一类无Lipschitz假设的非线性算子的带误差的Ishikawa迭代程序

１引言与预备知识 设Ｘ为一实赋范线性空间．Ｘ·是Ｘ的对偶空间,正规对偶映射Ｊ：Ｘ→２Ｘ定义为：其中＜·,·＞表示Ｘ和Ｘ的广义对偶组．由［１］知若Ｘ是一致光滑Ｂａｎａｃｈ空间,则Ｊ（·）单值且在Ｘ的任何有界子集上为一致连续．我们用ｊ（·）表示单值的正规对偶映射． 定义１［２］设Ｋ是Ｘ的一非空子集,算子Ｔ：Ｋ→Ｘ称为是　－强伪压缩的,如果存在一个严格增加函数　,存在使得 定义２［２,３］Ｔ称为　强增生算子的,如果（Ｉ－Ｔ）是　－强伪压缩算子（其中Ｉ是恒等算子）． 若定义１（相应地;定义２）中　（ｔ）＝ｋ…     

再生核空间二元函数展开

For convenience, we use D to denote ［0,1］×［0,1］. PutH2={u(x,y)|u∈L2(D) is a real and totally continuous function withux, uy, 2ux2, 2uy2, 2uxy, 3uxy2, 3ux2y, 4ux2y2∈L2(D)} For any u and v∈H2, we define an inner product〈u,v〉=Duv+2uxvx+2uyvy+42uxy2vxy+2ux22vx2+2uy22vy2+23ux2y3vx2y+23uxy23vxy2+4ux2y24vx2y2dxdy.(1)Selecting a norm as ‖·‖=〈·,·〉1/2, we find that, as the proof in ［1］, H2 is a reproducing kernel space (see ［2］), and (1) defines indeed an inner product on the …     

部分线性模型中估计的强相合性

考虑回归模型：ｙｉ＝ｘｉβ＋ｇ（ｔｉ）＋σｉｅｉ，１ｉｎ，其中σ２ｉ＝ｆ（ｕｉ），（ｘｉ，ｔｉ，ｕｉ）是固定非随机设计点列，ｆ（·）和ｇ（·）是未知函数，β是待估参数，ｅｉ是随机误差．对文［１］给出的基于ｇ（·）及ｆ（·）的一类非参数估计的β的最小二乘估计＾βｎ和加权最小二乘估计βｎ，我们在适当条件下证明了它们的强相合性．     

关于整数分拆的Alavi猜想的证明

Ｙ．Ａｌａｖｉ，Ｐ．Ｅｒｄｓ等人在［１］中提出猜想：设自然数α＿１，α＿２…α＿ｋ满足且，则可以划分成ｋ个互不相交子集Ｓ＿１，Ｓ＿２，···，Ｓ＿ｋ，满足．本文证明了这个猜想。     

具有分段常数变元的时滞微分方程解的振动性(英文)

我们获得了带有分段常数变元的时滞微分方程ｘ′（ｔ）＋ａ（ｔ）ｘ（ｔ）＋∑ｍｉ＝１ｂｉ（ｔ）ｘ（［ｔ－ｉ］）＝０，ｔ≥０所有解振动的新的充分条件，这里［·］定义为最大整数函数．我们的结果改进了文献中的某些已知结果．     

强拓扑的可赋范化与可度量化

作者之一在［１，２］中就序列空间Λ而言，讨论了关于强拓扑β（Λ，Λ^×）的可赋范化与可度量化问题，并给出了它的一些特征。本文在更广泛的序列空间一矢值序列空间Λ［Ｘ］上，讨论了Λ［ｘ］关于强拓扑β（Λ［Ｘ］，Λ［Ｘ］^×）的可赋范化与可度量化问题，同时给出了它的一个特征．     

求贝尔塞方程解的注记

求贝尔塞方程解的注记张自立（西安交通大学）书［１］是工科院校使用的教材。在该书第五章§５·２节中，叙述用广义幂级数方法求贝塞尔方程的解。求解过程有不严密之处，所得结论也不完整。现简要说明如下。１该书中解法摘要及存在的问题该书１０４页—１０６页研究ｎ阶...     

一类特殊函数的[n/n]Padé逼近

本文对［ｎ／ｎ］Ｐａｄé逼近进行探讨，证明了Ｐｎ（ｘ）／Ｑｎ（ｘ）是函数ｆ（ｘ）在ｘ＝０处的［ｎ／ｎ］Ｐａｄé逼近，而Ｑｎ（ｘ）＝Ｐｎ（－ｘ）的充要条件是ｆ（ｘ）ｆ（－ｘ）＝１，从而使这一类函数的［ｎ／ｎ］Ｐａｄé逼近计算量减少一半．     

同角三角函数间的基本关系式

同角三角函数间的基本关系式湖北工建三公司一中刘隄仿［基本概念］同角三角函数间的基本关系式有（１）倒数关系ｓｉｎａ·ｃｓｃａ＝１，ｃｏｓａ·ｓｅｃａ＝１，ｔｇａ·ｃｔｇａ＝１．（２）商数关系（３）平方关系ｓｉｎ２ａ＋ｃｏｓ＇ａ－１，１＋ｉｇ＇ａ一。。＇...     

