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1.
本文综合利用邻格方法及Siegel mass公式证明了实二次域Q(√d)上∨≌In(n≥4)内的偶幺模格类数为2当且仅当Q(√3),n=4及Q(√5),n=8。 相似文献
2.
本文综合利用邻格方法及Siegel mass公式证明了实二次域Q( )上 内的偶幺模 格类数为2当且仅当Q( ),n=4及Q( ).n=8. 相似文献
3.
本文给出了构作Z[m1/2i]上不可分的正定幺模n秩Hermite格当m?3(mod4)时的方法.对任何自然数n,除了n=2,3,4,5(n=2,3)的例外情形,证明了存在Gauss整环Z[i](整环Z[21/2i])上不可分的正定幺模n秩正规Hermi-te格并给出它们的明显结构.又对任何n=4k(n=2k)构作了Z[i][(Z21/2i])上不可分的正定幺模n秩偶Hermite格. 相似文献
4.
利用推广的邻格方法,完成了Q(√6)上秩4的在一个阿基米德除子上正定,在另一阿基米德除子上负定的所有幺模格种的分类. 相似文献
5.
设d,a,k,n是适合4k2n+1 =da2, k>1, n>2, d无平方因子的正整数;又设C(K)和h(K)分别是实二次域K=Q(√d)的理想类群和类数.本文证明了:当a<0.5k0.56n时,则h(K)≡0(mod n)和C(K)必有n阶循环子群. 相似文献
6.
众所周知,在实数系,符号n(√a)有明确的意义:如果a>0,n(√a)表示一个正数,它的n次方等于a,即n(√a)>0,且(n(√a))n=a.这时,n(√a)表示a的n次算术根.如果a=0,n(√a)=0,如果a<0.当n是奇数时,n(√a)=-n(√-a)这里的n(√-a)是正数-a的n次算术根,当n是偶数时,n(√a)没有意义. 相似文献
7.
In this paper, we give a lower bound exp(2.2 × 10~8 ) for those discriminants of real quadratic fields Q(√ d) with d= N~2-4 and h(d)=1. 相似文献
8.
《中国科学 数学(英文版)》2015,(7)
Suppose F = Q(√-p1 pt) is an imaginary quadratic number field with distinct primes p1,..., pt,where pi≡ 1(mod 4)(i = 1,..., t- 1) and pt ≡ 3(mod 4). We express the possible values of the 8-rank r8 of the class group of F in terms of a quadratic form Q over F2 which is defined by quartic symbols. In particular,we show that r8 is bounded by the isotropy index of Q. 相似文献
9.
Yan YONG 《应用数学学报(英文版)》2015,31(1):17-30
In this paper, we will show that under some smallness conditions, the planar diffusion wave v(√x11+) is stable for a quasilinear wave equation with nonlinear damping: vttt-f(v) + vt + g(vt) = 0, x =(xn1, x2,, xn)∈ R, where v(√x11+) is the unique similar solution to the one dimensional nonlinear heat equattion: vt-f(v)x1x1= 0, f ′(v) > 0, v(±∞, t) = v±, v+ = v-. We also obtain the L∞ time decay rate which rreads v-v L∞= O(1)(1 + t)-4, where r = min{3, n}. To get the main result, the energy method and a new inequality have been used. 相似文献
10.
设d是无平方因子正整数,hK是虚二次域K=Q(√-d)的类数.又设d满足1+ da2=4kn,其中a,k,n是适合k>1,n>2的正整数.运用初等数论方法给出了数组(d,a,k,n)可使n|hK成立的必要条件. 相似文献
11.
Hugh Thomas 《Order》2006,23(2-3):249-269
In this paper, we study lattices that posess both the properties of being extremal (in the sense of Markowsky) and of being left modular (in the sense of Blass and Sagan). We call such lattices trim and show that they posess some additional appealing properties, analogous to those of a distributive lattice. For example, trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sphere; the latter holds exactly if the maximum element of the lattice is a join of atoms. Any distributive lattice is trim, but trim lattices need not be graded. The main example of ungraded trim lattices are the Tamari lattices and generalizations of them. We show that the Cambrian lattices in types A and B defined by Reading are trim; we conjecture that all Cambrian lattices are trim. 相似文献
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O. A. Kuryleva 《Algebra and Logic》2008,47(1):42-48
A vector space V over a real field R is a lattice under some partial order, which is referred to as a vector lattice if u + (v ∨ w) = (u + v) ∨ (u + w) and u
+ (v ∧ w) = (u + v) ∧ (u + w) for all u, v, w ∈ V. It is proved that a model N of positive integers with addition and multiplications is relatively elementarily interpreted in the ideal lattice
ℱ
n
of a free vector lattice ℱ
n
on a set of n generators. This, in view of the fact that an elementary theory for N is hereditarily undecidable, implies that an elementary theory for
ℱ
n
is also hereditarily undecidable.
__________
Translated from Algebra i Logika, Vol. 47, No. 1, pp. 71–82, January–February, 2008. 相似文献
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15.
明平华 《数学的实践与认识》2004,34(6):159-161
由幂格的定义知 ,幂格与幂集格是不同的 ,然而它们却有一定的联系 .本文在幂格概念的基础上 ,进一步地讨论幂格和幂集格在一定条件下的联系 . 相似文献
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17.
幂格的同态与同余关系 总被引:1,自引:1,他引:0
本文在文[1]已引入幂格同态概念的基础上,进一步引入幂格同余关系的概念,并得到它们的一些相关性质.以及幂格同态与幂格同余关系的对应关系. 相似文献
18.
明平华 《数学物理学报(A辑)》2004,24(4):491-495
该文在文[1]中幂格概念的基础上,得到了幂格的一个充要条件,给出了正则幂格、相对幂格的概念,并讨论了商格与正则幂格、相对幂格的关系.〖HT5”H〗关键词:〖HT5”SS〗格;幂格;商格;正则幂格;相对幂格. 相似文献
19.
There are two results in the literature that prove that the ideal lattice of a finite, sectionally complemented, chopped lattice is again sectionally complemented. The first is in the 1962 paper of G. Grätzer and E. T. Schmidt, where the ideal lattice is viewed as a closure space to prove that it is sectionally complemented; we call the sectional complement constructed then the 1960 sectional complement. The second is the Atom Lemma from a 1999 paper of the same authors that states that if a finite, sectionally complemented, chopped lattice is made up of two lattices overlapping in an atom and a zero, then the ideal lattice is sectionally complemented. In this paper, we show that the method of proving the Atom Lemma also applies to the 1962 result. In fact, we get a stronger statement, in that we get many sectional complements and they are rather close to the componentwise sectional complement. 相似文献
20.
朱福祖 《中国科学A辑(英文版)》2001,44(1):7-14
Methods are presented for the construction of nondecomposable positive definite integral Hermitian forms over the ring of
integers Rm of an imaginary quadratic field ℚ(√−m). Using our methods, one can construct explicitly an n-ary nondecomposable positive
definite Hermitian Rm-lattice ( L, h) with given discriminant 2 for every n⩾2 (resp. n⩾13 or odd n⩾3) and square-free m = 12 k + t with k⩾1 and
t∈ (1,7) (resp. k⩾1 and t = 2 or k⩾0 and t∈ 5,10,11). We study also the case for discriminant different from 2. 相似文献