Some New uniform frames with block size four and index one or three

In this paper, some new uniform frames with block size four and index one or three are obtained. The known existence results for (4,1)‐frames and (4,3)‐frames are both improved to the extent that only a finite number of possible exceptions remain. © 2003 Wiley Periodicals, Inc.     

An exponential lower bound to the size of bounded depth frege proofs of the pigeonhole principle

We prove lower bounds of the form exp(n^{ε d}), ε_d > 0, on the length of proofs of an explicit sequence of tautologies, based on the Pigeonhole Principle, in proof systems using formulas of depth d, for any constant d. This is the largest lower bound for the strongest proof system, for which any superpolynomial lower bounds are known.     

TERAHERTZ QUALITY CONTROL OF POLYMERIC PRODUCTS

We report on experiments that evaluate the potential of terahertz (THz) time-domain spectroscopy (TDS) for quality control of polymeric compounds. We investigate specimens out of a polyethylene compound with silver-coated titanium dioxide nanospheres and a glass-fiber reinforced epoxy composite. We further examine an industrial polymer product produced by injection molding. Our data demonstrates that THz imaging is a powerful tool for contactless quality control in the polymer industry.     

A comparison of spin relaxation and local motion between symmetrically and asymmetrically ring-substituted bisphenol units in dissolved polycarbonates

Carbon-13 and proton spin-lattice relaxation times were measured at two field strengths on solutions 10% by weight of two polycarbonates in C₂D₂Cl₄ from ?20 to +120°C. The first polycarbonate is an asymmetrically substituted form with one chlorine on one of the two phenylene aromatic rings of the bisphenol unit, whereas the second polycarbonate is symmetrically substituted with two chlorines on each of the two rings. The nuclear spin relaxation data are interpreted in terms of several local motions likely in these polymers. Segmental motion was described by the Hall–Helfand correlation function. Segmental motion in the monosubstituted polycarbonate is somewhat slower than in unsubstituted polycarbonate, whereas segmental motion in the tetrasubstituted polycarbonate is considerably slower. Phenylene ring rotation is observed in unsubstituted polycarbonate and in the monosubstituted polycarbonate above 40°C. Below 40°C in the monosubstituted species, and at all temperatures in the tetrasubstituted species, ring rotation is replaced by ring libration as the predominant motion contributing to spin lattice relaxation. In addition, the rotational motion of the two types of rings in the asymmetric monosubstituted form are very similar although not identical. The substituted ring is slightly less mobile than the rings of unsubstituted polycarbonate. This indicates a strong coupling of ring motion, although the coupling leads to less than synchronous motion. Methyl group rotation is present in both polymers and is little affected by the various structural modifications.     

Global Optimal Image Reconstruction from Blurred Noisy Data by a Bayesian Approach

In this paper, a procedure is presented which allows the optimal reconstruction of images from blurred noisy data. The procedure relies on a general Bayesian approach, which makes proper use of all the available information. Special attention is devoted to the informative content of the edges; thus, a preprocessing phase is included, with the aim of estimating the jump sizes in the gray level. The optimization phase follows; existence and uniqueness of the solution is secured. The procedure is tested against simple simulated data and real data.