Tin-free intermolecular addition of primary alkyls to imines via the dimethylzinc-air radical process

[reaction: see text] A dimethylzinc-air initiator was applied to the generation of primary alkyl radicals from alkyl iodides. The addition of the generated primary alkyl radicals to N-tosylimines was accelerated by the action of boron trifluoride-diethyl etherate and copper(II) triflate to give the corresponding adducts in good yields after 2-3 h. Air oxygen was essential for the reaction to proceed, showing involvement of a radical process in the reaction.     

How many miles to βX? II — Approximations to βX versus cofinal types of sets of metrics

Kada, Tomoyasu and Yoshinobu proved that the Stone-?ech compactification of a locally compact separable metrizable space is approximated by the collection of d-many Smirnov compactifications, where d is the dominating number. By refining the proof of this result, we will show that the collection of compatible metrics on a locally compact separable metrizable space has the same cofinal type, in the sense of Tukey relation, as the set of functions from ω to ω with respect to eventually dominating order.     

Monatomic rarefied gas as a singular limit of polyatomic gas in extended thermodynamics

We show that, in the theory of extended thermodynamics, rarefied monatomic gases can be identified as a singular limit of rarefied polyatomic gases. Under naturally conditioned initial data we prove that the system of 14 field equations for polyatomic gases in the limit has the same solutions as those of the system of 13 field equations for monatomic gases where there exists no dynamic pressure. We study two illustrative examples in the process of the limit, that is, the linear waves and the shock waves in order to grasp the asymptotic behavior of the physical quantities, in particular, of the dynamic pressure.     

Effects of polyethylene spacer length in polymeric electrolytes on gelation of ionic liquids and ionogel properties

Polymer electrolytes containing N,N′-(trans-cyclohexane-1,4-diyl)dibenzamide linkages, polyethylene ((CH₂)_m, m = 2, 4, 10) spacers, and bis(trifluoromethanesulfonyl)amide (TFSA) or bis(fluorosulfonyl)amide (FSA) counteranions (polymer abbreviation: CDBAm•X; m = 2, 4, 10; X = TFSA, FSA) have been synthesized, adding to our previous report (m = 6). In addition, their ability to effect the gelation of six ionic liquids and the properties of the resulting ionogels have been examined. The polymers, except for CDBA10•TFSA, effect the gelation for all ionic liquids used in this study at fairly low concentrations (0.9–50 g/L). Ionogel ionic conductivity is not dependent on the spacer length, but does decrease slightly as increasing amounts of the gelatinizer are introduced. In contrast to ionic conductivity, the temperatures at which these ionogels transition into isotropic fluids is dependent on the spacer length; the gel composed of [EMI][FSA] and 100 g/L of CDBA6•FSA transforms at 120 °C, while the gel composed of [EMI][FSA] and 5 g/L of CDBA2•FSA does not transform into a sol even when temperatures become 155 °C. In brief, ionogel heat resistance can be improved by changing the spacer length of the polyelectrolyte. Finally, it has been determined using cyclic voltammetry that the potential window of the polyelectrolytes is particularly wide, ranging from −1.6 to 2.5 V. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2015 , 53, 249–255     

Strategic equivalence among hat puzzles of various protocols with many colors

We discuss puzzles of prisoners and hats with infinitely many prisoners and more than two hat colors. Assuming that the set of hat colors is equipped with a commutative group structure, we prove strategic equivalence among puzzles of several protocols with countably many prisoners.     

On the six-field model of fluids based on extended thermodynamics

We study the six-field model of fluids (ET6) derived from extended thermodynamics. The six fields are the mass density, the velocity, the temperature, and the dynamic pressure (nonequilibrium pressure). We present the basic system of field equations of ET6. And we elucidate its characteristic features through the studies of the singular limit from polyatomic to monatomic rarefied gases, of hydrodynamic fluctuation, and of a hard-sphere system. Open problems remained in ET6 at present are also pointed out.     

Ruthenium-catalyzed nitrogen-directed ortho CH borylation of aromatic imines with pinacolborane

An efficient ruthenium catalyst system for the direct ortho CH borylation of aromatic imines is described. The reaction of tert-butyl-1-arylmethanimines with pinacolborane in the presence of Ru(cod)(cot), followed by hydrolysis, to afford the ortho-formyl-substituted arylboronates. The borylation was achieved with complete mono-selectivity.     

Metallaphotoredox Difluoromethylation of Aryl Bromides

Herein, we report a convenient and broadly applicable strategy for the difluoromethylation of aryl bromides by metallaphotoredox catalysis. Bromodifluoromethane, a simple and commercially available alkyl halide, is harnessed as an effective source of difluoromethyl radical by silyl‐radical‐mediated halogen abstraction. The merger of this fluoroalkyl electrophile activation pathway with a dual nickel/photoredox catalytic platform enables the difluoromethylation of a diverse array of aryl and heteroaryl bromides under mild conditions. The utility of this procedure is showcased in the late‐stage functionalization of several drug analogues.     

Study of a random Heisenberg ferromagnet by the Molecular CPA method

The spin wave Green function of a random dilute Heisenberg ferromagnet is calculated by the Molecular CPA method for the bond model of the f.c.c. lattice. It is found that the ferromagnetic spin order atT=0 becomes unstable, if the concentration of the non-zero bondC _A decreases below the critical valueC _A ⁰ =0.1702, which is some-what larger than the percolation concentrationC _A ^P =0.125. In the regionC _A <C _A ⁰ , aδ function spectrum appears atE=0 corresponding to the free rotations of the total spins of the finite clusters. The peculiar structure of the spin wave state density near the critical concentration is analysed in detail and a speculation is made for the topological structure of the spin clusters.     

Ionic conduction in As2S3---Ag2S, GeS2---GeS---Ag2S and P2S5---Ag2S glasses

The glass-forming region in the system P---S---Ag was determined and density, thermal expansion, dc conductivity and the transport number of Ag ions were measured for P₂S₅---Ag₂S glasses found in the P---S---Ag system. The results for the transport number measurement show that P₂S₅---Ag₂S glasses are purely ionic conductors owing to the Ag ion migration, like most of the As₂S₃---Ag₂S and GeS₂---GeS---Ag₂S glasses reported previously. Glass structure and ionic conduction processes in As₂S₃---Ag₂S, GeS₂---GeS---Ag₂S and P₂S₅---Ag₂S glasses are discussed, based on their ionic conductivity and density data. The structural concept of -Ag₂S was applied to these glasses, which suggests that the Ag ions in the glasses are distributed in the available Ag ion sites in the non-conducting framework composed of both S anions and As, Ge or P cations. In each system the ionic conductivity increases linearly with increasing Ag⁺/total cation (%) in glass composition, the determining factor being the activation energy for ionic conduction alone. Thus, the activation energy in these glasses depends predominantly upon the molar ratio of Ag ions to total cation in the glass, irrespective of the kind of system. Small differences in the activation energy among the three systems can be interpreted as arising from differences in the field strength of As, Ge and P cations.