RANDOM EDGE can be exponential on abstract cubes

We prove that RANDOM EDGE, the simplex algorithm that always chooses a random improving edge to proceed on, can take a mildly exponential number of steps in the model of abstract objective functions (introduced by Williamson Hoke [Completely unimodal numberings of a simple polytope, Discrete Appl. Math. 20 (1988) 69-81.] and by Kalai [A simple way to tell a simple polytope from its graph, J. Combin. Theory Ser. A 49(2) (1988) 381-383.] under different names). We define an abstract objective function on the n-dimensional cube for which the algorithm, started at a random vertex, needs at least exp(const·n^1/3) steps with high probability. The best previous lower bound was quadratic. So in order for RANDOM EDGE to succeed in polynomial time, geometry must help.     

Semigroups of matrices of intermediate growth

Finitely generated linear semigroups over a field K that have intermediate growth are considered. New classes of such semigroups are found and a conjecture on the equivalence of the subexponential growth of a finitely generated linear semigroup S and the nonexistence of free noncommutative subsemigroups in S, or equivalently the existence of a nontrivial identity satisfied in S, is stated. This ‘growth alternative’ conjecture is proved for linear semigroups of degree 2, 3 or 4. Certain results supporting the general conjecture are obtained. As the main tool, a new combinatorial property of groups is introduced and studied.     

A Penrose-like inequality for maximal asymptotically flat spin initial data sets

We prove a Penrose-like inequality for the mass of a large class of constant mean curvature (CMC) asymptotically flat n-dimensional spin manifolds which satisfy the dominant energy condition and have a future converging, or past converging compact and connected boundary of non-positive mean curvature and of positive Yamabe invariant. We prove that for every n ≥ 3 the mass is bounded from below by an expression involving the norm of the linear momentum, the volume of the boundary, dimensionless geometric constants and some normalized Sobolev ratio.     

正态分布下任意秩有限总体中的Minimax预测

对于任意秩有限总体,在二次损失下,有关文献已给出了线性可预测变量在齐次线性预测类中的唯一线性Minimax预测．本文在正态假设下,证明了这个线性Minimax预测也是线性可预测变量在一切预测类中的唯一Minimax预测．     

确定线性偏微分方程组可积系统的对合特征集方法

基于Ritt-Wu特征集方法和Riquier-Janet理论,给出一种将线性微分方程组化成简单标准形式的有效算法．该算法通过消去冗余和添加可积条件获得线性微分方程组的完全可积系统(有形式幂级数解)或不相容判定．该算法不仅适用于常系数的线性偏微分方程组,而且对于变系数(以函数为系数)仍然有效．作者还给出了完全可积系统判定定理及其严格证明．     

Algorithmic and explicit determination of the Lovász number for certain circulant graphs

We consider the problem of computing the Lovász theta function for circulant graphs C_n,J of degree four with n vertices and chord length J, 2?J?n. We present an algorithm that takes O(J) operations if J is an odd number, and O(n/J) operations if J is even. On the considered class of graphs our algorithm strongly outperforms the known algorithms for theta function computation. We also provide explicit formulas for the important special cases J=2 and J=3.     

Classical, phenomenological analysis of the kinetics of reactions at the gas-exposed surface of mixed ionic electronic conductors

The kinetics of reactions occurring at the gas-exposed surfaces of charged mixed ionic electronic conductors (MIECs) are examined from theoretical first principles. Analysis based on the classical electrochemical potential-transition state theory model reveals that the nature of the reactions is electrochemical in general. However, the influence of the surface potential on the reaction rate is opposite for adsorption and incorporation reactions. Two-dimensional finite volume models of an MIEC as working electrode in a half-cell configuration are presented. The results for a simple, two-step reduction process show that the effect of the surface potential on the rate of reactions is minimal for incorporation-limited reactions but more influential for adsorption-limited reactions. An erratum to this article is available at .     

Interaction of indigo carmine dye with silica modified with humic acids at solid/liquid interface

Two distinct humic acids, one extracted from Brazilian peat soil, HA_PS, and another one obtained from commercial source, HA_FL, were attachment onto silica gel modified with aminopropyltrimethoxysilane, producing two material named SiHA_PS and SiHA_FL, respectively. The ability of these materials in removing indigo carmine dye from aqueous solution was followed through series of adsorption isotherms adjusted to modified Langmuir equation. The maximum number of moles adsorbed gave 6.82 ± 0.12 × 10⁻⁴ and 2.15 ± 0.17 × 10⁻⁴ mol g⁻¹ for SiHA_PS and SiHA_FL, respectively. Same interactions were calorimetrically followed and the thermodynamic data showed endothermic enthalpic values: 12.31 ± 0.55 and 24.69 ± 1.05 kJ mol⁻¹ for SiHA_PS and SiHA_FL surfaces, respectively. Gibbs free energies for two adsorption processes of indigo carmine dye presented negative values, reflecting dye/surface interactions must be accompanied by an increased in entropy values, which are 65 ± 3 and 98 ± 5 J mol⁻¹ K⁻¹ for SiHA_PS and SiHA_FL materials, respectively. The adsorption processes for both materials were spontaneous in nature although they presented an endothermic enthalpy for the interaction, resulting in an entropically favored process.     

Inner bounds for the spectrum of quasinormal operators

A linear operator in a separable Hilbert space is called a quasinormal one if it is a sum of a normal operator and a compact one. In the paper, bounds for the spectrum of quasinormal operators are established. In addition, the lower estimate for the spectral radius is derived. Under some restrictions, that estimate improves the well-known results. Applications to integral operators and matrices are discussed. Our results are new even in the finite-dimensional case.