On Planar Toeplitz Graphs

We describe several classes of finite, planar Toeplitz graphs and present results on their chromatic number. We then turn to counting maximal independent sets in these graphs and determine recurrence equations and generating functions for some special cases.     

Asymptotic expansion for vector-valued sequences of random variables with focus on Wiener chaos

We develop the asymptotic expansion theory for vector-valued sequences ${\left(F_N\right)}_{N\ge 1}$ of random variables in terms of the convergence of the Stein–Malliavin matrix associated with the sequence $F_N$. Our approach combines the classical Fourier approach and the recent Stein–Malliavin theory. We find the second order term of the asymptotic expansion of the density of $F_N$ and we illustrate our results by several examples.     

SPDE with generalized drift and fractional-type noise

We consider a stochastic partial differential equation involving a second order differential operator whose drift is discontinuous. The equation is driven by a Gaussian noise which behaves as a Wiener process in space and the time covariance generates a signed measure. This class includes the Brownian motion, fractional Brownian motion and other related processes. We give a necessary and sufficient condition for the existence of the solution and we study the path regularity of this solution.     

Obtaining and characterizing modified tannins by physical-chemical methods

After oxidation of tannins (Tannins 1–3) extracted from grape seeds, Tanoxil compounds with increased solubility and enhanced antioxidant activities were synthesized. In this research, ABTS^+· assay and a chemiluminescence method were used for antioxidant measurement of hydrophilic compounds (Tanoxils 1–3).

It was observed that the antioxidant activity (AA, %) is very similar for the three samples, while at the same time AA is quite high (93.16%–96.48%). The percentage of inhibition by ABTS^+· is higher for Tanoxil 2 (96.4%) as compared to Tannin 2 compound (14.34%). Moreover, the total content (T_CF) of carboxyl and phenolic groups was investigated. T_CF values, determined for Tanoxil products, revealed a double (Tanoxil 1) or triple (Tanoxil 2) increase as compared to the value of the T_CF of Tannin 1. Tanoxil products represent an interest for future research as they have a high AA (96.4%) and the content of acidic groups is significant (T_CF, 0.191 meq g^?1).

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Induced and coinduced Banach Lie–Poisson spaces and integrability

The Poisson induction and coinduction procedures are used to construct Banach Lie–Poisson spaces as well as related systems of integrals in involution. This general method applied to the Banach Lie–Poisson space of trace class operators leads to infinite Hamiltonian systems of k-diagonal trace class operators which have infinitely many integrals. The bidiagonal case is investigated in detail.     

Parameter estimation for stochastic equations with additive fractional Brownian sheet

We study the maximum likelihood estimator for stochastic equations with additive fractional Brownian sheet. We use the Girsanov transform for the the two-parameter fractional Brownian motion, as well as the Malliavin calculus and Gaussian regularity theory.