Coloring, location and domination of corona graphs

A vertex coloring of a graph G is an assignment of colors to the vertices of G so that every two adjacent vertices of G have different colors. A coloring related property of a graphs is also an assignment of colors or labels to the vertices of a graph, in which the process of labeling is done according to an extra condition. A set S of vertices of a graph G is a dominating set in G if every vertex outside of S is adjacent to at least one vertex belonging to S. A domination parameter of G is related to those structures of a graph that satisfy some domination property together with other conditions on the vertices of G. In this article we study several mathematical properties related to coloring, domination and location of corona graphs. We investigate the distance-k colorings of corona graphs. Particularly, we obtain tight bounds for the distance-2 chromatic number and distance-3 chromatic number of corona graphs, through some relationships between the distance-k chromatic number of corona graphs and the distance-k chromatic number of its factors. Moreover, we give the exact value of the distance-k chromatic number of the corona of a path and an arbitrary graph. On the other hand, we obtain bounds for the Roman dominating number and the locating–domination number of corona graphs. We give closed formulaes for the k-domination number, the distance-k domination number, the independence domination number, the domatic number and the idomatic number of corona graphs.     

In variance under translations

In this paper, the functions which are solutions of constant coefficient homogeneous linear differential (or difference) equations are characterized in terms of the vector space spanned by the set of their translates. For this, a result about the differentiable character of the continuous solutions of Polya's functional equation is used.     

A polyhedral study of the semi-continuous knapsack problem

We study the convex hull of the feasible set of the semi-continuous knapsack problem, in which the variables belong to the union of two intervals. Such structure arises in a wide variety of important problems, e.g. blending and portfolio selection. We show how strong inequalities valid for the semi-continuous knapsack polyhedron can be derived and used in a branch-and-cut scheme for problems with semi-continuous variables. To demonstrate the effectiveness of these inequalities, which we call collectively semi-continuous cuts, we present computational results on real instances of the unit commitment problem, as well as on a number of randomly generated instances of linear programming with semi-continuous variables.     

Leptoquark effects on ν τ propagation in the Earth

The proposal of pilgrim dark energy is based on the idea that phantom dark energy possesses enough resistive force to preclude black hole formation. We work on this proposal by choosing an interacting framework with cold dark matter and three cutoffs such as Hubble as well as event horizon and conformal age of the universe. We present a graphical analysis and focus our study on the pilgrim dark energy as well as interacting parameters. It is found that these parameters play an effective role on the equation of state parameter for exploring the phantom region of the universe. We also make the analysis of ω–ω′ and point out freezing region in the ω–ω′ plane. Finally, it turns out that the ΛCDM is achieved in the statefinders plane for all models.     

An [FeIII34] Molecular Metal Oxide

The dissolution of anhydrous iron bromide in a mixture of pyridine and acetonitrile, in the presence of an organic amine, results in the formation of an [Fe₃₄] metal oxide molecule, structurally characterised by alternate layers of tetrahedral and octahedral Fe^III ions connected by oxide and hydroxide ions. The outer shell of the complex is capped by a combination of pyridine molecules and bromide ions. Magnetic data, measured at temperatures as low as 0.4 K and fields up to 35 T, reveal competing antiferromagnetic exchange interactions; DFT calculations showing that the magnitudes of the coupling constants are highly dependent on both the Fe‐O‐Fe angles and Fe?O distances. The simplicity of the synthetic methodology, and the structural similarity between [Fe₃₄], bulk iron oxides, previous Fe^III–oxo cages, and polyoxometalates (POMs), hints that much larger molecular Fe^III oxides can be made.     

Effects of two-phase nanofluid model on MHD mixed convection in a lid-driven cavity in the presence of conductive inner block and corner heater

Journal of Thermal Analysis and Calorimetry - This paper investigates a steady mixed convection in a lid-driven square cavity subjected to an inclined magnetic field and heated by corner heater...     

Highly insulating alkane rings with destructive σ-interference

Science China Chemistry - Destructive quantum interference (DQI) provides a unique approach to controlling the leakage current in the OFF state of molecular devices. However, the DQI in...     

Remarkable facets for selective monitoring of biomolecules by morphologically tailored CuO nanostructures

Journal of Solid State Electrochemistry - Remarkable selective analysis of biomolecules i.e., glucose and ascorbic acid on copper oxide facets was reported for the first time. The copper oxide...     

Spectrophotometric determination of lithium with Quinizarin in drugs and serum

An endemic peripheral vascular disorder resulting in gangrene of the lower extremities, especially of the feet, is called 'Blackfoot disease (BFD)'. Clinically, the symptoms and signs of Blackfoot disease are similar to those of Buerger's disease. In this study, the objective is to examine the amount of arsenic, mercury, zinc, lead, and selenium in urine samples from BFD patients. After pre-treatment with acids, the samples were digested by means of a microwave oven. The determination of arsenic mercury, zinc, lead and selenium were by hydride atomic absorption spectrometry (HAAS), cold vapor atomic absorption spectrometry (CVAAS), flame atomic absorption spectrometry (FAAS), graphite furnace absorption spectrometry (GFAAS), respectively. The results indicated that urinary arsenic, mercury and lead of the BFD patients were significantly higher than those of the normal controls, while urinary zinc and selenium were significantly lower than those of the normal controls. The possibility that these elements are involved in the etiology of diseases is discussed.