Báo cáo toán học: "On Hopfian and Co-Hopfian Modules" potx

... necessary conditions of Hopfian and Co -Hopfian modules. In particular, we show that the weakly Co -Hopfian regular module R R is Hopfian, and the left R-module M is Co -Hopfian if and only if the left R[x]/(x n+1 )- module M[x]/(x n+1 ) ... R[x]/(x n+1 )- module M[x]/(x n+1 ) is Co -Hopfian, where n is a positive integer. 2000 Mathematics Subject Classification: Keywords: Hopfian modul...

Ngày tải lên: 06/08/2014, 05:20

... MacWilliams ([5]) and it states a funda- mental relation between the weight enumerators of C and of its dual C ∗ . Theorem 4.3 Let C be a linear code of length n and dimension k over GF [q] and 1+(q−1)t ... M. For example if G is a graph and N G the graphic matroid of G then T(G, x, y)= T(N G ,x,y). If M is a matroid and M ∗ its dual then r ∗ (E) − r ∗ (A)=|A|−r(A)andwe immediatel...

Ngày tải lên: 07/08/2014, 06:20

... MATHEMATICA. The PDF p C (r) and the CDF F C (r) of the capacity C(t) of N∗Nakagami-m channels are presented in Figures 2 and 3, respectively. Also, the approximation results obtained in (23) and (24) are shown ... values of the fading parameter m n and the numb er of hops N in N∗Nakagami-m channels. In Figures 4 and 5, we have also included the approximations obtained in (25) and...

Ngày tải lên: 20/06/2014, 20:20

Ngày tải lên: 05/08/2014, 09:46

Ngày tải lên: 05/08/2014, 15:20

Ngày tải lên: 05/08/2014, 15:21

... (x t ,x μ − )=(x t ,x ν + )=1, and (x s ,x μ + )=(x s ,x ν − )=1, and (x p ,x μ − )= (x p ,x ν − )=1, and (x r ,x μ + )=(x r ,x ν + )=1. Consider two new binomials, denoted by f u+v and f u−v , obtained from f u and f v as ... term of f u and the first term of f v , by x t the g.c.d. of the first term of f u and the second term of f v , by x r the g.c.d. of the second term of f u...

Ngày tải lên: 06/08/2014, 05:20

... plane and each pair of cycles C i and C j , i = j, intersects an even number of times. Hence the sum (modulo 2) of the number of crossings between pairs of cycles C i and C j , i = j, is 0 and ... 8 Note that both D 2 and D ∗ 1 are relevant orientations of proper g-graphs, H  2 is an alternating cycle of D 2 , H ∗ 1 is an alternating cycle of D ∗ 1 and CR(H ∗ 1 ) <CR(C )and...

Ngày tải lên: 07/08/2014, 06:20

... Σ n and having vertices x and y adjacent if and only if there is no i ∈{1, ,n} such that ix = iy. Similarly, Σ 0,1 n is the graph with vertex-set Σ n and having vertices x and y adjacent if and ... of computational group theory and graph theory in the discovery and classification of SOMAs. In particular, we discover and classify SOMA(3, 10)s with certain proper- ties, and d...

Ngày tải lên: 07/08/2014, 06:20

... as standard trees, and use them as equivalence class representatives. We will de- note the set of standard Catalan trees by standard(C) and the set of standard marked Catalan trees by standard(C, ... (2001), #R2 21 is standard if and only if T 1 = ,eachT i is standard, and . . . T T T 1 k k-1 ≥ T k+1 for all 1 ≤ k<n. Lemma 5.6. If the binary tree . . . T T n-1 n T 1 is standard an...

Ngày tải lên: 07/08/2014, 06:22