Efficient catalytic degradation of single and binary azo dyes by a novel triple nanocomposite of Mn3O4/Ag/SiO2

The strategy of structurally integrating noble metal and metal oxides is expected to offer exceptional opportunities toward emerging functions of all. We report the creation of an efficient hetero-structured nanocatalyst consisting of Mn₃O₄ core, SiO₂ shell impregnated with noble Ag nanoparticles. The triple nanocatalyst Mn₃O₄/Ag/SiO₂ was synthesized by using a facile three-step approach to disperse Ag nanoparticles between the surfaces of functionalized Mn₃O₄ and SiO₂. The physicochemical structural characterization was performed by XRD and FTIR. The surface morphologies were observed by SEM and TEM. The EDX measurements confirmed the composition of the composite. The nanocomposite has been used as a catalyst for the degradation of Direct blue 78 in the presence of sodium borohydride (NaBH₄). It has a drastic catalytic effect as compared to Mn₃O₄/Ag and Mn₃O₄. The rate constant of Direct blue 78 reduction followed the order: Mn₃O₄/Ag/SiO₂ (0.25166 min⁻¹) > Mn₃O₄/Ag (0.07971 min⁻¹) > Mn₃O₄ (0.00947 min⁻¹). The effects of different reaction conditions of the catalytic reaction have been determined. The catalytic activity of the as- synthesized nanocomposite was examined for the binary dyes system by incorporation of an additional dye (Sunset yellow). Its influence on the degradation rate and efficiency of Direct blue 78 was investigated. The nanocatalyst exhibited excellent catalytic activity towards the complete degradation of both the Direct blue 78 and Sunset yellow. The degradation percentage for these dyes reached 99.33 and 94.68%, respectively. The recovery and reusability of the Mn₃O₄/Ag/SiO₂ nanocomposite was studied in the reduction reaction of Direct blue 78. Five consecutive recovery reaction cycles were performed. They revealed high stability and constant efficiency of the catalyst for four cycles.     

Monometallic cyanide cluster fullerene YCN@C78: A theoretical prediction

Stimulated by the recent experimental success in production and characterization of YCN@C_s(6)‐C₈₂, the possibility of encapsulating YCN cluster in the C₇₈ fullerene has been performed using density functional theory. Six isomers of YCN@C₇₈ are considered based on six lowest energy C₇₈^2? isomers. The results reveal that YCN@D_3h(24109)‐C₇₈ and YCN@C_2v(24107)‐C₇₈, both of which satisfy the isolated‐pentagon rule, present excellent thermodynamic stability with very small energy differences. Moreover, the large HOMO‐LUMO gaps (1.55 and 1.47 eV for YCN@D_3h(24109)‐C₇₈ and YCN@C_2v(24107)‐C₇₈, respectively) indicate their high kinetic stabilities. Significantly, in both the structures, the encapsulated YCN cluster is triangular, similar to the cases of YCN@C_s(6)‐C₈₂ and TbCN@C₂(5)‐C₈₂. In addition, electronic absorption spectra, infrared spectra, and ¹³C nuclear magnetic resonance spectra of two stable structures have also been explored to further disclose the molecular structures and properties. © 2015 Wiley Periodicals, Inc.     

The 1‐2‐3‐Conjecture for Hypergraphs

A weighting of the edges of a hypergraph is called vertex‐coloring if the weighted degrees of the vertices yield a proper coloring of the graph, i.e. every edge contains at least two vertices with different weighted degrees. In this article, we show that such a weighting is possible from the weight set for all hypergraphs with maximum edge size and not containing edges solely consisting of identical vertices. The number is best possible for this statement.     

Neighbor Distinguishing Edge Colorings Via the Combinatorial Nullstellensatz Revisited

Consider a simple graph 783438c5d0e/jgt21852-math-0001.png"> and its proper edge coloring c with the elements of the set . We say that c is neighbor set distinguishing (or adjacent strong) if for every edge , the set of colors incident with u is distinct from the set of colors incident with v. Let us then consider a stronger requirement and suppose we wish to distinguishing adjacent vertices by sums of their incident colors. In both problems the challenging conjectures presume that such colorings exist for any graph G containing no isolated edges if only . We prove that in both problems is sufficient. The proof is based on the Combinatorial Nullstellensatz, applied in the “sum environment.” In fact the identical bound also holds if we use any set of k real numbers instead of as edge colors, and the same is true in list versions of the both concepts. In particular, we therefore obtain that lists of length ( in fact) are sufficient for planar graphs.     

Dimension gap under Sobolev mappings

We prove an essentially sharp estimate in terms of generalized Hausdorff measures for the images of boundaries of Hölder domains under continuous Sobolev mappings, satisfying suitable Orlicz–Sobolev conditions. This estimate marks a dimension gap, which was first observed in [2] for conformal mappings.     

First and second moments for self‐similar couplings and Wasserstein distances

We study aspects of the Wasserstein distance in the context of self‐similar measures. Computing this distance between two measures involves minimising certain moment integrals over the space of couplings, which are measures on the product space with the original measures as prescribed marginals. We focus our attention on self‐similar measures associated to equicontractive iterated function systems consisting of two maps on the unit interval and satisfying the open set condition. We are particularly interested in understanding the restricted family of self‐similar couplings and our main achievement is the explicit computation of the 1st and 2nd moment integrals for such couplings. We show that this family is enough to yield an explicit formula for the 1st Wasserstein distance and provide non‐trivial upper and lower bounds for the 2nd Wasserstein distance for these self‐similar measures.     

First total synthesis of prunustatin A

In this study, we achieved the first total synthesis of natural prunustatin A (1), a novel inhibitor of glucose-regulated protein 78 (GRP78) expression. A key feature included a 15-membered ring macrocyclization, which was successfully accomplished by employing Shiina macrolactonization using 2-methyl-6-nitrobenzoic anhydride (MNBA) and 4-dimethylaminopyridine (DMAP).     

A multi-frequency inverse source problem

This paper is concerned with an inverse source problem that determines the source from measurements of the radiated fields away at multiple frequencies. Rigorous stability estimates are established when the background medium is homogeneous. It is shown that the ill-posedness of the inverse problem decreases as the frequency increases. Under some regularity assumptions on the source function, it is further proven that by increasing the frequency, the logarithmic stability converts to a linear one for the inverse source problem.     

The graph and range singularity spectra of b-adic independent cascade functions

With the “iso-Hölder” sets of a function we naturally associate subsets of the graph and the range of the function. We compute the Hausdorff dimension of these subsets for a class of statistically self-similar multifractal functions, namely the b-adic independent cascade functions.     

Stabilities and Electronic Spectra for C78O2 Isomers

1 INTRODUCTION Functional derivatives of fullerenes have aroused chemists’ interest and monofunctional products are accompanied by difunctional derivatives[1～3]. Diede- rich[1] prepared and detected C70O2 by the FAB mass spectrum. Kalsbeck[2] synthesized C60On (n = 1～4) by electrochemical oxidation of C60. Wood[3] investi- gated photolysis of a crude fullerene mixture and obtained C60On (n = 2～5) and C70O2. Menon[4] stu- died the optimized structures and electronic proper- ties o…