Graph-Theoretical Method to the Existence of Stationary Distribution of Stochastic Coupled Systems

In this paper, by linking Fokker–Planck equations with stochastic coupled systems, a new method is provided to investigate the existence of a stationary distribution of stochastic coupled systems. Based on the graph theory and the Lyapunov method, an appropriate Lyapunov function associated with stationary Fokker–Planck equations is constructed. Moreover, a Lyapunov-type theorem and a coefficients-type criterion are obtained to guarantee the existence of a stationary distribution. Furthermore, theoretical results are applied to explore the existence of a stationary distribution of stochastic predator–prey models with dispersal and a sufficient criterion is presented correspondingly. Finally, a numerical example is given to illustrate the effectiveness of our results.     

Another refinement of the right-hand side of the Hermite–Hadamard inequality for simplices

We establish a new refinement of the right-hand side of the Hermite–Hadamard inequality for convex functions of several variables defined on simplices.     

Efficient synthesis of 3,4-dihydropyrano[3,2-c]chromenes catalyzed by Ni(II)-functionalized Li<Superscript>+</Superscript>-Montmorillonite in a one-pot fashion under solvent-free conditions

A family of 3,4-dihydropyrano[3,2-c]chromenes were synthesized from 4-hydroxycoumarin and malononitrile via a one-pot reaction under solvent-free conditions at 100 °C catalyzed by Ni@Imine-Li⁺-MMT. This methodology tolerates most of the substrates and has the merits of lower loading of the catalyst, absence of solvents, excellent yields and reusability of the catalyst. A reasonable mechanism is also proposed. This catalytic system can be reused for at least five times with a negligible loss of activity. The prepared catalyst was characterized by using FTIR, TGA, SEM, TEM, uv-DRS, EDX and XRD.     

Evolving groups

The class of evolving groups is defined and investigated, as well as their connections to examples in the field of Galois cohomology. Evolving groups are proved to be Sylow Tower groups in a rather strong sense. In addition, evolving groups are characterized as semidirect products of two nilpotent groups of coprime orders where the action of one on the other is via automorphisms that map each subgroup to a conjugate.     

Oxoanionic Noble Metal Compounds from Fuming Nitric Acid: The Palladium Examples Pd(NO3)2 and Pd(CH3SO3)2

The oxidation of elemental palladium at 100 °C in a mixture of fuming nitric acid and a pyridine‐SO₃ complex leads to the anhydrous nitrate Pd(NO₃)₂ (monoclinic, P2₁/n, Z=2, a=469.12(3) pm, b=593.89(3) pm, c=805.72(4) pm, β=105.989(3)°, V=215.79(2) ų). The Pd²⁺ ions are in square‐planar coordination with four monodentate nitrate groups which are connected to further palladium atoms, leading to a layer structure. The reaction of elemental palladium with a mixture of fuming nitric acid and methanesulfonic acid at 120 °C leads to single crystals of Pd(CH₃SO₃)₂ (monoclinic, P2₁/n, Z=2, a=480.44(1) pm, b=1085.53(3) pm, c=739.78(2) pm, β=102.785(1)°, V=376.254(17) ų). Also in this structure the Pd²⁺ ions are in square‐planar coordination with four monodentate anions; however, the connection to adjacent palladium atoms leads to a chain‐type structure. The thermal decomposition of the compounds has been investigated by means of DSC/TG measurements. Furthermore, IR and Raman spectra have been recorded, and an assignment of the observed vibrational frequencies has been carried out based on theoretical investigations.     

Monitoring fuel quality: a case study for quinizarin marker content of unleaded petrol marketed in Greece

Fuel adulteration and cross-contamination lead to low-quality fuel products, which may cause increased environmental pollution, loss of taxes and engine problems. An establishment of a quality monitoring mechanism based on laboratory measurements may reveal problematic areas of the fuel supply chain. For the purposes of this work, 97 unleaded petrol samples were measured in order to quantify mass concentration of quinizarin, a substance used in Greece to easily mark the presence of 95 Research Octane Number unleaded petrol in other types of automotive fuels. The samples were obtained from petroleum retail stations selling different brands of fuels and located in different geographic regions of Greece. Statistical analysis of the results revealed quinizarin mass concentrations below the 3 mg L^?1 legislation specification limit and significant differences between brands and geographic regions, which may attributed to the structure of the fuel supply chain in Greece in combination with quinizarin properties and way of handling. Moreover, certain approaches were used for the calculation of decision limits for assessing compliance or non-compliance. These approaches take measurement reproducibility or estimated in-house uncertainty into account, in order to minimize the probability of false rejection.