An inverse coefficient problem for a parabolic equation in the case of nonlocal boundary and overdetermination conditions

In this paper, the inverse problem of finding the time‐dependent coefficient of heat capacity together with the solution of heat equation with nonlocal boundary and overdetermination conditions is considered. The existence, uniqueness and continuous dependence upon the data are studied. Some considerations on the numerical solution for this inverse problem are presented with the examples. Copyright © 2010 John Wiley & Sons, Ltd.     

Fullerene containing norbornenes: synthesis and ring-opening metathesis polymerization

New norbornenes with the covalently bonded fullerene C₆₀ have been prepared as monomers for ring-opening metathesis polymerization. Under the Grubbs catalyst these monomers smoothly enter homopolymerization as well as co-polymerization reactions with the parent ‘non-fullerene’ monomers. Homopolymers are insoluble in organic solvents whereas co-polymers obtained by 1:1 co-polymerization of the norbornenes with their ‘non-fullerene’ analogues are well soluble.     

Convenient method for the synthesis of phthalazinones via carbonylation of 2-bromobenzaldehyde using Co2(CO)8 as a CO source

A simple one-pot synthesis of phthalazinones by the condensation and intra-molecular carbonylative cyclization of 2-bromobenzaldehydes with hydrazines is reported. This method utilizes solid Co₂(CO)₈ as carbonyl source making it readily accessible in small-scale laboratory applications.     

A simple and efficient synthesis of enantiomeric (3aRS,4RS,6aSR)-4-hydroxy-3,3a,4,6a-tetrahydro-1H-cyclopenta[c]furan-1-ones

Diastereomeric amides produced via the cleavage of easily available (±)-7,7-dichloro-4-exo-trimethylsilylbicyclo[3.2.0]hept-2-en-6-one by treatment with (+)-α-methylbenzylamine were transformed into bicyclic lactam-aminals, which can easily be separated by column chromatography on SiO₂. The latter products lead to enantiomeric (3a,6a)-4-hydroxy-3,3a,4,6a-tetrahydro-1H-cyclopenta[c]furan-1-ones after the removal of the chiral auxiliary and epoxidation.     

A minimizing property of homographic solutions

In this paper, we prove that the homographic solutions to the rhombus four body prob- lem are the variational minimizers of the Lagrangian action restricted on a holonomically constrained rhombus loop space.     

A CQM-based BEM for transient heat conduction problems in homogeneous materials and FGMs

A method for numerical solution of time-domain boundary integral formulations of transient problems governed by the heat equation is presented. The heat conduction problem is analyzed considering homogeneous and non-homogeneous media. In the case of the non-homogeneous media, the conductor material is assumed to be a functionally graded material, i.e., the material properties vary spatially according to known smooth functions. For some specific spatial variations of the material properties, the fundamental solution and the boundary integral equation of the problem are obtained thanks to a change of variables that transforms the original problem to the standard heat conduction problem for homogeneous materials. For the treatment of time-dependent terms, the convolution quadrature method is adopted to approximate numerically the integral equation of the time-domain boundary element method. In the case that the responses are required at a large number of interior points, the convolution performed to calculate them is very time consuming. It is shown that the discrete convolution of the proposed formulation can be computed by means of the fast Fourier transform technique, which considerably reduces the computational complexity. Results for some transient heat conduction examples are presented to validate the numerical techniques studied.     

A 13C NMR study of pyridine in the presence of aqueous solutions of carbohydrates

Spin-lattice relaxation rates of the ¹³C responses of pyridine were measured in the presence of aqueous sucrose and sodium alginate solutions and calcium alginate gels. In each case the results indicated a reduction in the overall tumbling rate of pyridine compared with that in aqueous media due to molecular association with the carbohydrate. Although anisotropic motion about the C-4:N axis of pyridine was apparent in the sucrose solutions no consistent trends were observed for the alginate samples.     

The role of the t-SNARE SNAP-25 in action potential-dependent calcium signaling and expression in GABAergic and glutamatergic neurons

Background  

The soluble N-ethylmaleimide-sensitive factor attachment protein receptor (SNARE) complex, comprised of SNAP-25, syntaxin 1A, and VAMP-2, has been shown to be responsible for action potential (AP)-dependent, calcium-triggered release of several neurotransmitters. However, this basic fusogenic protein complex may be further specialized to suit the requirements for different neurotransmitter systems, as exemplified by neurons and neuroendocrine cells. In this study, we investigate the effects of SNAP-25 ablation on spontaneous neuronal activity and the expression of functionally distinct isoforms of this t-SNARE in GABAergic and glutamatergic neurons of the adult brain.