The relaxation spectra, from which other material functions used to describe mechanical properties of materials can be uniquely determined, are important for modeling the rheological properties of polymers used in chemistry, food technology, medicine, cosmetics, and many other industries. The spectrum, being not directly accessible by measurement, is recovered from relaxation stress or oscillatory shear data. Only a few models and identification methods take into account the non-negativity of the real spectra. In this paper, the problem of recovery of non-negative definite relaxation spectra from discrete-time noise-corrupted measurements of relaxation modulus obtained in the stress relaxation test is considered. A new hierarchical identification scheme is developed, being applicable both for relaxation time and frequency spectra. Finite-dimensional parametric classes of models are assumed for the relaxation spectra, described by a finite series of power-exponential and square-exponential basis functions. The related models of relaxation modulus are given by compact analytical formula, described by the products of power of time and the modified Bessel functions of the second kind for the time spectrum, and by recurrence formulas based on products of power of time and complementary error functions for frequency spectrum. The basis functions are non-negative. In result, the identification task was reduced to a finite-dimensional linear-quadratic problem with non-negative unknown model parameters. To stabilize the solution, an additional smoothing constraint is introduced. Dual approach was used to solve the stated optimal identification task resulting in the hierarchical two-stage identification scheme. In the first stage, dual problem is solved in two levels and the vector of non-negative model parameters is computed to provide the best fit of the relaxation modulus to experiment data. Next, in second stage, the optimal non-negative spectrum model is determined. A complete scheme of the hierarchical computations is outlined; it can be easily implemented in available computing environments. The model smoothness is analytically studied, and the applicability ranges are numerically examined. The numerical studies have proved that using developed models and algorithm, it is possible to determine non-negative definite unimodal and bimodal relaxation spectra for a wide class of polymers. However, the examples also demonstrated that if the basis functions are non-negative and the model is properly selected for a given type of the real spectrum (unimodal, multimodal), the optimal model determined without non-negativity constraint can be non-negative in the dominant range of its arguments, especially in the wide neighborhood of the spectrum peaks.

A significant source of polycyclic aromatic hydrocarbons (PAH) in human diet is vegetable oils, especially those produced from plants grown in regions where the soil and the atmosphere are contaminated with these chemicals. Contamination with PAH of vegetable oils may also occur in the process of plant material drying with smoke or exhaust fumes, or in the course of extraction of that material with solvents containing trace amounts of PAH. The objective of this study was to determine the relationship between the levels of PAH present in rape seeds and the occurrence of these compounds in cultivation region and the relationship of the levels of PAH in rape seeds to thermal treatment after harvest. Rape seeds and pods from experimental fields and rape seeds subjected to thermal treatment in dryers obtained from suppliers of the raw material were examined and compared. Cleanup of extracts was performed with high-resolution size exclusion chromatography (SEC) and final determinations were by Trace Ultra/PolarisQ gas chromatography–mass spectroscopy (GC-MS). The results obtained indicated that during thermal treatment of rape seeds the concentration of PAH increased, but the levels of benzo[a]pyrene did not exceed threshold permissible levels. Data demonstrate that rapeseed cultivation in the presence of PAH results in higher levels of contaminants; however, the PAH levels still did not exceed the maximal allowable levels in Poland.

Zaburzenia płodności mają związek nie tylko z wiekiem (starzenie się jajników i jąder oraz pogarszanie się jakości gamet), ale również wynikają z negatywnego wpływu czynników środowiskowych, zawodowych i stylu życia. Do elementów stylu życia zalicza się sposób żywienia, aktywność fizyczną oraz palenie papierosów i spożywanie alkoholu. W pracy omówiono rolę poszczególnych składników odżywczych, takich jak: białka, węglowodany, tłuszcze, witaminy i składniki mineralne w kontekście procesów reprodukcyjnych. Nieprawidłowy sposób żywienia, nadmiar lub niedobór masy ciała to czynniki, które w znacznym stopniu mogą wpływać na płodność zarówno kobiet, jak i mężczyzn.

Recovering the relaxation spectrum, a fundamental rheological characteristic of polymers, from experiment data requires special identification methods since it is a difficult ill-posed inverse problem. Recently, a new approach relating the identification index directly with a completely unknown real relaxation spectrum has been proposed. The integral square error of the relaxation spectrum model was applied. This paper concerns regularization aspects of the linear-quadratic optimization task that arise from applying Tikhonov regularization to relaxation spectra direct identification problem. An influence of the regularization parameter on the norms of the optimal relaxation spectra models and on the fit of the related relaxation modulus model to the experimental data was investigated. The trade-off between the integral square norms of the spectra models and the mean square error of the relaxation modulus model, parameterized by varying regularization parameter, motivated the definition of two new multiplicative indices for choosing the appropriate regularization parameter. Two new problems of the regularization parameter optimal selection were formulated and solved. The first and second order optimality conditions were derived and expressed in the matrix-vector form and, alternatively, in finite series terms. A complete identification algorithm is presented. The usefulness of the new regularization parameter selection rules is demonstrated by three examples concerning the Kohlrausch–Williams–Watts spectrum with short relaxation times and uni- and double-mode Gauss-like spectra with middle and short relaxation times.