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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Searching for Potential Markers of Glomerulopathy in Urine by HS-SPME-GC×GC TOFMS

Volatile organic compounds (VOCs) exiting in urine are potential biomarkers of chronic kidney diseases. Headspace solid phase microextraction (HS-SPME) was applied for extraction VOCs over the urine samples. Volatile metabolites were separated and identified by means of two-dimensional gas chromatography and time of flight mass spectrometry (GC × GC TOF MS). Patients with glomerular diseases (n = 27) and healthy controls (n = 20) were recruited in the study. Different VOCs profiles were obtained from patients and control. Developed methodology offers the opportunity to examine the metabolic profile associated with glomerulopathy. Four compounds found in elevated amounts in the patients group, i.e., methyl hexadecanoate; 9-hexadecen-1-ol; 6,10-dimethyl-5,9-undecadien-2-one and 2-pentanone were proposed as markers of glomerular diseases.     

Dynamics of particles with anisotropic mass depending on time and position

Representations of solutions of equations describing the diffusion and quantum dynamics of particles in a Riemannian manifold are discussed under the assumption that the mass of particles is anisotropic and depends on both time and position. These equations are evolution differential equations with secondorder elliptic operators, in which the coefficients depend on time and position. The Riemannian manifold is assumed to be isometrically embedded into Euclidean space, and the solutions are represented by Feynman formulas; the representation of a solution depends on the embedding.     

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.