Spatial critical points not moving along the heat flow II: The centrosymmetric case

We consider solutions of initial-boundary value problems for the heat equation on bounded domains in and their spatial critical points as in the previous paper [MS]. In Dirichlet, Neumann, and Robin homogeneous initial-boundary value problems on bounded domains, it is proved that if the origin is a spatial critical point never moving for sufficiently many compactly supported initial data being centrosymmetric with respect to the origin, then the domain must be centrosymmetric with respect to the origin. Furthermore, we consider spatial zero points instead of spatial critical points, and prove some similar symmetry theorems. Also, it is proved that these symmetry theorems hold for initial-boundary value problems for the wave equation. Received October 31, 1997; in final form February 3, 1998     

Metric Sample Spaces of Continuous Geometric Curves and Estimation of Their Centroids

The metric sample space of Fréechet curves (Fréechet , 1934,1951,1961) is based on a generalization of regular curves that covers continuous curves in full generality. This makes it possible to deal with both smooth and non-smooth, even non-rectifiable geometric curves in statistical analysis. In the present paper this sample space is further extended in two directions that are relevant in practice: to incorporate information on landmark points in the curves and to impose invariance with respect to an arbitrary group of isometric spatial transformations. Properties of the introduced sample spaces of curves are studied, specially those concerning to the generation and representation of random curves by random functions.In order to provide measures of central tendency and dispersion of random curves, centroids and restricted centroids ofrandom curves are defined in a general metric framework, and methods for their consistent estimation are derived.     

Structural study of hyaluronic acid oligomers and their complexes with copper in water by NMR and IR and molecular dynamics calculations

The hexasaccharide (trimer) and tetrasaccharide (dimer) oligomers of hyaluronic acid were investigated by ¹H and ¹³C high resolution Nuclear Magnetic Resonance. The dynamic behavior of the molecules and their complexation with copper(II) were analysed by ¹H NMR relaxation studies. A specific site for the complexation of the tetrasaccharide with Cu²⁺ was demonstrated by analysis of the paramagnetic effect of the metal on non-selective proton relaxation rates. A model for the complex involving two molecules of the tetrasaccharide is proposed.     

Photodegradation of 2-chloro substituted phenothiazines in alcohols

The mechanisms that trigger the phototoxic response to 2-chlorophenothiazine derivatives are still unknown. To better understand the relationship between the molecular structure of halogenated phenothiazines and their phototoxic activity, their photophysics and photochemistry were studied in several alcohols. The photodestruction quantum yields were determined under anaerobic conditions using monochromatic light (313 nm). Absorption- and emission-spectroscopy, ¹H- and ¹³C-NMR and GC-MS were used to characterize the photoproducts and reference compounds. An electron transfer mechanism had been previously proposed by Bunce et al . ( J. Med. Chem . 22 , 202–204) to explain the large difference between the photodestruction quantum yield of 2-chlorpromazine (φ = 0.46) and 2-chlorphenothiazine (φ = 0.20). According to these authors, the alkylamino chain transfers an electron to the phenothiazine moiety. Our results demonstrate that this mechanism is incorrect, because the photodestruction quantum yields of all chlorinated derivatives of this study are the same under the same conditions of solvent and irradiation wavelength. The quantum yield has no dependence on the 10-substituent, but it depends on the solvent. The percentage of each photoproduct, on the other hand, strongly depends on that substituent, but not very much on the solvent. Finally, it is demonstrated that the phototoxic effect of chlorinated phenothiazines is not related to the photodechlorination, although both processes share the same transient.     

Solutions of the average cost optimality equation for finite Markov decision chains: risk-sensitive and risk-neutral criteria

This work is concerned with controlled Markov chains with finite state and action spaces. It is assumed that the decision maker has an arbitrary but constant risk sensitivity coefficient, and that the performance of a control policy is measured by the long-run average cost criterion. Within this framework, the existence of solutions of the corresponding risk-sensitive optimality equation for arbitrary cost function is characterized in terms of communication properties of the transition law.     

