On the volume product of polygons

We present a method that allows us to prove that the volume product of polygons in ℝ² with at most n vertices is bounded from above by the volume product of regular polygons with n vertices. The same method shows that the volume product of polygons is bounded from below by the volume product of triangles (or parallelograms in the centrally symmetric case). These last results give a new proof of theorems of K. Mahler. The cases of equality are completely described.     

Temporal integration of the contralateral acoustic-reflex threshold and its age-related changes

Although numerous studies have investigated temporal integration of the acoustic-reflex threshold (ART), research is lacking on the effect of age on temporal integration of the ART. Therefore the effect of age on temporal integration of the ART was investigated for a broad-band noise (BBN) activator. Subjects consisted of two groups of adults with normal-hearing sensitivity: one group of 20 young adults (ten males and ten females, ages 18-29 years, with a mean age of 24 years) and one group of 20 older adults (ten males and ten females, ages 59-75 years, with a mean age of 67.5 years). Activating stimulus durations were 12, 25, 50, 100, 200, 300, 500, and 1000 ms. Significant main effects for duration and age were obtained. That is, as the duration increased, the acoustic reflex threshold for BBN decreased. The interactions of duration x age group and duration x hearing level were not significant. The result of pair-wise analysis indicated statistically significant differences between the two age groups at durations of 20 ms and longer. The observed age effect on temporal integration of the ART for the BBN activator is interpreted in relation to senescent changes in the auditory system.     

Synthesis of oxidized thienopyrroles using HOF·CH3CN

An efficient transformation of the sulfur atoms to the sulfonyl group in a range of thienopyrroles was achieved by using the HOF·CH(3)CN complex. Mild conditions, high yields, and easy purification are the main features of this novel route. Most new materials exhibit considerable red-shift absorptions in the UV/visible range relative to the parent compounds.     

Beyond Equal-Power Sparse NOMA: Two User Classes and Closed-Form Bounds on the Achievable Region

Non-orthogonal multiple access (NOMA) is a promising technology for future beyond-5G wireless networks, whose fundamental information-theoretic limits are yet to be fully explored. Considering regular sparse code-domain NOMA (with a fixed and finite number of orthogonal resources allocated to any designated user and vice versa), this paper extends previous results by the authors to a setting comprising two classes of users with different power constraints. Explicit rigorous closed-form analytical inner and outer bounds on the achievable rate (total class throughput) region in the large-system limit are derived and comparatively investigated in extreme-SNR regimes. The inner bound is based on the conditional vector entropy power inequality (EPI), while the outer bound relies on a recent strengthened version of the EPI. Valuable insights are provided into the potential performance gains of regular sparse NOMA in practically oriented settings, comprising, e.g., a combination of low-complexity devices and broadband users with higher transmit power capabilities, or combinations of cell-edge and cell-center users. The conditions for superior performance over dense code-domain NOMA (taking the form of randomly spread code-division multiple access), as well as a relatively small gap to the ultimate performance limits, are identified. The proposed bounds are also applicable for the analysis of interference networks, e.g., Wyner-type cellular models.     

A note on conjugate gradient convergence – Part II

Summary. Continuing our previous analysis, we derive the exact number of conjugate gradient iterations needed (to achieve a given tolerance) for the one-dimensional discrete Poisson equation on a uniform grid, and a particularly smooth solution vector. Received July 29, 1998 / Published online March 16, 2000     

all-S,S-dioxygenated star oligothiophenes

Star-shaped oligothiophenes are promising materials for applications in the organic electronics field. For the first time, a range of star-oligothiophenes was oxidized to the corresponding all-S,S-dioxides by using the HOF·CH(3)CN complex. These materials exhibit considerable thermal stability and red-shift absorptions in the UV/vis relative to the parent compounds.     

Ring stain effect at room temperature in silver nanoparticles yields high electrical conductivity

We demonstrate that metallic rings formed spontaneously at room temperature via evaporation of aqueous drops containing silver nanoparticles (20-30 nm in diameter) exhibit high electrical conductivity (up to 15% of that for bulk silver). The mechanism underlying this self-assembly phenomena is the "ring stain effect", where self-pinning is combined with capillary flow to form a ring consisting of close-packed metallic nanoparticles along the perimeter of a drying droplet. Our macroscopic and microscopic (applying conductive atomic force microscopy) transport measurements show that the conductivity of the ring, which has a metallic brightness, is orders of magnitude larger than that of corresponding aggregates developed without the ring formation, where high conductivity is known to appear only after annealing at high temperature.     

Photochromism of side-chain liquid crystal polymers containing spironaphthoxazines

Side-chain liquid crystal polyacrylates and polysiloxanes containing different photochromic spironaphthoxazine side groups were synthesized. Thermodynamic, spectral and kinetic properties of the polymers were investigated. The structure of the mesophase is discussed.     

Photostabilization of an entomopathogenic fungus using composite clay matrices

To provide photostabilization for entomopathogenic fungi by anionic dyes, composite matrices based on clay-biopolymer combinations were prepared. In the first step, the negative surface charge of various clays (montmorillonite, attapulgite, bentonite and kaolinite) was reversed to positive by adsorption to the polycationic biopolymer chitosan. The second step involved adsorption of the toxicologically safe anionic dyes fast green (FG) and naphthol yellow S (NYS) to the clay complexes. Compared with cytotoxic photoprotectants like berberine, palmatine and acriflavine, the anionic dyes have no adverse effects up to a concentration of 1 M. In assays using various clay-chitosan-dye matrices and UV irradiation from a lamp source, it was evident that both FG and NYS provided considerable photostabilization for conidia of the entomopathogenic fungus Aschersonia spp. that served as a model biocontrol agent. Apparently, because of the light-dispersing property, bentonite and attapulgite per se provided significant photoprotection. All clay matrices containing FG provided a substantial photostabilization effect.