Isolation and characterization of some very stable 1-phospha-allenes: sterically protected iminomethylene- and ethenylidenephosphines

Very stable iminomethylenephosphine (3) and ethenylidenephosphine (4) were obtained by steric protection with the 2,4,6-tri-tertbutylphenyl group and some of the spectroscopic data are described.     

Sterically Protected Unusual Phosphorus Compounds in Lower Coordination States: Diphosphenes,Phosphaethylenes, and 1-Phospha- and 1,3-Diphosphaallenes

Abstract

Physicochemical properties and chemical reactivities of some sterically protected unusual phosphorus compounds in lower coordination states are discussed such as diphosphenes, phosphaethylenes, and 1-phospha- and 1,3-diphosphaallenes.     

Negative Magneto-Resistance Beyond Weak Localization in Three-Dimensional Billiards:Effect of Arnold Diffusion

We investigate a semiclassical conductance for ballistic open three-dimensional (3-d) billiards. For partially or completely broken-ergodic 3-d billiards such as SO(2) symmetric billiards, the dependence of the conductance on the Fermi wavenumber is dramatically changed by the lead orientation. Application of a symmetry-breaking weak magnetic field brings about mixed phase-space structures of 3-d billiards which ensures a novel Arnold diffusion that cannot be seen in 2-d billiards. In contrast to the 2-d case, the anomalous increment of the conductance should inevitably include a contribution arising from Arnold diffusion as well as a weak localization correction. Discussions are devoted to the physical condition for observing this phenomenon.     

Helix formation of poly(phenylacetylene) derivatives bearing amino groups at the meta position induced by optically active carboxylic acids

Two novel phenylacetylene derivatives bearing diethylaminomethyl groups at the meta position on phenyl groups [3‐(N,N‐diethylaminomethyl)phenyl]acetylene ( 1 ) and [3,5‐bis(N,N‐diethylaminomethyl)phenyl]acetylene ( 2 ) were synthesized and polymerized with [Rh(nbd)Cl]₂ (nbd: norbornadiene). Both monomers gave highly cis–transoidal stereoregular polymers that exhibited an induced circular dichroism (ICD) in the UV–visible region, probably because of a prevailing one‐handed helical conformation upon complexation with optically active carboxylic acids such as mandelic acid and lactic acid. The sign of the Cotton effects reflected the absolute configuration of the chiral acids. Therefore, these polymers can be used as a novel probe for determining the configuration of chiral acids. The polymers were stable in the presence of chiral acids in solution. The poly‐ 1 complexed with chiral acids exhibited a split‐type ICD, whereas the poly‐ 2 complexed with chiral acids showed a different, non‐split‐type ICD. The ICD pattern of the poly‐ 1 /chiral acids complexes dramatically changed with an increase in the concentration of the chiral acids, thus showing a non‐split‐type ICD similar to those of the poly‐ 2 /chiral acid complexes. © 2001 John Wiley & Sons, Inc. J Polym Sci Part A: Polym Chem 39: 3180–3189, 2001     

Hamiltonian cycles in n-factor-critical graphs

A graph G is said to be n-factor-critical if G−S has a 1-factor for any SV(G) with |S|=n. In this paper, we prove that if G is a 2-connected n-factor-critical graph of order p with , then G is hamiltonian with some exceptions. To extend this theorem, we define a (k,n)-factor-critical graph to be a graph G such that G−S has a k-factor for any SV(G) with |S|=n. We conjecture that if G is a 2-connected (k,n)-factor-critical graph of order p with , then G is hamiltonian with some exceptions. In this paper, we characterize all such graphs that satisfy the assumption, but are not 1-tough. Using this, we verify the conjecture for k2.     

Commutativity of association schemes of prime square order having non-trivial thin closed subsets

Through a study of the structure of the modular adjacency algebra over a field of positive characteristic p for a scheme of prime order p and utilizing the fact that every scheme of prime order is commutative, we show that every association scheme of prime square order having a non-trivial thin closed subset is commutative. The second author was supported by Korea Research Foundation Grant (KRF-2006-003-00008).     

The denominators of Lagrangian surfaces in complex Euclidean plane

A quotient of two linearly independent quaternionic holomorphic sections of a quaternionic holomorphic line bundle over a Riemann surface is a conformal branched immersion from a Riemann surface to four-dimensional Euclidean space. On the assumption that a quaternionic holomorphic line bundle is associated with a Lagrangian-branched immersion from a Riemann surface to complex Euclidean plane, we shall classify the denominators of Lagrangian-branched immersion from a Riemann surface to complex Euclidean plane.