离散时间观测下的α-赋权分数桥的参数估计

本文研究了赋权分数桥dX_t=-α(X_t)/(T-t)dt+dB_t^a,b,0≤t < T,中未知参数α>0的参数估计问题,其中B^a,b是参数为a>-1,|b|<1,|b|≤a+1的赋权分数布朗运动.假设对随机过程X_t进行离散观测t_i=i△_n,i=0,…,n,且T_n=n△_n.本文构造了α的最小二乘估计α_n,证明了当n→∞时,α_n依概率收敛到α.     

关于P2(C)全纯曲线唯一性问题的注记*

本文讨论P²(C)中全纯曲线相交处于次一般位置超平面的唯一性.设f₁, f₂, · · · , f_λ为P²(C)中线性非退化的全纯曲线,H₁, H₁, · · · , H_q为P²(C)上处于m-次一般位置的超平面,满足A_j :f₁^-1(H_j) = · · · =f_λ^-1(H_j) (1 ≤ j ≤ q)且A_i ∩ A_j = ?(i = j).假设存在整数l (2 ≤ l ≤ λ),使得f_j1(z) ∧ f_j2(z) ∧ · · · ∧ f_jl(z) = 0 (z ∈ A_j)对任意l个指标1 ≤ j₁ < j₂ < · · · < j_l < λ成立.那么当 q > 2λ/λ-l+1 + 3/2 m时, f₁ ∧ · · · ∧ f_λ ≡ 0.关键技术是第二基本定理中不等式改进为: ∥(q - 3m/2)T_ft(r)≤ Pjq=1N²(f_t,H_j )(r, 0) + o(T_ft(r))(1 ≤ t ≤ λ).     

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。     

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。     

多变量的Cauchy问题的唯一性中的离散现象

本文讨论Cauchy问题sub from i,j=0 to n a_iju_xixj+sub from i=0 to n b_iu_xj+cu=0,x₀>0,u(0,x₁,…,x_n)=u_x0(0,x₁,…,x_n)=0的唯一性中的离散现象. 我们证明了,此问题在原点的一个邻域中只有平凡解的充要条件为b₀(0)-sub from i=1 to n(2a_i+1)λ_i≠0,其中λ_i>0是矩阵-(?²α₀₀/?_xi?_xj(0))(_i,j=1,…,n)与(a_ij(0))_i,j=1,…,n)的乘积的特征根的平方根.α_i是任意的非负整数.     

Reinhardt域的Bergman核函数(Ⅰ)

若D为Reinhardt域 D={z∈Cⁿ:||z||_α=sum from j=1 to n(|z_j|~(2/α_j)<1)}这里0<α_j,j=1,2,…,n。若K_D(z,)为D的Bergman核函数,证明了一系列结果以获得K_D(z,)的渐近表达式.     

Reinhardt域的Bergman核函数(Ⅱ)

若D为Reinhardt域 D={Z∈Cⁿ:‖z‖_α=sum from j=1 to n(|z_j|^2/α_j<1)},这里0<α_j,j=1,2,…,n.证明了:若K_D(z,)为D的Bergman核函数,则存在两个正的常数m与M,不依赖于z,而只依赖于α=(α₁,…,α_n)及n,使得 mF(z,)≤K_D(z,)≤MF(z,z)对任一z∈D都成立,这里 F(z,)=(-r(z))^-n-1 multiply from j=1 to n ((-r(z)+|z_j|~(2/α_j))^1-α_j),而r(z)=‖z‖_α-1为D的定义函数.     

多复变整函数与其关于全导数的微分多项式*

本文证明如下定理: 设f为Cⁿ上的一个非常数整函数,L_D(f) = a_kD^kf +a_k?1D^k?1f +· · · + a₁Df + a₀f,其中a_j ∈ C, a_k ≠ 0, D_j f是f的j阶全导数(j=1,2, · · ·,k).若f与L_D(f)两个有穷的CM分担值, 则f=L_D(f).     

二阶抛物方程组解的Lp-正则性和Hölder连续性

在可控和自然增长条件下,非线性抛物组 u''_t-D_aA_i^a(x,t,u,Du)= B_i(x,t,u,Du),i=1,…,N,(x,t)∈Q之解。u∈L²(0,T;H¹(Ω,R^N))∩L^∞(0,T;L²(Ω,R^N))(或∩L^∞(Q,R^N))的空间导数D_au事实上属于L_loc^p(Q,R^N),p>2;拟线性抛物组 u''_t-Dα[A_ij^αβ(x,t,u)D_βu^j+a_j^a(x,t,u)]=B_i(x,t,u,Du),i=1,…,N的每一个解都在一开集 Q₁?Q上 Holder连续,且H^n+2-p(Q\Q₁)=0;若当j>i时A_ij^αβ=0,且B_i(x,t,u,p)关于|p|的增长阶小于2,则Q₁=Q;若A_ij^αβ和a_i^a都Holder连续,则D_au也在Q₁上 Holdler连续.     

