Synthesis and photochemistry of beta,beta'-di(2-furyl)-substituted o-divinylbenzenes: intra- and/or intermolecular cycloaddition as an effect of annelation

New heteroaryl-substituted o-divinylbenzenes, 2,2'-(1,2-phenylenedivinylene)difuran (9), 2,2'-(1,2-phenylenedivinylene)bisbenzo[b]furan (10), and 2,2'-(1,2-phenylenedivinylene)bisnaphtho[2,1-b]furan (11), were prepared and irradiated at various concentrations; intramolecular photocycloaddition and intermolecular [2+2] twofold photoaddition reactions took place to give bicyclo[3.2.1]octadiene derivatives 12-14 and cyclophane derivatives 15-17, respectively. Compound 11 was the most selective of these o-divinylbenzenes, which, owing to pi-pi intra- or intermolecular complexation, gave only the exo-bicyclo[3.2.1]octadiene derivative 14 at low concentrations, and only the cyclophane derivative 17 at high concentrations.     

Kinetic Monte Carlo simulations of nucleation and growth in electrodeposition

Nucleation and growth during bulk electrodeposition is studied using kinetic Monte Carlo (KMC) simulations. Ion transport in solution is modeled using Brownian dynamics, and the kinetics of nucleation and growth are dependent on the probabilities of metal-on-substrate and metal-on-metal deposition. Using this approach, we make no assumptions about the nucleation rate, island density, or island distribution. The influence of the attachment probabilities and concentration on the time-dependent island density and current transients is reported. Various models have been assessed by recovering the nucleation rate and island density from the current-time transients.     

Positive definite solutions of some matrix equations

In this paper we investigate some existence questions of positive semi-definite solutions for certain classes of matrix equations known as the generalized Lyapunov equations. We present sufficient and necessary conditions for certain equations and only sufficient for others.     

Error estimates for some quadrature rules with maximal trigonometric degree of exactness

In this paper, we give error estimates for quadrature rules with maximal trigonometric degree of exactness with respect to an even weight function on ( ? π,π) for integrand analytic in a certain domain of complex plane. Copyright © 2013 John Wiley & Sons, Ltd.     

Mirror and synchronous couplings of geometric Brownian motions

The paper studies the question of whether the classical mirror and synchronous couplings of two Brownian motions minimise and maximise, respectively, the coupling time of the corresponding geometric Brownian motions. We establish a characterisation of the optimality of the two couplings over any finite time horizon and show that, unlike in the case of Brownian motion, the optimality fails in general even if the geometric Brownian motions are martingales. On the other hand, we prove that in the cases of the ergodic average and the infinite time horizon criteria, the mirror coupling and the synchronous coupling are always optimal for general (possibly non-martingale) geometric Brownian motions. We show that the two couplings are efficient if and only if they are optimal over a finite time horizon and give a conjectural answer for the efficient couplings when they are suboptimal.     

Mechanistic pathways for oxidative addition of aryl iodides to the low-ligated diethanolamine palladium(0) complex in phosphine-free Heck reactions

A set of reactions of different activated olefins and aryl iodides with the trans-dichlorobis(diethanolamine-N)palladium(II) complex (trans-[PdCl₂(DEA)₂]) as a precatalyst was performed, in the presence of diethanolamine (DEA) as a weak base, and NaOEt as a strong base. It was established that the presence of NaOEt slightly lowered the yields, but significantly accelerated the reactions. This experimental finding is in agreement with our computational investigation that shows that significantly higher activation barrier is required for the preactivation reaction in the presence of a weak base than in the presence of a strong base. The reaction between the catalytically active DEA-Pd(0)-Cl complex, formed in the preactivation reaction, and iodobenzene was investigated using density functional theory. Two mechanisms for the oxidative addition of the activated complex were found. The first mechanism is based on a nucleophilic attack of Pd on I of iodobenzene, and yields an intermediate tetracoordinated Pd complex (aI2). The second mechanism begins with a nucleophilic attack of Pd on the benzene ring, and yields a tricoordinated intermediate complex (bI4). It was concluded, on the basis of structural and energetical properties of aI2 and bI4, that the second mechanism is significantly more favorable. It was shown that the oxidative addition requires noticeable lower activation energy than that required for the preactivation process. Thus, our investigations indicate that oxidative addition is not the rate determining step for the Heck reactions investigated in this work, but preactivation step.     

Quaternionic operators with finite matrix trace

In this paper we consider bounded liner operators in quaternionic Hilbert space, having finite and invariant matrix trace. We prove that any such operator is selfadjoint. Besides, we prove that dual space of the real normed space of all such operators is isomorphic to the Banach space of all selfadjoint operators.This research was supported by Science Fund of Serbia, through the Mathematical Faculty of Belgrade.     

The stability of the extended model of hypothalamic-pituitary-adrenal axis examined by stoichiometric network analysis

Stoichiometric network analysis (SNA) represents a powerful mathematical tool for stability analysis of complex stoichiometric networks. Recently, the important improvement of the method has been made, according to which instability relations can be entirely expressed via reaction rates, instead of thus far used, in general case undefined, current rates. Such an improved SNA methodology was applied to the determination of exact instability conditions of the extended model of the hypothalamic-pituitary-adrenal (HPA) axis, a neuroendocrinological system, whose hormone concentrations exert complex oscillatory evolution. For emergence of oscillations, the Hopf bifurcation condition was utilized. Instability relations predicted by SNA showed good correlation with numerical simulation data of the HPA axis model.