A spectrophotometric method for plant pigments determination and herbs classification

Twenty herbs, showing medicinal benefits on human life, like Taraxacum officinale, Plantago lanceolata, Hypericum perforatum, Ocimum basilicum, Melissa officinalis, Mentha piperita, and others, were tested. The percentage content of pigments, i.e. chlorophylls, carotenoids, and flavonoids, in the chosen herbs was determined. The spectrophotometric method, which is quick and readily available, was used. Measurements required pigment extraction with a solvent. Ethanol was used for the determination of chlorophylls and carotenoids, and acetone for the determination of flavonoids. Hierarchical agglomerative cluster analysis was performed in order to confirm the experimental results. The study of flavonoids content showed an interesting regularity which can be used for the classification of herbs. Plants belonging to the Lamiaceae family showed the flavonoids content in the range from 0.18 % to 0.68 %, whereas those belonging to the Apiaceaehas family showed the flavonoids content in the 0.75–1.20 % range.     

Estimation of platinum in environmental water samples with solid phase extraction technique using inductively coupled plasma mass spectrometry

A solid phase extraction technique for the determination of platinum(IV) at trace levels by inductively coupled plasma mass spectromA solid phase extraction technique for the determination of platinum(IV) at trace levels by inductively coupled plasma mass spectrometry (ICP-MS) was developed. The method was based on retention of platinum in a sample on silica gel modified with aminepropyl groups. The retention of platinum(IV) from the sample solution and the recovery of platinum with 1.0 mol L⁻¹ thiourea solution were quantitative. The relative standard deviation (RSD) was calculated as 5% (n = 7) at the 10 ng L⁻¹ level. The enrichment factor was found to be (50-fold) for 250 mL of water sample. Under optimum conditions, the method detection limit (MDL) was found to be 1 ng L⁻¹ for platinum in water matrices. Recoveries of Pt from spike addition to atmospheric water samples were quantitative (80–95%). The present method was used for the determination of platinum in precipitation, throughfall and runoff water samples.      

Generalized dimension compression under mappings of exponentially integrable distortion

We prove a dimension compression estimate for homeomorphic mappings of exponentially integrable distortion via a modulus of continuity result by D. Herron and P. Koskela [Mappings of finite distortion: gauge dimension of generalized quasicircles, Illinois J. Math., 2003, 47(4), 1243–1259]. The essential sharpness of our estimate is demonstrated by an example.     

On extensions of the Bessel operator on a finite interval and a half-line

The minimum and maximum operators generated by a Bessel differential expression are studied. The boundary triplets for the maximum operator A _??,max are constructed, and the corresponding Weyl functions are found. All non-negative self-adjoint extensions of the minimum operator A _??,min are described.     

Unified encoding for hyper-heuristics with application to bioinformatics

This paper introduces a new approach to applying hyper-heuristic algorithms to solve combinatorial problems with less effort, taking into account the modelling and algorithm construction process. We propose a unified encoding of a solution and a set of low level heuristics which are domain-independent and which change the solution itself. This approach enables us to address NP-hard problems and generate good approximate solutions in a reasonable time without a large amount of additional work required to tailor search methodologies for the problem in hand. In particular, we focused on solving DNA sequencing by hybrydization with errors, which is known to be strongly NP-hard. The approach was extensively tested by solving multiple instances of well-known combinatorial problems and compared with results generated by meta heuristics that have been tailored for specific problem domains.     

Multi-dimensional scalar balance laws with discontinuous flux

We consider scalar balance laws with a dissipative source term. The flux function may be discontinuous with respect to both the space variable x and the unknown quantity u. We formulate the definition of entropy weak solutions and provide existence and uniqueness to the considered problem. The problem is formulated in the framework of multi-valued mappings. The notion of entropy measure-valued solutions is used to prove the so-called contraction principle and comparison principle.     

Dimension gap under Sobolev mappings

We prove an essentially sharp estimate in terms of generalized Hausdorff measures for the images of boundaries of Hölder domains under continuous Sobolev mappings, satisfying suitable Orlicz–Sobolev conditions. This estimate marks a dimension gap, which was first observed in [2] for conformal mappings.