n参数d维随机游动(RW_n~d)

本文研究了ｎ参数ｄ随机游动（记为ＲＷ~ｄ_ｎ）的各种多参数Ｍａｒｋｏｖ性、单 点转移函数和宽过去转移函数,得到了基本型Ｒ叫（Ｂ~１（ｐ,ｑ））的一个弱大数定律．     

稳定随机游动二重时集的离散Hausdorff维数

设（Ｘ）ｎ≥０是ｄ维格子点上相应于正则变差函数ｂ（ｎ）＝ｎ＾１／βＳ（ｎ）的稳定随机游动，称为（Ｘｎ）ｎ≥０的二重时集，时文讨论了Ａ＾ｄβ的离散Ｈａｕｓｄｏｆｒｒ维数，并且在较弱的条件下证明了：ｄｉｍＨ（Ａ＾ｄβ）（１当ｄ＞β时，２－ｄ／β当ｄ≤β时     

带Hardy空间函数核的Marcinkiewicz积分的L~p有界性

本文证明了一类分别相应于 Ｌｉｔｔｌｅｗｏｏｄ－Ｐａｌｅｇ ｇ函数, 函数和面积积分Ｓ的 Ｍａｒｃｉｎｋｉｅｗｉｃｚ积分算子,μΩ,μ~*Ω,λ和μΩ,ｓ的 Ｌ~p（Ｒ~n）有界性．其中核函数Ω∈Ｈ~１（Ｓ（ｎ－１））这里Ｈ~１（Ｓ（ｎ－１））记Ｒ~ｎ（ｎ ≤２）中的单位球面 Ｈａｒｄｒ空间．本文结果是已知结果的本质改进和推广．     

带Hardy空间函数核的Marcinkiewicz积分的L~p有界性

本文证明了一类分别相应于 Ｌｉｔｔｌｅｗｏｏｄ－Ｐａｌｅｇ ｇ函数, 函数和面积积分Ｓ的 Ｍａｒｃｉｎｋｉｅｗｉｃｚ积分算子,μΩ,μ~*Ω,λ和μΩ,ｓ的 Ｌ~p（Ｒ~n）有界性．其中核函数Ω∈Ｈ~１（Ｓ（ｎ－１））这里Ｈ~１（Ｓ（ｎ－１））记Ｒ~ｎ（ｎ ≤２）中的单位球面 Ｈａｒｄｒ空间．本文结果是已知结果的本质改进和推广．     

带有中止检查规则（n－i）的CSP－1方案

本文引人转移概率母函数及幂级数等方法讨论带有中止规则（ｎ＊－ｉ）的连续抽样方案ＣＳＰ－１的中止概率Ｐ＊得到了Ｐ＊作为ＣＳＰ－１方案的度量的理论特性，证明了Ｄｏｄｇｅ型ＣＳＰ－１方案与带有中止规则（ｎ＊－ｉ）的ＣＳＰ－１方案具有相同的ＡＯＱ，ＡＦＩ，ＯＣ函数．文末还给出了一些数值结果．     

回归函数非线性小波估计的一致强相合性

设（Ｘ_１,Ｘ_１）,…,（Ｘ_ｎ,Ｙ_ｎ）是从总体（Ｘ,Ｙ）中抽取的ｉ．ｉ．ｄ样本且服从［０,１］上的均匀分布．本文在平方积分损失下得到了回归函数ｇ（ｘ）＝Ｅ（Ｙ｜Ｘ＝ｘ）的非线性小波估计的一致相合性．     

关于f(f~(k)~n-a(z)的零点

本文讨论了杨重骏和杨乐等提出的一个猜想：设ｆ是一超越整函数，ｎ，ｋ是两个正整数，则当ｎ２时，ｆ（ｆ（ｋ）ｎ取任何非零有限值无穷多次，并证明了这个猜测，而且证明了，当ｆ是亚纯函数时的情形也成立，即有，设ｆ是超越亚纯函数，ｎ，ｋ是两个正整数，则当ｎ２时，ｆ（ｆ（ｋ）ｎ－ａ（ｚ）有无穷多个零点，其中ａ（ｚ）是ｆ的一个小函数     

