Syntheses, structures, spectroscopy, and chromotropism of new complexes arising from the reaction of nickel(II) nitrate with diphenyl(dipyrazolyl)methane

The complexes [(dpdpm)Ni(2-NO3)2] (1), [(dpdpm)Ni(2-NO3)(1-NO3)(CH3CN)] (2), [(dpdpm)2Ni(1-NO3)(H2O)]NO3 (3), and [(dpdpm)2Ni(H2O)2][NO3]2 (4) (dpdpm = diphenyl(dipyrazolyl)methane, Ph2C(C3N2H3)2), have been prepared and characterized by IR and UV-vis-NIR spectroscopy and X-ray diffraction studies. X-ray studies have confirmed that complexes 1-4 all adopt variously distorted octahedral structures in the solid state, the largest distortions arising from the small bite-angle of the bidentate nitrate ligand in 1 and 2. Magnetic moment measurements indicate that these solids are paramagnetic with two unpaired electrons. The solution 1H NMR data show that the paramagnetism is maintained in solution. Absorption spectra of 1-4 show three main bands in the region of 350-1000 nm representing spin allowed (d-d) transitions from the ground state 3A2g to the excited states 3T2g, 3T1g(3F), and 3T1g(3P). A weak shoulder was also detected at about 700-800 nm in most spectra, representing spin-forbidden transitions 3A2g 1Eg. A comparison of the crystal field parameters 10Dq and B for 1-4 to the corresponding values for related complexes indicated that these parameters are fairly insensitive to structural variations within this family of complexes. The 10Dq/B ratios show greater variations, but no clear correlations are apparent between 10Dq/B and such structural features as the nature of ligator atoms (N:O ratio), the bonding mode of the nitrate ligand, or the overall charge. Complexes 1 (green) and 2 (blue) interconvert as a function of temperature (solutions and solid samples), concentration of CH3CN (solutions), or CH3CN vapor pressure (solid samples).     

Controlled growth of standing Ag nanorod arrays on bare Si substrate using glancing angle deposition for self-cleaning applications

A facile approach to manipulate the hydrophobicity of surface by controlled growth of standing Ag nanorod arrays is presented. Instead of following the complicated conventional method of the template-assisted growth, the morphology or particularly average diameter and number density (nanorods cm^?2) of nanorods were controlled on bare Si substrate by simply varying the deposition rate during glancing angle deposition. The contact angle measurements showed that the evolution of Ag nanorods reduces the surface energy and makes an increment in the apparent water contact angle compared to the plain Ag thin film. The contact angle was found to increase for the Ag nanorod samples grown at lower deposition rates. Interestingly, the morphology of the nanorod arrays grown at very low deposition rate (1.2 Å?sec^?1) results in a self-cleaning superhydrophobic surface of contact angle about 157° and a small roll-off angle about 5°. The observed improvement in hydrophobicity with change in the morphology of nanorod arrays is explained as the effect of reduction in solid fraction within the framework of Cassie–Baxter model. These self-cleaning Ag nanorod arrays could have a significant impact in wide range of applications such as anti-icing coatings, sensors and solar panels.     

Uniform in bandwidth exact rates for a class of kernel estimators

Given an i.i.d sample (Y _i , Z _i ), taking values in \({\mathbb{R}^{d'}\times\mathbb{R}^d}\), we consider a collection Nadarya–Watson kernel estimators of the conditional expectations \({\mathbb{E}( <\,c_g(z),g(Y)>+d_g(z)\mid Z=z)}\), where z belongs to a compact set \({H\subset \mathbb{R}^d}\), g a Borel function on \({\mathbb{R}^{d'}}\) and c _g (·), d _g (·) are continuous functions on \({\mathbb{R}^d}\). Given two bandwidth sequences \({h_n<\mathfrak{h}_n}\) fulfilling mild conditions, we obtain an exact and explicit almost sure limit bounds for the deviations of these estimators around their expectations, uniformly in \({g\in\mathcal{G},\;z\in H}\) and \({h_n\le h\le \mathfrak{h}_n}\) under mild conditions on the density f _Z , the class \({\mathcal{G}}\), the kernel K and the functions c _g (·), d _g (·). We apply this result to prove that smoothed empirical likelihood can be used to build confidence intervals for conditional probabilities \({\mathbb{P}( Y\in C\mid Z=z)}\), that hold uniformly in \({z\in H,\; C\in \mathcal{C},\; h\in [h_n,\mathfrak{h}_n]}\). Here \({\mathcal{C}}\) is a Vapnik–Chervonenkis class of sets.     

