m步非线性多重分裂Newton法的收敛性

本文讨论了多重分裂算法在求解一类非线性方程组的全局收敛性和单侧收敛性．当用研步Newton法来代替求得每个非线性多重分裂子问题的近似解时，同样给出相应收敛性结论．数值算例证实了算法的有效性．     

线性规划多重最优解判别准则刍议

本构造了一些线性规划问题来探讨多重最优解的判别准则，补充了现行献中关于多重最优解判别准则描述的不足，并指出多重最优解判别准则在出现退化解时可能失效的例外情况。     

带启动时间的多重休假的GI/Geom/1离散时间排队

本文通过矩阵几何解方法分析了带启动时间的多重休假的GI／Geom／1离散时间排队，得到了稳态队长和等待时间的分布、母函数及随机分解结果，推广了以前的结论。此外，本文考虑的休假都是服从几何分布．我们还可讨论更一般的分布。     

具有多重解的非线性奇摄动问题

利用边界层法,研究了一类具有多重解的非线性奇摄动问题．在适当的假设下,通过给出外部解展开式系数及其对应边界条件的一般表达式,根据退化问题的边值作为某方程的根的重数,得到了此问题不同形式的渐近解．特别地,当这种根的重数为偶数时,问题具有二重解．另外,将相关结果应用于化学反应器理论,并通过对具有多重解的例子的渐近解和精确解的数值模拟说明如此构造的渐近解具有较高的精度．     

多重分派问题

系统分析了多重分派问题的线性规划模型的性质和特点，得到一个直接求解多重分派问题的算法，利用该算法来求解古典题，无需要求完全二部图，特别是求解过程不会受到已化解的影响。     

含内生生育率的RCK模型

本文在经典的Ｒａｍｓｅｙ－Ｃａｓｓ－Ｋｏｏｐｍａｎｓ（ＲＣＫ）经济增长模型中 内生生育率、建立了一个能刻划经济增长和人口增长相互作用的ＲＣＫ模型,证明此模型在生产函数满足一定条件下存在最优增长路径和稳态解。     

带有止步和N-策略的M/H2/1多重休假排队系统

本文研究一个带有止步和N-策略的M/H2/1多重休假排队系统。利用拟生灭过程与矩阵几何解的方法求出了系统的稳态平衡条件和稳态概率分布。此外,本文还求出了系统的一些性能指标。     

R~n上分形集的多重维数

本文推广Ｈａｕｓｄｏｒｆｆ测度和维数的概念，引入了被称作为多重维测度和多重维数的概念．文中证明了关于多重维测度的Ｆｒｏｓｔｍａｎ定理，构造了一个例子说明存在一类点集，其Ｈａｕｓｄｏｒｆｆ测度是零或十∞，但其多重维测度是一个正数，并说明了多重维数除第一个分量是正数外，其它分量可以取到任何实数．     

一类拟线性椭圆方程的多重解(英文)

本文考虑一类包含拟线性椭圆算子当非线性项在无穷远处是(p-1)-次线性增长时多重解的存在性.结果,利用三临界点定理,我们证明了该类方程多重解的存在性.     

一类二阶常微分方程奇异边值问题多重解的至少个数

本文利用变分原理和Z2不变群指标研究了二阶常微分方程边值问题的多重解．得出了这类解个数的下界估计     

Multiple cover time

Motivated by applications in Markov estimation and distributed computing, we define the blanket time of an undirected graph G to be the expected time for a random walk to hit every vertex of G within a constant factor of the number of times predicted by the stationary distribution. Thus the blanket time is, essentially, the number of steps required of a random walk in order that the observed distribution reflect the stationary distribution. We provide substantial evidence for the following conjecture: that the blanket time of a graph never exceeds the cover time by more than a constant factor. In other words, at the cost of a multiplicative constant one can hit every vertex often instead of merely once. We prove the conjecture in the case where the cover time and maximum hitting time differ by a logarithmic factor. This case includes almost all graphs, as well as most “natural” graphs: the hypercube, k-dimensional lattices for k ≥ 2, balanced k-ary trees, and expanders. We further prove the conjecture for perhaps the most natural graphs not falling in the above case: paths and cycles. Finally, we prove the conjecture in the case of independent stochastic processes. © 1996 John Wiley & Sons, Inc. Random Struct. Alg., 9 , 403–411 (1996)     

Multiple fractional integrals

Multiple integrals with respect to fractional Brownian motion (with H > 1/2) are constructed for a large class of functions. The first and second moments of the multiple integrals are explicitly identified. Received: 23 February 1998 / Revised version: 31 July 1998     

Least Common Multiple

<正>Work with a partner.Use 9 centimeter cubes to model the first floor of Building 1 and 12 centimeter cubes to model the first floor of Building 2,as shown.1.Add a second floor to each building.Record the total number of cubes used in a table like the one shown below.     

