The main purpose of this paper is to establish some common fixed point theorems for single and set-valued maps in complete metric spaces, under contractive conditions by using minimal type commutativity and without continuity. These theorems generalize, extend and improve the result due to Elamrani and Mehdaoui () and others. Also, common fixed point theorems in metric spaces under strict contractive conditions are given.
Non-markovian queueing systems can be extended to piecewise-deterministic Markov processes by appending supplementary variables to the system. Then their analysis leads to an infinite system of partial differential equations with an infinite number of variables and non-local boundary conditions. We show how one can study such systems by using the theory of stochastic semigroups.
Ramesh Sirisetti and G. Jogarao
In this paper, the concept of relative complementation in almost distributive lattice is generalized. We obtain several properties on the sets of weak relative complement elements. We prove a sufficient condition for a weakly relatively complemented almost distributive lattice with dense elements to become a generalized stone almost distributive lattice.
Vita Šterna, Sanita Zute and Zaiga Vicupe
Consumption of dietary fibre has potential in improving nutrition and health. For further breeding of oats, it is necessary to increase knowledge on variation in the content of fibre and bioactive components in oats. Therefore, the aim of the present investigation was to study the extent of variation in β-glucan concentration of oats grown in Latvia and to evaluate association of β-glucan concentration with protein and fat concentration in newly created oat breeding lines. In 2015 and 2016, concentration of protein, fat, and β-glucan in grain of hulled oat varieties ‘Laima’, ‘Peppi’, and ten breeding lines was determined. The obtained results showed a wide range of fat concentration among varieties, with a range from 5.9 to 8.3%. The concentration of β-glucan ranged from 1.8 to 3.6% depending on the year. The β-glucan concentration had medium close positive correlation with lipid and weak significant positive correlation with protein concentration, which significantly differed among genotypes.
Arpita Das and Pratima Panigrahi
The R-graph R(G) of a graph G is the graph obtained from G by intro- ducing a new vertex ue for each e ∈ E(G) and making ue adjacent to both the end vertices of e. In this paper, we determine the adjacency, Lapla- cian and signless Laplacian spectra of R-vertex join and R-edge join of a connected regular graph with an arbitrary regular graph in terms of their eigenvalues. Moreover, applying these results we construct some non-regular A-cospectral, L-cospectral and Q-cospectral graphs, and find the number of spanning trees.
Akbar Rezaei and Arsham Borumand Saeid
Hilbert algebras are important tools for certain investigations in algebraic logic since they can be considered as fragments of any propositional logic containing a logical connective implication and the constant 1 which is considered as the logical value “true” and as a generalization of this was defined the notion of g-Hilbert algebra. In this paper, we investigate the relationship between g-Hilbert algebras, gi-algebras, implication gruopoid and BE-algebras. In fact, we show that every g-Hilbert algebra is a self distributive BE-algebras and conversely. We show cannot remove the condition self distributivity. Therefore we show that any self distributive commutative BE-algebras is a gi-algebra and any gi-algebra is strong and transitive if and only if it is a commutative BE-algebra. We prove that the MV -algebra is equivalent to the bounded commutative BE-algebra.
Ilze Beitāne, Gita Krūmiņa-Zemture, Zanda Krūma and Ingmārs Cinkmanis
The objective of the current study was to analyse the total phenolic concentration (TPC), total flavonoid concentration (TFC), individual phenolic compound concentration and DPPH′ radical scavenging activity of four buckwheat (raw, roasted, white and dark) flour samples obtained from the Latvian market, in comparison to those of wheat flour, which is the most common ingredient in production of cereal products. TPC, TFC, and DPPH′ radical scavenging activity values were determined using spectrophotometric methods. Phenolic compounds were determined based on the high performance liquid chromatographic method (HPLC). All buckwheat flour samples had significantly higher TPC and TFC than wheat flour. The highest TPC (974.74 mg GAE·100 g−1 DW) and TFC (495.31 mg CE·100 g−1 DW) was found in raw buckwheat flour (p < 0.05). Buckwheat flour samples demonstrated similar DPPH′ radical scavenging activity, which ranged from 21.067 to 22.644 mM TE·100 g−1 dry matter, and was significantly higher (p < 0.05) than in wheat flour (0.731 mM TE·100 g−1 of dry matter). Dark buckwheat flour contained the highest level of rutin (4.613 mg·100 g−1), whereas raw buckwheat flour displayed the highest level of 3.5-dihydroxybenzoic acid (6.356 mg·100 g−1), sinapic acid (0.947 mg·100 g−1) and epicatechin (2.608 mg·100 g−1).
Ida Jākobsone, Sanita Zute, Māra Bleidere, Ināra Kantāne and Vadims Bartkevičs
The aim of the study was to determine concentrations of 13 macro and trace elements in different barley genotypes depending on the year of growth (2011, 2012, and 2013) and agricultural practice (conventional/organic). Cd, Pb, Cr, Ni, and Al concentrations were determined by electrothermal atomic absorption spectrometry and K, Na, Zn, Cu, Ca, Mg, Mn, and Fe concentrations by flame atomic absorption spectrometry. Statistically different concentrations of Cr, Cu, and Zn occurred among genotypes; for Ca, Mn, and Fe concentrations between barley grains, grown conventionally and organically; for Cr and Ni concentrations between hulled and hull-less grain and for Cd, Cr, Ni, Cu, Zn, Al, K, and Na concentrations among the study years. Concentrations of potentially hazardous elements were low (Cd < 0.005–0.027, Pb 0.013–0.066, Cr 0.111–0.327, Ni 0.161–1.264, Cu 2.8–4.7 and Al 1.62–6.09 mg·kg−1). Barley products can provide necessary macro and trace elements, especially of Mn, Mg, Fe, and Zn (7.8–16.1; 1024–1249; 29.2–52.9, and 20.5–33.7 mg·kg−1, respectively).
Māra Kūka, Ilze Čakste and Pēteris Kūka
Oxidation of fats and oils reduces the nutritional value of food and causes various health problems. The addition of antioxidants prevents the oxidation of fats in the food. The antioxidant activity of antioxidants represents the ability to inhibit the process of oxidation. The antioxidant activity of herbal extracts has usually been assessed in a linoleic acid emulsion system. The aim of the present study was to evaluate inhibition of conjugated diene formation in Latvian linseed oil. Ethanol extract of the calyx of Hibiscus sabdariffa L., vanillin, α-tocopherol and 2,6-di-tert-butyl-4-methylphenol as additives were compared for their antioxidative activity. The samples of linseed oil with additives were incubated for 24 h at 60 °C and then analysed using UV spectrophotometry (λ = 234 nm). The antioxidant activity of additives was characterised by the percentage of formation of conjugated dienes. The ability of additives to inhibit oxidation in linseed oil decreases as follows: vanillin, 2,6-di-tert-butyl-4-methylphenol and α-tocopherol. Our results indicate that linseed oil can be used to test antioxidative activity of substances.