Theoretical studies on aromaticity of selected hydroxypyrones. Part 3#. Chelatoaromaticity phenomenon in metalcomplexes of hydroxypyrones

The aim of this project is to study the aromatic properties of various forms (neutral, cationic, and anionic) of selected hydroxypyrones (pyromeconic acid, maltol, and ethylmaltol) and their metalcomplexes with aluminum, gallium, and indium ions. Aromaticity of hydroxypyrone metalcomplexes is important because it can influence the stability of such complexes, which is crucial for their applications in medicinal and environmental chemistry. Results from ten different indices of aromaticity (HOMA, NICS(0), NICS(1), NICS_scan, ASE_iso, PDI, FLU, I_ring, MCI, and KMCI) show that aromaticity in hydroxypyrones decreases in the order cations > neutral molecules > anions. Performed calculations situate the aromaticities of ligands in metalcomplexes close to their respective cations. This means that complexation causes a significant increase of the aromaticity of ligands, which stabilizes formed chelatocomplexes. On the other hand, we clearly show that rings that are involved in binding metal ions are not aromatic. Copyright © 2010 John Wiley & Sons, Ltd.     

How random is your heart beat?

We measure the content of random uncorrelated noise in heart rate variability using a general method of noise level estimation using a coarse-grained entropy. We show that usually, except for atrial fibrillation, the level of such noise is within 5-15% of the variance of the data and that the variability due to the linearly correlated processes is dominant in all cases analyzed but atrial fibrillation. The nonlinear deterministic content of heart rate variability remains significant and may not be ignored.     

A Fleming–Viot Particle Representation¶of the Dirichlet Laplacian

We consider a model with a large number N of particles which move according to independent Brownian motions. A particle which leaves a domain D is killed; at the same time, a different particle splits into two particles. For large N, the particle distribution density converges to the normalized heat equation solution in D with Dirichlet boundary conditions. The stationary distributions converge as N→∞ to the first eigenfunction of the Laplacian in D with the same boundary conditions. Received: 11 November 1999 / Accepted: 19 May 2000     

Concepts of lower semicontinuity and continuous selections for convex valued multifunctions

We discuss several concepts of continuity, weaker than lower semicontinuity, but still implying the existence of a continuous selection for a closed convex valued multifunction from a paracompact Hausdorff topological space into a Banach space. In this way, an extension of Michael's celebrated selection theorem is given. The behavior of -envelop approximations, as well as the localization of continuous selections, is also discussed.     

Aromatic and Antiaromatic Pathways in Triphyrin(2.1.1) Annelated with Benzo[b]heterocycles

Understanding of the aromatic properties and magnetically induced current densities of highly conjugated chromophores is important when designing molecules with strongly delocalized electronic structure. Linear extension of the triphyrin(2.1.1) skeleton with an annelated benzo[b]heterocycle fragment modifies the aromatic character by extending the electron delocalization pathway. Two-electron reduction leads to an antiaromatic triphyrin(2.1.1) ring and an aromatic benzo[b]heterocycle subunit. Current-density calculations provide detailed information about the observed pathways and their strengths.     

Dynamic response of the spherical pendulum subjected to horizontal Lissajous excitation

Nonlinear Dynamics - This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the...     

SU(2) Chern-Simons theory at genus zero

We present a detailed study of the Schrödinger picture space of states in theSU(2) Chern-Simons topological gauge theory in the simplest geometry. The space coincides with that of the solutions of the chiral Ward identities for the WZW model. We prove that its dimension is given by E. Verlinde's formulae.