A globally convergent Newton method for solving strongly monotone variational inequalities

Variational inequality problems have been used to formulate and study equilibrium problems, which arise in many fields including economics, operations research and regional sciences. For solving variational inequality problems, various iterative methods such as projection methods and the nonlinear Jacobi method have been developed. These methods are convergent to a solution under certain conditions, but their rates of convergence are typically linear. In this paper we propose to modify the Newton method for variational inequality problems by using a certain differentiable merit function to determine a suitable step length. The purpose of introducing this merit function is to provide some measure of the discrepancy between the solution and the current iterate. It is then shown that, under the strong monotonicity assumption, the method is globally convergent and, under some additional assumptions, the rate of convergence is quadratic. Limited computational experience indicates the high efficiency of the proposed method.     

Primal-dual proximal point algorithm for linearly constrained convex programming problems

A primal-dual version of the proximal point algorithm is developed for linearly constrained convex programming problems. The algorithm is an iterative method to find a saddle point of the Lagrangian of the problem. At each iteration of the algorithm, we compute an approximate saddle point of the Lagrangian function augmented by quadratic proximal terms of both primal and dual variables. Specifically, we first minimize the function with respect to the primal variables and then approximately maximize the resulting function of the dual variables. The merit of this approach exists in the fact that the latter function is differentiable and the maximization of this function is subject to no constraints. We discuss convergence properties of the algorithm and report some numerical results for network flow problems with separable quadratic costs.     

Construction of self-assembled monolayer terminated with N-heterocyclic carbene-rhodium(I) complex moiety

Functionalization of self-assembled monolayer (SAM) of alkanethiolate with metal containing unit is one of the versatile methods to obtain functional surfaces such as heterogeneous catalysts. However, organic molecules that strongly bind to transition metals at SAM terminal are limited. Recently N-heterocyclic carbenes (NHCs) such as cyclic diaminocarbenes have emerged as strongly σ-donating ligands forming a robust bond with broad spectrum of transition metals. In the present study, for the purpose of establishment of a new robust basement for heterogeneous metal catalysts, a SAM of the alkanethiolate terminated with NHC-rhodium(I) complex moiety was prepared by utilizing a newly designed disulfide molecule bearing NHC-metal complex terminals. X-ray photoelectron spectroscopy (XPS) analysis and angle resolved XPS measurement revealed successful formation of the Rh-complex-terminated SAM on a gold substrate. Infrared reflection absorption spectroscopy (IRRAS) analysis suggested that the linker methylene chains connecting the rhodium complex moiety and the gold surface are in a loosely packed structure. This unique chemical species, NHC, would be a promising candidate as a basement for the construction of functional surface.     

Regioselective allylation reactions using crotyl Grignard reagent-CeCl3 systems

Regioselective allylation reactions using crotyl Grignard reagent-CeCl₃ systems are described. Regioselectivity depends on the lanthanide salts: α-product was predominantly produced with light rare earth elements such as La, Ce, Pr, Nd, whereas γ-product was formed when heavy rare earth elements were used.     

Spurious Shell Closures in the Relativistic Mean Field Model

Following a previous systematic theoretical study of the ground-state properties of over 7000 nuclei from the proton drip line to the neutron drip line in the relativistic mean field model [Prog. Theor. Phys. 113 （2005） 785], which is in fair agreement with existing experimental data, we observe a few spurious shell closures, i.e. proton shell closures at Z = 58 and Z = 92. These spurious shell closures are found to persist in all the effective forces of the relativistic mean field model, e.g. TMA, NL3, PKDD and DD-ME2.     

Catalytic property of Europium supported on alumina from its ammoniacal solution

Europium supported on alumina (Eu/Al₂O₃) was prepared by impregnation from an ammoniacal solution of the metal. The catalytic activity of Eu/Al₂O₃ for the isomerization of 2,3-dimethylbut-1-ene to 2,3-dimethylbut-2-ene was examined. Eu/Al₂O₃ showed the highest catalytic activity for the isomerization when heated under a vacuum at 523 K, the yield of 2,3-dimethylbut-2-ene in 20 min being 81.6% at 314 K. IR spectrum shows the presence of two kinds of Eu amides. The change of the IR spectra and the catalytic activities with evacuation temperature suggest that only one of the two Eu amides is catalytically active for this base-catalyzed isomerization.     

