商高确实证明了勾股定理——兼论这里的“矩”不宜理解为长方形

严格遵守"矩"是古代中国的测量仪器,"矩"在古文字中的含义为"矩线",或为"磬折形",将"矩"理解为长方形(包含正方形)是不可取的.商高确实证明了一般勾股定理.古证应该是最原始、最简单的.     

Complete q-Moment Convergence of Moving Average Processes under ψ-mixing Assumption

In this paper,we study the complete q-moment convergence of moving average processes under ψ-mixing assumption.The results obtained not only extend some previous known results,but also improve them.     

Theoretical study with vibration–rotation and dipole moment calculations of quartet states of the CrCl molecule

The potential energy curves have been investigated for the 10 lowest quartet electronic states in the ^2s+1Λ^± representation below 30,000 cm^?1 of the molecule CrCl via CASSCF and MRCI (singly and doubly excitation with Davidson correction) calculations. The harmonic frequency ω_e, the internuclear distance r_e, the rotational constant B_e, the electronic energy with respect to the ground state T_e, and the permanent dipole moment μ have been calculated. By using the canonical functions approach, the eigenvalues E_v, the rotational constant B_v, and the abscissas of the turning points r_min and r_max have been calculated for the considered electronic states up to the vibrational level v = 19. Seven electronic states have been studied here theoretically for the first time. The comparison of these values to the theoretical results available in the literature shows a good agreement. © 2010 Wiley Periodicals, Inc. Int J Quantum Chem, 2011     

Cluster tilting for higher Auslander algebras

The concept of cluster tilting gives a higher analogue of classical Auslander correspondence between representation-finite algebras and Auslander algebras. The n-Auslander–Reiten translation functor τn plays an important role in the study of n-cluster tilting subcategories. We study the category Mn of preinjective-like modules obtained by applying τn to injective modules repeatedly. We call a finite-dimensional algebra Λ n-complete if for an n-cluster tilting object M. Our main result asserts that the endomorphism algebra EndΛ(M) is (n+1)-complete. This gives an inductive construction of n-complete algebras. For example, any representation-finite hereditary algebra Λ(1) is 1-complete. Hence the Auslander algebra Λ(2) of Λ(1) is 2-complete. Moreover, for any n?1, we have an n-complete algebra Λ(n) which has an n-cluster tilting object M(n) such that Λ(n+1)=EndΛ(n)(M(n)). We give the presentation of Λ(n) by a quiver with relations. We apply our results to construct n-cluster tilting subcategories of derived categories of n-complete algebras.     

广义Pareto模型统计推断及其应用

广义Pareto分布能很好地拟合数据分布的尾部,广泛地应用于金融市场的风险管理、风险经营问题的研究。利用概率加权矩法得到了三参数广义Pareto模型的参数估计式,给出了阈值的选取方法和风险值的计算公式;利用计算机模拟,计算得出了KS检验统计量的临界值。     

随机利息力下的一类年金的时间价值

对于年金的时间价值的研究,往往假定利率在整个期间内是固定不变的,但事实上,由于受到多种因素的影响,利率通常具有不确定性.因此,本文采用可逆MA(1)模型对随机利息力进行建模,在此基础上,研究了期末付虹式年金和期末付平顶虹式年金的时间价值问题,给出了上述两种形式年金现值的期望和方差的递推公式.通过数值仿真分析了相关参数对...     

随机变量数学期望的一个注记

介绍一种计算随机变量数学期望的方法,利用这种方法容易得到数学期望的相关性质,很多概率与矩的不等式证明也因之变得更为简洁.     

Quasi-hereditary covers of higher zigzag algebras of type A

In this paper we define and study some quasi-hereditary covers for higher zigzag algebras of type A. We show how these algebras satisfy three different Koszul properties: they are Koszul in the classical sense, standard Koszul and Koszul with respect to the standard module Δ, according to the definition given in [24]. This last property gives rise to a well defined duality and we compute the Δ-Koszul dual as the path algebra of a quiver with relations.     

CASPT2 and CCSD(T) calculations of dipole moments and polarizabilities of acetone in excited states

The acetone molecule is investigated in its ground state and valence ^1,3n-π*, ^1,3π-π*, and ^1,3σ-π* excited states and Rydberg ^1,3n-3s, ^1,3π-3?, ^1,3n-3p_y and ^1,3π-3p_y states using the CASSCF, CASPT2, and CCSD(T) methods. Equilibrium geometries of excited states are obtained and their changes with respect to the ground state are discussed. For most excited states the C_2v symmetry of the ground state is lowered to the C_s symmetry. A series of valence vertical and adiabatic excitation energies is presented along with excitation energies for Rydberg states. The main body of the paper contains Finite-Field Perturbation Theory (FFPT) calculations of electric properties of the vertically as well as geometry relaxed excited states. Dipole moments of valence excited states decrease significantly upon excitation, being about one half of the ground state dipole moment. Polarizabilities usually change upon excitation much less (increase by about 30%) but hyperpolarizabilities are enhanced up to one or two orders of magnitude. The orientation of the dipole moment is reversed in some vertically excited Rydberg states. Properties of the ground and excited states are discussed considering alterations of the electronic structure and shifts in the geometry.