双代数余循环的余同调变换

在［８］中,作者讨论余循环交叉积和扭积之间的关系（见定理 ５．３）．设 Ａ＃ＸＨ为余循环交叉积,ｒ∈Ｈｏｍ（Ｈ,Ａ）,是卷积可逆的,且ｒ（１）＝１．在］［６］中,Ｓ．Ｍａｊｉｄ对任意地余循环Ｘ定义了余同调变换 ｘｒ·在本文中,首先证明了［８］中的定理 ５．３以及它的对偶在一般情况下成立． Ｓ． Ｍａｊｉｄ在［５］中给出了余循环交叉积和余循环交叉余积形成双代数的充要条件,这种结构称为Ｂｉｃｒｏｓｓｐｒｏｄｕｃｔ积．这里讨论了余循环余同调变换如何具体地保持这种双代数结构．     

Sufficient and Necessary Conditions for Stochastic Comparability of Jump Processes

Abstract This note is devoted to the study of the stochastic comparability of jump processes. On the basis of [2] and [3], it is proved that two jump processes are stochatically comparable if and only if their q-pairs are comparable. Meanwhile, the result concerning the uniqueness given in [6] is also improved upon. Research supported in part by DPFIHE(Grant No.96002704), NNSFC(Grant No.19771008), MCSEC, Ying-Tung Fok Educational Foundation and Youth Science Foundation of BNU     

State estimation for partially observed jump processes

In this paper partially observed jump processes are considered and optimal filtering equations are given for the conditional expectation of a functional on the past of the process.Rudemo [6] derived filtering equations for a partially observed jump Markov process. Snyder [3] gives equations for the conditional characteristic function of a jump process. Segall et al. [2] discuss filtering for processes with counting observations. Their work carries over to processes with counting observations the martingale methods that Fujisaki et al. [1] had used to derive nonlinear filtering equations for processes governed by Ito equations. Many further references to filtering for processes with discrete state measurements are given in the references cited.The objective of this paper is to show that by making use of the concept of a representation of a functional the idea of Rudemo's proof of [6, pp. 595–599] can be carried over to jump processes. The author feels that this is a very interesting proof because of its simplicity. It involves only calculations with conditional expectations and the rule for differentiation of a quotient.     

ON COUPLING OF JUMP PROCESSES

This is a sequel to the paper [3] in which the marginality, regularity and orderpreservation for couplings of jump processes are studied. The main purpose of this note is to present a criterion and some practical suffcient conditions for the success of couplings and some criteria for the monotonicity of jump processes.     

Scaling limits of coupled continuous time random walks and residual order statistics through marked point processes

A continuous time random walk (CTRW) is a random walk in which both spatial changes represented by jumps and waiting times between the jumps are random. The CTRW is coupled if a jump and its preceding or following waiting time are dependent random variables (r.v.), respectively. The aim of this paper is to explain the occurrence of different limit processes for CTRWs with forward- or backward-coupling in Straka and Henry (2011) [37] using marked point processes. We also establish a series representation for the different limits. The methods used also allow us to solve an open problem concerning residual order statistics by LePage (1981) [20].     

Analysis of jump processes with nondegenerate jumping kernels

We prove regularity estimates for functions which are harmonic with respect to certain jump processes. The aim of this article is to extend the method of Bass–Levin (2002) [3] and Bogdan–Sztonyk (2005) [6] to more general processes. Furthermore, we establish a new version of the Harnack inequality that implies regularity estimates for corresponding harmonic functions.     

Mean first passage times of two-dimensional processes with jumps

In this paper, we incorporate a jump component into the model based on a two-dimensional degenerate diffusion process for the remaining lifetime of machines in the recent paper [Lefebvre, M., 2010. Mean first-passage time to zero for wear processes. Stochastic Models 26, 46-53] by the second author. We calculate explicitly the expected value of first passage times associated to the two-dimensional process when the jump component is taken to be a compound Poisson process with exponential jumps and random proportion of jumps.     

Harnack Inequalities for Jump Processes

We consider a class of pure jump Markov processes in R ^d whose jump kernels are comparable to those of symmetric stable processes. We establish a Harnack inequality for nonnegative functions that are harmonic with respect to these processes. We also establish regularity for the solutions to certain integral equations.     

Convergence to diffusions with regular boundaries

Earlier results on weak convergence to diffusion processes [8] are generalized to cases where the limiting diffusions may have regular boundaries. The boundaries may be adhesive or reflecting, and in each case we give two different sets of conditions for convergence. It is shown that these conditions are necessary and sufficient for convergence in the same sense as the conditions in [8]. We also extend our results to cases where the coefficients of the diffusions have simple discontinuities, in particular we thereby answer an open question by Keilson and Wellner [9]. Finally we formulate alternative sets of conditions for convergence, with these new sets being more convenient for instance when the sequence under investigation consists of pure jump Markov processes in continuous time.     

Continuity of Harmonic Functions for Non-local Markov Generators

We consider a class of pure jump Markov processes in ${\mathbb R}^d$ whose jump kernels are comparable to those of symmetric stable processes. We prove a support theorem, a lower bound on the occupation times of sets, and show that we can approximate resolvents using smooth functions.     

A non-inversion theorem for the jump operator

R.W. Robinson's [15] interpolation theorem shows that the Sacks [16] jump inversion theorem can be extended to invert the jump and preserve order on any finite linearly ordered set of degrees r.e. in and above (REA in) 0′. We show that although the Friedberg inversion theorem can be extended to partial orders, the Sacks theorem cannot be extended to even the simplest ones even if we allow the inversion to carry us into rather than just the r.e. degrees. This strong non-inversion theorem also decides the problem that Lerman [12] has called the main obstacle to deciding the theory of the degrees with jump. It is a corollary to our main result:

Theorem 1.1. There are a₀ and a₁ REA in 0′ such that a₀ a₁<0” and if u<0′, then not both a₀ and a₁ are r.e. in u.

Other corollaries include a solution to a problem suggested by Jockusch and Soare: not every a REA in 0′ is the jump of a degree which is half of an r.e. minimal pair. The proof introduces a new type of 0 priority argument in which the tree of strategies is ω+1 branching and so simply determining the true path requires a 0 oracle.