Electrical conducting and magnetic properties of (ethylenedithiotetrathiafulvalenothioquinone-1,3-diselenolemethide)2.FeBr4 (GaBr4) crystals with two different interlayer arrangements of donor molecules

Two donor molecules newly synthesized, dimethylthio- and ethylenedithio-tetrathiafulvalenothioquinone-1,3-diselenolemethides (1 and 2), were used to prepare their charge-transfer (CT) salts with a magnetic FeBr(4)(-) counteranion. For 1, a low electrical conducting 1:1 salt (1.FeBr(4)) was obtained, in which molecules of 1 are tightly dimerized in a one-dimensional (1D) stacking column. On the other hand, 2 gave a 2:1 salt (2(2).FeBr(4)) as two different kinds of plate crystals (I and II). Both I and II possess similar stacking structures of molecules of 2 in each 1D column with a half-cut pipelike structure along the c axis. However, for I, the stacking columns are aligned in the same direction along the a and b axes, while for II they are in the same direction along the a axis, but in the reverse direction along the b axis, resulting in the difference in the relative arrangement of molecules of 2 and FeBr(4)(-) ions between the two crystals. The room-temperature electrical conductivities of the single crystals of I and II were 13.6 and 12.7 S cm(-)(1), respectively. The electrical conducting behavior in I was metallic above 170 K but changed to be semiconducting with a very small activation energy of 7.0 meV in the temperature range 4-170 K. In contrast, II showed the semiconducting behavior in the whole temperature range 77-285 K. The corresponding nonmagnetic GaBr(4)(-) salts with almost the same crystal structure as I and II showed definitively different electrical conducting properties in the metal to semiconductor transition temperature in I as well as in the magnitude of activation energy in the semiconducting region of I and II. The interaction between the d spins of FeBr(4)(-) ions was weak and antiferromagnetic in both I and II, but the magnitude of the spin interaction was unexpectedly larger compared with that in the FeBr(4)(-) salt of the corresponding sulfur derivative of 2 with closer contact between the neighboring FeBr(4)(-) ions. These electrical conducting and magnetic results suggest a significant interaction between the conducting pi electrons and the d spins of FeBr(4)(-) ions located near the columns or layers.     

Secondary hypervalent I(III)...O interactions: synthesis and structure of hypervalent complexes of diphenyl-lambda3-iodanes with 18-crown-6

Reported here for the first time are the synthesis and characterization of supramolecular complexes between diaryl-lambda(3)-iodanes and 18-crown-6 (18C6). Slow evaporation of solvents afforded 1:1 and 2:1 complexes between Ph(2)IBF(4) and 18C6 as stable crystals, depending on the conditions. X-ray crystal structures of these complexes indicated that each iodine atom contacts with the three adjacent oxygen atoms of 18C6 through two hypervalent secondary bonding and a weak interaction. (1)H NMR analyses and CSI-MS spectra showed that, in dichloromethane solution, Ph(2)IBF(4) exclusively forms the 1:1 complex with 18C6 (binding constant K(a), 1.02 x 10(3) M(-)(1)). The binding constants decrease with the increased solvent donor ability (Gutmann's DN). Changing the heteroatom ligand from BF(4) to the less nucleophilic PF(6) and AsF(6) increased the binding constant by about six times. Substitution of an electron-withdrawing group onto the para position of Ph(2)IBF(4) tends to increase in the complex stability. A linear Hammett relationship (rho = 0.59) between log K(a) and sigma(p)(+) values of substituents indicates that the diaryl-lambda(3)-iodanes with electropositive iodine(III) interact more efficiently with 18C6. Decreased binding magnitude was measured with 15C5, dibenzo-18C6, dibenzo-21C7, and dibenzo-30C10.