有限重位移

It is shown in this paper that a weighted unilateral Shift T of multiplicity k (0n}₀^∞ converge, is unitarily equialent to a Toeplitz operator if and only if (1-|a_n|²)=(1-|a₀|²) (1-|a_n-k|²)(n>k) and |a₀|= |a₁|=…|a_k-1| where we assume ‖T‖=1.     

关于S.Axler的一个猜想的注记

In this note, we prove that a^p,q,a(0-1) is a self-con jugate spacl, so a^p ( =a^p,q,a) is self-conjugate, in other words, we prove that the conjecture of S. Axler istrue.     

二值回归模型中自变量误差的处理

In this paper the binary regression model, in which the response Y is binary, i.e. Y takes the value 0 or 1 only, is considered. The conditional probability P{Y=1|X=x} is assumed to be of the form G(a₀+a₁x), where x is the measurement of the factor, a= (a₀,a₁)′ is the vector of the unknown parameter being estimated and G(a) = (1+e^a)^-1. The measurement x is assu-med to be contaminated when the value of x is out of certain limit. M-estimation is employed to estimate the unknown a of the model. In this paper, the consistent M-estimation is proved to be asymptotically normal and the optimal M-equation is obtained. Finally, a computation method is introduced to solve the M-equation and to get the optimal solution.     

On a Supercongruence Conjecture of Z.-W. Sun

In this paper, the author partly proves a supercongruence conjectured by Z.-W.Sun in 2013. Let p be an odd prime and let a ∈ Z⁺. Then, if p ≡ 1 (mod 3),k=0 6p^a 2k k/16^k ≡ 3/p^a(modp²) is obtained, where is the Jacobi symbol.     

Landau定理中的一个新上界

设f(z)=a₀+a₁z+…是单位圆内不取0与1的全纯函数.著名的Landau定理断言:存在一个与f无关的常数C使得|a₁|≤2|a₀|{|log|a₀||+C}.曾有许多数学家致力于估计此常数C.最后在1980年前后,由赖万才、Hempel及Jenkins独立地给出C的精确值:C=Γ⁴(1/4)/4π².本文的主要目的是要建立一种新形式的上界估计式以表明上述结果仍可改进.本文证明了: |a₁|≤2|a₀|{|log|a₀||+C-M|a₀ⁿ+1|²},其中M是一个与f无关的正的常数,而n取值为-1或1,依照|a₀|>1或≤1而定.     

关于算子─（▽—ia）2＋Ⅴ的性质（Ⅰ）

In this paper,we consider Schrodinger forms (operators) with singular magnetic vectorpotentials ─(▽—ia）²+Ⅴ. We prove that when the negative part V_{_} of electric potentialV satisfies(?) in dependentof V and a=(a₁,a₂,…,a_N)∈L_loc²(R^N)^N, ─(▽—ia）²+Ⅴ has essential self-adjointextension F and it is the only self-adjoint realization of ─(▽—ia）²+Ⅴ. Moreover,We consider the continuity of (a,V) respect to a and V in the sense of strong resolvent.     

关于赋值环的单元群

Let K be a field, K^* be the multiplicative group of nonzero elements of K and S be a subgroup of K^*. In this paper we show that S is a group of units of a valuation ring of K if and only if S satisfies the following conditions:1.a∈S implies -a∈S;2. for any a∈K^*\S either a+S?S or a^-1+S?S. Additional properties cf such groups are included.     

Hermite—Fejér插值算子的平均收敛

本文讨论了以第二类多项式U_a(x)的零点为插值节点的Hermite-Fejér插值算子H_a(f,x)及若干非一致收敛的Hermite-Fejér型插值算子在区间[-1,1]上关于权函数(1-x²)^1/2的平均收敛问题.我们主要证得:当0[-1,1]都有(?),并给出了收敛阶.此外也指明，当p=3时，该式对某些连续函数未必成立.     

齐次乘子算子的交换子

记H^l={w∈C^∞(R^k\{0}):w是l次齐次函数),R^_(-a)(m)是Taylor级数余项算子的n重叠合:m=(m₁,…,m_n)∈Zⁿ,Z记非负整数的集,α∈(R^k)ⁿ,定义 其中a=(a₁,…,a_n),a_i,f∈(R^k), 主要结果如下: 1.证明了几个介于算子T_^R(-a)^{(m)_w(ξ)),(a,f})的类与多线性奇异积分算子的类之间的对等定理; 2.作为应用,算子及 的某些有界性结果被给出,其中Ω∈H⁰,|β|≤|m|,且,m_i≥1。     

强拟星函数的Fekete-Szeg?不等式

令T(β)表示β级强拟星函数类,f(z)=z+a₂z²+a₃z³+…∈T(β),对任意实参数μ,本文得到了|a₃-μa₂²|的准确上界.     

