Polynomially convex hulls of graphs on the sphere

Let be the graph of a continuous map of the unit sphere of into , and the polynomially convex hull of . Several examples of for are given, which have different properties from the known ones for .

     

Novel amphiphilic network polymers consisting of nonpolar,short primary polymer chains and polar,long crosslink units: Influence of characteristic dangling chains on swelling behavior of resulting amphiphilic gels

Novel amphiphilic network polymers consisting of nonpolar, short primary polymer chains and polar, long crosslink units were prepared, and the swelling behavior of resulting amphiphilic gels is discussed by focusing on the influence of characteristic dangling chains; that is, benzyl methacrylate (BzMA) was copolymerized with tricosaethylene glycol dimethacrylate [CH₂?C(CH₃)CO(OCH₂CH₂)₂₃OCOC(CH₃)?CH₂, PEGDMA‐23] in the presence of lauryl mercaptan as a chain‐transfer agent because BzMA forms nonpolar, short primary polymer chains and PEGDMA‐23 as a crosslinker contains a polar, long poly(oxyethylene) unit. The enhanced incorporation of dangling chains into the network polymer was brought by shortening the primary polymer chain length, and copolymerization with methoxytricosaethylene glycol methacrylate, a mono‐ene counterpart of PEGDMA‐23, enforced the incorporation of flexible dangling poly(oxyethylene) chains into the network polymer, although the former dangling chains as terminal parts of primary poly(BzMA) chains were rather rigid. Then, the influence of characteristic dangling chains on the swelling behavior of amphiphilic gels was examined in mixed solvents consisting of nonpolar t‐butylbenzene and polar methanol. The profiles of the solvent‐component dependencies of the swelling ratios were characteristic of amphiphilic gels. The introduction of dangling poly(oxyethylene) chains led not only to an increased swelling ratio but also to sharpened swelling behavior of amphiphilic gels. The swelling response of amphiphilic gels was checked by changing the external solvent polarity. The dangling chains with freely mobile end segments influenced the swelling response of gels. The amphiphilic gels with less entangled, collapsed crosslink units exhibited faster swelling response than the ones with more entangled, collapsed primary polymer chains. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2192–2201, 2004     

Coherent optical neural networks and the generalization characteristic

Coherent optical neural-network systems are presented by which we are to realize (1) control of optical neural-network behavior by carrier frequency modulation and (2) frequency-domain multiplexing as a new degree of neural parallelism. In the coherent optical neural network, lightwave carries amplitude, phase, and frequency signals which are processed through optical neural connections consisting of transparency, delay, and optical nonlinear neurons. The neural learning process is realized by adjusting the delay time and the transpar-ency of the optical connections by regarding the carrier frequency as a learning parameter. A simulation experiment demonstrates that the proposed system learns desired output signals depending on the optical carrier frequencies, which leads to the above advantages. It is also found that the generalization characteristics depends on built-in input delays. The generalization quality is discussed from the viewpoint of function approximation or synthesis using sinusoidal basis functions.     

The transition from the spin-glass to the ferromagnetic state in the bond-random Ising model in the face-centred cubic lattice

The boundary between the spin-glass state and the ferromagnetic state (p_F-G) of the bond-random (±J) Ising model in the face-centred cubic lattice at T = 0 is calculated by the method of tetrahedron approximation in the simple version. The obtained value is, p_F-G = 0.682, which is a little larger than the triple point p_t = 0.654, and the model shows the reentrant behavior.     

[3]Parycyclo− and [3]metacyclo[3](3,7)-p-tropoquinonophanes

The title phanes were synthesized. Examination of their physical properties including X-ray crystallography disclosed that 1) the p-tropoquinone ring is still bent in both compounds though to a lesser extent than in the corresponding [2.2]phanes, 2) the metacyclo compound prefers syn conformation in solution, and 3) the intramolecular CT interaction is very similar in two compounds.