Convexifactors,generalized convexity and vector optimization

In this article we study a recently introduced notion of non-smooth analysis, namely convexifactors. We study some properties of the convexifactors and introduce two new chain rules. A new notion of non-smooth pseudoconvex function is introduced and its properties are studied in terms of convexifactors. We also present some optimality conditions for vector minimization in terms of convexifactors.     

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.     

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.     

Determination of the swelling behavior of superabsorbent polymers by a tracer-assisted on-line spectroscopic measurement

This work reports on a method for the accurate determination of kinetic swelling behavior and properties of superabsorbent polymers by a tracer-assisted on-line spectroscopic measurement. Based on monitoring the spectral absorption of a tracer compound (blue dextran 2000) at 610 nm in a superabsorbent polymer containing solution, the swelling (water absorption) of the polymer during the process can be followed, from which the parameters in a kinetic equation can be obtained. The results showed that the data obtained by the present method has a good measurement precision and accuracy, in which the relative differences were less than 4.0% when comparing the data measured by a reference method (i.e., the tea bag method). Since the present method can perform an on-line measurement, it is much superior to the current tea bag method and therefore is very suitable to be used in the process related study for the swelling behavior of superabsorbent polymers in many applications.     

新一代运载火箭时序仿真系统信号完整性分析

新一代运载火箭时序仿真系统具有数字电路速度快、集成度高的特点,系统要求发出多路高精度时序、时串信号以满足新一代运载火箭地面测试设备的检查与校准需求,因此信号完整性问题在系统设计中不容忽视。针对仿真系统的典型模块(USB 3.0 Super-speed差分线、FPGA外设数据走线、时钟走线)进行建模分析仿真得出PCB硬件电路设计参数,给出时序仿真系统设计信号完整性问题的抑制和解决方法,优化了板级信号质量,改善系统可靠性、工作连续性和输出精度,可有效提高新一代运载火箭测试效率和测试可靠性。     

Optimal Groomings with Grooming Ratios Six and Seven

Grooming uniform all‐to‐all traffic in optical (SONET) rings with grooming ratio C requires the determination of a decomposition of the complete graph into subgraphs each having at most C edges. The drop cost of such a grooming is the total number of vertices of nonzero degree in these subgraphs, and the grooming is optimal when the drop cost is minimum. The determination of optimal C‐groomings has been considered for , and completely solved for . For , it has been shown that the lower bound for the drop cost of an optimal C‐grooming can be attained for almost all orders with 5 exceptions and 308 possible exceptions. For , there are infinitely many unsettled orders; especially the case is far from complete. In this paper, we show that the lower bound for the drop cost of a 6‐grooming can be attained for almost all orders by reducing the 308 possible exceptions to 3, and that the lower bound for the drop cost of a 7‐grooming can be attained for almost all orders with seven exceptions and 16 possible exceptions. Moreover, for the unsettled orders, we give upper bounds for the minimum drop costs.