Novel Method for HPLC Analysis of Triterpenic Acids Using 9-Anthryldiazomethane Derivatization and Fluorescence Detection

Triterpenic acids are a group of secondary plant metabolites which are part of the cuticular waxes covering fruits, leaves, and flowers. To date, quantitative analysis of these compounds has often been conducted using high-performance liquid chromatography coupled with spectrophotometric detection or mass spectrometry; however, these methods have some major drawbacks. This paper reports a new method of analysis implementing derivatization with 9-anthryldiazomethane and fluorescence detection. The method consists of the extraction of analytes from a matrix, purification with anion exchanging SPE columns, and an optional step of the alkaline hydrolysis of triterpenic acid esters. The paper also describes a fast and easy method for the synthesis of the derivatization agent. The detection limits of the method presented are approximately 100-fold lower than in a similar method using ultraviolet spectrophotometry as the mode of detection. The recovery and repeatability of the method are at satisfactory levels.     

Physicochemical,Antioxidant, Microstructural Properties and Bioaccessibility of Dark Chocolate with Plant Extracts

In this study, dark chocolates (DCh) containing zinc lactate (ZnL) were enriched with extracts from elderberries (EFrE), elderflowers (EFlE), and chokeberries (ChFrE) to improve their functional properties. Both dried plant extracts and chocolates were analyzed for antioxidant capacity (AC) using four different analytical methods: 2,2-diphenyl-1-picrylhydrazyl (DPPH), 2,2′-azino-bis(3-ethylbenzothiazoline-6-sulfonic acid) (ABTS), cupric ion-reducing antioxidant capacity (CUPRAC), and ferric-reducing antioxidant power (FRAP), while total phenolic content (TPC) was determined by Folin–Ciocalteu (F–C) assay. An increase in antioxidant properties of fortified chocolates was found, and the bioaccessibility of their antioxidants was evaluated. The highest AC and TPC were found in ChFrE and chocolate with chokeberries (DCh + ChFrE) before and after simulated in vitro digestion. Bioaccessibility studies indicated that during the simulated digestion the AC of all chocolates reduced significantly, whereas insignificant differences in TPC results were observed between chemical and physiological extracts. Moreover, the influence of plant extracts on physicochemical parameters such as moisture content (MC), fat content (FC), and viscosity of chocolates was estimated. Furthermore, scanning electron microscopy with dispersive energy spectroscopy (SEM-EDS) was used to analyze surface properties and differences in the chemical composition of chocolates without and with additives.     

Uncatalyzed peptide bond formation between two double amino acid molecules in the gas phase

The gas phase mechanism for peptide bond formation between two double amino acid (DAA) molecules ((NH₂)₂C(COOH)₂) is investigated in the absence of any catalysts. Two different paths, concerted and stepwise, each leading to both cis and trans DAA‐DAA dipeptide products (four mechanisms total) are examined on the basis of theoretical calculations carried out at the CCSD(T)/aug‐cc‐pVDZ//MP2/aug‐cc‐pVDZ level. The investigation indicates that the concerted mechanism leading to the trans configuration of the peptide bond in the DAA‐DAA dipeptide product is thermodynamically favored by about 5 kcal mol^?1 and requires slightly less energy than the remaining pathways considered. Moreover, the peptide bond formation process between two DAA molecules in the gas phase resembles the analogous reactions between two natural amino acids.     

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.     

Decomposition of bipartite graphs into closed trails

Let Lct(G) denote the set of all lengths of closed trails that exist in an even graph G. A sequence (t ₁,..., t _p ) of elements of Lct(G) adding up to |E(G)| is G-realisable provided there is a sequence (T ₁,..., t _p ) of pairwise edge-disjoint closed trails in G such that T _i is of length T _i for i = 1,..., p. The graph G is arbitrarily decomposable into closed trails if all possible sequences are G-realisable. In the paper it is proved that if a ⩾ 1 is an odd integer and M _a,a is a perfect matching in K _a,a , then the graph K _a,a -M _a,a is arbitrarily decomposable into closed trails.      

