The L resolvents of elliptic operators with uniformly continuous coefficients

We consider the strongly elliptic operator A of order 2m in the divergence form with bounded measurable coefficients and assume that the coefficients of top order are uniformly continuous. For 1<p<∞, A is a bounded linear operator from the L^p Sobolev space H^m,p into H^−m,p. We will prove that (A−λ)⁻¹ exists in H^−m,p for some λ and estimate its operator norm.     

The Markov Model Based Algorithm to Predict Networking Load on the Computational Grid

The computational Grid is currently gaining in popularity, and it enables computers scattered all over the world to be connected by the Internet as if they are part of a large computational infrastructure. While the computational Grid gathers more and more computational resources and the number of the applications for the computational Grid is increasing, load balancing for the computational Grid is still not effective enough. Because the computers are connected by a wide area network on the computational Grid, the significant communication latency and the frequency of large wave throughputs make it difficult to achieve effective load balancing. Thus, in this paper, we propose an algorithm to predict networking loads on the computational Grid to make the use of computational resources more efficient. The proposed algorithm based on the Markov model is evaluated using an actual networking load. As a result, the Markov model based algorithm offers the most accurate predictions compared with the related work. This revised version was published online in July 2006 with corrections to the Cover Date.     

Photochemical intramolecular nitrene insertion of 6-azidouridine derivatives

A highly efficient intramolecular nitrene insertion was observed upon irradiation of 6-azidouridine derivatives. The N⁶,2′-cyclo structure of the product was determined unequivocally by X-ray crystallography.     

A Strategy to Control the Reactivation of Frustrated Lewis Pairs from Shelf‐Stable Carbene Borane Complexes

N‐Phosphine oxide substituted imidazolylidenes (PoxIms) have been synthesized and fully characterized. These species can undergo significant changes to the spatial environment surrounding their carbene center through rotation of the phosphine oxide moiety. Either classical Lewis adducts (CLAs) or frustrated Lewis pairs (FLPs) are thus formed with B(C₆F₅)₃ depending on the orientation of the phosphine oxide group. A strategy to reactivate FLPs from CLAs by exploiting molecular motions that are responsive to external stimuli has therefore been developed. The reactivation conditions were successfully controlled by tuning the strain in the PoxIm–B(C₆F₅)₃ complexes so that reactivation only occurred above ambient temperature.     

Moment convergence of <Emphasis Type="Italic">Z</Emphasis>-estimators

The problem to establish the asymptotic distribution of statistical estimators as well as the moment convergence of such estimators has been recognized as an important issue in advanced theories of statistics. This problem has been deeply studied for M-estimators for a wide range of models by many authors. The purpose of this paper is to present an alternative and apparently simple theory to derive the moment convergence of Z-estimators. In the proposed approach the cases of parameters with different rate of convergence can be treated easily and smoothly and any large deviation type inequalities necessary for the same result for M-estimators do not appear in this approach. Applications to the model of i.i.d. observation, Cox’s regression model as well as some diffusion process are discussed.     

On the Conservativeness of Some Markov Processes

We give a unified method to obtain the conservativeness of a class of Markov processes associated with lower bounded semi-Dirichlet forms on L ²(X;m), including symmetric diffusion processes, some non-symmetric diffusion processes and jump type Markov processes on X, where X is a locally compact separable metric space and m is a positive Radon measure on X with full topological support. Using the method, we give an example in each section, providing the conservativeness of the processes, that are given by the “increasingness of the volume of some sets(balls)” and “that of the coefficients on the sets” of the Markov processes.     

Proposal for generation of high-intensity monochromatic Cherenkov radiation in THz range by femtosecond electron bunches in impurity-doped semiconductor tube

A novel method to generate high-power THz radiation is proposed. If a beam with a bunch length on the order of 100 fs is injected into an electron–hole plasma of a semiconductor with a plasma frequency on the order of THz, THz wake fields are coherently generated. If the beam moves on the axis of a hollow tube covered by a metal, the frequency spectrum of the radiation is composed of discrete components. Monochromatic radiation is obtained by making only the lowest frequency component coherent.     

18O assisted analysis of a γ,δ-epoxyketone cyclization: synthesis of the C16-C28 fragment of ammocidin D

The C16-C28 fragment common to the cytotoxic macrolide ammocidin D has been prepared by a stereospecific 5-exo closure of a γ,δ-epoxyketone followed by a rearrangement to a pyran acetal. The reaction pathway was traced by (18)O labeling of the keto carbonyl and observation of (18)O induced (13)C shifts in the pyran acetal product. NMR data of the synthetic C16-C28 fragment compared favorably to the natural product providing support of the assigned stereochemistry.     

Enantioenriched synthesis of cyclopropenes with a quaternary stereocenter, versatile building blocks

Ir(salen) complexes were found to catalyze enantioselective cyclopropenation efficiently. Cyclopropenation can be carried out using either a donor/acceptor- or an acceptor/acceptor-substituted diazo compound such as α-aryl-α-diazoacetates, α-phenyl-α-diazophosphonate, 2,2,2-trifluoro-1-phenyl-1-diazoethane, and α-cyano-α-diazoacetamide as carbenoid precursors. The reactions provide highly enantioenriched cyclopropenes (84-98% ee) with a functionalized quaternary carbon as versatile building blocks.     

Stereoselective vinylogous Mukaiyama aldol reaction of α-haloenals

We have developed a high-yielding and stereoselective vinylogous Mukaiyama aldol reaction (VMAR) of α-haloenals. Contrary to the simple α,β-unsaturated aldehyde, α-haloenals were found to be reactive affording the corresponding VMAR adducts in excellent yields. Some transformations of VMAR adducts by Pd-mediated cross-coupling were also examined in order to demonstrate the synthetic utility of VMAR of α-haloenals.