纳米MOSFET迁移率解析模型

从玻尔兹曼方程出发，重新计算了纳米MOSFET沟道内的载流子所服从的分布函数，特别是考虑了纳米MOSFET横向电场和纵向电场之间的相互作用，并且以得到的非平衡状态下的分布函数为基础，考虑载流子寿命和速度的统计分布，给出了纳米MOSFET载流子迁移率的解析表达式.通过与数值模拟结果进行比较和分析，该迁移率解析模型形式简洁、物理概念清晰，且具有相当精度. 关键词： 玻尔兹曼方程 纳米MOSFET 迁移率 沟道有效电场     

On completely irreducible operators

Let T be a bounded linear operator on Hilbert space H, M an invariant subspace of T. If there exists another invariant subspace N of T such that H = M + N and M ∩ N = 0, then M is said to be a completely reduced subspace of T. If T has a nontrivial completely reduced subspace, then T is said to be completely reducible; otherwise T is said to be completely irreducible. In the present paper we briefly sum up works on completely irreducible operators that have been done by the Functional Analysis Seminar of Jilin University in the past ten years and more. The paper contains four sections. In section 1 the background of completely irreducible operators is given in detail. Section 2 shows which operator in some well-known classes of operators, for example, weighted shifts, Toeplitz operators, etc., is completely irreducible. In section 3 it is proved that every bounded linear operator on the Hilbert space can be approximated by the finite direct sum of completely irreducible operators. It is clear that a completely irreducible operator is a rather suitable analogue of Jordan blocks in L(H), the set of all bounded linear operators on Hilbert space H. In section 4 several questions concerning completely irreducible operators are discussed and it is shown that some properties of completely irreducible operators are different from properties of unicellular operators. __________ Translated from Acta Sci. Nat. Univ. Jilin, 1992, (4): 20–29     

离子交换富集-导数火焰原子吸收法测定自来水中Cu,Fe和Zn

本文研究了用 2 0 1× 7阳离子交换树脂对自来水中的微量元素进行交换富集 ,采用微量脉冲进样 导数火焰原子吸收法测定富集后溶液中的Cu ,Fe和Zn ,该方法灵敏度分别为 0 2 9,0 5 9和 0 0 6 μg·L- 1 ,精密度分别为 4 2 8% ,1 95 %和 2 2 8% ,检测限分别为 1 2 8,5 85和 0 6 8μg·L- 1 ,回收率分别为 91 13% ,10 1 34%和99 84 % ,本方法大大减少了需样量 ,简便快速 ,灵敏度高。     

Kolmogorov Width of Classes of Smooth Functions on the Sphere

Let ^d−1{(x₁,…,x_d) ^d:x²₁+···+x²_d=1} be the unit sphere of the d-dimensional Euclidean space ^d. For r>0, we denote by B^r_p (1p∞) the class of functions f on ^d−1 representable in the formwhere dσ(y) denotes the usual Lebesgue measure on ^d−1, and P^λ_k(t) is the ultraspherical polynomial.For 1p,q∞, the Kolmogorov N-width of B^r_p in L^q( ^d−1) is given bythe left-most infimum being taken over all N-dimensional subspaces X_N of L^q( ^d−1).The main result in this paper is that for r2(d−1)²,where A_NB_N means that there exists a positive constant C, independent of N, such that C⁻¹A_NB_NCA_N.This extends the well-known Kashin theorem on the asymptotic order of the Kolmogorov widths of the Sobolev class of the periodic functions.     

Two-dimensional Anhydrous Cadmium(II) Phthalate

The in situ hydrolysis of phthalyl-γ-glutaminyl-histidine with Cd(ClO₄)₂·6H₂O in the presence of water and methanol affords a novel two-dimensional cadmium coordination polymer, a new phase, anhydrous cadmium(II) phthalate, ( 1 ). The structure was determined by single crystal X-ray diffraction. Crystal data: P2₁/c, a = 13.8168(14), b = 7.0351(7), c = 8.2054(8) Å, β = 105.540(2)°, V = 768.43(13) ų, Z = 4, R₁ = 0.0380, wR₂ = 0.1111.     

Elektrische und thermische Eigenschaften von Salzlösungen

Ohne Zusammenfassung     

Singlet-Triplet Transition in Quantum Dots Confined by Triangular and Bowl-Like Potentials： the Effect of Electric Fields

We theoretically investigate the energy spectra of two-electron two-dimensional （2e 2D） quantum dots （QDs） confined by triangular potentials and bowl-like potentials in a magnetic field by exact diagonalization in the framework of effective mass theory. An in-plane electric field is found to contribute to the singlet-triplet transition of the ground state of the 2e 2D QDs confined by triangular or bowl-like potentials in a perpendicular magnetic field. The stronger the in-plane electric field, the smaller the magnetic field for the total spin of the ground states in the dot systems to change from S = 0 to S = 1. However, the influence of an in-plane electric field on the singlettriplet transition of the ground state of two electrons in a triangular QD modulated by a perpendicular magnetic field is quite small because the triangular potential just deviates from the harmonic potential well slightly. We find that the strength of the perpendicular magnetic field needed for the spin singlet-triplet transition of the ground state of the QD confined by a bowl-like potential is reduced drastically by applying an in-plane electric field.     

Patterns—a fundamental idea of mathematical thinking and learning

Taking advantage of patterns is typical of our everyday experience as well as our mathematical thinking and learning. For example a working day or a morning at school displays a certain structure, which can be described in terms of patterns. On the one hand regular structures give us the feeling of permanence and enable us to make predictions. On the other hand they also provide a chance to be creative and to vary common procedures. School students usually encounter patterns in math classes either as number patterns or geometric patterns. There are also patterns that teachers can find in analyzing the errors students make during their calculations (error patterns) as well as patterns that are inherent to mathematical problems. One could even go so far as to say that identifying and describing patterns is elementary for mathematics (cf. Devlin 2003). Practising good interacting with patterns supports not only the active learning of mathematics but also a deeper understanding of the world in general. Patterns can be explored, identified, extended, reproduced, compared, varied, represented, described and created. This paper provides some examples of pattern utilization and detailed analyses thereof. These ideas serve as “hooks” to encourage the good use of patterns to facilitate active learning processes in mathematics.