Simple and Efficient Method for the Protection of Hydroxyl Groups as 4-Methoxybenzyl Ethers

PMB ethers of alcohols are obtained in good yields and under mild conditions using the 4-methoxybenzyl N-allyl thiocarbamate and N-bromosuccinimide (NBS)/TfOH as the catalyst. The present method is very fast, simple, and efficient.     

Microporous {[Ni(cyclam)]3[W(CN)8]2}n affording reversible structural and magnetic conversions

Methanol adsorption into the porous 2D bimetallic coordination network {[Ni(cyclam)](3)[W(CN)(8)](2)}(n) (cyclam = 1,4,8,11-tetraazacyclotetradecane) causes significant modification of its structure and magnetic properties. Fully reversible transformations between the three states of the network: anhydrous, hydrated and methanol-modified are observed with the transition to the magnetic ordered state at T(c) equal to 4.9 K, 8.3 K and 11.4 K respectively. All three phases have a metamagnetic character but the methanol-modified one most easily turns to ferromagnetic and shows a hysteresis loop with coercivity field of 250 Oe. The differences in magnetic behaviour of the anhydrous and guest-induced forms of the compound are discussed in terms of changes in the structure: CN-bridge geometry and distance between the layers.     

On the weak topology of Banach spaces over non-archimedean fields

It is known that within metric spaces analyticity and K-analyticity are equivalent concepts. It is known also that non-separable weakly compactly generated (shortly WCG) Banach spaces over R or C provide concrete examples of weakly K-analytic spaces which are not weakly analytic. We study the case which totally differs from the above one. A general theorem is provided which shows that a Banach space E over a locally compact non-archimedean non-trivially valued field is weakly Lindelöf iff E is separable iff E is WCG iff E is weakly web-compact (in the sense of Orihuela). This provides a non-archimedean version of a remarkable Amir-Lindenstrauss theorem.     

Mathematical modelling of rate-independent pseudoelastic SMA material

The paper presents a procedure for the formulation of constitutive equations for rate-independent pseudoelastic SMA material models. The procedure applies a rheological scheme representing mechanical properties of the material. An additive decomposition of strains into two parts is proposed. The first part describes strains of a perfectly elastic body while the second part may be represented by a combination of a rigid perfectly elastic body and a rigid perfectly plastic body. It is demonstrated that the key problem of formulation of constitutive relationships is to derive the 1st order differential equation with respect to the tensor describing the second part of the strain field. This equation may be obtained in explicit form starting from the variational inequalities defining non-elastic parts of rheological model. The uniqueness of the obtained differential equation has been proved. A numerical implementation of the constitutive relationships of SMA material was done through the user subroutine module VUMAT within the FE commercial code ABAQUS/Explicit. As an example we analyzed the problem of vibration of a simple 3D structure made of SMA.     

Analysis of a time-dependent scheduling problem by signatures of deterioration rate sequences

In the paper a single machine time-dependent scheduling problem is considered. The processing time p_j of each job is described by a function of the starting time t of the job, p_j=1+α_jt, where the job deterioration rate α_j?0 for j=0,1,…,n and t?0. Jobs are nonpreemptable and independent, there are no ready times and no deadlines. The criterion of optimality of a schedule is the total completion time.First, the notion of a signature for a given sequence of job deterioration rates is introduced, two types of the signature are defined and their properties are shown. Next, on the basis of these properties a greedy polynomial-time approximation algorithm for the problem is formulated. This algorithm, starting from an initial sequence, iteratively constructs a new sequence concatenating the previous sequence with new elements, according to the sign of one of the signatures of this sequence.Finally, these results are applied to the problem with job deterioration rates which are consecutive natural numbers, α_j=j for j=0,1,…,n. Arguments supporting the conjecture that in this case the greedy algorithm is optimal are presented.     

Sheaves of Einstein algebras

To include all types of singularities into a geometrically tractable theoretical scheme we change from Einstein algebras, an algebraic generalization of general relativity, to sheaves of Einstein algebras. The theory of such spaces, called Einstein structured spaces, is developed. Both quasiregular and curvature singularities are studied in some detail. Examples of the closed Friedmann world model and the Schwarzschild spacetime show that Schmidt'sb-boundary is a useful theoretical tool when considered in the category of structured spaces.     

Magnetic-field-induced radiationless transitions

A quantum-mechanical theory of the magnetic field effect on radiationless transitions in an isolated molecule is presented. The mechanism of this phenomenon is a second-order process relying on the simultaneous radiationless relaxation of an excited electronic state and the interaction of the molecule with a constant uniform magnetic field.     

Kerr effect in the critical solutions of propionitrile

The electrooptical Kerr effect (EKE) has been measured in four critical propionitrile-hydrocarbon systems covering a wide range of refractive indices as well as the density mismatch between the components. Precritical EKE anomalies are strongly solvent-dependent and they have been observed only in the mixtures with distinctly pronounced critical opalescence and different electric permittivities of the components. The solvent influences the critical amplitude, but not the critical exponent, the latter being close to 0.7 for the examined systems. The possible mechanisms of the field-induced optical anisotropy of the solutions are discussed.     

Spectrochemical and Thermal Behaviour of the 5-chloro-2-nitrobenzoates of Rare Earth Elements

The conditions of the formation of yttrium and lanthanide 5-chloro-2-nitrobenzoates were studied and their quantitative composition and solubilities in water at 298 K were determined. They are anhydrous or hydrated complexes and their solubilities are of the order of 10-3 mol dm-3. The IR and X-ray spectra for the complexes were recorded. All complexes are crystalline compounds. Their thermal decomposition was studied. It was found that on heating above 523 K the complexes decompose explosively. Therefore their thermal decomposition was carried out in the temperature range 273-523 K. Hydrated complexes lose crystallization water molecules in one step. From the results it appeared that during dehydration process no transformation of nitro group to nitrito took place. Some of physico-chemical properties of rare earth element 5-chloro-2-nitrobenzoates were compared with 2-nitro- and 3-chlorobenzoates of those elements. This revised version was published online in July 2006 with corrections to the Cover Date.