Lower Bounds on the Lowest Spectral Gap of Singular Potential Hamiltonians

We analyze Schr?dinger operators whose potential is given by a singular interaction supported on a sub-manifold of the ambient space. Under the assumption that the operator has at least two eigenvalues below its essential spectrum we derive estimates on the lowest spectral gap. In the case where the sub-manifold is a finite curve in two dimensional Euclidean space the size of the gap depends only on the following parameters: the length, diameter and maximal curvature of the curve, a certain parameter measuring the injectivity of the curve embedding, and a compact sub-interval of the open, negative energy half-axis which contains the two lowest eigenvalues. Dedicated to Krešimir Veselić on the occasion of his 65^th birthday. Submitted: February 20, 2006; Accepted: May 8, 2006     

Stationary Oberbeck–Boussinesq model of generalized Newtonian fluid governed by multivalued partial differential equations

A generalization of the Oberbeck–Boussinesq model consisting of a system of steady state multivalued partial differential equations for incompressible, generalized Newtonian of the p-power type, viscous flow coupled with the nonlinear heat equation is studied in a bounded domain. The existence of a weak solution is proved by combining the surjectivity method for operator inclusions and a fixed point technique.     

Edge-disjoint Open Trails in Complete Bipartite Multigraphs

Let ^r K _a,b be a complete bipartite multigraph. We show a necessary and sufficient condition for a multigraph ^r K _a,b to be arbitrarily decomposable into open trails. We extend the results obtained by Balister for complete graphs (Balister in Probab Comput 10:463–499, 2001). Moreover we show that a multigraph ^r K _a,b with even r and a ≥ 3 or b ≥ 3 is arbitrarily decomposable into open and closed trails.     

Note on Group Distance Magic Graphs G[C 4]

A group distance magic labeling or a ${\mathcal{G}}$ -distance magic labeling of a graph G =  (V, E) with ${|V | = n}$ is a bijection f from V to an Abelian group ${\mathcal{G}}$ of order n such that the weight ${w(x) = \sum_{y\in N_G(x)}f(y)}$ of every vertex ${x \in V}$ is equal to the same element ${\mu \in \mathcal{G}}$ , called the magic constant. In this paper we will show that if G is a graph of order n =  2 ^p (2k + 1) for some natural numbers p, k such that ${\deg(v)\equiv c \mod {2^{p+1}}}$ for some constant c for any ${v \in V(G)}$ , then there exists a ${\mathcal{G}}$ -distance magic labeling for any Abelian group ${\mathcal{G}}$ of order 4n for the composition G[C ₄]. Moreover we prove that if ${\mathcal{G}}$ is an arbitrary Abelian group of order 4n such that ${\mathcal{G} \cong \mathbb{Z}_2 \times\mathbb{Z}_2 \times \mathcal{A}}$ for some Abelian group ${\mathcal{A}}$ of order n, then there exists a ${\mathcal{G}}$ -distance magic labeling for any graph G[C ₄], where G is a graph of order n and n is an arbitrary natural number.     

The Liouville-type theorem for problems with nonstandard growth derived by Caccioppoli-type estimate

Let u be a nonnegative solution to the PDI $$-\,\mathrm{div} \mathcal {A}(x, u, \nabla u)\geqslant \mathcal {B}(x,u, \nabla u)$$ in $$\Omega $$, where $$\mathcal {A}$$ and $$\mathcal {B}$$ are differential operators with p(x)-type growth. As a consequence of the Caccioppoli-type inequality for the solution u, we obtain the Liouville-type theorem under some integral condition. We simplify the assumptions on functions $$ \mathcal {A}$$ and $$ \mathcal {B}$$, and we do not restrict the range of p(x) by the dimension n, therefore we can cover quite general family of problems.