ERP的局限

目前,ERP生产计划管理模型多采用制造资源计划（ManufacturingReⅫuweP1anning,MRPⅡ）,这是在物料需求计划（MaterialRequirementPlanning,MRP）的基础上逐渐优化形成的,但仍存在较大的局限性。具体来说体现在以下几点：     

Limitations of learning in automata-based systems

In this article, we aim to analyze the limitations of learning in automata-based systems by introducing the L⁺$L^{+}$ algorithm to replicate quasi-perfect learning, i.e., a situation in which the learner can get the correct answer to any of his queries. This extreme assumption allows the generalization of any limitations of the learning algorithm to less sophisticated learning systems. We analyze the conditions under which the L⁺$L^{+}$ infers the correct automaton and when it fails to do so. In the context of the repeated prisoners’ dilemma, we exemplify how the L⁺$L^{+}$ may fail to learn the correct automaton. We prove that a sufficient condition for the L⁺$L^{+}$ algorithm to learn the correct automaton is to use a large number of look-ahead steps. Finally, we show empirically, in the product differentiation problem, that the computational time of the L⁺$L^{+}$ algorithm is polynomial on the number of states but exponential on the number of agents.     

Limitations on the size of semigroups of matrices

If a nonzero linear functional has finite, countable, or bounded range when restricted to an irreducible semigroup of complex matrices, it is shown that itself has the same property. Similar results are proven under the hypothesis that a nontrivial ideal of is finite, countable, or bounded.     

Limitations of the L-curve method in ill-posed problems

This paper considers the Tikhonov regularization method with the regularization parameter chosen by the so-called L-curve criterion. An infinite dimensional example is constructed for which the selected regularization parameter vanishes too rapidly as the noise to signal ratio in the data goes to zero. As a consequence the computed reconstructions do not converge to the true solution. Numerical examples are given to show that similar phenomena can be observed under more general assumptions in discrete ill-posed problems provided the exact solution of the problem is smooth.This work was partially supported by NATO grant CRG 930044.     

On Limitations and Insufficiency of the Trotter-Kato Theorem

We exhibit examples of convergence of equibounded semigroups that cannot be captured by means of the classical Trotter-Kato theorem. This is done to substantiate the need for semigroup-theoretical tools that would supplement the Trotter-Kato theorem in dealing with convergence problems.     

Local Limitations of the Ext Functor Do Not Exist

In this note it is shown that for k a field, and for the four-dimensionalalgebra = kx, y/x², y², xy + qyx when qⁿ 1, 0 for all n, thereexist a two-dimensional module M and a family of two-dimensionalmodules M_i, i = 1, 2, ..., such that for i equal to 0, j and j + 1, and otherwise. This is probably the most straightforward examplegiving a negative answer to a question raised by Maurice Auslander.2000 Mathematics Subject Classification 16D10, 16E10, 16E30,16G10, 16G20.     

Limitations imposed on elasticity coefficients of anisotropic solid bodies

A theoretical analysis has been made of the previously published results [1] on the determination of the tensor components of the elasticity constants of one of the modifications of an orthotropic glass-fiber-reinforced plastic to clarify the required agreement with fundamental laws of physics.     

关于和式极限的两个定理及其应用

从2017年3月第八届全国大学生数学竞赛决赛(数学类)的一道题入手,介绍了两个相关和式极限的定理,推广了一些结果.这些结论有助于完善相关教学内容.     

C—D生产函数在经济理论上的局限性

本文通过对经济系统机理分析,建立起反映生产力──生产关系的数学模型．指出了应用Ｃ－Ｄ生产函数分析科技进步存在的局限性,从而从观念上指出了“只追求科技进步就能提高经济效益”认识的片面性。     

等价无穷小代换在求和式极限中的应用

等价无穷小代换经常用于求函数乘积的极限,讨论了如何利用等价无穷小代换求函数和式的极限.     

High-order Explicit Runge-Kutta Formulae, Their Uses and Limitations

On page 53, the value given for the coefficient c16, approximatelyhalf-way down the right-hand column, is incorrect as printed.The correct figure is as follows:     

Scheduling Jobs of Equal Durations with Tardiness Costs and Resource Limitations

In this paper it is shown that the combinatorial problem of scheduling jobs of equal duration with tardiness costs and resource limitations can be solved by formulating the problem as a classical transportation model which is here highly degenerate. A new algorithm derived from the classical stepping stone method is given. The algorithm produces a strict decrease of the objective at each iteration. A special case which could be called the simplest problem of scheduling is also studied.     

一类多元函数极限不存在性判别法

为一类二元及三元广义齐次有理分式函数极限的不存在性建立一个判别准则.     

Limitations of the approximation capabilities of neural networks with one hidden layer

Lets1 be an integer andW be the class of all functions having integrable partial derivatives on [0, 1] ^s . We are interested in the minimum number of neurons in a neural network with a single hidden layer required in order to provide a mean approximation order of a preassigned>0 to each function inW. We prove that this number cannot be if a spline-like localization is required. This cannot be improved even if one allows different neurons to evaluate different activation functions, even depending upon the target function. Nevertheless, for any>0, a network with neurons can be constructed to provide this order of approximation, with localization. Analogous results are also valid for otherL ^p norms.The research of this author was supported by NSF Grant # DMS 92-0698.The research of this author was supported, in part, by AFOSR Grant #F49620-93-1-0150 and by NSF Grant #DMS 9404513.