Polynomial identities of bicommutative algebras,Lie and Jordan elements

ABSTRACT

An algebra with identities a(bc)?=?b(ac), (ab)c?=?(ac)b is called bicommutative. We construct list of identities satisfied by commutator and anti-commutator products in a free bicommutative algebra. We give criterions for elements of a free bicommutative algebra to be Lie or Jordan.     

An Exact Order of Discrepancy of the Smolyak Grid and Some General Conclusions in the Theory of Numerical Integration

This paper examines the relationship between the degree of uniformity of distribution of grids, including Smolyak grids, with the intention of choosing weights to obtain efficient quadrature formulas.     

硫胺素-三维荧光法测定水中汞离子的研究

汞是一种具有显著积累效应和遗传毒性的重金属元素,对人体健康和生态环境危害极大。我国水环境中汞污染严重,开发快速、高效、经济的汞离子检测方法可以有效推动水环境中汞污染的源头治理。该研究创新性地提出利用硫胺素-三维荧光法来实现水环境中汞离子的检测。研究结果表明,硫胺素与汞离子发生氧化还原反应前后,其荧光峰的位置与数量发生了明显改变,可作为检测水中汞离子的特征性信号。此外,在利用该法检测水中汞离子时,硫胺素的浓度不宜过高,体系应保持碱性环境,反应温度与反应时间可由一级动力学模型来优化,以期降低检测成本,提高检测效率。在指定的检测条件（硫胺素浓度为10 μmol·L-1、pH为9.7、反应时间为120 min、温度为20 ℃）下,汞离子浓度的线性检测范围为4～15 μmol·L-1。硫胺素-三维荧光法与传统的水中汞离子的检测方法相比具有突出优势和良好的实际应用价值,可以有效助力水环境中汞污染的源头监管,极大提升环境执法效率。     

The boundary rigidity problem in the presence of a magnetic field

For a compact Riemannian manifold with boundary, endowed with a magnetic potential α, we consider the problem of restoring the metric g and the magnetic potential α from the values of the Mañé action potential between boundary points and the associated linearized problem. We study simple magnetic systems. In this case, knowledge of the Mañé action potential is equivalent to knowledge of the scattering relation on the boundary which maps a starting point and a direction of a magnetic geodesic into its end point and direction. This problem can only be solved up to an isometry and a gauge transformation of α.For the linearized problem, we show injectivity, up to the natural obstruction, under explicit bounds on the curvature and on α. We also show injectivity and stability for g and α in a generic class G including real analytic ones.For the nonlinear problem, we show rigidity for real analytic simple (g,α), rigidity for metrics in a given conformal class, and locally, near any (g,α)∈G. We also show that simple magnetic systems on two-dimensional manifolds are always rigid.     

Entropy Production in Thermostats II

We show that an arbitrary Anosov Gaussian thermostat close to equilibrium has positive entropy poduction unless the external field E has a global potential. The configuration space is allowed to have any dimension and magnetic forces are also allowed. We also show the following non-perturbative result. Suppose a Gaussian thermostat satisfies for every 2-plane σ, where K _w is the sectional curvature of the associated Weyl connection and is the orthogonal projection of E onto σ. Then the entropy production of any SRB measure is positive unless E has a global potential. A related non-perturbative result is also obtained for certain generalized thermostats on surfaces.     

The decays $\tau \rightarrow [\omega (782), \phi (1020)] K^{-} \nu_{\tau}$ in the extended NJL model

The European Physical Journal A - The nuclear optical model potential (OMP) is generally assumed to be independent of the orbital angular momentum, l , of the interacting nuclei. Nucleon-nucleus...     

Local boundary rigidity of a compact Riemannian manifold with curvature bounded above

This paper considers the boundary rigidity problem for a compact convex Riemannian manifold with boundary whose curvature satisfies a general upper bound condition. This includes all nonpositively curved manifolds and all sufficiently small convex domains on any given Riemannian manifold. It is shown that in the space of metrics on there is a -neighborhood of such that is the unique metric with the given boundary distance-function (i.e. the function that assigns to any pair of boundary points their distance -- as measured in ). More precisely, given any metric in this neighborhood with the same boundary distance function there is diffeomorphism which is the identity on such that . There is also a sharp volume comparison result for metrics in this neighborhood in terms of the boundary distance-function.