两类广义Petersen 图的Euler亏格

广义 Petersen 图 P(n, m) 是这样的一个图:它的顶点集是{u_i, v_i | i=0,1, ^… , n-1}, 边集是 {u_iu_i+1, v_iv_i+m, u_iv_i | i=0,1, ^…, n-1}, 这里 m, n 是正整数、加法是在模n 下且 m<|n/2| . 这篇文章证明了P(2m+1, m)(m≥ 2) 的 Euler 亏格是1, 并且 P(2m+2, m)(m≥ 5) 的 Euler 亏格是2.     

Hilbert空间上线性算子广义逆A(2)T,S的存在性及其表示式

设H₁和H₂是两个Hilbert空间, B(H₁,H₂)表示从H₁到H₂的所有有界线性算子的集合, T和S分别是H₁和H₂的两个闭子空间. 如果存在线性算子X ∈ B(H₂,H₁)满足XAX=X, R(X)=T, N(X)=S,则称X为线性算子$A$的具有指定像空间T和零空间S的外逆,记为A⁽²⁾_T,S. 该文进一步研究了线性算子广义逆A⁽²⁾_T,S存在的若干等价条件及其性质,建立了算子广义逆A⁽²⁾_T,S的表示形式.     

∑e1型Banach空间上C0半群稳定性的谱特征

讨论一类不可分解的∑_e¹型Banach空间上有界线性算子的谱的特殊性质;给出了∑_e¹型Banach空间上一致有界C₀半群稳定性的一个谱特征,并给出稳定性定理的一个应用.     

误差为鞅差序列的部分线性模型中估计的强相合性

考虑回归模型:y_i=x_{i ^β} +g(ti)+σ_ie_i ,i=1,2,...,n,其中 σ_i=f(u_i), (x_i,t_i,u_i)是固定非随机设计点列,f(^.),\ g(^.)$\ 是未知函数,β是待估参数,e_i是随机误差且关于非降σ -代数列{F_i,i≥1} 为鞅差序列.对文献[1]给出的基于f^(.)及g(^.)的一类非参数估计的β的最小二乘估计β_n和加权最小二乘估计β_n,在适当条件下证明了它们的强相合性,推广了文献[6]在e_i为iid情形下的结果.     

Gd2SiO5: Eu3+中VUV激发的量子剪裁

在北京同步辐射装置的真空紫外光谱站, 对Gd₂SiO₅: Eu³⁺激发谱、发射谱进行了研究. 基于Gd³⁺-Eu³⁺体系通过能量传递发生可见光量子剪裁的原理, 对实验结果进行了讨论. 当直接激发Gd³⁺的⁶GJ态时, 有2个来自Eu³⁺的可见光光子发射, 粗略的估算表明Gd₂SiO₅: Eu³⁺是一种有效的量子剪裁材料.     

不含4圈的平面图的全色数

用Δ(G), χ_ve(G)分别表示图G的顶点最大度和全色数.Vizing猜想: 对任何 简单图G, Δ(G) +1≤χ_ve(G)≤Δ(G)+2. 即使对于平面图, 这一猜想仍未获得完整的证明, 唯一待完成的困难情形是Δ(G)=6. 本文证明:若Δ(G)=6的平面图G不含有4圈, 则χ_ve(G)≤8.这一结果和以前在该问题上的已知结果表明：对于不含有4圈的平面图，Vizing猜想是正确的.     

弱 (K1, K2) -拟正则映射的正则性

给出空间弱(K₁, K₂) -拟正则映射的定义, 并以Hodge分解及弱逆Hölder不等式为工具, 得到了其正则性结果：对任意满足 的q1, 都存在可积指数 使得对任意弱 (K₁, K₂) -拟正则映射 都有 即f为通常意义下的(K₁, K₂) -拟正则映射.     

偶数阶Sturm-Liouville边值问题的多个正解

该文讨论了偶数阶边值问题 (-1)^m y^(2m)₌f(t,y), 0≤t≤1,a_i+1y⁽²ⁱ⁾ (0)-β_i+1y ⁽²ⁱ⁺¹⁾ (0)=0, γ_i+1y⁽²ⁱ⁾ (1)+δ_i+1y⁽²ⁱ⁺¹⁾ (1)=0,0≤i ≤m-1正解的存在性.借助于Leggett-Williams 不动点定理,建立了该问题存在三个及任意奇数个正解的充分条件.     

