Long paths and cycles in random subgraphs of graphs with large minimum degree

For a given finite graph G of minimum degree at least k, let G_p be a random subgraph of G obtained by taking each edge independently with probability p. We prove that (i) if for a function that tends to infinity as k does, then G_p asymptotically almost surely contains a cycle (and thus a path) of length at least , and (ii) if , then G_p asymptotically almost surely contains a path of length at least k. Our theorems extend classical results on paths and cycles in the binomial random graph, obtained by taking G to be the complete graph on k + 1 vertices. © Wiley Periodicals, Inc. Random Struct. Alg., 46, 320–345, 2015     

The effect of uni-axial stretching on the roughness of microfiltration membranes

Atomic force microscopy (AFM) was used to characterize the surface morphology of uni-axially stretched and non-stretched microporous microfiltration (MF) membranes. The effect of stretching on the pore structure and bulk properties of MF membranes has been previously reported [J.A. Morehouse, L.S. Worrel, D.L. Taylor, D.R. Lloyd, B.D. Freeman, D.F. Lawler, The effect of uni-axial orientation on macroporous membrane structure, J. Porous Mater. 13 (2006) 63–75.]; this paper focuses solely on the use of AFM to characterize the surface of stretched and non-stretched MF membranes. A new way of representing surface roughness that may prove useful in relating roughness to performance in cross-flow applications is presented.     

Cs6Nb4Se22 and K12Nb6Se35.3: two new compounds containing the M4Q22 building block

The title compounds, namely hexacaesium tetraniobium docosaselenide and dodecapotassium hexaniobium pentatriacontaselenide, were formed from their respective alkali chalcogenide reactive flux and niobium metal. Both compounds fall into the larger family of solid‐state compounds that contain the M₂Q₁₁ building block (M = Nb, Ta; Q = Se, S), where the metal chalcogenide forms dimers of face‐shared pentagonal bipyramids. Cs₆Nb₄Se₂₂ contains two Nb₂Se₁₁ building blocks linked by an Se—Se bond to form isolated Nb₄Se₂₂ tetrameric building blocks surrounded by caesium ions. K₁₂Nb₆Se_35.3 contains similar Nb₄Se₂₂ tetramers that are linked by an Se—Se—Se unit to an Nb₂Se₁₁ dimer to form one‐dimensional anionic chains surrounded by potassium ions. Further crystallographic studies of K₁₂Nb₆Se_35.3 demonstrate a new M₂Se₁₂ building block because of disorder between an Se²⁻ site (85%) and an (Se—Se)²⁻ unit (15%). The subtle differences between the structures are discussed.     

Salting coefficients of fluorobenzoic acids

The Setschenow parameter and thermodynamic parameters of transfer of 2-, 3- and 4-fluorobenzoic acid from water to salt solution are reported. The data have been rationalized by considering the structure breaking effects of the ions of the salts, the localized hydrolysis model and the internal pressure theory.     

Boundary estimates for solutions to operators of p-Laplace type with lower order terms

In this paper we study the boundary behavior of solutions to equations of the form

∇⋅A(x,∇u)+B(x,∇u)=0,     

A reliable method to determine methylmercury and ethylmercury simultaneously in foods by gas chromatography with inductively coupled plasma mass spectrometry after enzymatic and acid digestion

A reliable and sensitive method for determination simultaneously of monomethylmercury (MeHg) and monoethylmercury (EtHg) in various types of foods by gas chromatography inductively coupled plasma mass spectrometry (GC-ICP/MS) was developed and validated. Samples were digested with pancreatin and then hydrochloric acid. MeHg and EtHg in the extract were derivatized in an aqueous buffer with sodium tetraphenylborate. After phase separation, the extract was directly transferred to analysis. The analyses were conducted by GC-ICP/MS with monopropylmercury chloride (PrHgCl) as surrogate standard. Concentrations of 254±5.1, 13.7±0.69 and 162±6.2 μg Hg kg(-1) (one standard deviation, n=3) were obtained for MeHg in NIST SRM 1947 (Superior Lake fish), SRM 1566b (oyster tissue) and NRC Tort-2 (lobster Hepatopancreas), respectively. These are in good agreement with the certified values of 233±10, 13.2±0.7 and 152±13 μg Hg kg(-1) (as 95% confidence interval), respectively. The method detection limits (3σ) for MeHg and EtHg are 0.3 μg Hg kg(-1). The method detection limit was estimated by using a 0.5 g of subsample, sufficiently low for the risk assessment of MeHg and EtHg in foods. The spiked recoveries of MeHg and EtHg in different food matrices were between 87 and 117% and the RSDs were less than 15%. When isotopic dilution mass spectrometry (IDMS) analysis was performed with a commercial available (201)Hg-enriched monomethylmercury (Me(201)Hg) solution as internal standard, concentrations of 244±13.4, 13.9±0.25 and 161±1.3 μg Hg kg(-1) were obtained for MeHg in NIST SRM 1947, SRM 1566b and NRC Tort-2, respectively. It shown clearly that IDMS analysis got improvement in precision and accuracy, however, EtHg cannot be analyze simultaneously and the cost of analysis is higher.