坡代数上的模糊软子坡

借助模糊软集的概念, 在坡代数上定义了模糊软子坡, 并对其性质进行研究. 此外, 定义了坡代数上模糊软子坡间的模糊软同态和模糊软同构, 给出了坡代数上模糊软子坡的同构像定理和同态逆像定理, 并证明了坡代数上模糊软子坡范畴是坡代数范畴上的拓扑范畴.     

模糊子坡代数、模糊理想、模糊滤子及模糊同余关系的刻画

定义了坡代数（X,＋,＊）的模糊滤子的概念,给出了X上的模糊集A是（X,＋,＊）的模糊子坡代数（resp.,模糊理想,模糊滤子）的若干个等价刻画以及X×X上的模糊集E是（X,＋,＊）上的模糊同余关系的若干个等价刻画,另外还证明了模糊子坡代数范畴[0,1]-SInc是坡代数范畴Inc上的拓扑范畴。     

模糊Quantale范畴的性质

引入了模糊Quantale的概念,证明了模糊Quantale范畴同构于L-代数范畴,于是从范畴论的角度说明L-代数也可以看成是Quantale的模糊化结构;给出了模糊Quantale范畴中的极限的具体结构,同时证明了该范畴是完备范畴;给出模糊Quantale范畴中逆系统的逆极限结构,引入了两个逆系统之间映射的定义,由此导出两个逆系统的逆极限之间的极限映射.     

L-序代数的内射壳

讨论L-序代数范畴的内射性, 证明L-序代数范畴中的M^≤-内射对象恰是L-并代数, 并给出L-序代数范畴中一类特殊L-序代数的M^≤-内射壳的具体形式.     

L-序代数的内射壳

讨论L-序代数范畴的内射性, 证明L-序代数范畴中的M^≤-内射对象恰是L-并代数, 并给出L-序代数范畴中一类特殊L-序代数的M^≤-内射壳的具体形式.     

M-阶化广义李超代数H(n)的导子超代数

给出了M-阶化广义李超代数H(n)的定义,证明了M-阶化广义李超代数H(n)是Z-阶化的,刻画了H(n)的导子超代数的Z-阶化成分,进而确定了M-阶化广义李超代数H(n)的导子超代数.     

Heyting代数中同余关系的简化

给出了Heyting代数中同余关系的一种简单定义,这种定义并不改变全体滤子和全体同余关系之间的一一对应性,并且借助滤子证明了这种定义是Heyting代数作为泛代数的同余关系的简化。最后证明了全体滤子之集作为完备格同构于全体同余关系之集。     

两类代数Domain范畴的等价

首先证明了一个Domain范畴与它的等价范畴有相同的笛卡儿闭性，其次通过引入两类新的偏序集即L-偏序集和B-偏序集，构造了范畴LPOSa（由L-偏序集与逼近关系组成）和范畴BPOSA（由B-偏序集与逼近关系组成），并证明了它们分别与代数L-domain范畴ALD和代数be-domain范畴ABD等价．     

连通代数domain上相容紧元及范畴的研究

基于连通集的定义,引入了c-理想的概念,得出了连通代数domain中每一个元都是相容紧元,当且仅当它的每个c-理想都是主c-理想,给出了连通代数domain满足升链条件.研究了连通完备偏序集A中的每个元是相容紧元的充要条件是A与A的c-理想格同构.最后,证明了连通代数domain范畴与偏序集范畴等价.     

一类对称范畴上的Hom-Hopf模

设L是一个余三角Hopf代数.通过余模范畴LM中Hom-Hopf代数的概念,证明了Hom-Hopf代数的对偶也是LM中的Hom-Hopf代数.进一步给出了范畴LM中Hom-Hopf模的余不变子空间的定义并得到LM中的Hom-Hopf模基本定理.     

A categorical interpretation of Yetter-Drinfel’d modules

It is known that any strict tensor category (C,⊗,I) can determine a strict braided tensor categoryZ(C), the centre ofC. WhenA is a finite Hopf algebra, Drinfel’d has proved thatZ( _AM) is equivalent to_D(A)M as a braided tensor category, where_AM is the left A-module category, andD(A) is the Drinfel’d double ofA. This is the categorical interpretation ofD(A). Z( _AM) is proved to be equivalent to the Yetter-Drinfel’d module category,_AYD ^A as a braided tensor category for any Hopf algebraA. Furthermore, for right A-comodule categoryM ^A, Z(M^A) is proved to be equivalent to the Yetter-Drinfel’d module category_AY D^A as a braided tensor category. But,in the two cases, the Yetter-Drinfel’d module category_AY D^A has different braided tensor structures.     

