Some geometrical aspects of semidefinite linear complementarity problems

This article studies some geometrical aspects of the semidefinite linear complementarity problem (SDLCP), which can be viewed as a generalization of the well-known linear complementarity problem (LCP). SDLCP is a special case of a complementarity problem over a closed convex cone, where the cone considered is the closed convex cone of positive semidefinite matrices. It arises naturally in the unified formulation of a pair of primal-dual semidefinite programming problems. In this article, we introduce the notion of complementary cones in the semidefinite setting using the faces of the cone of positive semidefinite matrices and show that unlike complementary cones induced by an LCP, semidefinite complementary cones need not be closed. However, under R₀-property of the linear transformation, closedness of all the semidefinite complementary cones induced by L is ensured. We also introduce the notion of a principal subtransformation with respect to a face of the cone of positive semidefinite matrices and show that for a self-adjoint linear transformation, strict copositivity is equivalent to strict semimonotonicity of each principal subtransformation. Besides the above, various other solution properties of SDLCP will be interpreted and studied geometrically.     

Critical dynamics of the Potts model in several dimensionalities

We study critical dynamics of general q-state Potts models on d-dimensional hypercubic lattices. The master equation is formulated according to a theory recently presented by the author. A simple bond moving technique, followed by decimation, is used to obtain the dynamical exponents. Although this approximation yields poor results for the static exponents, the dynamic behaviour is closer to Monte Carlo simulations. We compare our results with those obtained with a different formulation of dynamics. A final discussion is included.     

Markarian 8星系的包层辐射

使用美国甚大天线阵(VLA).对Markarian 8星系进行了多频观测.多频VLA观测表明,Markarian 8星系有三个主要的射电子成份,它们浸在一个弥漫的星系包层中.包层的射电谱是陡的非热谱.本文根据VLA观测确定了包层的物理参量,并讨论了包层中相对论性电子的可能起因.本文估计了包层非热辐射所要求的超新星爆发率.     

Nickel peroxide: A more probable intermediate in the Ni(II)‐catalyzed decomposition of peroxomonosulfate

The Ni(II) ion catalyzed thermal decomposition of peroxomonosulfate (PMS) was studied in the pH range 3.42–5.89. The rate is first order in [PMS] and Ni(II) ion concentrations. At pH greater than or equal to 5.23, the reaction becomes zero order in [PMS] and this changeover in the order of the reaction occurs at a higher concentration of nickel ions. The first‐order kinetics in PMS can be explained as a rate‐limiting step and is the transformation of nickel peroxomonosulfate into nickel peroxide. This peroxide intermediate reacts rapidly with another PMS to give oxygen and Ni(II). The formation of nickel peroxide is associated with a small negative or nearly zero entropy of activation. The zero‐order kinetics in [PMS] can be explained by the fact that the hydrolysis of aquated nickel(II) ions into hydroxocompounds is the rate‐limiting step. The turnover number is 2 at pH 3.42 and increases with pH. © 2007 Wiley Periodicals, Inc. Int J Chem Kinet 39: 320–237, 2007     

Inner-sphere oxidation of iron(II) by tris(malonato)cobaltate(III)

The kinetics of oxidation of Fe²⁺ by [Co(C₃H₂O₄)₃]^3? in acidic solutions at 605 nm showed a simple first-order dependence in each reactant concentration. The second-order rate constant dependence on [H⁺] is in accordance with eqn (i) k₂ = k′₂ + k₃[H⁺] (i) where k′₂ and k₃ have values of 73.4 ± 14.0 M ^?1 s^?1 and 353 ± 41 M^?2 s^?1, respectively, at 1.0 M ionic strength (NaClO₄) and 25°C. At 310 nm the formation and decomposition of an intermediate, believed to be [FeC₃H₂O₄]⁺, was observed. The increase in the rate of oxidation with increasing [H⁺] was interpreted in terms of a “one-ended” dissociation mechanism which facilitates chelation of Fe₂₊ by the carbonyl oxygens of malonate in the transition state.     

Characteristics of thermoradiative destruction of BaS2O6·2H2O

Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 55, No. 4, pp. 613–618, October, 1991.     

Riemannian Hilbert submanifolds of nonpositive extrinsic curvature

We consider strongly parabolic, Hilbert submanifolds in Riemannian Hilbert manifolds. We prove that their properties are analogous to the known properties in the finite-dimensional case. The main geometric result consists of Theorem 3: a complete, Riemannian, Hilbert submanifold of nonpositive extrinsic curvature and finite codimension in a Hilbert sphere is a great sphere.Translated from Ukrainskii Geometricheskii Sbornik, No. 33, pp. 91–100, 1990.The author expresses his thanks to Professor A. A. Borisenko for posing the problem and guiding the work.