Roman domination subdivision number of graphs

A Roman dominating function on a graph G = (V, E) is a function f : V ? {0, 1, 2}f : V \rightarrow \{0, 1, 2\} satisfying the condition that every vertex v for which f(v) = 0 is adjacent to at least one vertex u for which f(u) = 2. The weight of a Roman dominating function is the value w(f) = ?_{v ? V} f(v)w(f) = \sum_{v\in V} f(v). The Roman domination number of a graph G, denoted by _gR(G)_{\gamma R}(G), equals the minimum weight of a Roman dominating function on G. The Roman domination subdivision number sd_gR(G)sd_{\gamma R}(G) is the minimum number of edges that must be subdivided (each edge in G can be subdivided at most once) in order to increase the Roman domination number. In this paper, first we establish upper bounds on the Roman domination subdivision number for arbitrary graphs in terms of vertex degree. Then we present several different conditions on G which are sufficient to imply that $1 \leq sd_{\gamma R}(G) \leq 3$1 \leq sd_{\gamma R}(G) \leq 3. Finally, we show that the Roman domination subdivision number of a graph can be arbitrarily large.     

An Expedient Synthesis of Novel Derivatives of Pyrido[2,3‐d]pyrimidines Using Magnetically Supported ZrO2 Nanocatalyst

An efficient synthesis of pyrido[2,3‐d]pyrimidine derivatives via one‐pot multicomponent reactions of 6‐amino‐2‐(alkylthio)pyrimidin‐4(3H)‐one, 3‐cyanoacetylindole and arylaldehydes using [Fe₃O₄@ZrO₂] as magnetically recyclable nanocatalyst is reported. This protocol furnished the desired products in good to excellent yields (70–93 %) and lower reaction times. The catalyst could be easily and efficiently separated from the final product solution by an external magnet and be reused in 5 consecutive runs without any significant activity decrease.     

On zero-divisors of near-rings of polynomials

In this paper, we are interested to study zero-divisor properties of a 0-symmetric nearring of polynomials R₀[x], when R is a commutative ring. We show that for a reduced ring R, the set of all zero-divisors of R₀[x], namely Z(R₀[x]), is an ideal of R₀[x] if and only if Z(R) is an ideal of R and R has Property (A). For a non-reduced ring R, it is shown that Z(R₀[x]) is an ideal of Z(R₀[x]) if and only if ann_R({a, b}) ∩ N i?(R) ≠ 0, for each a, b ∈ Z(R). We also investigate the interplay between the algebraic properties of a 0-symmetric nearring of polynomials R₀[x] and the graph-theoretic properties of its zero-divisor graph. The undirected zero-divisor graph of R₀[x] is the graph Γ(R₀[x]) such that the vertices of Γ(R₀[x]) are all the non-zero zero-divisors of R₀[x] and two distinct vertices f and g are connected by an edge if and only if f ? g = 0 or g ? f = 0. Among other results, we give a complete characterization of the possible diameters of Γ(R₀[x]) in terms of the ideals of R. These results are somewhat surprising since, in contrast to the polynomial ring case, the near-ring of polynomials has substitution for its “multiplication” operation.     

Spectrofluorometric study of complexation of some amino derivatives of 9,10-anthraquinone with beta-cyclodextrin

Complexation reactions between 1-amino-9,10-anthraquinone (AA1), 1-amino-2-methyl-9,10-anthraquinone (AA2), 1-amino-2,4-dimethyl-9,10-anthraquinone (AA3) and 1-amino-2-ethyl-9,10-anthraquinone (AA4) and beta-cyclodextrin were studied spectrofluorometrically, under optimized experimental conditions. The formation constants of the resulting 1:1 beta-cyclodextrin complexes were evaluated and found to decrease in the order AA4>AA1>AA3>AA2. Possible reasons for the observed stability sequence are discussed based on the structures proposed for the resulting inclusion complexes.     

Electrocatalytic properties of [Ru(bpy)(tpy)Cl]PF6 at carbon ceramic electrode modified with nafion sol-gel composite: application to amperometric detection of l-cysteine

A two-step sol-gel technique was used here to prepare a carbon ceramic electrode modified with nafion and [Ru(bpy)(tpy)Cl]PF₆. This involves two steps: first, forming a bulk-modified carbon ceramic electrode with nafion, and then immersing the electrode into a Ru-complex solution (electroless deposition) for a short period of time (5-25 s). Cyclic voltammograms of the resulting surface-modified carbon ceramic electrode show stable and a well-defined redox couple due to Ru(II)/Ru(III) system with surface-confined characteristic. l-Cysteine (CySH) has been chosen as a model to elucidate the electrocatalytic ability of Ru-complex nafion sol-gel composite electrode. Not only the modified electrode shows excellent catalytic activity toward l-cysteine electrooxidation in pH range 3-9, but the antifouling effect of nafion film also increases the reproducibility of results in comparison with CCE modified with homogeneous mixing of graphite powder and Ru-complex (one step sol-gel method). Under the optimized conditions in amperometry method, the concentration calibration range, detection limit and sensitivity were 0.1-100 μM, 20 nM and 50 nA/μM, respectively. The advantages of this modified electrode are good reproducibility, excellent catalytic activity, simplicity of preparation and especially its antifouling properties towards l-cysteine and its oxidation products. Additionally, it is promising as a detector in flow system or chromatography systems.     

Simultaneous Investigation of the Laser Intensity and Magnetic Field Effects on Laser-Induced Plasma Spectroscopy

Journal of Russian Laser Research - In this paper, we use laser-induced breakdown spectroscopy (LIBS) to investigate the laser-induced copper plasma with and without an external magnetic field,...