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31.
Let a and b be fixed positive integers.In this paper,using some elementary methods,we study the diophantine equation(a~m-1)(b~n-1)= x~2.For example,we prove that if a ≡ 2(mod 6),b ≡ 3(mod 12),then(a~n-1)(b~m-1)= x~2 has no solutions in positive integers n,m and x. 相似文献
32.
In this paper we study the closed subsemigroups of a Clifford semigroup. It is shown that {∪α∈Y′ Gα | Y′∈ P(Y) } is the set of all closed subsemigroups of a Clifford semigroup S = [Y; Gα; ?α, β], where Y′denotes the subsemilattice of Y generated by Y′. In particular, G is the only closed subsemigroup of itself for a group G and each one of subsemilattices of a semilattice is closed. Also, it is shown that the semiring P(S) is isomorphic to the semiring P(Y) for a Clifford semigroup S = [Y; Gα; ?α, β]. 相似文献
33.
34.
35.
This paper characterizes directed graphs which are Cayley graphs of strong semilattices of groups and, in particular, strong chains of groups, i.e. of completely regular semigroups which are also called Clifford semigroups. 相似文献
36.
周绍艳 《云南师范大学学报(自然科学版)》2008,28(1):8-11
文章[4]给出了Dn中的半格置换相似于Tn中的某个半格的充要条件.对于这个充要条件,本文在[5]的基础上给出另一个更简洁的等价描述. 相似文献
37.
Thomas Zaslavsky 《Discrete and Computational Geometry》2002,27(3):303-351
For each pair (Q
i
,Q
j
) of reference points and each real number r there is a unique hyperplane h \perp Q
i
Q
j
such that d(P,Q
i
)
2
- d(P,Q
j
)
2
= r for points P in h . Take n reference points in d -space and for each pair (Q
i
,Q
j
) a finite set of real numbers. The corresponding perpendiculars form an arrangement of hyperplanes. We explore the structure
of the semilattice of intersections of the hyperplanes for generic reference points. The main theorem is that there is a real,
additive gain graph (this is a graph with an additive real number associated invertibly to each edge) whose set of balanced
flats has the same structure as the intersection semilattice. We examine the requirements for genericity, which are related
to behavior at infinity but remain mysterious; also, variations in the construction rules for perpendiculars. We investigate
several particular arrangements with a view to finding the exact numbers of faces of each dimension. The prototype, the arrangement
of all perpendicular bisectors, was studied by Good and Tideman, motivated by a geometric voting theory. Most of our particular
examples are suggested by extensions of that theory in which voters exercise finer discrimination. Throughout, we propose
many research problems.
Received July 20, 2000, and in revised form September 29, 2001, and October 12, 2001. Online publication March 4, 2002. 相似文献
38.
给出了左C-半群的另一种结构,所谓左交错积结构,并刻画了它的特殊情形.这种结构为左C-半群在广义正则半群类中的再推广奠定了基础. 相似文献
39.
Liu Quan Wang 《数学学报(英文版)》2017,33(1):37-50
Let p_3(n) be the number of overpartition triples of n. By elementary series manipulations,we establish some congruences for p_3(n) modulo small powers of 2, such as p_3(16 n + 14) ≡ 0(mod 32), p_3(8 n + 7) ≡ 0(mod 64).We also find many arithmetic properties for p_3(n) modulo 7, 9 and 11, involving the following infinite families of Ramanujan-type congruences: for any integers α≥ 1 and n ≥ 0, we have p_3 (3~(2α+1)(3n + 2))≡ 0(mod 9 · 2~4), p_3(4~(α-1)(56 n + 49)) ≡ 0(mod 7),p_3 (7~(2α+1)(7 n + 3))≡ p_3 (7~(2α+1)(7 n + 5))≡ p_3 (7~(2α+1)(7 n + 6))≡ 0(mod 7),and for r ∈ {1, 2, 3, 4, 5, 6},p_3(11 · 7~(4α-1)(7 n + r)≡ 0(mod 11). 相似文献
40.
Francis Pastijn 《代数通讯》2017,45(11):4979-4991
Every regular band can be isomorphically embedded into a regular band which has a semilattice transversal. The latter constitute the variety of regular split bands, whose subvariety lattice is isomorphic to the lattice of regular band varieties. 相似文献