Geometric Permutations of Non-Overlapping Unit Balls Revisited

Given four congruent balls $A, B, C, D$ in $R^{d}$ that have disjoint interior and admit a line that intersects them in the order $ABCD$, we show that the distance between the centers of consecutive balls is smaller than the distance between the centers of $A$ and $D$. This allows us to give a new short proof that $n$ interior-disjoint congruent balls admit at most three geometric permutations, two if $n\ge 7$. We also make a conjecture that would imply that $n\geq 4$ such balls admit at most two geometric permutations, and show that if the conjecture is false, then there is a counter-example of a highly degenerate nature

Thermal conductivity of suspended pristine graphene measured by Raman spectroscopy

The thermal conductivity of suspended single-layer graphene was measured as a function of temperature using Raman scattering spectroscopy on clean samples prepared directly on a prepatterned substrate by mechanical exfoliation without chemical treatments. The temperature at the laser spot was monitored by the frequency of the Raman 2$D$ band of the Raman scattering spectrum, and the thermal conductivity was deduced by analyzing heat diffusion equations assuming that the substrate is a heat sink at ambient temperature. The obtained thermal conductivity values range from $\sim$1800 Wm$^{-1}$K$^{-1}$ near 325 K to $\sim$710 Wm$^{-1}$K$^{-1}$ at 500 K.Comment: 4pages, 3 figure

Cache-based Query Processing for the Boolean Retrieval Model

We propose a new method of processing general Boolean queries utilizing previous query results stored in a result cache in a mediator architecture. A simple but noble normalization form is developed to describe keyword-based Boolean queries and the content of the result cache. We propose Boolean query processing algorithms based on this form of presentation that utilizes the result cache. We show that the proposed method theoretically guarantees improved performance over the conventional query processing method without using a cache

On Benzofuroindole Analogues as Smooth Muscle Relaxants

At least two laboratories have independently reported the synthesis of benzofuroindole compounds having potential therapeutic implications in many disease states including those that involve smooth muscle hyperactivity. Through a series of in vitro screenings, they demonstrated the efficacy (and selectivity) of these compounds to potentiate large conductance calcium- (Ca2+-) activated K+ (BKCa) channels, by far, the most characterized of all Ca2+-dependent K+ channels. Interestingly, promising benzofuroindole derivatives such as compound 7 (10H-benzo[4,5]furo[3,2-b]indole) and compound 22 (4-chloro-7-trifluoromethyl-10H-benzo[4,5]furo[3,2-b]indole-1-carboxylic acid) both exhibited high bladder (versus aorta) selectivity, making them attractive alternative treatments for bladder overactivity. In recent reports, compound 22 (LDD175 or TBIC) also showed inhibition of ileum and uterine contractions, indicating multiple target tissues, which is not surprising as BKCa channels are ubiquitously expressed in the animal and human tissues. In this paper, the authors discuss the value of benzofuroindole compounds and the challenges that need to be overcome if they were considered as smooth muscle relaxants