不完全三值逻辑在语言表达上的相互比较

深入讨论各种命题联结词含量不完全的三值逻辑的语言表达的能力,完全弄明白了三值系统L3,L3,B3,B3,K3,K3,MP的语言表达能力的等效或不等效关系,特别应当指出的一个结论是：中介命题逻辑MP作为一种命题联结词含量不完全的三值系统而言,它和其他命题联结含量不完全的三值逻辑L3,L3Δ,B3,B3Δ,K3,K3Δ的语言表达能力都不等效,从而也由此体现出MP的一种自身特色。     

ON SCHWARZ-PICK TYPE INEQUALITY FOR MAPPINGS SATISFYING POISSON DIFFERENTIAL INEQUALITY

Let f be a twice continuously differentiable self-mapping of a unit disk satisfying Poisson differential inequality |△f(z)|≤B·|Df(z)|2 for some B＞0 and f(0)= 0....     

THE TRACE SPACE INVARIANT AND UNITARY GROUP OF C^＊—ALGEBRA

Let A be a unital C-algebra, n ∈ N ∪ {∞}. It is proved that the isomorphism △n : is isometric for some suitable distances. Asan application, the author has the split exact sequence with iA contractive (and isometric if n = ∞) under certain condition of A.     

Gorenstein-Projective Modules over Morita Rings

Let △(φ,ψ) =(A BMA ANBB) be a Morita ring which is an Artin algebra.In this paper we investigate the relations between the Gorenstein-projective modules over a Morita ring △(φ,ψ) and the algebras A and B.We prove that if △(φ,ψ) is a Gorenstein algebra and both MA and AN (resp.,both NB and BM) have finite projective dimension,then A (resp.,B) is a Gorenstein algebra.We also discuss when the CM-freeness and the CM-finiteness of a Morita ring △(φ,ψ) is inherited by the algebras A and B.     

完全图中的正常染色的路和圈

令$K_{n}^{c}$表示$n$ 个顶点的边染色完全图.
令 $\Delta^{mon}
(K_{n}^{c})$表示$K^c_{n}$的顶点上关联的同种颜色的边的最大数目.
如果$K_{n}^{c}$中的一个圈（路）上相邻的边染不同颜色,则称它为正常染色的.
B. Bollob\'{a}s和P. Erd\"{o}s (1976) 提出了如下猜想：若 $\Delta^{{mon}}
(K_{n}^{c})<\lfloor \frac{n}{2} \rfloor$, 则$K_{n}^{c}$中含有一个正常染
色的Hamilton圈. 这个猜想至今还未被证明.我们研究了上述条件下的正常染色的路和圈.     

具有跳扩散的美式期权二叉树计算格式的收敛速率

American put option with jump-diffusion can be modelled as a vari- ational inequality problem with an integral term.Under the stability condition (σ~2Δt)/(Δx~2)≤1,whereΔx=ln(S_n 1)/(S_n),the convergence rate O((Δx)~(2/3) (Δt)~(1/3))of the explicit finite scheme for this problem is obtained by using penalization technique. The binomial tree scheme of this model,which is equivalent to the explicit scheme, is convergent by the same rate.     

HARNACK''S INEQUALITY FOR GENERALIZED SUBELLIPTIC SCHR(O)DINGER OPERATORS

We prove a uniform Hamack inequality for nonnegative solutions of △Gu- μμ=0, where △G is a sublaplacian, μ is a non-negative Radon measure and satisfying scale-invariant Kato condition.     

解抛物型方程的高精度显式差分格式

在渗流、扩散、热传导等邻域中经常会遇到求解抛物型方程的问题.在一维情形,其模型为如下初边值问题:     

解二维抛物型方程的高精度显式差分格式

<正> 1 引言从扩散、渗流、热传导等问题中可以提出很多抛物型方程。对于一维的抛物型方程u_1=σu_(xx)(σ>0),文[1]给出了一个截断误差为O(△t~2+△x~4)的高精度显式差分格式,对于二维的抛物型方程u_t=σ(u_(xx)+u_(yy))(σ>0),文[2]给出了截断误差为O(△t~2+△x~2+△y~2)的绝对稳定的显     

关于3维Minkowski空间中类空曲面的若干结果

在本文，我们证明２维黎曼流形能实现为Ｌ３中的类空极大曲面的充要条件是相应的Ｒｉｃｃｉ条件成立，此外还确定了Ｌ３中其平均曲率向量ｈ满足条件△ｈ＝λｈ（λ∈Ｒ）的类空曲面     

带有无界势和一般时间频率的非周期离散非线性Schr#246;dinger方程：无穷多个孤立子

本文研究下面的非周期离散非线性Schrödinger 方程：
-Δu_n + v_nu_n - ωun = g_n（u_n）,n ∈ Z,
其中V = {v_n}_n∈Z 和g_n 都是非周期的,当|n| → +∞ 时,v_n → +∞,并且时间频率ω ∈ R 可以满足下面的任何一种情形：（1）ω 属于算子-Δ + V 的一个有限谱间隔;（2）ω < inf σ（-Δ + V）;（3）ω ∈ σ（-Δ+ V）,其中σ（-Δ+ V）表示-Δ+ V的谱. 本文将用一些局部条件（在无穷远或零处）来代替一些全局条件. 利用变化的喷泉定理,当非线性项在无穷远处是超线性时,本文得到这个方程的无穷多个非平凡孤立子,并且,也得到指数衰减的孤立子的存在性.     