非线性抛物椭圆方程组的正则解和奇异解

该文用单模方法在Lorentz空间研究了抛物椭圆方程组奇异解和正则解的存在性, 其中初值属于Lorentz空间L^{n/2,∞ ₍}Rⁿ), n≥ 3. 利用时间加权的Lorentz空间, 还得到了其正则解. 此外, 如果初值满足自相似结构, 也得到了自相似解的存在性.     

完全二部图Km,n的Kp,q-因子分解

如果完全二部图K_m,n的边集可以划分为K_m,n的K_p,q-因子, 则称K_m,n存在K_p,q-因子分解. 给出K_m,n存在K_p,q-因子分解的一个充分条件. 同时证明: 对于任意正整数k, 当p:q = k:(k + 1)时, K_m,n存在K_p,q-因子分解, 即Martin的BAC猜想成立.     

POSITIVE SOLUTION TO FOURTH-ORDER IMPULSIVE DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN

In order to study three-point BVPs for fourth-order impulsive differential equation of the form(\phi_p(u'(t)))'- f(t,u(t))=0, t≠ t_i,△ u(t_i)=-I_i(u(t_i)), i=1, 2, ..., k,△u'(t_i)=-L_i(u(t_i)), i=1, 2, ..., k,(\star)with the following boundary conditionsu'(0)=u(1)=0, u'(0)=0=u'(1)-\phi_q(α)u'(η),the authors translate the fourth-order impulsive differential equations with p-Laplacian (\star) into three-point BVPs for second-order differential equation without impulses and two-point BVPs for second-order impulsive differential equation by a variable transform. Based on it, existence theorems of positive solutions for the boundary value problems (\star) are obtained.     

The finiteness of the reward function and the optimal value function in Markov decision processes

This paper studies the discrete time Markov decision processes (MDP) with expected discounted total reward, where the state space is countable, the action space is measurable, the reward function is extended real-valued, and the discount rate may be any real number. Two conditions (GC) and (C) are presented, which are weaker than that presented in literature. By eliminating some worst actions, the state space S can be partitioned into sets S_X, S_mX, S₀, on which the optimal value function equals +X , mX or is finite, respectively. Furthermore, the validity of the optimality equation is shown when its right hand side is well defined, especially, when it is restricted to the subset S₀. The reward function r (i, a) is finite and bounded above in a for each i]S₀. Finally, some sufficient conditions for (GC) and (C) are given.     

State estimation for cox processes with unknown probability law

Let N_i, i?1, be i.i.d. observable Cox processes on a compact metric space E, directed by unobservable random measures M_i. Assume that the probability law of the M_i is completely unknown. Techniques are developed for approximation of state estimators using data from the processes N₁,…,N_n to estimate necessary attributes of the unknown probability law of the time M_i. The techniques are based on representation of the state estimators in terms of reduced Palm distributions of the N_i and on estimation of these Palm distributions. Estimators of Palm distributions are shown to be strongly consistent and asymptotically normal. The difference between the true and the pseudo-state estimators converges to zero in L² at rate n^{?$\text{1}\text{4+δ}$} for each δ > 0.     

Steady-state solution for electroplating

At steady state, electroplating processes are governed by thedimensionless equations where d_i, e_i, and u_i arerespectively the diffusion coefficient, charge, and concentrationof the ith species. The extra electroneutrality condition will determine the electric potential. This system of nonlinear differential equations is subjectto the nonlinear boundary conditions modelling the actual electrodekinetics. The authors prove the existence of the solution andconstruct a computational algorithm. Numerical experiments areperformed on practical data.     

On the existence of certain measures appearing in distance geometry

Abstract. We prove the following result: Let X be a compact connected Hausdorff space and f be a continuous function on X x X. There exists some regular Borel probability measure m\mu on X such that the value of¶¶ ò\limit _X f(x,y)dm(y)\int\limit _X f(x,y)d\mu (y) is independent of the choice of x in X if and only if the following assertion holds: For each positive integer n and for all (not necessarily distinct) x₁,x₂,...,x_n,y₁,y₂,...,y_n in X, there exists an x in X such that¶¶ ?_i=1ⁿ f(x_i,x)=?_i=1ⁿ f(y_i,x).\sum\limits _{i=1}^n f(x_i,x)=\sum\limits _{i=1}^n f(y_i,x).