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1.
In this paper, we study cyclic codes over the rings Z
2 + uZ
2 and Z
2 + uZ
2 + u
2
Z
2 . We find a set of generators for these codes. The rank, the dual, and the Hamming distance of these codes are studied as
well. Examples of cyclic codes of various lengths are also studied.
相似文献
2.
3.
Ming-Chang Kang 《Israel Journal of Mathematics》2005,146(1):77-92
LetK be any field which may not be algebraically closed,K(x
1
,x
2
,x
3
) be the rational function field of three variables overK, and σ:K(x
1
,x
2
,x
3
) → K(x
1
,x
2
,x
3
) be aK-automorphism defined by
wherea
i
,b
i
,c
i
,d
i
∈K anda
i
d
i
−b
i
c
i
≠0. Let
,f
i
(T)=T
2
−(a
i
+d
i
)T+(a
i
d
i
−b
i
c
i
)∈K[T] be the “characteristic polynomial” of σ
i
.
Theorem:Assume that charK≠2.Then the fixed field K(x
1
,x
2
,x
3
)
<σ>
is not rational (=purely transcendental) over K if and only if (i) for each 1≤i≤3, f
i
(T) is irreducible; (ii) the Galois group of f
1
(T)f
2
(T)f
3
(T) over K is of order 8; and (iii) for each 1≤i≤3,ord (σ
[itn]
)is an even integer. 相似文献
4.
We prove that in a Banach space admitting a separating polynomial, each weakly null normalized sequence has a subsequence which is equivalent to the usual basis of some , p an even integer. We show that for each even integer p, the Schatten class admits a separating polynomial. For a space with a basis admitting a 4-homogeneous separating polynomial, we relate the unconditionality of the basis with the existence of certain type of polynomials defined in terms of infinite symmetric matrices. We find relations between the properties of the entries of these matrices and the geometrical structure of the space. Finally we study the existence of convex 4-homogeneous separating polynomials. 相似文献
6.
The decomposition of the complete graph Kv into Kr×Kc's, the products of Kr and Kc,is originated from the use of DNA library screening. In this paper, we consider the case where r=2 and c = 5, and show that such a decomposition exists if and only if v ≡ 1 (mod 25). 相似文献
7.
M. LASHKARIZADEH BAMI 《数学学报(英文版)》2008,24(3):439-454
The author gives a characterization of the Fourier transforms of bounded bilinear forms on C*(S1)×C*(S2) of two foundation semigroups S1 and S2 in terms of Jordan *-representations, hemimogeneous random fields, and as well as weakly harmonizable random fields of S1 and S2 into Hilbert spaces. 相似文献
8.
《K-Theory》2005,35(3-4):375-394
We discuss the local index formula of Connes–Moscovici for the isospectral noncommutative geometry that we have recently constructed
on quantum SU(2). We work out the cosphere bundle and the dimension spectrum as well as the local cyclic cocycles yielding the index formula.
(Received: January 2005) 相似文献
9.
10.
We bring to light a G
2 structure existing on the unit sphere tangent bundle S
M
of any given orientable Riemannian 4-manifold M. The associated 3-form φ is co-calibrated if, and only if, M is an Einstein manifold—a result which leads to new examples of co-calibrated G
2 spaces. We hope to be contributing both to the knowledge of special geometries and to the study of 4-manifolds. 相似文献
11.
A. S. Kondratev 《Siberian Mathematical Journal》2007,48(6):1001-1018
We prove that if L is one of the simple groups E
6(q) and 2
E
6(q) and G is some finite group with the same spectrum as L, then the commutant of G/F(G) is isomorphic to L and the quotient G/G′ is a cyclic {2,3}-group.
Original Russian Text Copyright ? 2007 Kondrat’ev A. S.
The author was supported by the Russian Foundation for Basic Research (Grant 04-01-00463) and the RFBR-NSFC (Grant 05-01-39000).
