Entropy for Symbolic Dynamics with Overlapping Alphabets

We consider shift spaces in which elements of the alphabet may overlap nontransitively. We define a notion of entropy for such spaces and show that it is equal to a limit of entropies of standard (non-overlapping) shifts when the underlying shift is of finite type. When a shift space with overlaps arises as a model for a discrete dynamical system with a finite set of overlapping neighborhoods, the entropy gives a lower bound for the topological entropy of the dynamical system.     

Single- and multi-shot laser-induced damages of Ta_2O_5/SiO_2 dielectric mirrors at 1064 nm

Ta2O5/SiO2 dielectric mirrors deposited by ion beam sputtering (IBS) are studied. The multi-shot laserinduced damage threshold (LIDT) and its dependence on the number of shots are investigated, after which we find that the multi-shot LIDT is lower than that of single-shot. The accumulation effects of defects play an important role in the multi-shot laser damage. A simple model, which includes the conduction band electron production vsa multiphoton and impact ionizations, is presented to explain the experimental phenomena.     

2-Butyl-4-iodoimidazole-5-carboxaldehyde: A Versatile Intermediate for the Synthesis of Highly Functionalized Imidazoles

The facile preparation of 2-butyl-4-iodoimidazole-5-carboxaldehyde 1 is described. The versatility of this intermediate in the synthesis of highly tunctionalized imidazoles is demonstrated with the synthesis of two potent and selective angiotensin II receptor antagonists.     

John’s Ellipsoid and the Integral Ratio of a Log-Concave Function

We extend the notion of John’s ellipsoid to the setting of integrable log-concave functions. This will allow us to define the integral ratio of a log-concave function, which will extend the notion of volume ratio, and we will find the log-concave function maximizing the integral ratio. A reverse functional affine isoperimetric inequality will be given, written in terms of this integral ratio. This can be viewed as a stability version of the functional affine isoperimetric inequality.     

Cytotoxic and NF-κB inhibitory sesquiterpene lactones from Piptocoma rufescens

Six new (1-6) and eight known germacranolide-type sesquiterpene lactones, along with several known phenylpropanol coumarates and methylated flavonoids, were isolated from the leaves of Piptocoma rufescens, collected in the Dominican Republic. The new compounds were identified by analysis of their spectroscopic data, with the molecular structure of 3 being established by single-crystal X-ray diffraction. The absolute configurations of the sesquiterpene lactones isolated were determined from their CD and NOESY NMR spectra, together with the analysis of Mosher ester reactions. Bioassay screening results showed the majority of the sesquiterpene lactones isolated (1-13) to be highly cytotoxic toward the HT-29 human colon cancer cell line, with the most potent compound being 15-deoxygoyazensolide (10, IC(50), 0.26 μM). In addition, several of the sesquiterpene lactones exhibited NF-κB (p65) inhibitory activity.