New polyphenylene‐g‐polystyrene and polyphenylene‐g‐polystyrene/poly(ε‐caprolactone) copolymers by combined controlled polymerization and cross‐coupling processes

1,4‐Dibromo‐2‐(bromomethyl)benzene and 1,3‐dibromo‐5‐(bromomethyl)benzene were used as initiators in the atom transfer radical polymerization of styrene in conjunction with CuBr/2,2′‐bipyridine as a catalyst. The resulting polystyrene (PSt)‐based macromonomers, possessing at one end a 2,5‐dibromophenylene or 3,5‐dibromophenylene moiety, were used in combination with 2,5‐dihexylbenzene‐1,4‐diboronic acid for Suzuki coupling in the presence of Pd(PPh₃)₄ as a catalyst or with the system NiCl₂/2,2′‐bipyridine/triphenylphosphine/Zn for Yamamoto polymerization. Polyphenylenes (PPs) with PSt chains as substitution groups were obtained. The same macromonomers were used in Yamamoto copolycondensation reactions, in combination with a poly(ε‐caprolactone) (PCL) macromonomer, and this resulted in PPs with PSt/PCL side chains. The obtained PPs had good solubility properties in common organic solvents at room temperature similar to those of the starting macromonomers. The new polymers were characterized with ¹H (¹³C) NMR, IR, and gel permeation chromatography. The optical properties of the polymers were monitored with UV and fluorescence spectroscopy. The thermal behaviors of the macromonomers and final PPs were investigated with differential scanning calorimetry and compared. The morphology of PPs containing PSt and PCL blocks was characterized with atomic force microscopy, and a microphase‐separated layered morphology was observed. © 2005 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 43: 879–896, 2005     

Group VA effects on surfactant aggregation number and dye solubilization efficiency

The effects of changing the charge-bearing atom in the polar head of a surfactant ion on micelle size and dye solubilization efficiency were investigated. Replacement of nitrogen in decyltrimethylammonium bromide by phosphorus or arsenic increases the micellar aggregation number by at least 20% in 0.5 m NaBr solutions. The ability of the surfactants to solubilize the dye Orange-OT is only slightly affected by the substitution of phosphorus for nitrogen, but it is lowered appreciably by the substitution of arsenic.     

On exotic nuclear decay of223Ra by emission of14C nuclei

Earlier work of the authors is extended and various new radioactivity decay modes of heavy nuclei are predicted.     

(E)-3-(2-Alkyl-10H-phenothiazin-3-yl)-1-arylprop-2-en-1-ones: Preparative, IR, NMR and DFT study on their substituent-dependent reactivity in hydrazinolysis and sonication-assisted oxidation with copper(II)nitrate

A series of novel 3(5)-aryl/ferrocenyl-5(3)-phenothiazinylpyrazoles and pyrazolines were obtained by substituent-dependent regioselective condensation of the corresponding (E)-3-(2-alkyl-10H-phenothiazin-3-yl)-1-aryl/ferrocenylprop-2-en-1-one with hydrazine or methylhydrazine in acetic acid. The different propensity of the primary formed beta-hydrazino adducts to undergo competitive retro-Mannich reaction was interpreted in terms of tautomerisation equilibrium constants calculated by DFT using a solvent model. The regioselectivity of the cyclisation reactions with methylhydrazine and the substituent-dependent redox properties of pyrazolines were also rationalized by comparative DFT calculations performed for simplified model molecules. On the effect of ultrasound-promoted oxidation with copper(II)nitrate phenothiazine-containing pyrazolines, enones and oxo-compounds were selectively transformed into sulfoxides. Only one sulfoxide enone was partially converted into an oxirane derivative. The structure of the novel products was determined by IR and NMR spectroscopy including COSY, HSQC, HMBC and DNOE measurements.     

MHD mixed convection flow near the stagnation-point on a vertical permeable surface

The steady magnetohydrodynamic (MHD) mixed convection boundary layer flow of a viscous and electrically conducting fluid near the stagnation-point on a vertical permeable surface is investigated in this study. The velocity of the external flow and the temperature of the plate surface are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically by a finite-difference method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. It is found that dual solutions exist for both cases, and the range of the mixed convection parameter for which the solution exists increases with suction.     

Convergence rates for forward–backward dynamical systems associated with strongly monotone inclusions

We investigate the convergence rates of the trajectories generated by implicit first and second-order dynamical systems associated to the determination of the zeros of the sum of a maximally monotone operator and a monotone and Lipschitz continuous one in a real Hilbert space. We show that these trajectories strongly converge with exponential rate to a zero of the sum, provided the latter is strongly monotone. We derive from here convergence rates for the trajectories generated by dynamical systems associated to the minimization of the sum of a proper, convex and lower semicontinuous function with a smooth convex one provided the objective function fulfills a strong convexity assumption. In the particular case of minimizing a smooth and strongly convex function, we prove that its values converge along the trajectory to its minimum value with exponential rate, too.     

A Bound of the Finslerian Ricci Scalar

In the Riemannian as well as in the Finslerian geometry, certain conditions on the Ricci scalar or the Ricci tensor provide obstructions on the topology of the base manifold and so on the configuration of cut points by limitations of the injectivity radius, see the Bonnet–Myers theorem and its variants and generalizations. In this paper, we show that conversely, prescribing the injectivity radius of a Finsler manifold, some limitations of the Ricci scalar are obtained. Some consequences of the condition that the Ricci tensor is h-parallel with respect to the Chern–Rund connection are found. In addition, some classes of examples are provided.     

Gradient-type penalty method with inertial effects for solving constrained convex optimization problems with smooth data

We consider the problem of minimizing a smooth convex objective function subject to the set of minima of another differentiable convex function. In order to solve this problem, we propose an algorithm which combines the gradient method with a penalization technique. Moreover, we insert in our algorithm an inertial term, which is able to take advantage of the history of the iterates. We show weak convergence of the generated sequence of iterates to an optimal solution of the optimization problem, provided a condition expressed via the Fenchel conjugate of the constraint function is fulfilled. We also prove convergence for the objective function values to the optimal objective value. The convergence analysis carried out in this paper relies on the celebrated Opial Lemma and generalized Fejér monotonicity techniques. We illustrate the functionality of the method via a numerical experiment addressing image classification via support vector machines.     

Koszul incidence algebras, affine semigroups, and Stanley-Reisner ideals

We prove a theorem unifying three results from combinatorial homological and commutative algebra, characterizing the Koszul property for incidence algebras of posets and affine semigroup rings, and characterizing linear resolutions of squarefree monomial ideals. The characterization in the graded setting is via the Cohen-Macaulay property of certain posets or simplicial complexes, and in the more general nongraded setting, via the sequential Cohen-Macaulay property.