Loading Multiple Pallets

This paper addresses the problem of loading pallets with non-identical items, i.e. what has been called the ‘Distributor's Pallet Packing Problem’. It concentrates on the situation where the consignment to be loaded cannot be accommodated on a single pallet. A greedy procedure for tackling this problem, which is based on a published approach for loading single pallets, is described and evaluated. Also discussed is a series of possible modifications of the basic method, whereby the pallets involved are packed simultaneously. A detailed performance analysis is undertaken. The paper concludes with suggestions for further work in this area.     

Multiple commutator formulas

Let A be a quasi-finite R-algebra (i.e., a direct limit of module finite algebras) with identity. Let I _i , i = 0, …,m, be two-sided ideals of A, GL _n (A, I _i ) be the principal congruence subgroup of level I _i in GL _n (A) and E _n (A, I _i ) be the relative elementary subgroup of level I _i . We prove the multiple commutator formula $$\left[ {{E_n}(A,{I_0}),{\rm{G}}{{\rm{L}}_n}(A,{I_1}),{\rm{G}}{{\rm{L}}_n}(A,{I_2}), \ldots ,{\rm{G}}{{\rm{L}}_n}(A,{I_m})} \right] = \left[ {{E_n}(A,{I_0}),{E_n}(A,{I_1}),{E_n}(A,{I_2}), \ldots ,{E_n}(A,{I_m})} \right],$$ , which is a broad generalization of the standard commutator formulas. This result contains all the published results on commutator formulas over commutative rings and answers a problem posed by A. Stepanov and N. Vavilov.     

Immense Multiple Realization

In his latest book Physicalism, or Something near Enough, Jaegwon Kim argues that his version of functional reductionism is the most promising way for saving mental causation. I argue, on the other hand, that there is an internal tension in his position: Functional reductionism does not save mental causation if Kim’s own supervenience argument is sound. My line of reasoning has the following steps: (1) I discuss the supervenience argument and I explain how it motivates Kim’s functional reductionism; (2) I present what I call immense multiple realization, which says that macro-properties are immensely multiply realized in determinate micro-based properties; (3) on that background I argue that functional reductionism leads to a specified kind of irrealism for mental properties. Assuming that such irrealism is part of Kim’s view, which Kim himself seems to acknowledge, I argue that Kim’s position gets the counterfactual dependencies between macro-causal relata wrong. Consequently, his position does not give a conservative account of mental causation. I end the paper by discussing some alternative moves that Kim seems to find viable in his latest book. I argue on the assumption that the supervenience argument is sound, so the discussion provides further reasons to critically reevaluate that argument because it generalizes in deeply problematic ways.     

Multiple zeta values

The definition of multiple zeta values is extended in the paper. The preservation of the main properties known for multiple zeta values in the sense of their classic definition is proved.     

Multiple ergodic theorems

Given measure preserving transformationsT ₁,T ₂,...,T _s of a probability space (X,B, μ) we are interested in the asymptotic behaviour of ergodic averages of the form $$\frac{1}{N}\sum\limits_{n = 0}^{N - 1} {T_1^n f_1 \cdot T_2^n f_2 } \cdot \cdots \cdot T_s^n f_s $$ wheref ₁,f ₂,...,f _s ?L ^∞(X,B,μ). In the general case we study, mainly for commuting transformations, conditions under which the limit of (1) inL ²-norm is ∫ _x f ₁ dμ·∫ _x f ₂ dμ...∫ _x f _s dμ for anyf ₁,f ₂...,f _s ?L ^∞(X,B,μ). If the transformations are commuting epimorphisms of a compact abelian group, then this limit exists almost everywhere. A few results are also obtained for some classes of non-commuting epimorphisms of compact abelian groups, and for commuting epimorphisms of arbitrary compact groups.     

Multiple criteria linear regression

The unknown parameters in multiple linear regression models may be estimated using any one of a number of criteria such as the minimization of the sum of squared errors MSSE, the minimization of the sum of absolute errors MSAE, and the minimization of the maximum absolute error MMAE. At present, the MSSE or the least squares criterion continues to be the most popular. However, at times the choice of a criterion is not clear from statistical, practical or other considerations. Under such circumstances, it may be more appropriate to use multiple criteria rather than a single criterion to estimate the unknown parameters in a multiple linear regression model. We motivate the use of multiple criteria estimation in linear regression models with an example, propose a few models, and outline a solution procedure.