加性函数的一个结果的简单证明

以‖ｘ‖表示ｘ与其最近的整数的距离．本文给出了如下结果的一个简化证明：如果一实值加性函数ｆ（ｎ）满足条件‖ｆ（ｎ＋１）─ｆ（ｎ）‖＝Ｏ（１）（ｎ→∞）；则存在一常数Ｃ，使得ｆ（ｎ）—Ｃｌｏｇｎ为整值加性函数．     

一般增长曲线模型回归系数线性估计的泛容许性

本文讨论一般的增长曲线模型；Ｘ＝ＡＢＣ＋ε，Ｅ（ε）＝０，Ｖａｒ（ε）＝σΣＶ，其中Ｘ和ε是ｐ×ｎ价随机阵，Ａ、Ｃ分别为ｐ×ｑ，ｋ×ｎ已知阵，Σ、Ｖ分别Ｐ、ｎ阶已知非负定阵，Ｂ和σ为未知参数．在损失函数（ｄ（Ｘ）－ＫＢＬ）＇（ｄ（Ｘ）－ＫＢＬ）下，我们给出了可估函数ＫＢＬ的线性估计的泛（Φ）容许性定义，得到了ＤＸＦ（ＤＸＦ＋Ｍ）在某些估计类中是ＫＢＬ的泛容许性估计的充要条件．     

Littlewood—Paley的gλ函数与面积函数在Lipα（R^n）上的有界性

本文证明，对于Ｌｉｐｓｃｈｉｔｚ空间Ｌｉｐａ（Ｒ＾ｎ）的函数ｆ，若相应Ｌｉｔｔｌｅｗｏｏｄ－Ｐａｌｅｙ的ｇλ函数ｇλ（ｆ）（ｘ）（或面积函数Ｓ（ｆ）（ｘ））在Ｒ＾ｎ中一点有限，则它必处处有限，并且作为Ｌｉｐａ（Ｒ＾ｎ）上的算子，ｇλ和Ｓ在一定意义下有界，这对一切ａ，０＜ａ＜１，和适当的λ成立。     

Layer dynamics and phase transition for non-linear thermoviscoelasticity

In this article, we study the dynamics of transition layers for a system of 1D non-linear thermoviscoelasticity with non-monotone stress–strain relation.     

中国电力可持续转型的效率与潜力是多少?省级数据的实证分析

聚焦电力可持续转型领域,考虑能源安全(期望产出)和环境污染(非期望产出)问题,利用坏产出动态DEA模型与熵权法-TOPSIS模型,采集并整理2009~2018年省级“结构性要素指标”(投入~产出类指标)和“跨期活动变量指标”(政策性指标)的转型期数据,对中国电力可持续转型的“效率~潜力”空间进行测算、排序与优化。结果表明:中国电力转型仍处于发展较为缓慢的量变阶段,而转型的质变拐点仍未可期;就转型效率而言,电力可持续转型在省际间仍存在着较为明显的“不平衡不充分”现象;就转型潜力而言,现行的诸多诱因既提供了转型潜力的存在保障,又成为转型潜力的发展限制。     

成绩转移权系数法在教学效果评价中的应用

研究了评价教学效果的成绩转移权系数法,给出了成绩转移权系数法的评价步骤,并通过具体实例验证了该法的合理性。     

Hysteresis in discrete systems of possibly interacting elements with a double-well energy

Summary We study in this paper the hysteretic behavior of a discrete system constituted by a finite number of elements (snap-springs) whose energy has two parabolic wells. The guideline idea is that, in many circumstances, hysteresis can be due to the presence of relative minimizers of a potential (metastable states) in which the system might get locked during its quasistatic evolution. A careful investigation is thus carried out of the relative minimizers of the total energy of our system of snap-springs under imposed total displacement, and of the barriers separating them. This is done both in the case of noninteracting elements and in the case in which some interaction is present that gives rise in the energy to an extra coherence term of special form. The results allow discussion of various hysteretic phenomena, also in the presence of vibrational motion of the elements. This study of a simple but suggestive discrete system will hopefully prove itself of help in understanding the implications regarding hysteresis of certain continuum theories recently proposed to model phase transitions in the solid state, in which the energy density is assumed, as here, to be biparabolic, and in which the coherence energy term we adopt arises in a natural way when equilibria involving mixtures of kinematically noncoherent phases are considered. In these cases the optimal microstructures are known to be layered, and physically this gives a good basis to our discrete calculation.     

