Multilinear interpolation between adjoint operators

Multilinear interpolation is a powerful tool used in obtaining strong-type boundedness for a variety of operators assuming only a finite set of restricted weak-type estimates. A typical situation occurs when one knows that a multilinear operator satisfies a weak L^q estimate for a single index q (which may be less than one) and that all the adjoints of the multilinear operator are of similar nature, and thus they also satisfy the same weak L^q estimate. Under this assumption, in this note we give a general multilinear interpolation theorem which allows one to obtain strong-type boundedness for the operator (and all of its adjoints) for a large set of exponents. The key point in the applications we discuss is that the interpolation theorem can handle the case q?1. When q>1, weak L^q has a predual, and such strong-type boundedness can be easily obtained by duality and multilinear interpolation (cf. Interpolation Spaces, An Introduction, Springer, New York, 1976; Math. Ann. 319 (2001) 151; in: Function Spaces and Applications (Lund, 1986), Lecture Notes in Mathematics, Vol. 1302, Springer, Berlin, New York, 1988; J. Amer. Math. Soc. 15 (2002) 469; Proc. Amer. Math. Soc. 21 (1969) 441).     

Structural hierarchy of rock masses and the mechanisms of its formation

The formation mechanisms for the structural hierarchy in geological media are discussed. It is shown that the formation of such a hierarchy is caused by certain external and internal circumstances. The first ones consist in the fact that, because of external actions, the Earth’s poles continuously execute the translational and rotational motions responsible for a regular structure of rock fracture and for the appearance of the scale factor √2. The second ones consist in the fact that, under the action of many random factors and because of external actions, during the formation of geological media there appear dissipative structures and, hence, some self-similar fractal structures are formed.     

基于进化人工神经网络的组合系统滤波技术

在组合系统运用Kalman滤波器技术时,准确的系统模型和可靠的观测数据是保证其性能的重要因素,否则将大大降低Kalman滤波器的估计精度,甚至导致滤波器发散.为解决上述Kalman应用中的实际问题,提出了一种新颖的基于进化人工神经网络技术的自适应Kalman滤波器.仿真试验表明该算法可以在系统模型不准确时、甚至外部观测数据短暂中断时,仍能保证Kalman滤波器的性能.     

作业成本法数学模型的创新

随着企业产品价格竞争愈演愈烈，成本的合理分配、计算日显重要，但在间接费用的分摊上，传统成本会计对成本信息反映失真的局限性日益显露，会计理论界和实务界开始寻求一种新的准确的成本计算方法，作业成本法应运而生。本将由作业成本法基本原理推导出其数学模型，并将对其数学模型进一步改进，建立比较数学模型。使作业成本法向实际应用更进一步。     

线性规划问题的规范型算法

提出了线性规划问题的两种规范标准形式；证明了任意一个线性规划问题都可化为这两种形式之一；给出了不需引入人工变量的线性规划问题的求解算法。     

MC模式下顾客需求与厂商供应的纳什均衡

在大规模定制(MC，Mass Customization)模式下，基于市场需求的复杂化，厂商对个性化的顾客需求很难做出及时准确的反应，而且由于其自身生产能力的限制，不可能对所有的个性化用户进行一一地满足，只可能对已经存在的个性化需求，根据自身的生产能力和规模，以利润最大化及顾客对产品的满意度为目标，对个性化需求进行较准确地预测，从而正确指导生产。本通过博弈论的方法，提出了一个基于顾客对产品的满意度及企业的利润的一个非合作博弈模型，并给出求解纳什均衡的方法。     

基于实数编码的免疫遗传算法研究

针对标准遗传算法(SGA)搜索效率低、收敛速度慢等缺陷，在免疫遗传算法的基础上提出了基于实数编码的免疫遗传算法(RIGA)。研究表明，RIGA对SGA的改进是有效可行的，显示出稳健的全局优化、计算量少而解的精度高等特点，具有较高的应用价值。     

农户信用评估系统的设计与运用研究

农户信用评估的研究对推动农村消费信用的发展，促进农村经济良好运行十分重要。本在构造农户信用评估的指标体系的基础上，提出了农户信用评估神经网络模型的算法，利用实际搜集到的农户资料进一步建立了农户信用评估模型，继而构造了农户信用评估系统，并举例说明了该系统的实际运用，以期能为农村经济发展中的农户信用评价及相关研究提供一丝基础性启发。