Infinitary first-order categorical logic

We present a unified categorical treatment of completeness theorems for several classical and intuitionistic infinitary logics with a proposed axiomatization. This provides new completeness theorems and subsumes previous ones by Gödel, Kripke, Beth, Karp and Joyal. As an application we prove, using large cardinals assumptions, the disjunction and existence properties for infinitary intuitionistic first-order logics.     

Completeness of general solutions for three-dimensional transversely isotropic piezoelectricity

In this paper, a general solution for three-dimensional transversely isotropic piezoelectricity in terms of four quasi-quadri-harmonic functions is established first. Owing to complexity of the higher-order equation, it is difficult to obtain rigorous analytic solutions and in most cases this general solution is not applicable. By virtue of the generalized Almansi’s Theorem, the simplified generalized LHN solution and E–L solution expressed by lower order functions are achieved, respectively, by taking a decomposition and superposition technique. In the absence of piezoelectric coupling, these two simplified general solutions can be degenerated into those for transversely isotropic elasticity, i.e. LHN and E–L solutions. More importantly, the completeness of these two generalized solutions is proved if the domain is z-convex, no matter whether the characteristic roots are distinct or possibly equal to each other.     

STRONGLY ALGEBRAIC LATTICES AND CONDITIONS OF MINIMAL MAPPING PRESERVING INFS

ＳＴＲＯＮＧＬＹ ＡＬＧＥＢＲＡＩＣ ＬＡＴＴＩＣＥＳ ＡＮＤ ＣＯＮＤＩＴＩＯＮＳ ＯＦ ＭＩＮＩＭＡＬ ＭＡＰＰＩＮＧ ＰＲＥＳＥＲＶＩＮＧ ＩＮＦＳ ￥ＸＵＸＩＡＯＱＵＡＮＡｂｓｔｒａｃｔ：Ｔｈｅｔａｂｏｒｇｉｖｅｓｓｏｍｅｃｈａｒａｃｔｅｒｉ...     

连续态波函数归一化问题及其完备性检验

本文探讨了连续态波函数归一化问题,给出了正确、有效的归一化算法.采用改进的Numerov格式计算氢原子的连续态波函数,并利用基矢完备性条件对此进行了检验.利用最小二乘法,分别得出了束缚态部分和及连续态部分积分的渐近函数形式.并由此采用积分处理方法得到了余项的近似计算结果.     

Federations and transitive group choice

The following is a brief English summary of the paper Mirkin (1979), in which he discusses social welfare functions where the relations involved are solely assumed to be reflexive. Under axioms of independence and neutrality, monotonicity, and two domain assumptions the author shows that such a social welfare function is determined by a ‘federation’,i.e., the set of coalitions such that if that each member considers a not worse than b so does the group. The author then characterizes transitive, completeness, definiteness, (a sort of non-indifference assumption), and majority rule in this framework. He also characterizes those domains on which social welfare functions determined by federations F satisfying I ∈ F if and only if ī ? F, are transitive. We omit proofs, which are given in the Russian version, as well as the author's discussion of these results.     

Global hyperbolicity and completeness

We prove global hyperbolicity of spacetimes under generic regularity conditions on the metric. We then show that these spacetimes are timelike and null geodesically complete if the gradient of the lapse and the extrinsic curvature K are integrable. This last condition is required only for the tracefree part of K if the universe is expanding.     

区间值模糊集之间一种新距离的完备性

定义区间值模糊集之间的一种新距离d*∞,讨论了这种距离的基本性质,并证明区间值模糊数的距离空间(IΦ*(R),d*∞)是完备的,但它却是不可分的。     

两参数变形量子代数SU(1,1)q,s的相干态及其性质

利用SU(1,1)_q,s量子代数的两参数变形振子构造出归一化的SU(1,1)_q,s相干态,证明了SU(1,1)_q,s量子代数的表示基是正交的,并讨论了它的相干态的归一性和完备性。指出(SU(1,1)_q,s相干态的相干性受参数q、s的影响。     

Completeness and an extension theorem for continuous fuzzy linear order-homomorphisms

In this paper, the notions of λ-Cauchy net and completeness in L-topological vector spaces are introduced, and some of their properties are studied. An extension theorem for continuous fuzzy linear order homomorphisms is proved.