Dynamic Transition and Pattern Formation in Taylor Problem

The main objective of this article is to study both dynamic and structural transitions of the Taylor-Couette flow, by using the dynamic transition theory and geometric theory of incompressible flows developed recently by the authors. In particular, it is shown that as the Taylor number crosses the critical number, the system undergoes either a continuous or a jump dynamic transition, dictated by the sign of a computable, nondimensional parameter R. In addition, it is also shown that the new transition states have the Taylor vortex type of flow structure, which is structurally stable.     

k步转移矩阵的频谱插值计算法

本文较全面研究了系统状态转移矩阵的各种计算方法，在分析这些方法在实用计算中各自特点的同时，提出了较为有效的频谱插值计算法，作为应用与比较，文中给出了几个特殊转移矩阵的计算结果．     

一类逻辑环站点双态转移的研究

本对于容量有限和具有优先队列的逻辑环随机运作系统,研究其站点双态转移的有关问题,转移规律的探讨,零转移和非零转移的判断及其数目函数的推导;中还提出若干相关的新概念。章有别于以往寻求传统的工作特性参数表达式的思路,从另一个侧面揭示该类系统的数学特征。     

Self-adjusting stochastic processes

Let A_t(i, j) be the transition matrix at time t of a process with n states. Such a process may be called self-adjusting if the occurrence of the transition from state h to state k at time t results in a change in the hth row such that A_t+1(h, k) ? A_t(h, k). If the self-adjustment (due to transition h → kx) is A_{t + 1}(h, j) = λA_t(h, j) + (1 ? λ)δ_jk (0 < λ < 1), then with probability 1 the process is eventually periodic. If A₀(i, j) < 1 for all i, j and if the self-adjustment satisfies A_{t + 1}(h, k) = ?(A_t(h, k)) with ?(x) twice differentiable and increasing, x < ?(x) < 1 for 0 ? x < 1,?(1) = ?′(1) = 1, then, with probability 1, lim A_t does not exist.     

Kinetically constrained spin models

We analyze the density and size dependence of the relaxation time for kinetically constrained spin models (KCSM) intensively studied in the physics literature as simple models sharing some of the features of the glass transition. KCSM are interacting particle systems on with Glauber-like dynamics, reversible w.r.t. a simple product i.i.d Bernoulli(p) measure. The essential feature of a KCSM is that the creation/destruction of a particle at a given site can occur only if the current configuration around it satisfies certain constraints which completely define each specific model. No other interaction is present in the model. From the mathematical point of view, the basic issues concerning positivity of the spectral gap inside the ergodicity region and its scaling with the particle density p remained open for most KCSM (with the notably exception of the East model in d = 1; Aldous and Diaconis in J Stat Phys 107(5–6):945–975, 2002). Here for the first time we: (i) identify the ergodicity region by establishing a connection with an associated bootstrap percolation model; (ii) develop a novel multi-scale approach which proves positivity of the spectral gap in the whole ergodic region; (iii) establish, sometimes optimal, bounds on the behavior of the spectral gap near the boundary of the ergodicity region and (iv) establish pure exponential decay at equilibrium for the persistence function, i.e. the probability that the occupation variable at the origin does not change before time t. Our techniques are flexible enough to allow a variety of constraints and our findings disprove certain conjectures which appeared in the physical literature on the basis of numerical simulations.      

Existence and Regularity of a Nonhomogeneous Transition Matrix under Measurability Conditions

This paper is about the existence and regularity of the transition probability matrix of a nonhomogeneous continuous-time Markov process with a countable state space. A standard approach to prove the existence of such a transition matrix is to begin with a continuous (in t≥0) and conservative matrix Q(t)=[q _ij (t)] of nonhomogeneous transition rates q _ij (t) and use it to construct the transition probability matrix. Here we obtain the same result except that the q _ij (t) are only required to satisfy a mild measurability condition, and Q(t) may not be conservative. Moreover, the resulting transition matrix is shown to be the minimum transition matrix, and, in addition, a necessary and sufficient condition for it to be regular is obtained. These results are crucial in some applications of nonhomogeneous continuous-time Markov processes, such as stochastic optimal control problems and stochastic games, and this was the main motivation for this work. Supported by NSFC and RFDP. The research of O. Hernández-Lerma was partially supported by CONACYT grant 45693-F.