Combined perturbation bounds: Ⅱ. Polar decompositions

In this paper, we study the perturbation bounds for the polar decomposition A= QH where Q is unitary and H is Hermitian. The optimal (asymptotic) bounds obtained in previous works for the unitary factor, the Hermitian factor and singular values of A are σ2r||△Q||2F ≤ ||△A||2F,1/2||△H||2F ≤ ||△A||2F and ||△∑||2F ≤ ||△A||2F, respectively, where ∑ = diag(σ1, σ2,..., σr, 0,..., 0) is the singular value matrix of A and σr denotes the smallest nonzero singular value. Here we present some new combined (asymptotic)perturbation bounds σ2r ||△Q||2F+1/2||△H||2F≤ ||△A||2F and σ2r||△Q||2F+||△∑ ||2F ≤||△A||2F which are optimal for each factor. Some corresponding absolute perturbation bounds are also given.     

一类（p,q）-Laplacian椭圆方程组解的存在性

研究了P,q—Laplacian椭圆方程组-△pu=λf（x）u^8v^n,-△qv=μg（x）u^tv^m的Dirichlet边界值问题的正弱解的存在性．首先根据两个方程组构造了弱上解和弱下解,然后利用弱上下解方法得到了方程组正弱解的存在性．利用特征值和特征函数构造了弱上下解具有一定的创新性,结果推广了p=q=2的情...     

关于Poisson群胚的结构

令（ΓP,α,β）是Poisson群胚．如果它的每个α-纤维与β-纤维至多交于一点,则Γ在任一点x的特征分布有直和分解△（x）=△α（x）+△β（x）,其中△α（x）Txα－1（u）,△β（x）Txβ-1（u）且它们都是△（x）的辛子空间．由此得到辛叶Sx的辛子流形S和S,使在映射α之下,S辛微分同胚于P中辛叶Su,在映射β之下,S反辛微分同胚于P中辛叶Sv（定理4和5）．对于一般的Poisson群胚,也可得到类似的S和S,它们差一局部辛微分同胚是唯一确定的（定理6）．把以上结果用于辛群胚,还可得到一些更具体的性质（定理7及其推论）．     

幂零李群上的薛定谔算子的加权估计

In this paper we consider the SchrSdinger operator -△G ＋ W on the nilpotent Lie group G where the nonnegative potential W belongs to the reverse H51der class Bq1 for some q1 ≥ D and D is the dimension at infinity of G. The weighted L^p -L6q estimates for the operators W^a（-△G ＋ W）^-β and W^a△G（-△G ＋ W）^-β are obtained.     

可和系数的二阶差分方程解的渐近性

考虑非线性差分方程△(Pn-1△（yn-1)^σ） qnf(yn)=0,n=1,2,3…其中linn→∞∑s=1^nqs存在且为有限给出了方程（E）具有渐近于非零常数解的必要（充分）条件。     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

Poisson半群的边界值

在空间Ｌｐ（Ｒｎ），１≤ｐ＜∞中，Ｐｏｉｓｏｎ算子半群ｅ－－△ｚ是右半平面Ｒｅｚ＞０上的解析半群．本文考虑它的边界值，证明了闭稠定算子－ｉ－△对某个α≥０生成了一个指数有界（Ｉ＋－△）－α 半群．     

THE FIRST BOUNDARY VALUE PROBLEM FOR A CLASS OF QUASILINEAR DEGENERATE ELLIPTIC EQUATIONS

In this paper, the first boundary value problem for quasilinear equation of the form △A（u,x）＋∑i=1^m δb^i（u,x）/δxi＋c（u,x）=0,Au（u,x） ≥0is studied. By using the compensated compactness theory, some results on the existence of weak solution are established. In addition, under certain condition the uniqueness of solution is proved.     

求解Riesz空间分数阶扩散方程的一种新的数值方法

本文利用Diethelm方法构造了一种逼近Riesz空间分数阶导数的O（△x^3-α）格式,其中1 < α < 2,△x是空间步长.进一步对一阶时间导数采用Crank-Nicolson方法离散,得到了求解Riesz空间分数阶扩散方程的一种新的有限差分格式,并用矩阵方法证明了稳定性和收敛性,其误差估计为O（△t²+△x^3-α）,其中△t为时间步长.最后,数值算例验证了差分格式的正确性和有效性.