电感耦合等离子体质谱(ICP-MS)法测定离子吸附型稀土矿中的浸出稀土元素

对浙江某地大量的离子吸附型稀土样品进行了稀土元素(Y,La,Ce,Pr,Nd,Sm,Eu,Gd,Tb,Dy,Ho,Er,Tm,Yb,Lu)的浸提和测定实验,实验对比了氯化铵和硫酸铵溶液对矿石中稀土元素的浸出性能,选择了杂质浸出较少的硫酸铵溶液作为浸出剂,对不同稀土含量的吸附型稀土矿进行了实验,浸出方法稳定,符合工业开采要求。实验了电感耦合等离子体质谱法测定浸出液中稀土元素分量的方法,浸出液经大比例稀释并酸化后测定,精密度较好,能满足离子吸附型稀土矿评价的质量要求,方法检出限(6σ)0.005~0.26μg/g,单元素测定精密度(n=6,RSD≤6.0%),浸出稀土元素总量测定RSD≤4.0%。实际样品的实验及测定结果满意。     

Exploring students' mathematical performance,metacognitive experiences and skills in relation to fundamental theorem of calculus

Several studies have explored students’ understanding of the relationships between definite integrals and areas under curve(s). So far, however, there has been less attention to students’ understanding of the Fundamental Theorem of Calculus (FTC). In addition, students’ metacognitive experiences and skills whilst solving FTC questions have not previously been explored. This paper explored students’ mathematical performance, metacognitive experiences and metacognitive skills in relation to FTC questions by interviewing nine university and eight Year 13 students. The findings show that several students had difficulty solving questions related to the FTC and that students’ metacognitive experiences and skills could be further developed.     

On Cartan's theorem for linear operators

In this paper, we describe a second main theorem of holomorphic curves in , of hyper‐order strictly less than 1, that involves a general linear operator . As an application, we derive a truncated second main theorem of degenerate holomorphic curves of hyper‐order strictly less than 1 using Nochka weights.     

Some gradient estimates and Harnack inequalities for nonlinear parabolic equations on Riemannian manifolds

In this paper, by the method of J. F. Li and X. J. Xu (Differential Harnack inequalities on Riemannian manifolds I: Linear heat equation, Adv. in Math., 226 (2011), 4456–4491 ), we shall consider the nonlinear parabolic equation on Riemannian manifolds with , . First of all, we shall derive the corresponding Li–Xu type gradient estimates of the positive solutions for . As applications, we deduce Liouville type theorem and Harnack inequality for some special cases. Besides, when , our results are different from Li and Yau's results. We also extend the results of J. F. Li and X. J. Xu, and the results of Y. Yang.     

A fresh approach to the Paley–Wiener theorem for Mellin transforms and the Mellin–Hardy spaces

Here we give a new approach to the Paley–Wiener theorem in a Mellin analysis setting which avoids the use of the Riemann surface of the logarithm and analytical branches and is based on new concepts of polar‐analytic function in the Mellin setting and Mellin–Bernstein spaces. A notion of Hardy spaces in the Mellin setting is also given along with applications to exponential sampling formulas of optical physics.     

Candidates for nonzero Betti numbers of monomial ideals

Let I be a monomial ideal in the polynomial ring S generated by elements of degree at most d. In this paper, it is shown that, if the i-th syzygy of I has no elements of degrees j,…,j+(d?1) (where j≥i+d), then (i+1)-th syzygy of I does not have any element of degree j+d. Then we give several applications of this result, including an alternative proof for Green–Lazarsfeld index of the edge ideals of graphs as well as an alternative proof for Fröberg’s theorem on classification of square-free monomial ideals generated in degree 2 with linear resolution. Among all, we deduce a partial result on subadditivity of the syzygies for monomial ideals.     

Clifford theory for infinite dimensional modules

Clifford theory of possibly infinite dimensional modules is studied.     

On eight-dimensional unital division algebras over finite fields

The purpose of this paper is to investigate the eight-dimensional non-associative unital division algebras {0}≠A over finite fields, admitting elementary abelian 2-group of automorphisms E≤Aut(A), of order 8, using tools from algebraic geometry.     

A summation‐integral type modification of Szász–Mirakjan operators

In this paper, we introduced a summation‐integral type modification of Szász–Mirakjan operators. Calculation of moments, density in some space, a direct result and a Voronvskaja‐type result, are obtained. Copyright © 2016 John Wiley & Sons, Ltd.