A New View on Fuzzy Hypermodules

We describe the relationship between the fuzzy sets and the algebraic hyperstructures. In fact, this paper is a continuation of the ideas presented by Davvaz in （Fuzzy Sets Syst., 117： 477- 484, 2001） and Bhakat and Das in （Fuzzy Sets Syst., 80： 359-368, 1996）. The concept of the quasicoincidence of a fuzzy interval value with an interval-valued fuzzy set is introduced and this is a natural generalization of the quasi-coincidence of a fuzzy point in fuzzy sets. By using this new idea, the concept of interval-valued （α,β）-fuzzy sub-hypermodules of a hypermodule is defined. This newly defined interval-valued （α,β）-fuzzy sub-hypermodule is a We shall study such fuzzy sub-hypermodules and sub-hypermodules of a hypermodule. generalization of the usual fuzzy sub-hypermodule. consider the implication-based interval-valued fuzzy     

L-型模糊格蕴涵代数

This paper introduced the concept of L-fuzzy sub lattice implication algebra and discussed its properties. Proved that the intersection set of a family of L-fuzzy sub lattice implication algebras is a L-fuzzy sub lattice implication algebra, that a L-fuzzy sub set of a lattice implication algebra is a L-fuzzy sub lattice implication algebra if and only if its every cut set is a sub lattice implication algebra, and that the image and original image of a L-fuzzy sub lattice implication algebra under a lattice implication homomorphism are both L-fuzzy sub lattice implication algebras.     

Ultra <Emphasis Type="Italic">LI</Emphasis>-ideals in lattice implication algebras and <Emphasis Type="Italic">MTL</Emphasis>-algebras

A mistake concerning the ultra LI-ideal of a lattice implication algebra is pointed out, and some new sufficient and necessary conditions for an LI-ideal to be an ultra LI-ideal are given. Moreover, the notion of an LI-ideal is extended to MTL-algebras, the notions of a (prime, ultra, obstinate, Boolean) LI-ideal and an ILI-ideal of an MTL-algebra are introduced, some important examples are given, and the following notions are proved to be equivalent in MTL-algebra: (1) prime proper LI-ideal and Boolean LI-ideal, (2) prime proper LI-ideal and ILI-ideal, (3) proper obstinate LI-ideal, (4) ultra LI-ideal. This work was supported by the Zhejiang Provincial Natural Science Foundation of China (Grant No. Y605389) and K. C. Wong Magna Fund in Ningbo University.     

Representation of Cubic Lattices by Symmetric Implication Algebras

In this paper a cubic lattice L(S) is endowed with a symmetric implication structure and it is proved that L(S) \ {0} is a power of the three-element simple symmetric implication algebra. The Metropolis–Rota’s symmetries are obtained as partial terms in the language of symmetric implication algebras.     

开展化学教育硕士学位试点工作的实践和思考

本文结合近几年我们开展化学教育硕士学位试点工作的实践 ,介绍了一些成功的经验 ,同时对存在的问题也提出了一些建议和思考。     

ON THE INCOMPLETENESS OF A DESCENDING CHAIN OF EXTENSIONS OF IMPLICATIONAL S5

C5.ω is obtained by adding, schematically, to the strict-implicational fragment C5 of S5 the axiom ((p → q) → (q → p)) → (q → p). This paper presents a fully general proof that neither C5.ω nor any of a descending chain of its extensions is complete with respect to any class of frames, correcting the garbled details of a version skeched in an earlier paper (same Zeitschrift 31 (1985), 201-208).     

On a Boolean-valued Model of the Strict Implication System(Continuous)

The reference [4] proved the consistency of S1 and S2 among Lewis' five strict implication systems in the modal logic by using the method of the Boolean-valued model. But, in this method, the consistency of S3, S4 and S5 in Lewis' five strict implication systems is not decided. This paper makes use of the properties: (1) the equivalence of the modal systems S3 and P3, S4 and P4; (2) the modal systems P3 and P4 all contained the modal axiom T(□p → p); (3) the modal axiom T is correspondence to the reflexive property in VB. Hence, the paper proves: (a) ‖As31‖ = 1; (b) ‖AS41‖ = 1; (c) ‖AS5l‖ = 1 in the model (where B is a complete Boolean algebra, R is reflexive property in VB). Therefore, the paper finally proves that the Boolean-valued model VB of the ZFC axiom system in set theory is also a Boolean-valued model of Lewis' the strict implication system S3, S4 and S5.     

Hilbert algebras as implicative partial semilattices

The infimum of elements a and b of a Hilbert algebra are said to be the compatible meet of a and b, if the elements a and b are compatible in a certain strict sense. The subject of the paper will be Hilbert algebras equipped with the compatible meet operation, which normally is partial. A partial lower semilattice is shown to be a reduct of such an expanded Hilbert algebra i ?both algebras have the same ?lters.An expanded Hilbert algebra is actually an implicative partial semilattice (i.e., a relative subalgebra of an implicative semilattice),and conversely.The implication in an implicative partial semilattice is characterised in terms of ?lters of the underlying partial semilattice.     

An experimental and theoretical study on the kinetics of the reaction between 4‐hydroxy‐3‐hexanone CH3CH2C(O)CH(OH)CH2CH3 and OH radicals

Experimental and theoretical rate coefficients are determined for the first time for the reaction of 4‐hydroxy‐3‐hexanone (CH₃CH₂C(O)CH(OH)CH₂CH₃) with OH radicals as a function of temperature. Experimental studies were carried out using two techniques. Absolute rate coefficients were measured using a cryogenically cooled cell coupled to the pulsed laser photolysis‐laser‐induced fluorescence technique with temperature and pressure ranges of 280‐365 K and 5‐80 Torr, respectively. Relative values of the studied reaction were measured under atmospheric pressure in the range of 298‐354 K by using a simulation chamber coupled to a FT‐IR spectrometer. In addition, the reaction of 4H3H with OH radicals was studied theoretically by using the density functional theory method over the range of 278‐350 K. Results show that H‐atom abstraction occurs more favorably from the C–H bound adjacent to the hydroxyl group with small barrier height. Theoretical rate coefficients are in good agreement with the experimental data. A slight negative temperature dependence was observed in both theoretical and experimental works. Overall, the results are deliberated in terms of structure–reactivity relationship and atmospheric implications.     

国内外化学教师PCK评价量规的实证研究述评*

主要从化学教师PCK评价量规的建立方式、测查内容、特征属性,以及应用量规测查PCK水平实证研究的研究设计、研究目的等维度梳理了相关文献。综述表明:(1)国内外研究均较多基于已有成果建立量规,较少基于原始数据生成量规,对比国外,国内有关后者的研究更为稀缺;(2)国内外研究均较多测查KoC,KoL,KoS,而较少测查KoA,CTO以及整合水平;(3)国内外研究均较多应用化学学科专属型评价量规,少部分国内研究开发了化学主题专属型评价量规;(4)与国外相比,国内研究较少应用概念图法和定性定量混合型分析方法;(5)相对而言,国内研究更关注调查型研究,但较少探查PCK水平与其他变量的关系,较少关注干预型研究。文末据此对我国开发本土化的化学教师PCK评价量规用于实证研究与化学教师教育提出建议。