Intramolecular hemiacetals. The acid-base-catalyzed ring-chain interconversion of 2-substituted 2-hydroxy-4,4-dimethylmorpholinium cations in aqueous solution.

The ring-chain tautomerism in aqueous solution of some aryl-substituted morpholinium salts (bromides), has been studied and equilibrium constants are reported. In the crystals the substrates exist entirely in their cyclic forms as hemiacetals, but in aqueous solution NMR measurements reveal that an equilibrium is established between the cyclic (hemiacetal) and the noncyclic (ketone) form, the degree of ring-opening being more pronounced with electron-donating aryl substituents at the carbonyl carbon. The kinetics of the ring-chain interconversion in water has been investigated spectrophotometrically by a 'pH jump' stopped-flow technique. General base catalysis is observed with a Br?nsted beta value apparently independent of substituent and equal to 0.60. The Hammett rho values for various base catalysts are close to those for very similar intermolecular reactions involving hemiacetal breakdown, leading to the suggestion of a 'normal' class n mechanism for base catalysis. For acid catalysis, however, a quite different situation is encountered, since no general acid but only (weak) catalysis by the hydronium ion can be detected. We believe this deviation from 'normal' general acid catalysis is caused by an electrostatic interaction, and we suggest that it might result from a change in the usual class e mechanism for general acid catalysis by a situation in which rate-limiting concerted proton transfer is replaced by rate-limiting preprotonation. This is supported by the observed drastic change in Hammett rho value for catalysis by the hydronium ion, compared with the 'normal' case. An interesting case is encountered for the 4-aminophenyl-substituted substrate, in which the amino group becomes protonated in acid solution, thus representing a new substituent. Despite this complication, the various equilibrium and rate constants may also be evaluated experimentally for this substrate.     

Monitoring genomic alterations with a panel of oligonucleotide probes specific for various simple repeat motifs

Germline and somatic instability of the human genome was studied, using synthetic oligonucleotides specific for simple repeat motifs. The following probes were used: (GTG)5, (GACA)4, (GATA)4, (CT)8, (TTAGGG)3, (GT)8, (GAA)6 and (GGAT)4. Each of them is unique with respect to the target regions recognized in the genome. Thus compilation of the various fingerprint data provides a complex map of the genome (and its deviations). While the fingerprints of differentiated somatic tissues never showed any alterations, in tumor tissues (namely gliomas) many changes could be detected. Most of the latter reflect secondary karyological aberrations. In nearly one third of the gliomas, drastically amplified and apparently monomorphic DNA fragments were identified. This marker should make it possible to deal with causal pathogenetic mechanisms as well as novel diagnostic strategies.     

Anomalous anisotropies and field dependencies of the muon Knight shift and the relaxation rate in monocrystalline Bi

The angular dependence of the muon Knight shift,K _μ, and the muon relaxation rate in Bi at 11 K were measured in external magnetic fields up to 1 T. BothK _μ and the second moment,M ₂, are field dependent and involveP ₄ ⁰(cos θ) andP ₄ ³(cos θ) terms in the angular dependence. The Knight shift behaviour is discussed in terms of the dipole-dipole interaction and the de Haas-van Alphen effect, a consistent interpretation was not achieved in either case. The field dependence ofM ₂ is in complete contrast to the second moment calculations and points to a field dependent redistribution of the charge distribution around the interstitial site.     

π π andK¯K channel coupling

We investigate the origin of the attraction in theK¯K channel around the threshold by introducing an additional channel to theππ andK¯K channels in a separable potential formalism assuming, in general, no direct interaction in theK¯K channel. To reproduce the features of the data, we find that the threshold of the additional channel is much above thef ₀(975) meson position. We show that this three-channel problem can be reduced to an effective two-channel problem where thef ₀(975) behaves as if it were aK¯K molecule bound by the coupling to the exotic channel. This picture is also supported by the fact that a single pole only, in the complexK¯K momentum plane, is associated to thef ₀(975) meson. Various physical observables, like the decay branching ratio and theK¯K scattering length, are then discussed in an effective two-channel framework.     

An invariance of geometric mean with respect to Lagrangian means

The invariance of the geometric mean G with respect to the Lagrangian mean-type mapping (Lf,Lg), i.e. the equation G○(Lf,Lg)=G, is considered. We show that the functions f and g must be of high class regularity. This fact allows to reduce the problem to a differential equation and determine the second derivatives of the generators f and g.     

Monotonic solutions of a quadratic integral equation of fractional order

In the paper we indicate an error made in the proof of the main result of the paper [M.A. Darwish, On quadratic integral equation of fractional orders, J. Math. Anal. Appl. 311 (2005) 112-119]. Moreover, we provide correct proof of a slightly modified version of the mentioned result. The main tool used in our proof is the technique associated with the Hausdorff measure of noncompactness.     

A model for the interaction of near-infrared laser pulses with metal powders in selective laser sintering

A thermal model of the interaction of pulsed near-infrared laser radiation from a Nd:YAG laser was made, taking the measured powder properties such as reflectance, optical penetration depth and thermal conductivity into account. It allows an estimation of the evolution of two different temperatures: the average temperature of the powder (taken over the grains in a volume given by the laser beam diameter and the optical penetration depth) and the temperature distinction within a single grain. It showed that in pulsed mode consolidation can be achieved at much lower average power as the surface of the powder particles are molten but their cores remain at nearly room temperature. This leads to a much lower average temperature and therefore a dramatic decrease in residual thermal stresses in the finished piece. The results of the model were experimentally tested and confirmed. Received: 26 July 2001 / Accepted: 23 November 2001 / Published online: 23 January 2002     

Nonlinear second-order equations with functional implicit impulses and nonlinear functional boundary conditions

In this paper we deal with nonlinear second-order boundary value problems with impulses. The impulsive functions depend implicitly on the different considered variables and the boundary value conditions are nonlinear. In both cases functional dependence on the solution is allowed. The existence results follow from the existence of a pair of well-ordered lower and upper solutions.     

Shadowing with multidimensional time in Banach spaces

We study linear dynamical systems with multidimensional time in Banach spaces. Using Taylor functional calculus we prove that under additional assumptions hyperbolic systems have shadowing property.