Hénon映射的奇怪吸引子和吸引域的结构

考虑Hnon映射T_a.b,对于正测度的参数集合,构造了T_a.b的拓扑可迁的奇怪吸引子Λ_a.b的一个捕捉区G,证明Λ_a.b=T_a.bⁿG,同时证明Λ_a.b的吸引域恰好就是那些边界包含在W^u(P)∪W^s(P)中的区域的并以及W^s(P),从而肯定地回答了Benedicks和Carleson关于奇怪吸引子的吸引域的猜测。     

关于一阶具分布型偏差变元微分方程的振动性

In this paper we study the oscillation of the retarded differential equation x′(t)+∫_a^bp(t,ξ)x[g(t,ξ)]dσ(ξ)=0 (b>a) (1)and the advanced differential equation x′(t)-∫_a^bp(t,ξ)x[g(t,ξ)]dσ(ξ)=0 (b>a) (2) We improved the main results of [1-4].     

紧Lie群上Fourier级数的Gauss-Weierstrass型平均的逼近性质

Let G be a compact, connected semisimple Lie group and f∈L¹(G) . De note by G_R^a(f,g) the Gauss-Weierstrass type means of Fourier series of f.     

论Szegǒ的定理

设f(z)=Z+a₂z²+…∈S.Szegǒ证明:S_n(z)=z+a₂z²+…+a_nzⁿ(n=2,3…)在|z|<1/4内单叶。ρ₀=1/4最好的,我们证明了更强的结果: 定理:若f(z)∈s.则s_n(z)(n=2,3…)在|z|<1/4内关于原点成星形。 当f∈S^*时为吴卓人所得。     

p-值星形函数的子类

Let M_n+p-1 denote the class of functions f(z) = 1/z^p+a₀/z^p-2+a₁/z^p-2+…+a_n+p-1zⁿ+…, regular and p-valent in the annulus 0<|z|<1 and satisfying Re((D^n+p f(z))/(D^n+p-1 f(z)))-2)<-(n+p-1)/(n+p),|z|<1,n>-p where D^n+p-1 f(z)=1/z^p((z^n+2p-1f(z))/(n+p-1)!)^(n+p-1).M_n+p?M_n+p-1 is proved. Since M₀ is the subclass of p-valent meromorphically starlike functions, all functions in Mn + p-1 are p-valent meromorphically star-like functions. Further the integrals of functions in M_n+p-1, are considered.     

关于加权位移的酉等价问题

In this paper, we study the unilateral weighted shift which is unitarily equivalent to a Toeplitz operator and prove a similar result to that in [ 1 ] without the hypothesis that the shift must be hyponormal. As a corollary, we show that if the weight sequence {a_n}_n=0^∞ of the shift is convergent, then 1-a_n²=(1-a₀²)ⁿ⁺¹ ?n≥0     

环Z/(2e)上本原序列最高权位的0,1分布

研究环Z/(2^e)上本原序列的最高权位序列a_e-1的0,1分布问题,给出了序列a_e-1在1个周期中0,1个数的比值的上下界,并显示出当e越大时,a_e-1的0,1个数的比值越接近1。     

类2的常数联络黎曼空间

A non-flat Riemannian space V_n is called Riemannian space with constant connection if its Christoffel symbols of the second kind are constant in some coordinate system {xⁱ}. Following G. Vranceanu [3], a Riemannian space V_n with constant connection is said to be of genus p, if the components of the fundamental tensor in the coordinate system {x^{i/sup>} can be written in the form g_ij=c_ijat_a(a=1,…,p) where c_ija are constant, and p is least.In this paper we prove the following}     

多体问题中惯量矩的演变

本文得到了多体问题中在(p,t)平面上允许区域与禁区之间的分歧曲线,其中p为“平方平均距离”(正比于惯量矩的平方根)。这说明了,例如对负能量系统在大于T/2的时间间隔内ρ不能保持小于α,其中α为广义半长轴,T为对应的周期,即T=2π(a³/μ)^1/2,μ为引力常数。     

关于鞅的两类空间

本文证明了鞅的空间_aK_Φ与_aL_Φ,它们是分别由Garsia与Herz定义的空间的Φ-推广,都等价于^aL^Φ(一个Orlicz型的空间),这里0...