Almost all triple systems with independent neighborhoods are semi-bipartite

The neighborhood of a pair of vertices u, v in a triple system is the set of vertices w such that uvw is an edge. A triple system H is semi-bipartite if its vertex set contains a vertex subset X such that every edge of H intersects X in exactly two points. It is easy to see that if H is semi-bipartite, then the neighborhood of every pair of vertices in H is an independent set. We show a partial converse of this statement by proving that almost all triple systems with vertex sets [n] and independent neighborhoods are semi-bipartite. Our result can be viewed as an extension of the Erd?s-Kleitman-Rothschild theorem to triple systems.The proof uses the Frankl-Rödl hypergraph regularity lemma, and stability theorems. Similar results have recently been proved for hypergraphs with various other local constraints.     

List coloring triangle‐free hypergraphs

A triangle in a hypergraph is a collection of distinct vertices u, v, w and distinct edges e, f, g with , and . Johansson [Tech. report (1996)] proved that every triangle‐free graph with maximum degree Δ has list chromatic number . Frieze and Mubayi (Electron J Comb 15 (2008), 27) proved that every linear (meaning that every two edges share at most one vertex) triangle‐free triple system with maximum degree Δ has chromatic number . The restriction to linear triple systems was crucial to their proof. We provide a common generalization of both these results for rank 3 hypergraphs (edges have size 2 or 3). Our result removes the linear restriction from 8 , while reducing to the (best possible) result [Johansson, Tech. report (1996)] for graphs. In addition, our result provides a positive answer to a restricted version of a question of Ajtai Erd?s, Komlós, and Szemerédi (combinatorica 1 (1981), 313–317) concerning sparse 3‐uniform hypergraphs. As an application, we prove that if is the collection of 3‐uniform triangles, then the Ramsey number satisfies for some positive constants a and b. The upper bound makes progress towards the recent conjecture of Kostochka, Mubayi, and Verstraëte (J Comb Theory Ser A 120 (2013), 1491–1507) that where C₃ is the linear triangle. © 2014 Wiley Periodicals, Inc. Random Struct. Alg., 47, 487–519, 2015     

Inertial Sensitivity of Porous Microstructures

Fluid flows through porous media are subject to different regimes, ranging from linear creeping flows to unsteady, chaotic turbulence. These different flow regimes at the pore scale have repercussions at larger scales, with the macroscale drag force experienced by a fluid moving through the medium becoming a nonlinear function of the average velocity beyond the creeping flow regime. Accurate prediction of the transition between different flow regimes is an important challenge with repercussions onto many engineering applications. Here, we are interested in the first deviation from Darcy’s law, when inertia effects become sizeable. Our goal is to define a Reynolds number, \(Re_{\mathrm{C}}\), so that the inertial deviation occurs when \(Re_{\mathrm{C}}\sim 1\) for any microstructure. The difficulty in doing so is to reduce the multiple length scales characterizing the geometry of the porous structure to a single length scale, \(\ell \). We analyze the problem using the method of volume averaging and identify a length scale in the form \(\ell =C_\lambda \sqrt{\nicefrac {K_\lambda }{\epsilon _\beta }}\), with \(C_\lambda \) a parameter that indicates the sensitivity of the microstructure to inertia. The main advantage of this definition is that an explicit formula for \(C_\lambda \) is given; \(C_\lambda \) is computed from a creeping flow simulation in the porous medium; and \(Re_{\mathrm{C}}\) can be used to predict the transition to a non-Darcian regime more accurately than by using Reynolds numbers based on alternative length scales. The theory is validated numerically with data from flow simulations for a variety of microstructures.     

Multiple vertex coverings by specified induced subgraphs

Given graphs H₁,…, H_k, let f(H₁,…, H_k) be the minimum order of a graph G such that for each i, the induced copies of H_i in G cover V(G). We prove constructively that f(H₁, H₂) ≤ 2(n(H₁) + n(H₂) − 2); equality holds when H₁ = H ₂ = K_n. We prove that f(H₁, K _n) = n + 2√δ(H₁)n + O(1) as n → ∞. We also determine f(K_{1, m −1}, K _n) exactly. © 2000 John Wiley & Sons, Inc. J Graph Theory 34: 180–190, 2000