Epidifferentiability of the map of infima in Hilbert spaces

This article deals with derivatives for set-valued maps that take values in ordered vector spaces, in particular it concerns about the relationship between the epiderivatives of a set-valued map and its associated map of infima. When the image space is a real separable Hilbert space ordered by an orthonormal basis, by using a variational technique based on a decoupling of the ordering cone into half-spaces, we show that both epiderivatives coincide under certain hypothesis of compactness and stability. Furthermore we obtain some computation formulas for these derivatives in terms of associated scalar set-valued maps.     

Fixed point theorems for generalized contractions in ordered metric spaces

The purpose of this paper is to present some fixed point results for self-generalized contractions in ordered metric spaces. Our results generalize and extend some recent results of A.C.M. Ran, M.C. Reurings [A.C.M. Ran, M.C. Reurings, A fixed point theorem in partially ordered sets and some applications to matrix equations, Proc. Amer. Math. Soc. 132 (2004) 1435-1443], J.J. Nieto, R. Rodríguez-López [J.J. Nieto, R. Rodríguez-López, Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations, Order 22 (2005) 223-239; J.J. Nieto, R. Rodríguez-López, Existence and uniqueness of fixed points in partially ordered sets and applications to ordinary differential equations, Acta Math. Sin. (Engl. Ser.) 23 (2007) 2205-2212], J.J. Nieto, R.L. Pouso, R. Rodríguez-López [J.J. Nieto, R.L. Pouso, R. Rodríguez-López, Fixed point theorem theorems in ordered abstract sets, Proc. Amer. Math. Soc. 135 (2007) 2505-2517], A. Petru?el, I.A. Rus [A. Petru?el, I.A. Rus, Fixed point theorems in ordered L-spaces, Proc. Amer. Math. Soc. 134 (2006) 411-418] and R.P. Agarwal, M.A. El-Gebeily, D. O'Regan [R.P. Agarwal, M.A. El-Gebeily, D. O'Regan, Generalized contractions in partially ordered metric spaces, Appl. Anal., in press]. As applications, existence and uniqueness results for Fredholm and Volterra type integral equations are given.     

Fully ordered groups in partially ordered linear algebras

No abstract. Received September 2, 1999; accepted in final form October 23, 2000.     

A fuzzy-stochastic OWA model for robust multi-criteria decision making

All realistic Multi-Criteria Decision Making (MCDM) problems face various kinds of uncertainty. Since the evaluations of alternatives with respect to the criteria are uncertain they will be assumed to have stochastic nature. To obtain the uncertain optimism degree of the decision maker fuzzy linguistic quantifiers will be used. Then a new approach for fuzzy-stochastic modeling of MCDM problems will be introduced by merging the stochastic and fuzzy approaches into the OWA operator. The results of the new approach, entitled FSOWA, give the expected value and the variance of the combined goodness measure for each alternative. Robust decision depends on the combined goodness measures of alternatives and also on the variations of these measures under uncertainty. In order to combine these two characteristics a composite goodness measure will be defined. The theoretical results will be illustrated in a watershed management problem. By using this measure will give more sensitive decisions to the stakeholders whose optimism degrees are different than that of the decision maker. FSOWA can be used for robust decision making on the competitive alternatives under uncertainty.     

一种“冻地”鸡血石相似玉石的宝石学及谱学研究

研究对象是一种与“冻地”鸡血石外观高度相似的玉石,该种玉石半透明“地”中含有橙红色矿物。利用X射线粉晶衍射仪、扫描电子显微镜、红外光谱仪、拉曼光谱仪对该玉石的宝石学及谱学特征进行研究。结果表明：该玉石“地”的主要组成矿物为有序度较高的地开石、橙红色矿物为雄黄;地开石晶体为自形假六边形片状,约15～20 μm,厚2～4 μm,粒径均一且形态一致,集合体在三维空间无序排列;部分样品“地”中含有少量黄铁矿、萤石、石英、方解石等矿物。“地”的红外光谱指纹区具有高岭石族矿物的主要特征峰,分别位于430,470,540,698,755,795,913,937,1 002,1 034和1 118 cm-1;官能团区以3 622,3 653和3 706 cm-1处的吸收峰为特征,3 622 cm-1吸收峰由内羟基OH1的面内伸缩振动引起,3 653 cm-1归属于内表面羟基OH2和OH4的同相伸缩振动;从高频峰到低频峰强度依次增大,且内表面羟基OH3伸缩振动引起的吸收峰位于3 706 cm-1,表明“地”为有序地开石;拉曼光谱测试表明“血”为雄黄,具有186,222,235,273,346和355 cm-1的特征拉曼位移,其中186和222 cm-1归属于S-As-S的弯曲振动,346和355 cm-1由As-S的伸缩振动引起;拉曼光谱同样可用于“地”的矿物组成研究,低频区具有133,241,266,336,436,463,747,792和914 cm-1的高岭石族矿物的特征位移,高频区可见三个与红外光谱相似的阶梯状谱峰,3 624 cm-1强度最大,归属于OH1的伸缩振动,次强峰3 646 cm-1由OH2和OH4的同相伸缩振动引起,归属于OH3的伸缩振动峰强度最小且位于3 706 cm-1,高频区拉曼位移特点指示“地”为地开石,且有序度较高,与红外光谱测试结论一致。尽管研究样品的“地”与“冻地”鸡血石的主要组成矿物相同,为地开石,且具有外观细腻、温润等特点,但其“血”并非辰砂而是雄黄,所以不应与鸡血石混淆,其正确的珠宝玉石名称应为“粘土矿物质玉”。     

