求极限的等价无穷大代换

给出等价无穷大代换的法则,并由此得到求某些未定式极限的计算方法.     

Theoretical and experimental studies on mesoscale flame propagation and extinction

Mesoscale flame propagation and extinction of premixed flames in channels are investigated theoretically and experimentally. Emphasis is placed on the effect of wall heat loss and the wall–flame interaction via heat recirculation. At first, an analytical solution of flame speed in mesoscale channels is obtained. The results showed that channel width, flow velocity, and wall thermal properties have dramatic effects on the flame propagation and lead to multiple flame regimes and extinction limits. With the decrease in channel width, there exist two distinct flame regimes, a fast burning regime and a slow burning regime. The existence of the new flame regime and its extended flammability limit render the classical quenching diameter inapplicable. Furthermore, the results showed that at optimum conditions of flow velocity and wall thermal properties, mesoscale flames can propagate faster than the adiabatic flame. Second, numerical simulation with detailed chemistry demonstrated the existence of multiple flame regimes. The results also showed that there is a non-linear dependence of the flame speed on equivalence ratio. Moreover, it is shown that the Nusselt number has a significant impact on this non-linear dependence. Finally, the non-linear dependence of flame speed on equivalence ratio for both flame regimes is measured using a C₃H₈–air mixture. The results are in good agreement with the theory and numerical simulation.     

一类稀疏效应下捕食┐被捕食者系统极限环的存在性和唯一性

本文研究捕食者种群具有线性密度制约的一类稀疏效应下捕食－被捕食者系统ｘ＝ｘ（ａｘ－ｃｘ３－ｂｙ），ｙ＝ｙ（－α＋βｘ－γｙ）．（＊）得到：（１）当Ａ１＜Ａ１，Ａ２＜Ａ２，Ａ３＞Ａ３时，系统（＊）在第一象限内存在极限环；（２）当Ａ２＜Ａ２，Ａ３＞Ａ３时，系统（＊）在第一象限内存在唯一极限环     

On martingale tail sums for the path length in random trees

For a martingale (X_n) converging almost surely to a random variable X, the sequence (X_n– X) is called martingale tail sum. Recently, Neininger (Random Structures Algorithms 46 (2015), 346–361) proved a central limit theorem for the martingale tail sum of Régnier's martingale for the path length in random binary search trees. Grübel and Kabluchko (in press) gave an alternative proof also conjecturing a corresponding law of the iterated logarithm. We prove the central limit theorem with convergence of higher moments and the law of the iterated logarithm for a family of trees containing binary search trees, recursive trees and plane‐oriented recursive trees. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 493–508, 2017     

非单C~*-代数α-比较性的等价刻画

给出非单C~*-代数α-比较性的等价刻画:当每个τ∈QT(■H)均为忠实时,■具有α-比较性,当且仅当对于任意的〈a〉,〈b〉∈Cu(■)且∝,若α·d_τ(a)≤在Cu(■)中成立;一般地,当QT(■H)≠Φ时,■具有α-比较性,当且仅当对于任意的,∈Cu(■),若存在η>0,使得d_τ(α)≤(α~(-1)-η)d_τ(b)(_τ∈QT(■H)),则≤在Cu(■)中成立.     

部分均匀荷载作用下圆板塑性极限统一解

本文采用俞茂宏双剪统一屈服准则求解部分均匀荷载下简支圆板的塑性极限，已有的最大主应力准则、Ｔｒｅｓｃａ准则，Ｍｉｓｅｓ准则的解答均是该解答的特例或线性逼近。该解答可以适合于多种工程材料，具有普遍性和适用性，从得出的解析解和图示中可得出一些新的有益的认识     

PLASTIC LIMIT LOAD ANALYSIS OF DEFECTIVE PIPELINES

The integrity assessment of defective pipelines represents a practically important task of structural analysis and design in various technological areas, such as oil and gas industry, power plant engineering and chemical factories. An iterative algorithm is presented for the kinematic limit analysis of 3-D rigid-perfectly plastic bodies. A numerical path scheme for radial loading is adopted to deal with complex multi-loading systems. The numerical procedure has been applied to carry out the plastic collapse analysis of pipelines with part-through slot under internal pressure, bending moment and axial force. The effects of various shapes and sizes of part-through slots on the collapse loads of pipelines are systematically investigated and evaluated. Some typical failure modes corresponding to different configurations of slots and loading forms are studied.     

The spherical limit forn-vector correlations

We investigate then limit of then-vector model single-spin and pairspin correlation functions. In this limit we show that the correlation functions become those of the corresponding spherical model.     

具常数存放的非线性功能反应捕食模型的定性分析

研究一类食饵具常数存放且功能反应函数为次线性函数的食饵-捕食者模型,获得了一些平衡点全局渐近稳定,极限环存在惟一的充分条件.利用数值仿真检验了我们的结论.     

Brown运动增量在H(o)lder范数下关于(r,p)-容度的泛函极限定理

利用Brown运动在H\"older 范数下关于$(r,p)$-容度的大偏差,证明了Brown运动增量在H\"older范数下关于$(r,p)$-容度的泛函极限定理.