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1.
得到离散时间正规鞅平方可积泛函空间L2(M)中广义计数算子Nh的5种表示:(1)量子Bernoulli噪声(quantum Bernoulli noises,QBN){?k,?k*;k0}的加权表示;(2)Nh的谱表示,广义计数算子Nhh-计数测度#h的值域为其点谱;(3)Nh的“对角化”表示,Nh可表示为L2(M)的标准正交基{Zσ;σΓ}所生成的一维对角化正交投影算子的加权极限;(4)广义Skorohod积分-广义随机梯度表示,Nh可表示为互共轭算子δh?h的复合算子;(5)对N上的任意非负函数h,可构造一列有界广义计数算子,Nh恰为该有界广义计数算子的强极限,当h可和时,Nh为该有界广义计数算子的一致极限。  相似文献   
2.
The study aims to explore the structural aspects of generic examples, to get better insight into what makes them potentially opaque for learners. We have analyzed 27 written arguments, for which student teachers (grades 1–10) were asked to use a generic example to prove a given statement in multiplication. Using Toulmin’s framework, we developed five categories of arguments based on their structure: examples, empirical arguments, leap arguments, embedded arguments, and other arguments. Also, we conclude that none of the student teachers provided arguments that we recognize as complete generic examples. The results bring us to a discussion about features of generic examples making them difficult to come to grips with, having implications for how teacher educators can support student teachers’ learning to prove. From this, we propose a definition of generic examples that attends to the criteria suggested in previous research, yet, emphasizing their structural nature.  相似文献   
3.
In this paper, we investigate local and global asymptotic stability of a positive equilibrium point of system of differential equations where t ≥ 0, the parameters r1, k1, α1, α2, r2, k2, and d1 are positive, and [t] denotes the integer part of t ∈ [0, ∞ ). x(t) and y(t) represent population density for related species. Sufficient conditions are obtained for the local and global stability of the positive equilibrium point of the corresponding difference system. We show through numerical simulations that periodic solutions arise through Neimark–Sacker bifurcation. Copyright © 2014 John Wiley & Sons, Ltd.  相似文献   
4.
This work deals with the convergence and stability of Runge–Kutta methods for systems of differential equation with piecewise continuous arguments x(t) = Px(t)+Qx([t+1∕2]) under two cases for coe?cient matrix. First, when P and Q are complex matrices, the su?cient condition under which the analytic solution is asymptotically stable is given. It is proven that the Runge–Kutta methods are convergent with order p. Moreover, the su?cient condition under which the analytical stability region is contained in the numerical stability region is obtained. Second, when P and Q are commutable Hermitian matrices, using the theory of characteristic, the necessary and su?cient conditions under which the analytic solution and the numerical solution are asymptotically stable are presented, respectively. Furthermore, whether the Runge–Kutta methods preserve the stability of analytic solution are investigated by the theory of Padé approximation and order star. To demonstrate the theoretical results, some numerical experiments are adopted.  相似文献   
5.
Herein, the spin dynamics for various magnetic configurations arranged on a Kagome lattice is investigated. Using a Holstein–Primakoff expansion of the isotropic Heisenberg Hamiltonian with multiple exchange parameters, the development and evolution of magnetic Dirac nodes with both anisotropy and magnetic field are examined. From the classical energies, the phase diagrams for the ferromagnetic (FM), antiferrimagnetic (AfM), and the 120°  phases are shown as functions of J1, J2, J3, and anisotropy. Furthermore, the production of bosonic Dirac and Weyl nodes in the spin-wave spectra is shown. Through frustration of the magnetic geometry, a connection to the asymmetric properties of the Kagome lattice and the various antiferromagnetic configurations is discerned. Most interesting is the 120°  phase, which does not have Dirac nodes when considering only J1 due to the formation of an analogous antiferromagnetic honeycomb lattice, but gains Dirac symmetry with next-nearest neighbor interactions. Additionally, the presence of flat modes that are characteristic of cluster excitations is shown. Further study of external frustrations from a magnetic field and anisotropy reveals a tunability of the exchange interactions and nodal points.  相似文献   
6.
In this paper, we deal with the strong convergence of numerical methods for stochastic differential equations with piecewise continuous arguments (SEPCAs) with at most polynomially growing drift coefficients and global Lipschitz continuous diffusion coefficients. An explicit and time-saving tamed Euler method is used to solve this type of SEPCAs. We show that the tamed Euler method is bounded in pth moment. And then the convergence of the tamed Euler method is proved. Moreover, the convergence order is one-half. Several numerical simulations are shown to verify the convergence of this method.  相似文献   
7.
In this work, we present some existence theorems of weighted pseudo almost periodic solutions for N-th order neutral differential equations with piecewise constant argument by means of weighted pseudo almost periodic solutions of relevant difference equations.  相似文献   
8.
分情形讨论递推数列求通项的问题,介绍相应的矩阵解法,并借助实例说明其应用。  相似文献   
9.
10.
Abstract

Radiation defects created by γ-irradiation of Co60 and fast neutrons in high purity p-Si (p = 5×103 to 4 × 104 Ω.cm) and n-Si (p = 4 × 102 to 5 × 103 Ω.cm) are investigated by measurements of Hall effect, resistivity and minority carrier lifetime. The oxygen concentration in the crystals is in the range of 5 × 1014 to 5 × 1015 cm?3.

It is shown that stable γ-defects at 300 °K are divacancies and complexes of vacancies with donor or acceptor impurities. Divacancies introduced by γ-irradiation are the secondary defects. They become predominant after ‘exhaustion’ of the dopant. When divacancies become the predominant defects the Fermi level occupies its boundary position Ev +0.39 eV in the gap. At low doses (Φ<1016 photons/cm2) vacancy-impurity complexes and at heavy doses (Φ>1017 photons/cm2) divacancies play the main role in the recombination process.

In neutron irradiation disordered regions are introduced and the level at Ev +0.35 eV is observed. The Fermi level in both n- and p-Si shifts to the middle of the gap. At the annealing of disordered regions in the interval 200 to 250 °C the level at Ev +0.27 eV appears and Fermi level occupies its boundary position at Ev +0.39 eV. This indicates that divacancies become the predominant defects which can be formed as secondary defects at the destruction of the disordered regions.  相似文献   
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