Boron macrocycles having a calix-like shape. Synthesis, characterization, X-ray analysis, and inclusion properties

The syntheses, structure, and inclusion properties of trinuclear boron compounds having a calix-like shape are described. The compounds have been obtained via self-assembly reactions between salicylaldehyde derivatives and 3-aminophenylboronic acid, whereby the formation of three N --> B coordination bonds favored the oligomerization. The products have high melting points (>370 degrees C), are stable to moisture, and have good solubility in organic solvents; the latter property is useful for host-guest recognition experiments. The structural analysis by X-ray diffraction revealed that diverse conformations are possible because of the presence of two different units of aromatic rims. A cone-cone (double-cone) conformation is observed for three of these compounds, while the remaining one has a cone-partial cone conformation. An analysis of the molecular packing showed that the molecules are stacked in columns in two different orientations in relation to the organization of the macrocycles when referred to the N-B bonds. The inclusion properties toward primary amines and ammonium chlorides were analyzed by titration experiments and monitored by UV spectroscopy, whereby association constants on the order of 10(2)-10(3) M(-1) were determined.     

A straightforward synthesis and structure of unprecedented iminium salts of dihydropyrido[3,2-e][1,3]thiazines

Unprecedented 2-iminium chloride salts of 5,8-dihydro-2H-pyrido[3,2-e][1,3]thiazines derivatives (8) were easily synthesized in one step from the corresponding o-chloroformyl-1,4-dihydropyridine (2) and thiourea. The structural study has been carried out by X-ray crystallography and theoretical calculations at the B3LYP/6-31G* levels and reveal that the new salts exhibit appropriate structural features to behave as calcium channel modulators.     

Calculation of CLD Using Population Balance Equations of Generating Functions: Linear and Non‐Linear Ideal Controlled Radical Polymerization

Population balance equations in terms of generating functions (GF) are used to predict chain length distributions (CLD) of linear and non‐linear ideal controlled radical polymerization (CRP) systems. It is here shown that under simplified conditions analytical solutions for the CLD can be found and moreover the fundamental CLD derived by H. Tobita in 2006 is a limiting case of the more general solutions here presented. In order to deal with more complex CRP systems, solutions based upon the numerical inversion of GF are presented. These studies are also extended to the non‐linear CRP of vinyl/divinyl monomers where multimodal CLDs are predicted to occur.

     

Molecular Architecture of Non-Linear Polymers: Kinetic Modeling and Experimental Characterization of the System Methyl Methacrylate + Ethylene Glycol Dimethacrylate

A general kinetic approach allowing the prediction of the molecular architecture of non-linear polymers is applied to the study of the copolymerization of methyl methacrylate (MMA) with ethylene glycol dimethacrylate (EGDMA). Dynamic predictions of molecular weight distributions, sequence length distributions and mean square radius of gyration are possible before and after gelation. A set of experiments concerning the copolymerization of MMA and EGDMA was carried out in toluene solution at 60 °C for which classic radical kinetics is a good approximation. The time evolution of key polymer properties was followed using a SEC system with a refractive index detector coupled with MALLS allowing the determination of absolute weight average molecular weight and apparent molecular size distributions as well as z-average radius of gyration. Special focus was given to assess the influence of the initial amount of cross-linker on the dynamics of the non-linear structure build-up of these products. A kinetic scheme comprising 23 different chemical species and 76 chemical reactions was used in the modeling studies of this chemical system. Most of the kinetic parameters used in the simulations have been collected from previous studies. For experiments at low monomer conversion (up to about 0.5) a good agreement between predictions and experimental measurements is observed for molecular weights and z-average radius of gyration by fitting a small number of parameters describing gel effect (with a conversion dependent but chain length independent termination rate parameter) and the relative propagation on pendant double bonds. However, predicted values of weight-average molecular weights and z-average radius of gyration before gelation are too low at higher monomer conversions with non-linear systems. The likely cause is the presence of intramolecular reactions which should not be neglected in these circumstances.