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.     

Precise asymptotics in the deviation probability series of self-normalized sums

Let X,X₁,X₂,… be a sequence of nondegenerate i.i.d. random variables with zero means. Set Sn=X₁+?+Xn and . In the present paper we examine the precise asymptotic behavior for the general deviation probabilities of self-normalized sums, Sn/Wn. For positive functions g(x), ?(x), α(x) and κ(x), we obtain the precise asymptotics for the following deviation probabilities of self-normalized sums:

     

湍流中漫射目标偏振部分相干激光的闪烁特性

采用广义惠更斯-菲涅耳原理和矩阵光学理论,研究了湍流大气中偏振部分相干激光波束从发射机到目标和从目标到接收机双程路径的闪烁特性。将产生任意偏振光束的琼斯矩阵和ABCD传输矩阵进行结合,围绕接收机处波场四阶矩展开推导,得出双程路径下偏振部分相干激光波束在接收机处的闪烁指数表达式,数值分析了大气折射率结构常数、激光波束的波长、束宽、相干长度对接收机处光强闪烁指数的影响。结果表明:偏振部分相干激光波束的闪烁指数随着目标与发射机之间距离呈现先增大、到达峰值后逐渐减小的变化趋势;相干性差的光束产生的闪烁指数小,相干长度微小的变化将会产生较大的闪烁指数变化,相干性好的光束产生较大的闪烁指数,但是相干长度的变化对闪烁指数的影响很小。     

非负NOD随机变量序列的逆矩

仅在一阶矩有限的条件下获得了非负NOD随机变量序列正则和的逆矩的渐近逼近,特别得到了部分和的逆矩的渐近逼近.本文的结论推广了已有的结果.     

Quenched Fe moment in the collapsed tetragonal phase of Ca_(1-x)Pr_x Fe_2As_2

We report 75As NMR studies on single crystals of rare-earth doped iron pnictide superconductor Ca1-xPrxFe2As2 . In both cases of x = 0.075, 0.15, a large increase of νq upon cooling is consistent with the tetragonal-collapsed tetragonal structure transition. A sharp drop of the Knight shift is also seen just below the structure transition, which suggests the quenching of Fe local magnetism, and therefore offers important understanding of the collapsed tetragonal phase. At even low temperatures, the 1/75T1 is enhanced and forms a peak at T ≈ 25 K, which may be caused by the magnetic ordering of the Pr3+ moments or spin dynamics of mobile domain walls.     

Bonferroni-type inequalities; Chebyshev-type inequalities for the distributions on [0, n]

An elementary majorant-minorant method to construct the most stringent Bonferroni-type inequalities is presented. These are essentially Chebyshev-type inequalities for discrete probability distributions on the set {0, 1,..., n}, where n is the number of concerned events, and polynomials with specific properties on the set lead to the inequalities. All the known results are proved easily by this method. Further, the inequalities in terms of all the lower moments are completely solved by the method. As examples, the most stringent new inequalities of degrees three and four are obtained. Simpler expressions of Mrgritescu's inequality (1987, Stud. Cerc. Mat., 39, 246–251), improving Galambos' inequality, are given.     

NA序列部分和的完全收敛性

本文讨论了非平稳NA随机变量序列部分和的完全收敛性,获得了一般形式的完全收敛速度与矩条件之间的等价关系,其结果与独立情形一致,从而证实了NA序列与独立序列有着极为类似的完全收敛性．     

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.     

平面研磨中影响工件起动力矩的因素

本文针对平面研磨过程中工件运动的随机性，从理论上求出了在机床起动瞬间磨具作用于工件上的合力矩；探讨了影响这个力矩的主要因素，偏心距和工件几何尺寸的作用规律；为选择研磨参数提供一理论依据。     

Higher Harmonic Operations of Submillimeter Wave Gyrotrons (Gyrotron FU Series)

Higher harmonic operation of gyrotrons is necessary to obtain high frequencies. Some gyrotrons included in the Gyrotron FU series developed at Fukui University have achieved operation at the third and even fourth harmonics of the electron cyclotron frequency. The output lies in the millimeter to submillimeter wavelength range and the output powers are several watts to several tens of watts. In this paper, the gyrotrons and the conditions under which they operate are described in detail.