__________
Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 48, No. 6, pp. 1250–1271, November–December, 2007. 相似文献
12.
Sh. Makharadze 《Journal of Mathematical Sciences》2008,155(5):697-708
In the paper, the class of complete semigroups of binary relations is considered, each of whose elements is defined by a complete
B
X
(D)-semilattice of unions which belongs to the class of generalized elementary X-semilattices. Regular elements are described for each semigroup of this class.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 49, Algebra
and Geometry, 2007. 相似文献
13.
V. Chernousov 《Mathematische Annalen》2003,326(2):297-330
We prove that for a simple simply connected quasi-split group of type 3,6
D
4
,E
6
,E
7
defined over a perfect field F of characteristic ≠=2,3 the Rost invariant has trivial kernel. In certain cases we give a formula for the Rost invariant.
It follows immediately from the result above that if cd F≤2 (resp. vcd F≤2) then Serre's Conjecture II (resp. the Hasse principle) holds for such a group. For a (C
2
)-field, in particular ℂ(x,y), we prove the stronger result that Serre's Conjecture II holds for all (not necessary quasi-split) exceptional groups of
type 3,6
D
4
,E
6
,E
7
.
Received: 27 March 2002 /
Published online: 28 March 2003
The author gratefully acknowledge the support of TMR ERB FMRX CT-97-0107 and Forschungsinstitut für Mathematik, ETH in Zürich 相似文献
14.
15.
Xiao Hong Fu 《数学学报(英文版)》2008,24(9):1475-1482
This paper considers the isometric extension problem concerning the mapping from the unit sphere S
1(E) of the normed space E into the unit sphere S
1(l
∞(Γ)). We find a condition under which an isometry from S
1(E) into S
1(l
∞(Γ)) can be linearly and isometrically extended to the whole space. Since l
∞(Γ) is universal with respect to isometry for normed spaces, isometric extension problems on a class of normed spaces are
solved. More precisely, if E and F are two normed spaces, and if V
0: S
1(E) → S
1(F) is a surjective isometry, where c
00(Γ) ⊆ F ⊆ l
∞(Γ), then V
0 can be extended to be an isometric operator defined on the whole space.
This work is supported by Natural Science Foundation of Guangdong Province, China (Grant No. 7300614) 相似文献
16.
Most results on the crossing number of a graph focus on the special graphs, such as Cartesian products of small graphs with
paths Pn, cycles Cn or stars Sn. In this paper, we extend the results to Cartesian products of complete bipartite graphs K2,m with paths Pn for arbitrary m ≥ 2 and n ≥ 1.
Supported by the NSFC (No. 10771062) and the program for New Century Excellent Talents in University. 相似文献
17.
This paper classifies dual pairs (F,G′) in complex G2 where F is finite and G′ is infinite complex reductive. 相似文献
18.
G. Vanden Berghe H. De Meyer 《Journal of Computational and Applied Mathematics》2003,160(1-2):315-321
As a by-product of the calculation of eigenvalues of a particular SO(3) invariant operator in the enveloping algebra of SO(5), a three terms relation between three hypergeometric series emerges. 相似文献
19.
The ( . )
reg
construction was introduced in order to make an arbitrary semigroup S divide a regular semigroup (S)
reg
which shares some important properties with S (e.g., finiteness, subgroups, torsion bounds, J -order structure). We show that (S)
reg
can be described by a rather simple complete string rewrite system , as a consequence of which we obtain a new proof of the normal form theorem for (S)
reg
. The new proof of the normal form theorem is conceptually simpler than the previous proofs. 相似文献
20.
We give a construction of a family of CAP representations of the exceptional group G
2, whose existence is predicted by Arthur’s conjecture. These are constructed by lifting certain cuspidal representations of
PGS
p6. To show that the lifting is non-zero, we establish a Rankin-Selberg integral for the degree 8 Spin L-function of these cuspidal representations of PGS
p6. 相似文献