A study of aryl radical cyclization in enaminone esters

Aryl radical cyclization in N-phenyl, N-benzyl, and N-phenethyl enaminone esters 1a-f was studied. N-Benzyl and N-phenethyl enaminones afforded 5-exo and 6-exo cyclization products, respectively, but radical cyclization did not occur in N-phenyl enaminones. The rate constants for the 5-exo and 6-exo cyclization processes in secondary enaminones were estimated as being on the order of 10(7) s(-1) at 353 K; since DNMR experiments showed the rate constant for rotation around the enaminone C3-N bond to be on the order of 10(4) s(-1) at this temperature, the initial enaminone configuration is maintained throughout the cyclization process. PM3 calculations suggested that the nonoccurrence of endo and 4-exo cyclizations is due to the corresponding transition structures involving significant distortion of the conjugated enaminone system.     

Diffusion and annihilation of a particle on a disordered chain

We present an effective-medium approximation to a diffusion model of a particle in a one dimensional medium, that can be annihilated. This approximation is compared with results based on a multistate continuous-time random walk. The mean-square displacement and the annihilation rate in Laplace transformed form are computed in both schemes. We also analyse the small- and largetime asymptotic behavior of the effective hopping and annihilation probabilities per unit time. The effectivemedium approximation results are in full agreement with those of the multistate continuous-time random walk scheme only under a linear approximation of the square root that appears in the Green's function for a homogeneous medium.     

Generic integral manifolds for weight two period domains

We define the notion of a generic integral element for the Griffiths distribution on a weight two period domain, draw the analogy with the classical contact distribution, and then show how to explicitly construct an infinite-dimensional family of integral manifolds tangent to a given element.

     

Predicting nonlinear pseudorandom number generators

Let be a prime and let and be elements of the finite field of elements. The inversive congruential generator (ICG) is a sequence of pseudorandom numbers defined by the relation . We show that if sufficiently many of the most significant bits of several consecutive values of the ICG are given, one can recover the initial value (even in the case where the coefficients and are not known). We also obtain similar results for the quadratic congruential generator (QCG), , where . This suggests that for cryptographic applications ICG and QCG should be used with great care. Our results are somewhat similar to those known for the linear congruential generator (LCG), , but they apply only to much longer bit strings. We also estimate limits of some heuristic approaches, which still remain much weaker than those known for LCG.

     

Electronic contributions to the sigma(p) parameter of the Hammett equation

A statistical procedure to obtain the intrinsic electronic contributions to the Hammett substituent constant sigma(p) is reported. The method is based on the comparison between the experimental sigma(p) values and the electronic electrophilicity index omega evaluated for a series of 42 functional groups commonly present in organic compounds.     

Palladium-catalyzed intermolecular alpha-arylation of N-protected 2-piperidinones

[reaction: see text] The alpha-arylation of the zinc enolate of N-protected 2-piperidinones with aryl bromides in the presence of a palladium catalyst is described as a general method.     

Computer-assisted enhanced volumetric segmentation magnetic resonance imaging data using a mixture of artificial neural networks

An accurate computer-assisted method able to perform regional segmentation on 3D single modality images and measure its volume is designed using a mixture of unsupervised and supervised artificial neural networks. Firstly, an unsupervised artificial neural network is used to estimate representative textures that appear in the images. The region of interest of the resultant images is selected by means of a multi-layer perceptron after a training using a single sample slice, which contains a central portion of the 3D region of interest.The method was applied to magnetic resonance imaging data collected from an experimental acute inflammatory model (T(2) weighted) and from a clinical study of human Alzheimer's disease (T(1) weighted) to evaluate the proposed method. In the first case, a high correlation and parallelism was registered between the volumetric measurements, of the injured and healthy tissue, by the proposed method with respect to the manual measurements (r = 0.82 and p < 0.05) and to the histopathological studies (r = 0.87 and p < 0.05). The method was also applied to the clinical studies, and similar results were derived of the manual and semi-automatic volumetric measurement of both hippocampus and the corpus callosum (0.95 and 0.88).     

A pathological lattice of invariant subspaces

An explicit example of a Hilbert space operator whose lattice of invariant subspaces (under the metric topology “gap between subspaces”) contains an inaccessible point which is not isolated is constructed; the component of that inaccessible point is not arcwise connected and, moreover, no ball (of sufficiently small radius) about the point is connected.     

The distance to a similarity-invariant set of operators

A general argument is developed in order to construct approximants (and to obtain concrete expressions for the distance) for a given Hilbert space operator in a set of operators invariant under similarities and under compact perturbations. Several examples illustrate the main result.