Approximation in Banach space by linear positive operators

In this paper, we obtain a sufficient condition for the convergence of positive linear operators in Banach function spaces on \({\mathbb {R}}^n\) and derive a Korovkin type theorem for these spaces. Also, we generalized this result via statistical sense.     

Nonparametric Bayesian drift estimation for multidimensional stochastic differential equations*

We consider nonparametric Bayesian estimation of the drift coefficient of a multidimensional stochastic differential equation from discrete-time observations on the solution of this equation. Under suitable regularity conditions, we establish posterior consistency in this context.     

Synthesis of phenylalkyl-substituted polyhydroxypiperidines as potent inhibitors for α-l-fucosidase

Synthesis and inhibitory activities against α-l-fucosidase of phenylalkyl-substituted polyhydroxypiperidines have been described. Among the newly synthesized compounds, 2,4,6-trichloro derivative (16q) showed very high inhibitory activity against α-l-fucosidase with IC₅₀ value of 0.005 μM, and K_i values of 0.0011 μM, respectively.     

Efficient Synthesis of a Regioregular Oligothiophene Photovoltaic Dye Molecule,MK‐2, and Related Compounds: A Cooperative Hypervalent Iodine and Metal‐Catalyzed Synthetic Route

We have successfully established an efficient route to the core structure of donor–acceptor head‐to‐tail (H–T)‐linked regioregular oligothiophenes, which includes the following key synthetic steps, that is, hypervalent iodine induced direct and regioselective coupling of thiophenes and the use of the obtained bithiophenes as excellent coupling substrates for the Suzuki and Stille couplings. The versatility of this new approach is highlighted in the dramatic improvement of the yield (ca. 59 % overall yield) of MK‐2, a high‐performance organic dye, for photovoltaic applications.     

Morrey Spaces for Non-doubling Measures

The authors give a natural definition of Morrey spaces for Radon measures which may be non-doubling but satisfy certain growth condition, and investigate the boundedness in these spaces of some classical operators in harmonic analysis and their vector-valued extension.     

Application of a Palladium‐Catalyzed C−H Functionalization/Indolization Method to Syntheses of cis‐Trikentrin A and Herbindole B

We describe herein formal syntheses of the indole alkaloids cis‐trikentrin A and herbindole B from a common meso‐hydroquinone intermediate prepared by a ruthenium‐catalyzed [2+2+1+1] cycloaddition that has not been used previously in natural product synthesis. Key steps include a sterically demanding Buchwald–Hartwig amination as well as a unique C(sp³)?H amination/indole formation. Studies toward a selective desymmetrization of the meso‐hydroquinone are also reported.     

Stereospecific [2+2] cycloaddition reactions of diphosphorus with alkenes

[2+2] Cycloaddition reactions of P₂ with alkenes were predicted to have concerted paths, that is, pseudoexcitation, distorted 2π_s+2π_s, and 2π_s+2π_a processes without any interventions of intermediates. The pseudoexcitation and/or distorted 2π_s+2π_s paths with retention of configuration of alkenes are kinetically preferred to the 2π_s+2π_a path with inversion of configuration. The reactions were predicted from the appreciable difference in the calculated enthalpies of activation to be stereospecific.     

Multifunctional photo acid generator for fluorescence imaging based on self-contained photoreaction

We present N-(p-anilinesulfonyloxy)-1,8-naphthalimide (ASNI) as fluorescence imaging material based on a novel fluorescence imaging mechanism. ASNI is composed of two functional moieties in one molecule: an acid-reactive fluorescence probe and a photoacid generator (PAG). When ASNI is photoirradiated, a bond in the PAG moiety breaks and an acid is generated. The fluorescence probe moiety then detects the acid and fluoresces. We call this novel mechanism a self-contained photoreaction (SCP). The photophysical properties and photoreactivity of ASNI were measured and compared with those of a prototype PAG, N-(phenylsulfonyloxy)-1,8-naphthalimide. These were well represented by density functional theory calculations. SCP permits one-step fluorescence imaging without any wet or dry developing process.     

Photochemistry of naphthalimide photoacid generators

The photophysical properties of a series of 1,8-naphthalimide photoacid generators were studied by steady state fluorescence and phosphorescence spectroscopy. Emission and excitation anisotropies, triplet quantum yields in polar and nonpolar solvent and photoacid generation were evaluated. The singlet excited state exhibits a low polarity and is strongly deactivated by an efficient intersystem crossing process. In protic solvent, a homolytic singlet cleavage of the N-O bond occurs and leads to the acid production. The existence of a triplet state close to the singlet state was clearly evidenced. The presence of close singlet excited states is supported by fluorescence anisotropy and picosecond laser spectroscopy experiments. Results of DFT calculations well confirm the experimental contentions and yield important information about the cleavage process involved in such compounds.     

Real Inversion Formulas of the Laplace Transform on Weighted Function Spaces

We investigate compactness of linear operators associated with the real inversion formulas of the Laplace transform, coming with weighted Sobolev reproducing kernel Hilbert spaces on the half line R ⁺. We present concrete reproducing kernels along with several typical examples. Submitted: October 13, 2007. Accepted: November 11, 2007.