On zero sum subsequences of restricted size

Let G be a finite abelian group with exp(G) = e. Let s(G) be the minimal integer t with the property that any sequence of t elements in G contains an e-term subsequence with sum zero. Let n, mand r be positive integers and m ≥ 3. Furthermore, η(C _m ^r ) = a _r (m − 1) + 1, for some constant a _r depending on r and n is a fixed positive integer such that

Synthesis of pyridine-borane complexes via electrophilic aromatic borylation

Pyridine-borane complexes were synthesized from 2-arylpyridines through an electrophilic aromatic borylation reaction with BBr(3). The intermediate 2-(2-dibromoborylaryl)pyridines were stable enough to be handled in air and served as the synthetic platform for variously substituted pyridine-borane complexes. This facile method would be useful for the synthesis of aza-π-conjugated materials having boron-nitrogen coordination.     

Gas permeation properties of poly(silamine) membrane

The gas permeation characteristics of poly(silamine) membrane, which consists of alternating 3,3-dimethyl-3-silapentane and N,N′-diethylethylenediamine units in the main chain, were investigated. Though poly(silamine) shows high flexibility (glass transition temperature of −88°C), the gas permeabilities were much lower than those of other rubbery polymers such as poly(dimethylsiloxane) and natural rubber. The activation energies of diffusion in poly(silamine) were much higher than that of natural rubber. On the basis of these results, we propose a model such that the interaction between the Si atom and gas molecules (O₂ and N₂) prevents the free diffusion of the gas molecule in the poly(silamine) membrane. © 1997 John Wiley & Sons, Ltd.     

Tributylstannylated silicic acid as precursor of organofunctionalized silica gel

Tributylstannylated silicic acid (TBSA), which was regarded as a protected polymeric silanol against self-condensation to give silica gel, was newly prepared from the reaction of water glass (WG) and bis(tributyltin) oxide (TBO). The ratios of Si/Sn contained in TBSA were determined by gravimetric analysis to be in the range of 2–3. The gelation of TBSA in usual organic solvents such as hexane, benzene, and dichloromethane was not observed over 3 weeks. In addition, TBSA was shown to be a convenient precursor for the preparations of silica gel modified with organofunctional groups. From the reaction of TBSA with trimethoxysilanes and aromatic alcohols, the silica gels havingorganofunctional groups were obtained with the elimination of a tributyltin group. © 1998 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 36: 655–663, 1998     

Post-stimulus response in hemodynamics observed by functional magnetic resonance imaging--difference between the primary sensorimotor area and the supplementary motor area

The blood oxygen level dependency (BOLD) contrast is a useful tool for functional neuroimaging based on the hemodynamic response to neuronal activation. We observed different hemodynamic responses in the BOLD signal between the primary sensorimotor area (SM1) and the supplementary motor area (SMA) in the sequential finger movement task. In the SMA, a stronger initial overshoot and a post-stimulus overshoot were observed. It was hypothesized from the time course analysis that the stronger initial overshoot reflected the activation of the SMA for motor control programming in the initial phase. Although the post-stimulus overshoot may be partially explained by cerebral blood flow (CBF) cerebral blood volume (CBV) uncoupling, its mechanism remained unknown. In the SM1, only the initial overshoot was observed and the level of BOLD signal was almost constant after the initial overshoot during the task period. These observations suggested that the BOLD signal is characterized by both CBF-CBV uncoupling and the neuronal activation characteristics in each region.     

Radical ring‐opening copolymerization behavior of vinyloxirane: Synthesis of copolymer from 2‐isopropenyl‐3‐phenyloxirane and styrene and its functionalization

The radical ring‐opening copolymerization of 2‐isopropenyl‐3‐phenyloxirane (1) with styrene (St) was examined to obtain the copolymer [copoly(1‐St)] with a vinyl ether moiety in the main chain. The copolymers were obtained in moderate yields by copolymerization in various feed ratios of 1 and St over 120 °C; the number‐average molecular weights (M_n) were estimated to be 1800–4200 by gel permeation chromatography analysis. The ratio of the vinyl ether and St units of copoly(1‐St) was estimated with the ¹H NMR spectra and varied from 1/7 to 1/14 according to the initial feed ratio of 1 and St. The haloalkoxylation of copoly(1‐St) with ethylene glycol in the presence of N‐chlorosuccinimide produced a new copolymer with alcohol groups and chlorine atoms in the side group in a high yield. The M_n value of the haloalkoxylated polymer was almost the same as that of the starting copoly(1‐St). The incorporated halogen was determined by elemental analysis. The analytical result indicated that over 88% of the vinyl ether groups participated in the haloalkoxylation. © 2000 John Wiley & Sons, Inc. J Polym Sci A: Polym Chem 38: 3729–3735, 2000     

Liquid crystalline phase transitions in hexakis(4-(4'-heptyloxy)biphenoxy)cyclotriphosphazene

Hexakis(4-(4'-heptyloxy)biphenoxy)cyclotriphosphazene (HHCP) was synthesized from hexachlorocyclotriphosphazene and 4-heptyloxy-4'-hydroxybiphenyl. The mesogenicity of HHCP was studied by DSC, FTIR spectroscopy and polarizing microscopy. Enantiotropic smectic C and nematic phases were observed between 450 and 455 K and 455 and 456 K, respectively, on heating, and between 456 and 455 K (nematic) and 455 and 440 K (smectic C) on cooling from the isotropic liquid phase. The introduction of the heptyloxybiphenoxy groups as side chains into cyclotriphosphazene has generated the liquid crystalline phase. FTIR spectroscopy showed that the P=N and P-O-(C) stretching vibrations converted to lower frequencies from 1224 to 1210 cm^-1 and from 920 to 910cm^-1, respectively, at the crystalline (C)-S_c phase transition. This result suggests that the state of the cyclotriphosphazene ring dramatically changes near the C-S_c phase transition.     

Developments of the theory of spin fluctuations and spin fluctuation-induced superconductivity

Theory of spin fluctuations as developed in the past 30 years have played important roles in the theory of magnetism in metals, particularly in elucidating the properties around the magnetic instability or quantum critical points. Recently the theory has been extended to deal with the spin fluctuaion-mediated superconductivity with anisotropic order parameters in strongly correlated electron systems. These theoretical developments are briefly reviewed and the high temperature superconductivity of cuprates and organic and heavy electron superconductors are discussed in the light of these theories.