An application of the theorem of Rudin to the Toeplitz operators on odd spheres

Summary In this note we will prove a theorem on Toeplitz operators on odd spheres, using the recent result of Rudin [3, Th. 2.3] concerning space of typeH+C. This theorem is a generalization of the analogous fact for Toeplitz operators on the unit circle, proved by Douglas [2, Th. 7.29].     

Intensification of Double Kinetic Resolution of Chiral Amines and Alcohols via Chemoselective Formation of a Carbonate–Enzyme Intermediate

Chiral amines and alcohols are synthons of numerous pharmaceutically-relevant compounds. The previously developed enzymatic kinetic resolution approaches utilize a chiral racemic molecule and achiral acyl donor (or acyl acceptor). Thus, only one enantiodivergent step of the catalytic cycle is engaged, which does not fully exploit the enzyme’s abilities. The first carbonate-mediated example of simultaneous double chemoselective kinetic resolution of chiral amines and alcohols is described. Herein, we established a biocatalytic approach towards four optically-pure compounds (>99% ee, Enantioselectivity: E > 200) via double enzymatic kinetic resolution, engaging chiral organic carbonates as acyl donors. High enantioselectivity was ensured by extraordinary chemoselectivity in lipase-catalyzed formation of unsymmetrical organic carbonates and engaged in a process applicable for the synthesis of enantiopure organic precursors of valuable compounds. This study focused not only on preparative synthesis, but additionally the catalytic mechanism was discussed and the clear impact of this rarely observed carbonate-derived acyl enzyme was shown. The presented protocol is characterized by atom efficiency, acyl donor sustainability, easy acyl group removal, mild reaction conditions, and biocatalyst recyclability, which significantly decreases the cost of the reported process.     

HCSE method for detection of small carbon–carbon couplings and their signs,comparison with SLAP pulse sequence

Performance of homonuclear coupling sign edited (HCSE) experiment applied to detection of signed carbon–carbon couplings is discussed using a set of already measured samples of nine monosubstituted benzenes. It is shown that coupling sign detection is insensitive to the settings of carbon–carbon polarization transfer delays. The HCSE spectra of ten from the total of 43 measured carbon–carbon couplings were considerably influenced by relaxations and proton–proton strong couplings. These effects are quantitatively discussed. The results of HCSE and SLAP experiments are compared. It is shown that the two methods may complement each other in detection of signed carbon–carbon couplings. Copyright © 2013 John Wiley & Sons, Ltd.     

Broadband excitation pulses for high‐field solid‐state nuclear magnetic resonance spectroscopy

In nuclear magnetic resonance spectroscopy, experimental limits due to the radiofrequency transmitter and/or coil means that conventional radiofrequency pulses (“hard pulses”) are sometimes not sufficiently powerful to excite magnetization uniformly over a desired range of frequencies. Effects due to nonuniform excitation are most frequently encountered at high magnetic fields for nuclei with a large range of chemical shifts. Using optimal control theory, we have designed broadband excitation pulses that are suitable for solid‐state samples under magic‐angle‐spinning conditions. These pulses are easy to implement, robust to spinning frequency variations, and radiofrequency inhomogeneities, and only four times as long as a corresponding hard pulse. The utility of these pulses for uniformly exciting ¹³C nuclei is demonstrated on a 900 MHz (21.1 T) spectrometer. Copyright © 2012 John Wiley & Sons, Ltd.     

DMSA and its complexes with radioisotopes: review

Meso-2,3-dimercaptosuccinic acid (DMSA) forms stable complexes with a remarkable wide range of metal ions. This relatively small molecule has attracted increasing attention in the field of radiopharmacy, treatment of heavy metal intoxications and nanoparticles preparation. In this review detailed summary of all physical, chemical and biological properties of DMSA and its complex compounds with ^99mTc, ^186/188Re, ¹⁶⁶Ho, ¹⁷⁷Lu and ⁹⁰Y is provided. The clinical utilisation of DMSA complexes in the nuclear medicine and its use for treatment of heavy metal intoxication is briefly summarised. The aspects of its application in the field of nanoparticles preparation is behind the scope of this review, therefore it is only shortly described.     

Diffusion of biostimulators into plant tissues

Biostimulators are substances able to enhance the immune system of cultivated crops and support plant metabolism. Their utilization helps to reduce the amount of chemicals used in agriculture. To perform the desired effect, a biostimulator must be able to penetrate into the plant tissue. The time of penetration however, is limited, since the biostimulator must remain in a liquid state. This is of great importance—especially in field conditions, where the treated plants are exposed to different weather condition and other extrinsic factors. A mathematical model based on diffusion mechanisms has been elaborated to describe the biostimulator transport process from penetration of the leaves into the plant’s inner tissues. By means of the effective diffusion coefficient of the prepared specific protein hydrolyzate, this model can be used to estimate the time necessary for the uptake of the minimal active amount of the biostimulator.     

Colourings of cubic graphs inducing isomorphic monochromatic subgraphs

A -bisection of a bridgeless cubic graph is a -colouring of its vertex set such that the colour classes have the same cardinality and all connected components in the two subgraphs induced by the colour classes ( monochromatic components in what follows) have order at most . Ban and Linial Conjectured that every bridgeless cubic graph admits a -bisection except for the Petersen graph. A similar problem for the edge set of cubic graphs has been studied: Wormald conjectured that every cubic graph with has a -edge colouring such that the two monochromatic subgraphs are isomorphic linear forests (ie, a forest whose components are paths). Finally, Ando conjectured that every cubic graph admits a bisection such that the two induced monochromatic subgraphs are isomorphic. In this paper, we provide evidence of a strong relation of the conjectures of Ban-Linial and Wormald with Ando's Conjecture. Furthermore, we also give computational and theoretical evidence in their support. As a result, we pose some open problems stronger than the above-mentioned conjectures. Moreover, we prove Ban-Linial's Conjecture for cubic-cycle permutation graphs. As a by-product of studying -edge colourings of cubic graphs having linear forests as monochromatic components, we also give a negative answer to a problem posed by Jackson and Wormald about certain decompositions of cubic graphs into linear forests.