On fuzzy multi-valued functions, part 4: Fuzzy economic models

An application to fuzzy economic systems of the fuzzy multi-valued functions theory elaborated by both of us in our previous papers is presented. First, stationary and dynamic fuzzy economic models are defined. Next the optimality of fuzzy trajectories of these models is introduced and investigated.     

A NOTE ON THE BACKWARD ERRORS FOR INVERSE EIGENVALUE PROBLEMS

In this note,we consider the backward errors for more general inverse eigenvalus prob-lems by extending Sun‘‘‘‘s approach.The optimal backward errors defined for diagonal-ization matrix inverse eigenvalue problem with respect to an approximate solution,and the upper and lower bounds are derived for the optimal backward errors.The results may be useful for testing the stability of practical algorithms.     

可加广义代数格上的 Tietze 扩张定理

可加的广义代数格范畴与 T₀ 拓扑空间范畴相等价, 从这个观点出发, 作者把可加广义代数格作为一个闭集格, 在其上建立 Urysohn 引理和 Tietze 扩张定理. 这是拓扑理论在格上的一种新推广, 有助于格上拓扑理论的研究和广义连续格理论的应用.     

Study on interaction between Tb(III) and poly(N-isopropylacrylamide)

A new kind of the thermo-sensitive and fluorescent complex of poly(N-isopropylacrylamide) (PNIPAM) and Tb(III) was synthesized by free radical polymerization, in which PNIPAM was used as a polymer ligand. The complex was characterized by using X-ray photoelectron spectroscopy (XPS), ultraviolet-visual (UV), Fourier transform infrared (FT-IR) and fluorescence spectroscopy. The results from the experiments indicated that there is a strong interaction between PNIPAM and Tb(III), leading to a decrease in the electron density of nitrogen and oxygen atoms and an increase in the electron density of Tb(III) in the PNIPAM containing Tb(III) by contrast with PNIPAM and Tb(III), respectively, meanwhile, exhibiting that the Tb(III) is mainly bonded to oxygen atoms in the polymer chain of PNIPAM and formed the complex of PNIPAM-Tb(III). After forming the PNIPAM-Tb(III) complex, the emission fluorescence intensity of Tb(III) in the PNIPAM-Tb(III) complex is significantly enhanced because the effective intramolecular energy transfer from PNIPAM to Tb(III). Especially, the emission intensity of the fluorescence peak at 547 nm can be increased as high as 145 times comparing with that of the pure Tb(III). The intramolecular energy transfer efficiency for fluorescence peak at 547 nm can reach as high as 68%. The fluorescence intensity is related the weight ratio of Tb(III) and PNIPAM in the PNIPAM-Tb(III) complex. When the weight ratio is 1.4%, the maximum fluorescence enhancement can be obtained. Nevertheless, the lower critical solution temperature of PNIPAM containing a low content of Tb(III) has not obviously changed after the formation of the complex of PNIPAM-Tb(III) by the interaction between PNIPAM and Tb(III). This novel thermosensitive and fluorescence characterization of the PNIPAM-Tb(III) complex may be useful in the fluorescence systems and the biomedical field.     

Bounded knapsack sharing

A bounded knapsack sharing problem is a maximin or minimax mathematical programming problem with one or more linear inequality constraints, an objective function composed of single variable continuous functions called tradeoff functions, and lower and upper bounds on the variables. A single constraint problem which can have negative or positive constraint coefficients and any type of continuous tradeoff functions (including multi-modal, multiple-valued and staircase functions) is considered first. Limiting conditions where the optimal value of a variable may be plus or minus infinity are explicitly considered. A preprocessor procedure to transform any single constraint problem to a finite form problem (an optimal feasible solution exists with finite variable values) is developed. Optimality conditions and three algorithms are then developed for the finite form problem. For piecewise linear tradeoff functions, the preprocessor and algorithms are polynomially bounded. The preprocessor is then modified to handle bounded knapsack sharing problems with multiple constraints. An optimality condition and algorithm is developed for the multiple constraint finite form problem. For multiple constraints, the time needed for the multiple constraint finite form algorithm is the time needed to solve a single constraint finite form problem multiplied by the number of constraints. Some multiple constraint problems cannot be transformed to multiple constraint finite form problems.     

Existence of solutions for integral inclusions of Urysohn type with nonconvex-valued orientor field

In this paper, we prove the existence of solutions for an integral inclusion of Urysohn type with nonconvex orientor field and with delay. We make standard boundedness and continuity assumptions on the data, and we assume that the orientor field is l.s.c. in the state variable. Using a selection theorem of Fryszkowski, we are able to prove the existence of solutions, extending an earlier result of Angell.This research was supported by NSF Grant No. DMS-86-02313.     

Tight Lower Bounds on the Size of a Maximum Matching in a Regular Graph

In this paper we study tight lower bounds on the size of a maximum matching in a regular graph. For k ≥3, let G be a connected k-regular graph of order n and let α′(G) be the size of a maximum matching in G. We show that if k is even, then , while if k is odd, then . We show that both bounds are tight. Research supported in part by the South African National Research Foundation and the University of KwaZulu-Natal.     

HL-2M装置低杂波钛泵电流监测器的研制

选用Arduino nano开源硬件平台、OLED图形显示器和SD卡等器件,研制了钛泵电流监测器,实现了在非实验期间钛泵电流长期低速采集、存储和趋势图显示功能。同时启用内部中断和外部中断,提升采样频率到1k Hz,拓展了监测器的应用范围。测试结果表明,监测器趋势图与测试信号一致,最大采集误差为0.25μA。     

黄河下游堤防地质险段研究

由地质作用影响形成的易出险堤段称为地质险段 ,主要包括活断层作用影响形成的堤基易渗漏段、强地震高发区段和地基稳定性差段等。构造节点是识别地质险段的重要的河流地貌标志之一。根据成因 ,本文将黄河下游的地质险段分为三类 ,即新构造险段、沉降险段、断裂复活险段。针对黄河下游堤防地质特征 ,圈定出东坝头、大刘屯—董口黄河南岸和路那里—十里堡黄河南岸地质险段 ,提出了治理的有关措施     

Growth of meromorphic solutions of linear difference equations

In this paper, the authors continue to study the growth of meromorphic solutions of homogeneous or non-homogeneous linear difference equations with entire coefficients, and obtain some results which are improvement and extension of previous results in Chiang and Feng (2008) [7] and Laine and Yang (2007) [19]. Examples are also given to illustrate the sharpness of our results.