Stereochemistry of the reaction of ribonucleoside cyclic 3′,5′-phosphorothioates with oxiranes

The stereochemical course of the epoxide-induced oxidative rearrangement of ribonucleoside cyclic 3′,5′-phosphorothioates into the corresponding 2′,3′-phosphates has been determined using styrene [¹⁸O] oxide and (S_p)-uridine cyclic 3′,5′-phosphorothioate. The evidence of full stereoselectivity of this reaction is presented and mechanistic implications of the presence of the nucleoside 2′-hydroxyl group are discussed in terms of a classical Hamer Mechanism.     

Substituent effect in anionic polymerization of β-lactones initiated by alkali metal alkoxides

The influence of methyl substituent on the mechanism of the ring-opening polymerization of β-lactones initiated by alkali metal alkoxides is discussed. Attention has been paid to the effect of the substituent position in the monomer molecule on the ring-opening mechanism, the 3,3-dimethyl-2-oxetanone (pivalolactone), 4-methyl-2-oxetanone (β-butyrolactone) and 2-oxetanone (β-propiolactone) being chosen as model monomers. Moreover, it was found unexpectedly that in the case of pivalolactone polymerization, besides open-chain polymers, cyclic oligomers are produced.     

SHAH: SHape-Adaptive Haar Wavelets for Image Processing

We propose the shape-adaptive Haar (SHAH) transform for images, which results in an orthonormal, adaptive decomposition of the image into Haar-wavelet-like components, arranged hierarchically according to decreasing importance, whose shapes reflect the features present in the image. The decomposition is as sparse as it can be for piecewise-constant images. It is performed via a stepwise bottom-up algorithm with quadratic computational complexity; however, nearly linear variants also exist. SHAH is rapidly invertible. We show how to use SHAH for image denoising. Having performed the SHAH transform, the coefficients are hard- or soft-thresholded, and the inverse transform taken. The SHAH image denoising algorithm compares favorably to the state of the art for piecewise-constant images. A clear asset of the methodology is its very general scope: it can be used with any images or more generally with any data that can be represented as graphs or networks.     

Isoperimetric Inequalities and Imbedding Theorems in Irregular Domains

The paper proves several weighted imbedding theorems for domainswith fractal boundaries. The weights considered are distancesto the boundary to certain powers, and the domains are so-calleds-John domains. The paper also proves, in the general setting,that the existence of an imbedding implies compactness of theimbedding for lower exponents. Moreover, following Maz'ya, thepaper reformulates the imbedding theorems in the language oflocal isoperimetric and capacity estimates.     

On a problem of Rolewicz about Banach spaces that admit support sets

We construct an example of a nonseparable Banach space which does not admit a support set.² It is a consistent (and necessarily independent from the axioms of ZFC) example of a space C(K) of continuous functions on a compact Hausdorff K with the supremum norm. The construction depends on a construction of a Boolean algebra with some combinatorial properties. The space is also hereditarily Lindelöf in the weak topology but it doesn't have any nonseparable subspace nor any nonseparable quotient which is a C(K) space for K dispersed.     

Extending the coordination chemistry of 1,3,5-triaza-7-phosphaadamantane (PTA) to cobalt centers: first examples of co-PTA complexes and of a metal complex with the PTA oxide ligand

Water-soluble Co (III) and Co (II) complexes with P- or N-coordinated PTA or PTA oxide ligands, respectively, have been prepared and fully characterized, constituting the first examples of cobalt compounds bearing PTA or any ligand with a cage-like PTA core, the latter complex providing also the first PTA oxide coordination to a metal center.     

Anionic polymerization of β-lactones initiated with potassium hydride. A convenient route to polyester macromonomers

The anionic polymerization of 2-oxetanone and 4-methyl-2-oxetanone initiated with the potassium hydride/18-crown-6 complex was investigated. The α-proton abstraction of the monomer was found to proceed at the initiation step of this polymerization. The salt of the unsaturated carboxylic acid formed initiates further propagation, leading to functionalized polyesters with unsaturated, dead end-groups.