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1.
Aaron Clark 《代数通讯》2013,41(11):4097-4104
Let d be an odd integer, and let k be a field which contains a primitive dth root of unity. Let l 1 and l 2 be cyclic field extensions of k of degree d with norms n l 1/k and n l 2/k . Minà?'s approach which showed that quadratic Pfister forms are strongly multiplicative is applied to the form n l 1/k ? n l 2/k of degree d. Let K = k(X 1,…, X d 2 ). We compute polynomials which are similarity factors of a form of the kind N ? (n l 2/k ? k K) over K, where N is the norm of a certain field extension of K of degree d. These polynomials arise by specializing certain indeterminates of the homogeneous polynomial representing the form n l 1/k ? n l 2/k to be zero. Similar results are obtained for the tensor product of the norm of a cubic division algebra and a cubic norm n l 1/k . 相似文献
2.
Abstract The Iwasava decomposition is proved for the Steinberg groups of types 2
A
2l−1, 2
D
l
, 2
E
6, 3
D
4 over the field of fractions of a principal ideal ring. By using this decomposition, it is described that subgroups exist
between the Steinberg groups over the rings D and K under some restrictions on the ring D.
This work was partially supported by RFFI (Grant No. 08-01-00824) 相似文献
3.
For fixed generalized reflection matrix P, i.e. P
T
= P, P
2 = I, then matrix X is said to be generalized bisymmetric, if X = X
T
= PXP. In this paper, an iterative method is constructed to find the generalized bisymmetric solutions of the matrix equation A
1
X
1
B
1 + A
2
X
2
B
2 + ⋯ + A
l
X
l
B
l
= C where [X
1,X
2, ⋯ ,X
l
] is real matrices group. By this iterative method, the solvability of the matrix equation can be judged automatically. When
the matrix equation is consistent, for any initial generalized bisymmetric matrix group , a generalized bisymmetric solution group can be obtained within finite iteration steps in the absence of roundoff errors,
and the least norm generalized bisymmetric solution group can be obtained by choosing a special kind of initial generalized
bisymmetric matrix group. In addition, the optimal approximation generalized bisymmetric solution group to a given generalized
bisymmetric matrix group in Frobenius norm can be obtained by finding the least norm generalized bisymmetric solution group of the new matrix equation
, where . Given numerical examples show that the algorithm is efficient.
Research supported by: (1) the National Natural Science Foundation of China (10571047) and (10771058), (2) Natural Science
Foundation of Hunan Province (06JJ2053), (3) Scientific Research Fund of Hunan Provincial Education Department(06A017). 相似文献
4.
Let Σn be the symmetric group on n letters. For l ≤ n identify Σl with a subgroup of Σn in the natural way. Let k be an algebraically closed field of characteristic p. This article begins to develop a theory for modules over the centralizer algebras kΣnΣl that is analogous to James's theory of permutation modules, Specht modules, and simple modules over kΣn. We make a conjecture about how to construct all simple kΣnΣl-modules, we develop tools to test the conjecture, and we prove that it is correct for all n when l < p. 相似文献
5.
6.
Li Hao 《Journal of Graph Theory》1989,13(3):313-322
Ore proved in 1960 that if G is a graph of order n and the sum of the degrees of any pair of nonadjacent vertices is at least n, then G has a hamiltonian cycle. In 1986, Li Hao and Zhu Yongjin showed that if n ? 20 and the minimum degree δ is at least 5, then the graph G above contains at least two edge disjoint hamiltonian cycles. The result of this paper is that if n ? 2δ2, then for any 3 ? l1 ? l2 ? ? ? lk ? n, 1 = k = [(δ - 1)/2], such graph has K edge disjoint cycles with lengths l1, l2…lk, respectively. In particular, when l1 = l2 = ? = lk = n and k = [(δ - 1)/2], the graph contains [(δ - 1)/2] edge disjoint hamiltonian cycles. 相似文献
7.
8.
Robin Chapman 《Finite Fields and Their Applications》1997,3(4):353-369
For certain primeslandp, and characters χ:F*p→F*l2, we construct codesWof lengthp+ 1 overFl2which are linear overFl, but not overFl2, and which are invariant under a monomial action of the group SL(2,p). We consider the cases of cubic and quartic characters in detail and use theWto construct linear codes overFlin these cases. 相似文献
9.
V. V. Korableva 《Siberian Mathematical Journal》2008,49(2):273-286
We determine the ranks of the permutation representations of the simple groups B l (q), C l (q), and D l (q) on the cosets of the parabolic maximal subgroups. 相似文献
10.
We prove that every bipartite C2l‐free graph G contains a C4‐free subgraph H with e(H) ≥ e(G)/(l – 1). The factor 1/(l – 1) is best possible. This implies that ex(n, C2l) ≤ 2(l – 1)ex(n, {C4, C2l}), which settles a special case of a conjecture of Erd?s and Simonovits. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 147–156, 2005 相似文献
11.
Wolfgang Müller 《Monatshefte für Mathematik》2011,171(2):69-88
Denote by 0 = λ
0 < λ
1 ≤ λ
2 ≤ . . . the infinite sequence given by the values of a positive definite irrational quadratic form in k variables at integer points. For l ≥ 2 and an (l −1)-dimensional interval I = I
2×. . .×I
l
we consider the l-level correlation function K(l)I(R){K^{(l)}_I(R)} which counts the number of tuples (i
1, . . . , i
l
) such that li1,?,lil £ R2{\lambda_{i_1},\ldots,\lambda_{i_l}\leq R^2} and lij-li1 ? Ij{\lambda_{i_{j}}-\lambda_{i_{1}}\in I_j} for 2 ≤ j ≤ l. We study the asymptotic behavior of K(l)I(R){K^{(l)}_I(R)} as R tends to infinity. If k ≥ 4 we prove K(l)I(R) ~ cl(Q) vol(I)Rlk-2(l-1){K^{(l)}_I(R)\sim c_l(Q)\,{\rm vol}(I)R^{lk-2(l-1)}} for arbitrary l, where c
l
(Q) is an explicitly determined constant. This remains true for k = 3 under the restriction l ≤ 3. 相似文献
12.
