Generating primitive positive clones

Suppose is a set of operations on a finite set A. Define PPC() to be the smallest primitive positive clone on A containing . For any finite algebra A, let PPC#(A) be the smallest number n for which PPC(CloA) = PPC(Clo _n A). S. Burris and R. Willard [2] conjectured that PPC#(A) ≤|A| when CloA is a primitive positive clone and |A| > 2. In this paper, we look at how large PPC#(A) can be when special conditions are placed on the finite algebra A. We show that PPC#(A) ≤|A| holds when the variety generated by A is congruence distributive, Abelian, or decidable. We also show that PPC#(A) ≤|A| + 2 if A generates a congruence permutable variety and every subalgebra of A is the product of a congruence neutral algebra and an Abelian algebra. Furthermore, we give an example in which PPC#(A) ≥|A| - 1)² so that these results are not vacuous. Received August 30, 1999; accepted in final form April 4, 2000.     

Prime Ideal Theory for General Algebras

We introduce ideals, radicals and prime ideals in arbitrary algebras with at least one binary operation, and we show that various separation lemmas and prime ideal theorems are special instances of one general theorem which, in turn, is equivalent to the Boolean Prime Ideal Theorem (or Ultrafilter Principle).     

分配伪补格的主理想

本文给出了分配伪补格 ( L;∧ ,∨ ,* ,0 ,1 )中的主理想 I=( d]成为同余理想的充分必要条件 .当 L是局部有限时 (即 d∈ S( L) ,Fd={x|x* * =d}有限 ) ,对骨架 S( L)中的每个元素 d,我们找到了以 I=( d]为核心的最小同余关系 ,利用以上结果我们得到一个 Stone代数是布尔代数的一些等价条件 .     

分配P-代数的核理想与余核滤子

本文的主要结果是给出了分配P-代数中一个理想成为核理想的充要条件,同时提出了余核滤子的概念,研究了核理想与余核滤子之间的某些内在联系.     

Special Elements of the Lattice of Overcommutative Varieties of Semigroups

The distributive, codistributive, standard, costandard, and neutral elements of the lattice of overcommutative varieties of semigroups are completely described.     

Evolution of Classical and Quantum States in the Groupoid Picture of Quantum Mechanics

The evolution of states of the composition of classical and quantum systems in the groupoid formalism for physical theories introduced recently is discussed. It is shown that the notion of a classical system, in the sense of Birkhoff and von Neumann, is equivalent, in the case of systems with a countable number of outputs, to a totally disconnected groupoid with Abelian von Neumann algebra. The impossibility of evolving a separable state of a composite system made up of a classical and a quantum one into an entangled state by means of a unitary evolution is proven in accordance with Raggio’s theorem, which is extended to include a new family of separable states corresponding to the composition of a system with a totally disconnected space of outcomes and a quantum one.     

浑水中非均匀光场探测图像方法

分析了传统的水下观测和激光观测技术在能见度约为0.5~1.5 m的浑浊水域和0.2 m的特浑水域观测遇到的理论和技术上的局限性.叙述了一种非均匀光场集束光水下目标图像探测方法和系统,并在各种浑浊水质中进行其特性的试验.试验结果表明该系统基本上解决了浑浊水中的观测问题.     

SEMIGROUPS CHARACTERIZED BY THEIR FUZZY IDEALS

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Coproducts of bounded distributive lattices: infinite distributivity

Summary It is shown that, if two bounded distributive lattices satisfy the join-infinite distributive law (JID), then their coproduct also satisfies this law. In 1986, Yaqub proved that generalized Post algebras with a finite lattice of constants satisfy JID, and stated that, in general, it is not known whether a generalized Post algebra satisfies JID when its lattice of constants satisfies JID. In this note, the statement is proved.