Ratio-conjugation tool and its application in linear optimization models†

The ratio-conjugation-tool (RC) is constructed systematically, and its applicability for analysis of economic models is demonstrated. One of the main results establishes a general formula for RC of aggregative function. This tool is applied to the analysis of linear economic dynamics models of Neumann–Gale type which can be solved by a dynamic programming method: for each direct problem we construct the corresponding dual RC-problem. Moreover, we consider three examples of the most important economic dynamics models and look at these now from a unified general position.     

An Alternative Way to Generalize the Pentagon

We introduce the concept of a pentagonal geometry as a generalization of the pentagon and the Desargues configuration, in the same vein that the generalized polygons share the fundamental properties of ordinary polygons. In short, a pentagonal geometry is a regular partial linear space in which for all points x, the points not collinear with the point x, form a line. We compute bounds on their parameters, give some constructions, obtain some nonexistence results for seemingly feasible parameters and suggest a cryptographic application related to identifying codes of partial linear spaces.     

A variational approach to second-order approximability of sliding mode control systems

We consider robustness properties of second-order methods for the sliding mode control of nonlinear ordinary differential equations. A new approach is presented based on the theory of well-posed optimization problems. It is shown that the convergence of the real states of the control system to the ideal one is intimately related to Tykhonov well-posedness of suitably defined dynamic optimization problems.     

CDMA2000覆盖公路隧道的工程实例分析

简要介绍了公路隧道的孔径尺寸、电信运营商所需的电源、站点、管沟资源及隧道覆盖工程费用构成;详细论述了无线覆盖建设方案中的共建共享、公路隧道无线传播特点及信号源、天馈系统、天线、站点选择等有关问题,并通过多个具体实例对典型覆盖工程分别进行了测试验证。     

Cousin I condition and Stein spaces

Here we give a few n-dimensional extensions of a recent result of M. Abe concerning a Cousin I characterization of two-dimensional Stein manifolds.     

Analysis for some properties of discrete time Markov decision processes

This paper investigates properties of the optimality equation and optimal policies in discrete time Markov decision processes with expected discounted total rewards under weak conditions that the model is well defined and the optimality equation is true. The optimal value function is characterized as a solution of the optimality equation and the structure of optimal policies is also given.     

The projective dimension of three cubics is at most 5

Let R be a polynomial ring over a field and I an ideal generated by three forms of degree three. Motivated by Stillman's question, Engheta proved that the projective dimension $\mathrm{pd}(R/I)$ of $R/I$ is at most 36, although the example with largest projective dimension he constructed has $\mathrm{pd}(R/I)=5$. Based on computational evidence, it had been conjectured that $\mathrm{pd}(R/I)\le 5$. In the present paper we prove this conjectured sharp bound.