By the R-matrix of orthosymplectic quantum superalgebra U
q
(osp(2l+1|2n)) in the vector representation, we establish the corresponding quantum Hopf superalgebra OSP
q
(2l + 1|2n). Furthermore, it is shown that OSP
q
(2l + 1|2n) is coquasitriangular. 相似文献
13.
Extended affine Lie algebras are higher nullity generalizations of finite dimensional simple Lie algebras and affine Kac Moody Lie algebras. In this paper we completely describe the structure of the core modulo its centre and the root system for extended affine Lie algebras of type Bl (l 3 3) B_l (l\ge 3) , Cl (l 3 2) C_l (l \ge 2), F 4 and G 2 . 相似文献
14.
Joan F. Tent 《代数通讯》2013,41(11):4025-4032
Let G be a p-solvable group of p-length l, where p is any prime. We show that G has at least 2 l irreducible characters of degree coprime to p and having values inside ? p . This generalizes a previous result for p = 2 [6] to arbitrary primes. With the same notation, we prove that if p is odd then G has at least 2 l Galois orbits of conjugacy classes of p-elements having values in ? p . 相似文献
15.
In this paper, some properties of Ramsey numbers are studied, and the following results are presented.
- 1. (1) For any positive integers k1, k2, …, km l1, l2, …, lm (m> 1), we have .
- 2. (2) For any positive integers k1, k2, …, km, l1, l2, …, ln , we have . Based on the known results of Ramsey numbers, some results of upper bounds and lower bounds of Ramsey numbers can be directly derived by those properties.
16.
Takashi Kawamura 《Commentarii Mathematici Helvetici》2003,78(3):486-493
Mod l Galois representations of
1- and 2-dimensional abelian varieties with trivial endomorphism ring are
surjective for sufficiently large prime l
as Serre proved. But he did not give an effective lower bound of
l
0 such that
they are surjective for l >
l
0.
We supply an effective evaluation of
l
0 by an
elementary proof of the surjectivity. The proof
uses the Masser-Wüstholz theorem and Kleidman and Liebecks
classification of the maximal subgroups of
GL
2
F
l
)
and GSp
4
(F
l
). 相似文献
17.
Anl-ruler is a chain ofn links, each of lengthl. The links, which are allowed to cross, are modeled by line segments whose endpoints act as joints. A given configuration
of anl-ruler is said to fold if it can be moved to a configuration in which all its links coincide. We show thatl-rulers confined inside an equilateral triangle of side 1 exhibit the following surprising alternation property: there are
three valuesx
1≈0.483,x
2=0.5, andx
3≈0.866 such that all configurations ofn-linkl-rulers fold ifl∈[0,x
1] orl∈(x
2,x
3], but, for anyl∈(x
1,x
2] and anyl∈(x
3, 1], there are configurations ofl-rulers that cannot fold. In the folding cases, linear-time algorithms are given that achieve the folding. Also, a general
proof technique is given that can show that certain configurations—in the nonfolding cases—cannot fold.
Most of this research was done while the first author was at McGill University supported by an NSERC international fellowship.
The second author was supported by NSERC. The third author was supported by NSERC and FCAR. 相似文献
18.
Fred Ustina 《Annali di Matematica Pura ed Applicata》1970,85(1):21-47
Summary Let a2π-periodic function f(x, y) be continuous in some neighbourhood of the point (x, y) except possibly along finitely many lines
l
1
, l
2
, ..., lk terminating at (x, y). The problem of convergence of the Fourier series of f(x, y) at the point (x, y) is examined in some
detail. It is established that under certain restrictions on the variation of f(x, y), and also on the lines l
1
, l
2
, ..., lk, the fourier series converges to a value bounded above by the limit superior, and below by the limit inferior of f(x+u, y+v),
u, v →0, this value depending on the manner in which the series is summed.
The preparation of this paper was financed, in part, by a Canadian Mathematical Congress Summer Research Grant (1968).
Entrata in Redazione il 3 febbraio 1969. 相似文献
19.
Using strong subdifferentiability of convex functionals, we give a new sufficient condition for proximinality of closed subspaces of finite codimension in a Banach space. We apply this result to the Banach space K(l2) of compact operators on l2 and we show that a finite codimensional subspace Y of K(l2) is strongly proximinal if and only if every linear form which vanishes on Y attains its norm. 相似文献
20.
Xuding Zhu 《Journal of Graph Theory》2005,48(3):210-218
This paper discusses the circular version of list coloring of graphs. We give two definitions of the circular list chromatic number (or circular choosability) χc, l(G) of a graph G and prove that they are equivalent. Then we prove that for any graph G, χc, l(G) ≥ χl(G) ? 1. Examples are given to show that this bound is sharp in the sense that for any ? 0, there is a graph G with χc, l(G) > χl(G) ? 1 + ?. It is also proved that k‐degenerate graphs G have χc, l(G) ≤ 2k. This bound is also sharp: for each ? < 0, there is a k‐degenerate graph G with χc, l(G) ≥ 2k ? ?. This shows that χc, l(G) could be arbitrarily larger than χl(G). Finally we prove that if G has maximum degree k, then χc, l(G) ≤ k + 1. © 2005 Wiley Periodicals, Inc. J Graph Theory 48: 210–218, 2005 相似文献