Ferromagnetic Convection in a Heterogeneous Darcy Porous Medium Using a Local Thermal Non-equilibrium (LTNE) Model

The combined effects of vertical heterogeneity of permeability and local thermal non-equilibrium (LTNE) on the onset of ferromagnetic convection in a ferrofluid saturated Darcy porous medium in the presence of a uniform vertical magnetic field are investigated. A two-field model for temperature representing the solid and fluid phases separately is used. The eigenvalue problem is solved numerically using the Galerkin method for different forms of permeability heterogeneity function Γ(z) and their effect on the stability characteristics of the system has been analyzed in detail. It is observed that the general quadratic variation of Γ(z) with depth has more destabilizing effect on the system when compared to the homogeneous porous medium case. Besides, the influence of LTNE and magnetic parameters on the criterion for the onset of ferromagnetic convection is also assessed.     

Crystallographic studies and structural systematics of the C2c alkali metal metavanadates

Four compounds in the system (Li, Na)VO₃ were synthesized and their structures refined in the space group $\text{C2}\text{c}$. Site population analysis showed that their compositions are (Na_0.5Li_0.5)VO₃, (Na_0.62Li_0.38)VO₃, (Na_0.71Li_0.29)VO₃ and (Na_0.84Li_0.16)VO₃. All have the structure of LiVO₃ and α-NaVO₃ which are related to the $\text{C2}\text{c}$ silicate pyroxenes. Structural data of eight compounds in the system (K, Na, Li)VO₃ were compiled, and correlations were established by multiple regression analyses between the effective ionic radii r_M1 and r_M2 of the alkali metal ions and various structural parameters. The size of the M2 site and the relative displacement of the (VO₃)_∞ chains are found to depend primarily on r_M2 only. The size of the M1 site and the amount of chain rotation are affected by both r_M1 and r_M2. Changes in lattice parameters are related to the chain movements. The anomalous chain configuration of LiVO₃ is also discussed.     

Robust tensor train component analysis

Robust Principal Component Analysis plays a key role in various fields such as image and video processing, data mining, and hyperspectral data analysis. In this paper, we study the problem of robust tensor train (TT) principal component analysis from partial observations, which aims to decompose a given tensor into the low TT rank and sparse components. The decomposition of the proposed model is used to find the hidden factors and help alleviate the curse of dimensionality via a set of connected low-rank tensors. A relaxation model is to minimize a weighted combination of the sum of nuclear norms of unfolding matrices of core tensors and the tensor ${?}_1$ norm. A proximal alternating direction method of multipliers is developed to solve the resulting model. Furthermore, we show that any cluster point of the convergent subsequence is a Karush-Kuhn-Tucker point of the proposed model under some conditions. Extensive numerical examples on both synthetic data and real-world datasets are presented to demonstrate the effectiveness of the proposed approach.     

On Cauchy differences of all orders

Summary This paper deals with the problem of characterizing higher order Cauchy differences of mappings on groups and semigroups. Symmetric, first order Cauchy differencesf(x + y)–f(x)–f(y) for mapsf between groups were characterized by Jessen, Karpf, and Thorup [8] through the use of first partial Cauchy differences. Our results are similar and extend their result to higher order differences. Our results also extend those of Heuvers [6] for mappings between vector spaces over the rationals.     

Error Bounds of Constrained Quadratic Functions and Piecewise Affine Inequality Systems

We consider the error bounds for a piecewise affine inequality system and present a necessary and sufficient condition for this system to have an error bound, which generalizes the Hoffman result. Moreover, we study the error bounds of the system determined by a quadratic function and an abstract constraint.     

Monotonic Solutions of a Functional Equation Arising from Simultaneous Utility Representations

The functional equation ?(h(x)) ? ?(h(y)) + ?(y) = ?(h(x ? y) + y) was solved by Aczél, Luce and Marley on the assumption that the functions are different iable. They posed the question of its strictly monotonic continuous solutions. The problem is solved using a uniqueness theorem. The continuity assumption on the functions is removed and the equation is also solved on a restricted domain.     

Experimental evidence of highly energy relaxed products in the 35 MeV/u84Kr+197Au reaction

The Q_β-values of⁹⁹Rb,^99,100Sr and¹⁰⁰Y have been measured for the first time at the mass separator OSTIS of the ILL; for⁹⁹Y,^99,100Zr and¹⁰⁰Nb, the results of earlier experiments were confirmed with reduced experimental errors. The two-neutron binding energies derived from the experimental Q_β-values clearly indicate that the nuclei¹⁰⁰Sr and¹⁰⁰Y are strongly deformed.     

Error Bounds of Regularized Gap Functions for Nonsmooth Variational Inequality Problems

We study the Clarke–Rockafellar directional derivatives of the regularized gap functions (and of some modified ones) for the variational inequality problem (VIP) defined by a locally Lipschitz but not necessarily differentiable function on a closed convex set in an Euclidean space. As applications we show that, under the strong monotonicity assumption, the regularized gap functions have fractional exponent error bounds and consequently that the sequences provided by an algorithm of Armijo type converge to the solution of the (VIP). The research of this author was supported by an Earmarked Grant from the Research Council of Hong Kong.