Fourier multipliers on compact groups

In a recent paperIan Inglis gives some sufficient conditions for a function on a totally disconnected compact Abelian group to be anL ^p Fourier multiplier. His proof depends on an interpolation theorem ofE. M. Stein. In this note we prove a generalization ofInglis' theorem. Our result is deduced from a factorization theorem, the proof of which is elementary, and a standard multiplier theorem.This work was done while the second-named author held a visiting appointment at the University of Washington. He wishes to thank ProfessorsE. Hewitt andR. R. Phelps for making the visit possible.     

Maximal sum-free sets in finite Abelian groups,III

The main result of this paper is the complete characterization of maximal sum-free sets in Abelian groups of order 3^mn(m ≥ 1) where every prime divisor p of n (if n > 1) is congruent to 1 modulo 3. A few previous results of the author on addition theorems of group theory are also sharpened and/or improved.     

pH-Sensitive brush polymer-drug conjugates by ring-opening metathesis copolymerization

Representing a new category of polymer-drug conjugates, brush polymer-drug conjugates were prepared by ring-opening metathesis copolymerization. Following judicious structural design, these conjugates exhibited well-shielded drug moieties, significant water solubility, well-defined nanostructures, and acid-triggered drug release.     

A polynomial solution for the potato-peeling problem

The potato-peeling problem asks for the largest convex polygon contained inside a given simple polygon. We give anO(n ⁷) time algorithm to this problem, answering a question of Goodman. We also give anO(n ⁶) time algorithm if the desired polygon is maximized with respect to perimeter.Work in this paper has been supported in part by NSF grants #DCR-84-01898 and #DCR-84-01633, the Office of Naval Research Grant N00014-82-K-0381, and by grants from Digital Equipment Corporation, the Sloan Foundation, the System Development Foundation, and the IBM Corporation. This paper contains the main results of the paper A Polynomial Solution for Potato-Peeling and other Polygon Inclusion and Enclosure Problems presented in the 25th Foundation of Computer Science Conference, 1984, Florida. The second half of that paper is submitted for publication elsewhere [1].     

Controlling mode selectivity in palladium-catalyzed bisdiene carbocyclizations: optimizing for cyclization-trapping over cycloisomerization

[reaction: see text] Screening combinations of five catalyst precursors with 13 phosphorus ligands identified cyclization catalysts that favor carbocyclization-trapping with N-hydroxyphthalimide over a competing cycloisomerization mode.     

Alleviation of photoinduced damage in GdxY1-xCa4O(BO3)3 at elevated crystal temperature for noncritically phase-matched 355-nm generation

We developed a Gd(x)Y(1-x)Ca(4)O(BO(3))(3) (GdYCOB) crystal for control of optical birefringence. GdYCOB crystals were successfully used to generate noncritical phase-matched (NCPM) second and third harmonics of 1064-nm lights. However, we observed degradation of third-harmonic-generation (THG) output power and distortion of the beam pattern as a result of photoinduced damage and thermal dephasing. The photoinduced damage was classified into two types. One was gray-track and the other was photorefractive damage. It seems that these types of damage were similar to the types of damage that occurred with KTiOPO(4) and LiNbO(3) crystals. We tried to circumvent this problem by crystal heating. Photoinduced damage of GdYCOB was overcome by elevation of the crystal temperature, and NCPM THG (355-nm) output power from heated GdYCOB increased to 9 mW (62.5 kHz).