Two kinds of silicalites in Mount Ailao belt, Yunnan Province

Two kinds of radiolarian silicalites at the bottom and top of the ophiolite in the Mount (Mt.) Ailao belt, Yunnan Province, are dealt with in this work in terms of geology, micro-paleontology, isotope and REE. The first kind of silicalite was defined as the turbidite formation. In this category, the radiolarian species lived in the Late Devonian (D3). The corresponding ecologic assemblage, composed of δ 30Si (0.4‰-0.5‰, average 0.03‰), δ Ce (0.77- 0.97, average 0.85) and LaN /YbN (0.77-1.06, average 0.96) of silicalite, shows that it occurred in the abyssal environment. The second kind of silicalite was defined as the mud-siliceous formation. Contacting conformably with the basalt of the ophiolite suit, the radiolarian silicalite at the top of ophiolite was in the category of the component units of the ophiolite in the Mt. Ailao belt. In this category, the radiolarian species lived in the Early Carboniferous (C1-). The corresponding ecologic assemblage, composed of d 30Si (0.2‰-1.3‰, averaging 0.7‰), dδCe (0.88- 0.92, averaging 0.90) and LaN /YbN (0.77-1.45, averaging 1.22), of silicalites indicate that it occurred in the bathyal environment. All these facts domonstrate that the Mt. Ailao must have been a small ocean basin at that time.     

2类优美图

用构造法证明了Q²_m×n 和u·Q²_m×n 都是优美图。     

关于图P36k+5∪P3n的优美性

讨论了形如P³_6k+5∪P³_n的非连通并图的优美性,用构造性的方法给出了P³_6k+5∪P³_n的优美标号,并证明P³_6k+5∪P³_n是交错图.     

非连通图(K1∨(P(1)n∪ P(2)n)) ∪ P(3)n及(K1∨(P(1)n∪ P(2)n)) ∪ P(3)n∪ St(n)的优美性

 给出了非连通图(K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n和(K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n∪ St(n),且对其优美性进行了研究。证明了如下结论：设 n 为任意正整数,则当n≥4时,非连通图 (K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n和(K₁∨(P⁽¹⁾_n∪ P⁽²⁾_n)) ∪ P⁽³⁾_n∪ St(n)均是优美图;其中,Pn 是 n 个顶点的路,Kn 是n个顶点的完全图, St(n) 是 n+1 个顶点的星形树,G₁ ∨ G₂ 是图 G1 与 G2 的联图。     

Implicational lattices and generalization of Stone’s representation theorem

Let F(S) be the free algebra of type (,∨,→) generated by the non_empty set S, it is proved that the logical equivalent relation defined by means of R 0_semantics is a congruence relation on F(S) and the corresponding quotient algebra is said to be the R 0_semantic Lindenbaum algebra. Taking R 0_semantic Lindenbaum algebra as a prototype, the concepts of implicational lattices and regular implicational lattices which are generalizations of the concept of Boolean algebras are introduced. Besides, the concept of fuzzy implicational spaces is introduced and the representation theorem of regular implicational lattices is obtained by means of fuzzy implicational spaces. In case of Boolean algebras, the corresponding fuzzy implicational spaces are zero_dimensional compact Hausdorff spaces and herefrom it is proved that the famous Stone's representation theorem of Boolean algebras is a corollary of the representation theorem of regular implicational lattices.     

Enhanced dielectric performance of Dy - substituted YMn2O5 for high-frequency applications

The dielectric performances as well as the effects of Dy³⁺ ions content at A sites of YMn₂O₅ (YMO) [x ​= ​0 (YDM₀) and x ​= ​0.4 (YDM_0.4)] polycrystalline samples were explored. These compounds were synthesized via sol–gel method. X-Ray diffraction and Raman measurements proved the high quality of the compounds that crystallized in an orthorhombic structure with the Pbam space group. Besides, impedance spectroscopy and electrical modulus studies revealed that both samples exhibited a non-Debye's type of relaxation. The decrease of impedance for YDM_0.4 compared to the pure YDM₀, may be attributed to the decrease in charge transfer resistance. Concerning the fit of impedance spectra, they confirmed that both compounds were simultaneously capacitive and resistive. Furthermore, the activation energies obtained from Modulus and complex impedance were proven to be neighboring, suggesting that the relaxation process refers to electron hopping. For each compound, the evolution of ε' and tan ​δ with temperature indicated a clearer relaxor behavior, namely the existence of two relaxations. The first one detected at low temperature is related to the charge carriers hopping between Mn³⁺ and Mn⁴⁺ and the second at high temperature is associated with oxygen vacancies. The reduced hopping rate with Dy³⁺ substitution for Y³⁺ ions at A sites is responsible for the decrease in dielectric constant and dielectric loss. These significant findings demonstrate that these materials can be invested in a fruitful use in UV photo-detector and power applications in high frequency as microwave, millimeter wave signal processing, for civilian, military and space applications.     

几个三角求和算子的线性组合

通过对已有几个三角求和算子进行线性组合, 构造一个新算子T_n(f;x). 证明该算子在全实轴上一致收敛于任意以2π为周期的连续函数f(x), 得到了当f(x)∈C^j_2π(0≤j≤7)时算子的最佳收敛阶, 并且证明了算子的最高收敛阶不 会超过1/n⁸. 在收敛性方面, 所构造的新算子明显优于其他算子.     

一类解析Toeplitz算子的约化子空间与群的特征

设A_r为复平面中的圆环{z:r|z|1},L_a~2(A_r)为A_r上的Bergman空间.从局部逆的代数结构的新视角研究解析Toeplitz算子的约化子空间.首先证明L_a~2(A_r)上Toeplitz算子T_(z~N)的交换子的表示,再次证明zN的全体局部逆组成的集合在复合映射下是循环群,最后证明了循环群的特征与Toeplitz算子T_(z~N)的极小约化子空间是一一对应的.     

Surface state of molybdenum cations in MoO3/CeO2

Conclusion