全聚点集与(?)α-紧性

In this paper we introduce the concept for the set of complete cluster point and (?)_α-cormpactness in the metric space. We have proved several primitive properties relatedto the complete cluster point and set of complete cluster point. We have discussed the relationship among some kinds of (?)_α-compactness; and analysed the relationship among the (?)_α-compactness and the general compactness. We have found that the (?)_α-compactness and the general compactness are eqivalent to each other in the metric space.     

The Spaces ∧_αof Lipschitz Continuous Functions on Complete Riemannian Manifold with Nonnegative Curvature

We consider the spaces∧_αof Lipschitz continuous functions on completeRiemannian manifold with nonnegative Ricci curvature.We first give a characeriza-tion of f∈∧_αin terms of its Poisson integral u(x,t),then we show that the BesselPotential J_βmaPPs∧_αisomorphically onto∧_(α+β).     

按有理函数系展开函数成Fourier级数

In this paper we give some orthogonal system of rational functions on the unit circumference; We obtained the Riemann Lemma and some tests of convergence of Fourier series for this orthogonal system with the poles {α_k}₀^∞ satisfying some conditions, The conditions we obtained are weaker than those established in [2].     

具有负系数的单叶函数的推广

Let R_A,B(α,β,q) denote the class of functions f(z) = z(?) which are analytic and nnivalent in < 1, and satisfy the condition. Also let R_A,B(α,β,q,t) denote the class of functions (1 - t)z + tf(z), where f(z) ∈R_A,B(α,β, q) and t ∈(0, 1].Sharp results concerning representation, distortion theorems and radius of convexityfor the class R_A,B(α,β, q, t) are determined. It is shown that the class R_A,B(α,β,q, t)is closed under linear combinations. Furthermore extreme points and support points forthe class R_A,B(α,β,q, t) are also determined.     

关于组合合成阵

We define the r^th combinatorial compound C_r^*(A) of a matrix A, which can be viewed as the characteristic function of the subset of the rxr submatrices of A which are combinatorially nonsingular. We prove that for 1≤rr^*(A)is. We determine the minimum number of 2×2 and 3×3 combinatorially nonsingular submatrices over all n×n fully indecomposable matrices and make a jecture for general r.     

一类积分算子的近于凸性

Let CS^*(α,ρ) and SB_γ(β,σ) be the subclasses of close-to-starlike functions and Bazile-vic functions class respectively. It is proved that the integral operators is close-to-convex function under the same conditions, where f_i∈CS^*(a_i,ρ_i,) and g_j∈SB_γj(β_j, σ_j). In addition, we correct a mistake in [3].     

Cohn环与Grothendieck群

We introduce three classes of cohn rings C₁,C₂ and C₃). Let R and S are rings,φ : R→S is a ring homomorphism. We prove that R∈C_i if and only if R/J(R) ∈ C_i. In We also discuss the relation between the     

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.     

实赋范数性空间内的Lp-正交

In this paper we have proved the theorem: Let p>1, and E be a real normed linear space, if the L^p-orthogonality in E satisfies one of the following conditions 1) homogeneity 2) additivity 3) x⊥_L^py implies x⊥_Jy 4) x⊥_Jy implies x⊥_L^py, then E is an abstract Euclidean space and there must be p=2. We also proved anR. C. James' result-If for every element x of a normed linear space E therecan be found a nonzero element orthogonal to x by Roberts' definition in each two dimensional linear subset containing x, then E is an abstract Euclidean space——which had not been proved. Finally, we point out that if one of the James′,L^p-,isosceles, Pythagorean and (α,β)-orthogonalities defined in E implies Roberts′ orthogonality then E is an abstract Euclidean space.     

The monodromy of a series of hypersurface singularities

Let {f=0} be a hypersurface inC ⁿ⁺¹ with a 1-dimensional singular set Σ. We consider the series of hypersurfaces {f+ɛx ^N=0} wherex is a generic linear form. We derive a formula, which relates the characteristic polynomials of the monodromies off andf+ɛx ^N. Other ingredients in this formula are the horizontal and the vertical monodromies of the transversal (isolated) singularities on each branch of the singular set. We use polar curves and the carrousel method in the proof. The formula is a generalization of the Iomdin formula for the Milnor numbers: μ(f+ɛx ^N )=μ _n (f)−μ _n −1(f)+Ne ₀(Σ)     

Volterra Type Operators on Weighted Dirichlet*

The Carleson measures for weighted Dirichlet spaces had been characterized by Girela and Pel′aez, who also characterized the boundedness of Volterra type operators between weighted Dirichlet spaces. However, their characterizations for the boundedness are not complete. In this paper, the author completely characterizes the boundedness and compactness of Volterra type operators from the weighted Dirichlet spaces D^p_α to D^q_β (?1 < α, β and 0 < p < q < ∞), which essentially complete their works. Furthermore, the author investigates the order boundedness of Volterra type operators between weighted Dirichlet spaces.     

