Some results on Ramsey numbers using sumfree sets

Maximal sumfree sets chosen from the non-zero elements of galois group of order 2⁶ (i.e. GF(2⁶)?{0}) are found to be of size 13, 17, 18, 20 and 32 only. This gives a negative result to an investigation which would otherwise have delivered an exact value of the Ramsey number R(3,3,3,3;2).     

A Survey on Existence Results for Boundary Value Problems of Nonlinear Fractional Differential Equations and Inclusions

In this survey paper, we shall establish sufficient conditions for the existence and uniqueness of solutions for various classes of initial and boundary value problem for fractional differential equations and inclusions involving the Caputo fractional derivative. The both cases of convex and nonconvex valued right hand side are considered. The topological structure of the set of solutions is also considered.     

Unreliable M/G/1 retrial queue: monotonicity and comparability

In this paper we investigate the monotonicity properties of an unreliable M/G/1 retrial queue using the general theory of stochastic ordering. We show the monotonicity of the transition operator of the embedded Markov chain relative to the strong stochastic ordering and increasing convex ordering. We obtain conditions of comparability of two transition operators and we obtain comparability conditions of the number of customers in the system. Inequalities are derived for the mean characteristics of the busy period, number of customers served during a busy period, number of orbit busy periods and waiting times. Inequalities are also obtained for some probabilities of the steady-state distribution of the server state. An illustrative numerical example is presented.     

Large Amplitude Motions of Pyruvic Acid (CH3-CO-COOH)

Torsional and rotational spectroscopic properties of pyruvic acid are determined using highly correlated ab initio methods and combining two different theoretical approaches: Second order perturbation theory and a variational procedure in three-dimensions. Four equilibrium geometries of pyruvic acid, Tc, Tt, Ct, and CC, outcome from a search with CCSD(T)-F12. All of them can be classified in the C_s point group. The variational calculations are performed considering the three internal rotation modes responsible for the non-rigidity as independent coordinates. More than 50 torsional energy levels (including torsional subcomponents) are localized in the 406–986 cm⁻¹ region and represent excitations of the ν₂₄ (skeletal torsion) and the ν₂₃ (methyl torsion) modes. The third independent variable, the OH torsion, interacts strongly with ν₂₃. The A₁/E splitting of the ground vibrational state has been evaluated to be 0.024 cm⁻¹ as it was expected given the high of the methyl torsional barrier (338 cm⁻¹). A very good agreement with respect to previous experimental data concerning fundamental frequencies (ν^CAL − ν^EXP ~ 1 cm⁻¹), and rotational parameters (B₀^CAL − B₀^EXP < 5 MHz), is obtained.     

Photocatalytic Performance of H6P2W18O62/TiO2 Nanocomposite Encapsulated into Beta Zeolite under UV Irradiation in the Degradation of Methyl Orange

In this work, neat and supported H₆P₂W₁₈O₆₂ into nanocage of β‐zeolite were synthesized. However, H₆P₂W₁₈O₆₂ into nanocage of β‐zeolite was synthesized via template synthesis method. In addition, TiO₂ was supported on H₆P₂W₁₈O₆₂/β zeolite by impregnation method. The obtained materials were characterized by XRD, FT‐IR, UV‐Vis, FESEM and EDS techniques. Also, W and Ti contents of the catalyst were determined by ICP and EDS technique. The results reveal that the photocatalyst performance depends on catalyst loading, pH effect, and methyl orange concentration. Photocatalytic degradation of methyl orange follows a pseudo‐first order kinetic. The chemical oxygen demand (COD) experimental proved mineralization of methyl orange. Another reason for degradation and mineralization of methyl orange is the absence of hydrazine at the end of reaction which is one of the photodecolorization products. The plausible mechanism for photodegradation of MO was proposed.     

LC–DAD/ESI–MS/MS characterization of phenolic constituents in Rosa canina L. and its protective effect in cells

In an aim to prove the efficiency of polyphenols of Rosa canina fruits in promoting human health. A methanolic extract of R. canina fruits was prepared by successive maceration with solvents of increasing polarity. The polyphenol composition was analyzed by HPLC–DAD–ESI–MS. The biological activity of this extract on SH-SY5Y cells and HepG2 cells was then studied. The antioxidant activity was tested by various in vitro tests such as DPPH-radical-scavenging activity, FRAP assay, hydroxyl radical scavenging assay and total antioxidant capacity. The subacute toxicity of R. canina was tested on female rats by repeated intraperitoneal administration of various doses. The phenolic profiles showed 25 antioxidants distributed into three classes of phenolic compounds: glycosylated and agglomerated flavonoids/isoflavonoids, tannins and phenanthrenes. Qualitative phytochemical analyses showed that this extract lacks alkaloids. The methanolic extract of R. canina fruits has a total antioxidant capacity of 82.69 ± 1.18 μg EAA/mg of methanol extract and the IC₅₀ of the methods used is in the following increasing order: FRAP assay (61.88 μg/ml), then hydroxyl radical scavenging assay (67.45 μg/ml) and then DPPH radical-scavenging activity (129.81 μg/ml). The extract of R. canina did not cause any phenotypic signs of toxicity or mortality during and after treatment. The LD₅₀ was >5,000 mg/kg, hence, R. canina was considered nontoxic. An in vivo study proved the protective effect of R. canina against cardiac and hepato-renal toxicities. These results drew the importance of a healthy diet, where diets rich in R. canina fruits can be used as a rich natural source of antioxidants and anticarcinogenic phenolic compounds.     

Synthesis and pharmacological properties of polysubstituted 2-amino-4H-pyran-3-carbonitrile derivatives

Molecular Diversity - 2-Amino-3-cyano-4H-chromenes are structural core motifs that received increasing attention in the last years due to their interesting potential pharmacological properties. In...     

Transition-Metal-Mediated Glycosylation with Thioglycosides

Thioglycosides are among the most common glycosyl donors that find broad application in the synthesis of glycans and glycoconjugates. However, the requirement for toxic and/or large access of activators needed for common glycosylations with thioglycosides remains a notable drawback. Due to the increased awareness of the chemical waste impact on the environment, synthetic studies have been driven by the goal of finding non-toxic reagents. The main focus of this review is to highlight recent methods for thioglycoside activation that rely on transition metal catalysis.