Composition operators from large weighted Hardy spaces into the Dirichlet space

Given a large weighted Hardy space we show there exists a composition operatorC with that maps from that space into the unweighted Dirichlet space and lies in every Schatten p-class for 0<p<. This is in contrast to the situation in which the image space is a smaller weighted Dirichlet space. It is known that in that case it is not possible to find such a composition operator that is bounded.This research was supported in part by a summer stipend from Bellarmine College.     

Strong consistency of least squares estimates in multiple regression II

The strong consistency of least squares estimates in multiple regression models is established under minimal assumptions on the design and weak dependence and moment restrictions on the errors.     

Unified description of aging and rate effects in yield of glassy solids

The competing effects of slow structural relaxations (aging) and deformation at constant strain rate on the shear yield stress tau(y) of simple model glasses are examined using molecular simulations. At long times, aging leads to a logarithmic increase in density and tau(y). The yield stress also rises logarithmically with rate but shows a sharp transition in slope at a rate that decreases with increasing age. We present a simple phenomenological model that includes both intrinsic rate dependence and the change in properties with the total age of the system at yield. As predicted by the model, all data for each temperature collapse onto a universal curve.     

Copper-catalyzed hydroamination of propargyl imidates

Propargyl imidates derived from aromatic and aliphatic nitriles cyclize at room temperature in high yields when treated with a catalytic amount of copper (I) iodide. This 5-exo-dig process affords dihydrooxazoles which do not aromatize under the reaction conditions, and which are isolated without chromatography. Investigations of the reaction scope, subsequent functionalization of the reaction products, and preliminary mechanistic data are presented.     

All solid state ion-conducting cesium source for atomic clocks

Cesium containing glass with solid metal electrodes was used as a Cs atom source in a high vacuum system. A silver anode provides an injection source of highly mobile ions which sweep Cs to the cathode surface, from which they evaporate into the vacuum. Cathode metallization with finger patterns was used leaving bare glass for Cs evaporation. Laser absorption measurements show Cs vapor generation synchronous with an applied DC voltage.     

Ruthenium-caged antisense morpholinos for regulating gene expression in zebrafish embryos

Photochemical approaches afford high spatiotemporal control over molecular structure and function, for broad applications in materials and biological science. Here, we present the first example of a visible light responsive ruthenium-based photolinker, Ru(bipyridine)₂(3-ethynylpyridine)₂ (RuBEP), which was reacted stoichiometrically with a 25mer DNA or morpholino (MO) oligonucleotide functionalized with 3′ and 5′ terminal azides, via Cu(i)-mediated [3+2] Huisgen cycloaddition reactions. RuBEP-caged circular morpholinos (Ru-MOs) targeting two early developmental zebrafish genes, chordin and notail, were synthesized and tested in vivo. One-cell-stage zebrafish embryos microinjected with Ru-MO and incubated in the dark for 24 h developed normally, consistent with caging, whereas irradiation at 450 nm dissociated one 3-ethynylpyridine ligand (Φ = 0.33) and uncaged the MO to achieve gene knockdown. As demonstrated, Ru photolinkers provide a versatile method for controlling structure and function of biopolymers.