Fourier级数子列的可和性

Let H_α0^ω denote the set of functions f(x)∈L_2π such that ω(f,x₀;t)≤ω(t),ω(t) being a given modulus of continuity. Let {n_k} be a set of natural numbers satisfying the condition n_i+1/n_k>q>1, and let A= (α_πk) be a regular summation matrix.     

关于解析函数的一个不等式

Let P(Z) = 1 + P₁Z + P₂Z² +…be an analytic function in the unit disc D. In thispaper, we determine the value of φ(α,β) for which Re[P(Z) + αZP′(Z)] > β,Z ∈ D,α > 0,β < 1 implies that Re{P(Z)} >φ(α,β) for all Z ∈ D, and this result is sharp. Some of its interesting consequences are also given. In addition, we give a new univalence criterion.     

Boundedness of Iterated Spherical Average on α-Modulation Spaces*

For the iteration of spherical average (A₁)^N and the Laplace operator ?, we consider the boundedness of the operator ?(A₁)^N on the α-modulation spaces M_p,q ^s,α. The authors obtain some sufficient and necessary conditions to ensure the boundedness on the α-modulation spaces. The main theorems significantly improve some known results.     

Mt2上的强ω(α)轨道稳定性

In this paper we define the concept of strong ω-stability (α-stability) of trajectories on dynamical systems, and discuss some properties of them on M_t² Using those properties we discuss the existence of close orbits or singular close orbits on M_t².     

关于一类单叶函数

A sharp coefficient estimate,distortion theorem and the radius of convexityare determined for the class R(α,β,A,B) of function f(z)=z+(?)a_nzⁿ satisfyingthe condition |(f′(z)-1)/(Bf′(z)-[B+(A-B)(1-α)])|<β for some α,β(0≤α<1,0<β≤1) and -1≤A相似文献   

Flensted-Jensen’s functions attached to the Landau problem on the hyperbolic disc

We give an explicit expression of a two-parameter family of Flensted-Jensen’s functions Ψ _μα on a concrete realization of the universal covering group of U(1, 1). We prove that these functions are, up to a phase factor, radial eigenfunctions of the Landau Hamiltonian on the hyperbolic disc with a magnetic field strength proportional to μ, and corresponding to the eigenvalue 4α(α − 1).     

Transfer of absolute continuity by a flow generated by a stochastic equation with reflection

Let ϕ_t(x), x ∈ ℝ₊ be a value taken at time t ≥ 0 by a solution of a stochastic equation with normal reflection from a hyperplane starting at initial time from x. We characterize the absolutely continuous (with respect to Lebesgue measure) component and the singular component of a stochastic measure-valued process μ_t = μ ○ ϕ _t ⁻¹ that is the image of a certain absolutely continuous measure μ under random mapping ϕ_t(·). We prove that the restriction of the Hausdorff measure H ^d−1 to the support of the singular component is σ-finite and give sufficient conditions guaranteeing that the singular component is absolutely continuous with respect to H ^d−1. __________ Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 58, No. 12, pp. 1663–1673, December, 2006.     

四元数矩阵的特征值与奇异值估计

In this paper, we give accurate estimation of eigenvalues and singular values of A + B,C^*AC and AB, where A, B and C are quaternions matrices. These results improve and generalze the results in [4] and [5]. We also obtainsum (?),for k=1,…,n. Where A and B are self-conjugate quaternions matrices of order n, and λ₁≥…≥λ_n,μ₁≥μ_n,λ₁,(A + B)≥…≥λ_n(A+B) be the eigenvalues of A,B and A + B, respectively.     

一般Gauss—Markov模型下最小二乘估计是最佳估计的充要条件

In this paper, we discuss the decomposition of the space μ(X : V) and the invariance with respect to the choice of a generalized inverse of matrix X in the general Gauss-Markov model. In Theorem 1, we give necessary and sufficient conditions for the least squares estimator P_xy = BLUE(Xβ) under the general Gauss-Markov model M = {y,Xβ,σ²V}. In Theorem 2, we prove that P_xy= BLUE(Xβ) under model M and invariant with respect to the choice of a generalized inverse of matrix X are equivalent.