一类弱拟凸域上的Bergman型算子

得到了算子在空间 L^p(Ω_a,dv_λ)(1< p< ∞)上有界的充分必要条件,其中h(ξ)=(1-|z|²)^α-|w|²,K_s,_u,_v)( ξ , ξ'' )为一核函数.作为应用,证明了对所有多重指标α=( α₁,…,α_n)和β=(β₁,…,β_n),f∈L_H^p(Ωα, dv_λ)蕴含1≤ p<∞.     

Generalized B-vex functions and generalized B-vex programming

A class of functions called pseudo B-vex and quasi B-vex functions is introduced by relaxing the definitions of B-vex, pseudoconvex, and quasiconvex functions. Similarly, the class of B-invex, pseudo B-invex, and quasi B-invex functions is defined as a generalization of B-vex, pseudo B-vex, and quasi B-vex functions. The sufficient optimality conditions and duality results are obtained for a nonlinear programming problem involving B-vex and B-invex functions.The first author is thankful to the Natural Science and Engineering Research Council of Canada for financial support through Grant A-5319. The second author is grateful to the Faculty of Management, University of Manitoba for the financial support provided for her visit. The authors are thankful to Prof. R. N. Kaul, Department of Mathematics, Delhi University for his constructive criticism of the paper.     

复变函数中由调和函数求解析函数的方法

本文给出了由解析函数的实部或虚部求该解析函数的几个定理,再以例题说明其应用。这些方法及应用,解决了复变函数中这一问题的理论与计算,而且所给方法能广泛进行推广。     

Functional inequalities involving special functions

Let up(x) be the generalized and normalized Bessel function depending on parameters b,c,p and let σ(r)=up(1−r²)/up(r²), r∈(0,1). Motivated by an open problem of Anderson, Vamanamurthy, and Vuorinen we prove that for all r₁,r₂∈(0,1) for certain conditions on the parameters b,c,p.     

Indefinite integrals of products of special functions

A method is given for deriving indefinite integrals involving squares and other products of functions which are solutions of second-order linear differential equations. Several variations of the method are presented, which applies directly to functions which obey homogeneous differential equations. However, functions which obey inhomogeneous equations can be incorporated into the products and examples are given of integrals involving products of Bessel functions combined with Lommel, Anger and Weber functions. Many new integrals are derived for a selection of special functions, including Bessel functions, associated Legendre functions, and elliptic integrals. A number of integrals of products of Gauss hypergeometric functions are also presented, which seem to be the first integrals of this type. All results presented have been numerically checked with Mathematica.     

Coefficient estimates for bi-univalent Ma-Minda starlike and convex functions

Estimates on the initial coefficients are obtained for normalized analytic functions f in the open unit disk with f and its inverse g=f⁻¹ satisfying the conditions that zf^′(z)/f(z) and zg^′(z)/g(z) are both subordinate to a univalent function whose range is symmetric with respect to the real axis. Several related classes of functions are also considered, and connections to earlier known results are made.     

SUFFICIENT CONDITION FOR FUNCTIONS TO BE IN A CLASS OF MEROMORPHIC MULTIVALENT SAKAGUCHI TYPE SPIRAL-LIKE FUNCTIONS

In this article, we define a subclass of meromorphic multivalent Sakaguchi type functions and obtain certain sufficient conditions for functions to be in this class. The main result presented here includes a number of consequences as its special cases.     

A note on hyperharmonic and polyharmonic functions

We show that the spaces of harmonic functions with respect to the Poincaré metric in the unit ball B^N in have many different properties depending upon whether N is even or odd.     

On the extremality of maximal dual feasible functions

Dual feasible functions have been used to compute bounds and valid inequalities for combinatorial optimization problems. Here, we analyze the properties of some of the best functions proposed so far. Additionally, we provide new results for composed functions. These results will allow improving the computation of bounds and valid inequalities.     

Sufficient condition for functions to be in a class of meromorphic multivalent Sakaguchi type spiral-like functions

In this article, we define a subclass of meromorphic multivalent Sakaguchi type functions and obtain certain sufficient conditions for functions to be in this class. The main result presented here includes a number of consequences as its special cases.