Kato's square root problem in Banach spaces

Let L be an elliptic differential operator with bounded measurable coefficients, acting in Bochner spaces Lp(Rn;X) of X -valued functions on Rn. We characterize Kato's square root estimates and the H^∞-functional calculus of L in terms of R-boundedness properties of the resolvent of L, when X is a Banach function lattice with the UMD property, or a noncommutative Lp space. To do so, we develop various vector-valued analogues of classical objects in Harmonic Analysis, including a maximal function for Bochner spaces. In the special case X=C, we get a new approach to the Lp theory of square roots of elliptic operators, as well as an Lp version of Carleson's inequality.     

Comparison between the shifted-Laplacian preconditioning and the controllability methods for computational acoustics

Processes that can be modelled with numerical calculations of acoustic pressure fields include medical and industrial ultrasound, echo sounding, and environmental noise. We present two methods for making these calculations based on Helmholtz equation. The first method is based directly on the complex-valued Helmholtz equation and an algebraic multigrid approximation of the discretized shifted-Laplacian operator; i.e. the damped Helmholtz operator as a preconditioner. The second approach returns to a transient wave equation, and finds the time-periodic solution using a controllability technique. We concentrate on acoustic problems, but our methods can be used for other types of Helmholtz problems as well. Numerical experiments show that the control method takes more CPU time, whereas the shifted-Laplacian method has larger memory requirement.     

Selective Alkylation of C‐Rich Bulge Motifs in Nucleic Acids by Quinone Methide Derivatives

A quinone methide precursor featuring a bis‐cyclen anchoring moiety has been synthesized and its capacity to alkylate oligonucleotide targets quantified in the presence and absence of divalent metal ions (Zn²⁺, Ni²⁺ and Cd²⁺). The oligonucleotides were designed for testing the sequence and secondary structure specificity of the reaction. Gel electrophoretic analysis revealed predominant alkylation of C‐rich bulges, regardless of the presence of divalent metal ions or even the bis‐cyclen anchor. This C‐selectivity appears to be an intrinsic property of the quinone methide electrophile as reflected by its reaction with an equimolar mixture of the 2′‐deoxynucleosides. Only dA‐N1 and dC‐N3 alkylation products were detected initially and only the dC adduct persisted for detection under conditions of the gel electrophoretic analysis.     

Manipulation of Single‐Stranded DNA by Using an Artificial Site‐Selective DNA Cutter Composed of Cerium(IV)/EDTA and Phosphonate–Oligonucleotide Conjugates

An artificial site‐selective DNA cutter to hydrolyze single‐stranded DNA at a desired site was prepared from Ce^IV/ethylenediamintetraacetic acid (EDTA) and two ethylenediamine‐N,N,N′,N′‐tetrakis(methylenephosphonic acid)–oligonucleotide conjugates. By using this cutter, the sense strand of a blue fluorescent protein (BFP) gene was selectively cut at a predetermined site in the chromophore‐coding region. The upstream fragment obtained by the site‐selective scission was ligated with the downstream fragment of the closely related green fluorescent protein (GFP) gene so that the 5′‐ and 3′‐end portions of the chromophore came from the BFP fragment and the GFP fragment, respectively. The recombinant gene was successfully expressed in E. coli and the chimeric chromophore emitted green fluorescence as expected.     

Measuring tablet porosity using multispectral imaging system

A multispectral imaging system with computer controlled light source of 16 light emitting diodes is applied for measuring of tablet porosity. The system is based on a subspace vector model of surface reflection. The measured spectral data are compressed on the stage of measurement and used directly for the discrimination of tablets with different porosity. The experimental results demonstrate that the multispectral imaging system is a potential method for tablet porosity measurement.     

The Banach Space-valued BMO, Carleson’s Condition, and Paraproducts

We define a scale of L ^q Carleson norms, all of which characterize the membership of a function in BMO. The phenomenon is analogous to the John–Nirenberg inequality, but on the level of Carleson measures. The classical Carleson condition corresponds to the L ² case in our theory.     

The base sequence dependent flexibility of linear single-stranded oligoribonucleotides correlates with the reactivity of the phosphodiester bond

The effect of base sequence on the structure and flexibility of linear single-stranded RNA molecules and the influence of the base sequence on phosphodiester bond reactivity have been studied. Molecular dynamics simulations of 2.1 ns were carried out for nine chimeric oligonucleotides containing only one unsubstituted ribo unit, all the rest of sugars being 2'-O-methylated. The base sequence has recently been reported to make a big contribution to the reactivity of these compounds. A detailed examination of the interaction energies between the base moieties shows that base stacking is strongly context-dependent and cooperative. The strength of stacking at the site susceptible to chain cleavage by intramolecular transesterification was observed to be dependent on both the flanking bases of the cleavage site and those further apart in the molecule. The interaction energies between the bases in the vicinity of the scissile linkage were found to correlate well with the experimental phosphodiester bond cleavage rates: the stronger the bases close to the cleavage site are stacked, the slower the cleavage rate is.     

Axial super-resolution by mirror-reflected stimulated emission depletion microscopy

In stimulated emission depletion (STED) microscopy, the lateral resolution is in the range of tens of nanometers depending on the sample and the instrument. The axial resolution, however, is in standard systems limited by diffraction to about 500 nm. We present an approach to three-dimensional diffraction-unlimited resolution by observing the sample at two optical angles. The system is realized by using an atomic force microscope (AFM) chip as a microreflector to deflect the STED beams near the region-of-interest (ROI), thus allowing observations at an angle ∠. Consequently, the superior lateral resolution can be utilized to resolve details in the axial direction of the main optical axis of the microscope. Here, fluorescent nanoparticles 90 nm apart and biological structures 80 nm apart along axial direction were distinguished by utilizing an off-the-shelf, commercial STED microscope, coupled with an AFM and an AFM chip micro-reflector.