Dispersion in retentive pillar array columns

The method of volume averaging is applied to estimate the Taylor–Aris dispersion tensor of solute advected in columns consisting of ordered pillar arrays with wall retention of the type used in chromatographic separation. The appropriate closure equations are derived and solved in a unit cell with periodic boundary conditions to obtain the dispersion tensor (or the reduced plate height) as a function of the Peclet number (reduced velocity); pillar pattern, shape and size; partition coefficient; and resistance to mass transfer. The contributions of the velocity profile, the wall adsorption, and the mass transfer resistance to the dispersion tensor are identified and delineated. The model is verified by comparing its predictions and obtaining favorable agreement with results of direct numerical simulations and with experimental data for columns containing ordered pillars. The model is then used to study the effect of pillars’ shape and pattern on the longitudinal dispersion coefficient (plate height).     

Investigation of the mechanism of protein adsorption on ordered mesoporous silica using flow microcalorimetry

The adsorption of bovine serum albumin (BSA) and lysozyme (LYS) on siliceous SBA-15 with 24 nm pores was studied using flow microcalorimetry; this is the first attempt to understand the thermodynamics of protein adsorption on SBA-15 using flow microcalorimetry. The adsorption mechanism is a strong function of protein structure. Exothermic events were observed when protein–surface interactions were attractive. Entropy-driven endothermic events were also observed in some cases, resulting from lateral protein–protein interactions and conformational changes in the adsorbed protein. The magnitudes of the enthalpies of adsorption for primary protein–surface interactions decrease with increased surface coverage, indicating the possibility of increased repulsion between adsorbed protein molecules. Secondary exothermic events were observed for BSA adsorption, presumably due to secondary adsorption made possible by conformational changes in the soft BSA protein. These secondary adsorption events were not observed for lysozyme, which is structurally robust. The results of this study emphasize the influence of solution conditions and protein structure on conformational changes of the adsorbed protein and the value of calorimetry in understanding protein–surface interactions.     

序半群的阿基米德半群的半格分解

本文通过一个序半群S上的一些二元关系以及它的理想的根集的性质该序半群是阿基米德半群的半格,特别地是阿基米德半群的链的刻划,证明了S是阿基米德链当且仅当S是准素的.通过序半群的m-系的概念,证明了S的任意半素理想是含它的所有素理想的交,并通过该结论,证明了S是阿基米德半群的链当且仅当S是阿基米德半群的半格且S的所有素理想关于集包含关系构成链.作为应用,该结论在一般的半群（没有序）[1]中也成立.     

Relative polars in ordered sets

In the paper, the notion of relative polarity in ordered sets is introduced and the lattices of R-polars are studied. Connections between R-polars and prime ideals, especially in distributive sets, are found.     

On positive invertibility of operators and their decompositions

In Banach spaces ordered by a normal cone that contains interior points the positive invertibility of operators is studied. If there exists a uniformly positive functional then any positively invertible operator A possesses a B -decomposition, i.e., a positive decomposition A = U – V with the properties: U^–1 exists, VU^–1 ≥ 0, Ax ≥ 0, U x ≥ 0 imply x ≥ 0 and r (VU^–1) < 1. Earlier it was shown that the existence of a B -decomposition with r (VU^–1) < 1 is sufficient for the positive invertibility of the operator A. Peris' result is obtained as a special case of the main theorem. The decomposition is demonstrated for a positively invertible operator in a Banach space ordered by an ice cream cone (© 2009 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)