Conditions for Generic Initial Ideals to be Almost Reverse Lexicographic

Let $I$ be a homogeneous Artinian ideal in a polynomial ring $R=k[x_1,...,x_n]$ over a field $k$ of characteristic 0. We study an equivalent condition for the generic initial ideal \gin(I) with respect to reverse lexicographic order to be almost reverse lexicographic. As a result, we show that Moreno-Socias conjecture implies Fr\"{o}berg conjecture. And for the case \Codim I \le 3, we show that $R/I$ has the strong Lefschetz property if and only if \gin(I) is almost reverse lexicographic. Finally for a monomial complete intersection Artinian ideal $I=(x_1^{d_1},...,x_n^{d_n})$, we prove that \gin(I) is almost reverse lexicographic if $d_i > \sum_{j=1}^{i-1} d_j - i + 1$ for each $i \ge 4$. Using this, we give a positive partial answer to Moreno-Socias conjecture, and to Fr\"{o}berg conjecture.Comment: 10 page

Preparation of silica nanospheres and porous polymer membranes with controlled morphologies via nanophase separation

We successfully synthesized two different structures, silica nanospheres and porous polymer membranes, via nanophase separation, based on a sol-gel process. Silica sol, which was in situ polymerized from tetraorthosilicate, was used as a precursor. Subsequently, it was mixed with a polymer that was used as a matrix component. It was observed that nanophase separation occurred after the mixing of polymer with silica sol and subsequent evaporation of solvents, resulting in organizing various structures, from random network silica structures to silica spheres. In particular, silica nanospheres were produced by manipulating the mixing ratio of polymer to silica sol. The size of silica beads was gradually changed from micro- to nanoscale, depending on the polymer content. At the same time, porous polymer membranes were generated by removing the silica component with hydrofluoric acid. Furthermore, porous carbon membranes were produced using carbon source polymer through the carbonization process.open0

Topological Structure of Dense Hadronic Matter

We present a summary of work done on dense hadronic matter, based on the Skyrme model, which provides a unified approach to high density, valid in the large $N_c$ limit. In our picture, dense hadronic matter is described by the {\em classical} soliton configuration with minimum energy for the given baryon number density. By incorporating the meson fluctuations on such ground state we obtain an effective Lagrangian for meson dynamics in a dense medium. Our starting point has been the Skyrme model defined in terms of pions, thereafter we have extended and improved the model by incorporating other degrees of freedom such as dilaton, kaons and vector mesons.Comment: 13 pages, 8 figures, Talk given at the KIAS-APCTP Symposium in Astro-Hadron Physics "Compact Stars: Quest for New States of Dense Matter", November 10-14, 2003, Seoul, Korea, published by World Scientific. Based on talk by B.-Y. Par

Spin cast ferroelectric beta poly(vinylidene fluoride) thin films via rapid thermal annealing

We describe a method of fabricating ferroelectric beta-type poly(vinylidene fluoride) (PVDF) thin films on Au substrate by the humidity controlled spin casting combined with rapid thermal treatment. Our method produces thin uniform ferroelectric PVDF film with ordered beta crystals consisting of characteristic needlelike microdomains. A capacitor with a 160 nm thick ferroelectric PVDF film exhibits the remanent polarization and coercive voltage of similar to 7.0 mu C/cm(2) and 8 V, respectively, with the temperature stability of up to 160 degrees C. A ferroelectric field effect transistor also shows a drain current bistablility of 100 at zero gate voltage with +/- 20 V gate voltage sweep. (C) 2008 American Institute of Physicsopen485