The product was characterized as poly(ε‐caprolactone) (PCL) by ¹H NMR spectroscopy, Fourier transform infrared spectroscopy, ultraviolet spectroscopy, and gel permeation chromatography. The polymerization was significantly improved under microwave irradiation. The weight‐average molecular weight (M_w) of PCL reached 44,800 g/mol, with a polydispersity index [weight‐average molecular weight/number‐average molecular weight (M_w/M_n)] of 1.6, when a mixture of ε‐CL and benzoic acid (25/1 molar ratio) was irradiated at 680 W for 240 min, whereas PCL with M_w = 12,100 and M_w/M_n = 4.2 was obtained from the same mixture by a conventional heating method at 210 °C for 240 min. A degradation of the resultant PCL was observed during microwave polymerization with chlorinated acetic acids as initiators, and this induced a decrease in M_w of PCL. However, the degradation was hindered by benzoic acid at low concentrations. © 2002 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 41: 13–21, 2003