Staircase two-guard kernels of orthogonal polygons

Let S be a simply connected orthogonal polygon in the plane, and assume that S is two-guardable (but not starshaped) via staircase paths. If K is a component of two-kernel (S), then the set of partners of points in K determines a second component K' of two-kernel (S). Thus the components occur in pairs. Moreover, each component is geodesically convex. The results fail without the requirement that S be simply connected. Received 2 November 1999; revised 28 September 2000.     

Liquid chromatography determination of residue levels on apples treated with cetylpyridinium chloride

Cetylpyridinium chloride (CPC) has been found to be effective in reducing microbial contamination in apples. A sensitive and specific HPLC method was developed to determine CPC residues in apples treated with CPC. This method involves ion exchange solid-phase extraction, and the use of stearylpyridinium chloride (SPC) as internal standard. Limit of quantitation, was 0.5 microg/ml of CPC for the apple ethanolic extracts. The observed residues in apple (2.35-4.35 microg/g of apple) were lower than those previously reported for chicken and beef. The method is specific, sensitive, reproducible and accurate.     

Large-order estimates for ground-state energy perturbation series

A general treatment is given, using path integral methods, of obtaining accurate estimates on the rate of growth at large order of the perturbation coefficients for the lowest eigenvalue (ground-state energy) of a large class of anharmonic oscillators. Simple sufficient conditions are given on the potentialV(x) so that accurate upper and lower bounds on the perturbation coefficients may be derived. Several examples are given which generalize previous results. Examples from Euclidean quantum field theory are also considered.This paper is dedicated to the memory of Mark Kac.     

Covering in the set of principal ideals in the semigroup of binary relations

Communicated by Boris M. Schein     

A Helly-type theorem for countable intersections of starshaped sets

Let k and d be fixed integers, 0kd, and let be a collection of sets in If every countable subfamily of has a starshaped intersection, then is (nonempty and) starshaped as well. Moreover, if every countable subfamily of has as its intersection a starshaped set whose kernel is at least k-dimensional, then the kernel of is at least k-dimensional, too. Finally, dual statements hold for unions of sets.Received: 3 April 2004     

Illumination by translates of convex sets

Let S be a compact set in the plane. If every three points of S are illuminated clearly by some translate of the compact convex set T, then there is a translate of T which illumines every point of S. Various analogues hold for translates of flats in R ^das well.Supported in part by NSF grant DMS-8705336.     

Dual Illumination Enhances Transformation of an Engineered Green‐to‐Red Photoconvertible Fluorescent Protein

The molecular mechanisms for the photoconversion of fluorescent proteins remain elusive owing to the challenges of monitoring chromophore structural dynamics during the light‐induced processes. We implemented time‐resolved electronic and stimulated Raman spectroscopies to reveal two hidden species of an engineered ancestral GFP‐like protein LEA, involving semi‐trapped protonated and trapped deprotonated chromophores en route to photoconversion in pH 7.9 buffer. A new dual‐illumination approach was examined, using 400 and 505 nm light simultaneously to achieve faster conversion and higher color contrast. Substitution of UV irradiation with visible light benefits bioimaging, while the spectral benchmark of a trapped chromophore with characteristic ring twisting and bridge‐H bending motions enables rational design of functional proteins. With the improved H‐bonding network and structural motions, the photoexcited chromophore could increase the photoswitching‐aided photoconversion while reducing trapped species.     

Radon and Carathéodory type theorems for staircase convexity

Aequationes mathematicae - We establish the following analogues of the familiar Radon and Carathéodory theorems for staircase convex sets in $$\mathbb {R}^d$$ : Various “best...