Positive integer solutions of the diophantine equation x 2 − L n xy + (−1) n y 2 = ±5 r

In this paper, we consider the equation x ²?L _n x y+(?1) ⁿ y ² = ±5 ^r and determine the values of n for which the equation has positive integer solutions x and y. Moreover, we give all positive integer solutions of the equation x ²?L _n x y+(?1) ⁿ y ² = ±5 ^r when the equation has positive integer solutions.     

Characterization of free,restricted, and entrapped water environments in poly(N‐isopropyl acrylamide) hydrogels via 1H HRMAS PFG NMR spectroscopy

Different water environments in poly(N‐isopropyl acrylamide) (PNIPAAm) hydrogels are identified and characterized using ¹H high resolution magic angle spinning (HRMAS) nuclear magnetic resonance (NMR). Local water environments corresponding to a “free” highly mobile species, along with waters showing restricted dynamics are resolved in these swollen hydro‐gels. For photo‐initiated polymerized PNIPAAm gels, an additional entrapped water species is observed. Spin–spin R₂ relaxation experiments support the argument of reduced mobility in the restricted and entrapped water species. By combining pulse field gradient techniques with HRMAS NMR it is possible to directly measure the self‐diffusion rate for these different water environments. The behavior of the heterogeneous water environments through the lower critical solution temperature transition is described. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1521–1527     

Extraction spectrophotometric determination of niobium in rocks with sulfochlorophenol S

After acid decomposition and potassium pyrosulfate fusion, niobium (1—26 ppm) is separated from interfering elements by extraction into methyl isobutyl ketone from 6 M H₂SO₄—2 M HF and back-extracted into water. The niobium—sulfochloro-phenol S complex is extracted into amyl alcohol.     

Characterizing NF and RO membrane surface heterogeneity using chemical force microscopy

Chemical force microscopy (CFM) was used to characterize the chemical heterogeneity of two commercially available nanofiltration and reverse osmosis membranes. CFM probes were modified with three different terminal functionalities: methyl (CH₃), carboxyl (COOH), and hydroxyl (OH). Chemically distinct information about the membrane surfaces was deduced based on differences in adhesion between the CFM probes and the membrane surfaces using both traditional atomic force microscopy (AFM) force measurements and spatially resolved friction images. Contact angle titration and streaming potential measurements provided general information about surface chemistry and potential, which largely complemented the CFM analyses, but could not match the accuracy of CFM on the atomic level. Using CFM it was found that both membranes were characterized as chemically heterogeneous. Specifically, membrane chemical heterogeneity became more significant as the scan size approached colloidal or micron-sized dimensions. In many instances, the chemically unique regions, contributing to the overall chemical heterogeneity of the membrane surface, were substantially different in chemistry (e.g., hydrophobicity) from that determined for the surface at large from contact angel and streaming potential analyses. Topographical and corresponding CFM images supports previous adhesion studies finding a correlation between surface roughness and the magnitude of adhesion measured with AFM. However, chemical specificity was also significant and in turn measurable with CFM. The implication of these findings for future membrane development is discussed.