共查询到20条相似文献,搜索用时 22 毫秒
1.
This paper presents procedures for constructing irreducible polynomials over GF(2s) with linearly independent roots (or normal polynomials or N-polynomials). For a suitably chosen initial N-polynomial F0(x)GF(2s) of degree n, polynomials Fk(x)GF(2s) of degrees n2k are constructed by iteratively applying the transformation x→x+x-1, and their roots are shown to form a normal basis of GF(2sn2k) over GF(2s). In addition, the sequences are shown to be trace compatible, i.e., the trace map TGF(2sn2k+1)/GF(2sn2k) fromGF(2sn2k+1) onto GF(2sn2k) maps the roots of Fk+1(x) onto those of Fk(x). 相似文献
2.
Stanis
aw Lewanowicz 《Journal of Computational and Applied Mathematics》2003,150(2):193-327
Let {pk(x; q)} be any system of the q-classical orthogonal polynomials, and let be the corresponding weight function, satisfying the q-difference equation Dq(σ)=τ, where σ and τ are polynomials of degree at most 2 and exactly 1, respectively. Further, let {pk(1)(x;q)} be associated polynomials of the polynomials {pk(x; q)}. Explicit forms of the coefficients bn,k and cn,k in the expansions are given in terms of basic hypergeometric functions. Here k(x) equals xk if σ+(0)=0, or (x;q)k if σ+(1)=0, where σ+(x)σ(x)+(q−1)xτ(x). The most important representatives of those two classes are the families of little q-Jacobi and big q-Jacobi polynomials, respectively.Writing the second-order nonhomogeneous q-difference equation satisfied by pn−1(1)(x;q) in a special form, recurrence relations (in k) for bn,k and cn,k are obtained in terms of σ and τ. 相似文献
3.
Let ω be a primitive element of GF(2n), where . Let d=(22k+2s+1-2k+1-1)/(2s-1), where n=2k, and s is such that 2s divides k. We prove that the binary m-sequences s(t)=tr(ωt) and s(dt) have a four-level cross-correlation function and give the distribution of the values. 相似文献
4.
Fix integers n, x, k such that n≥3, k>0, x≥4, (n, x)≠(3, 4) and k(n+1)<(
n
n+x
). Here we prove that the order x Veronese embedding ofP
n
is not weakly (k−1)-defective, i.e. for a general S⊃P
n
such that #(S) = k+1 the projective space | I
2S
(x)| of all degree t hypersurfaces ofP
n
singular at each point of S has dimension (
n
/n+x
)−1− k(n+1) (proved by Alexander and Hirschowitz) and a general F∈| I
2S
(x)| has an ordinary double point at each P∈ S and Sing (F)=S.
The author was partially supported by MIUR and GNSAGA of INdAM (Italy). 相似文献
5.
6.
O. T. Mewomo 《Proceedings Mathematical Sciences》2008,118(4):547-555
Let S be a Rees matrix semigroup. We show that l
1(S) is (2k + 1)-weakly amenable for k ∈ ℤ+. 相似文献
7.
Let denote the set of continuous n×n matrices on an interval . We say that is a nontrivial k-involution if where ζ=e-2πi/k, d0+d1++dk-1=n, and with . We say that is R-symmetric if R(t)A(t)R-1(t)=A(t), , and we show that if A is R-symmetric then solving x′=A(t)x or x′=A(t)x+f(t) reduces to solving k independent dℓ×dℓ systems, 0ℓk-1. We consider the asymptotic behavior of the solutions in the case where . Finally, we sketch analogous results for linear systems of difference equations. 相似文献
8.
Hiroshi Nagamochi Toru Hasunuma 《Journal of Algorithms in Cognition, Informatics and Logic》2001,38(2)
We present an efficient
algorithm for finding a sparse k-edge-connectivity certificate of a multigraph G. Our algorithm runs in O((log kn)(log k)2(log n)2) time using O(k(n + m′)) processors on an ARBITRARY CRCW PRAM, where n and m′ stand for the numbers of vertices in G and edges in the simplified graph of G, respectively. 相似文献
9.
We address the probability that k or more Consecutive Customer Losses take place during a busy period of a queue, the so-called k-CCL probability, for oscillating GI
X
/M//n systems with state dependent services rates, also denoted as GI
X
/M(m)−M(m)//n systems, in which the service rates oscillate between two forms according to the evolution of the number of customers in
the system. We derive an efficient algorithm to compute k-CCL probabilities in these systems starting with an arbitrary number of customers in the system that involves solving a linear
system of equations. The results derived are illustrated for specific sets of parameters. 相似文献
10.
I. A. Yurov 《Mathematical Notes》1998,63(6):823-836
Let {a
n
}
n
=0/
be a uniformly distributed sequence ofp-adic integers. In the present paper we study continuous functions close to differentiable ones (with respect to thep-adic metric); for these functions, either the sequence {f(a
n
)}
n
=0/
is uniformly distributed over the ring ofp-adic integers or, for all sufficiently largek, the sequences {f
k
(k(an))}
n
=0/
are uniformly distributed over the residue class ring modp
k
, where
k
is the canonical epimorphism of the ring ofp-adic integers to the residue class ring modp
k
andf
k
is the function induced byf on the residue class ring modp
k
(i.e.,f k
(x)
=f(
k
(x)) (modp
k
)). For instance, these functions can be used to construct generators of pseudorandom numbers.Translated fromMatematicheskie Zametki, Vol. 63, No. 6, pp. 935–950, June, 1998.In conclusion, the author wishes to express his deep gratitude to V. S. Anashin for permanent attention to this research and for support. 相似文献
11.
Valentin Blomer 《Mathematische Zeitschrift》2008,260(4):755-777
Let S
k
(N, χ) be the space of cusp forms of weight k, level N and character χ. For let L(s, sym2
f) be the symmetric square L-function and be the Rankin–Selberg square attached to f. For fixed k ≥ 2, N prime, and real primitive χ, asymptotic formulas for the first and second moment of the central value of L(s, sym2
f) and over a basis of S
k
(N, χ) are given as N → ∞. As an application it is shown that a positive proportion of the central values L(1/2, sym2
f) does not vanish.
The author was supported by NSERC grant 311664-05. 相似文献
12.
Wesley Pegden 《Combinatorica》2006,26(5):577-585
We prove that the out-distance sequence {f+(k)} of a vertex-transitive digraph of finite or infinite degree satisfies f+(k+1)≤f+(k)2 for k≥1, where f+(k) denotes the number of vertices at directed distance k from a given vertex. As a corollary, we prove that for a connected vertex-transitive undirected graph of infinite degree
d, we have f(k)=d for all k, 1≤k<diam(G). This answers a question by L. Babai. 相似文献
13.
Hans Dobbertin 《Designs, Codes and Cryptography》1999,17(1-3):177-180
We give a short direct proof for a famous theorem published by Kasami in 1971. In terms of Walsh analysis it states that for d = 22k
- 2k + 1 the Walsh spectrum of the Boolean function Tr(x
d
) on GF(2
n
) consists precisely of the three values 0, ±2(n+s)/2 if s = gcd(k, n) = gcd(2k, n). 相似文献
14.
In this article we introduced the sequence spaces c
I
(p), c
0
I
(p), m
I
(p) and m
0
I
(p) for p = (p
k
), a sequence of positive real numbers. We study some algebraic and topological properties of these spaces. We prove the decomposition
theorem and obtain some inclusion relations.
相似文献
15.
Wenguang Zhai 《中国科学A辑(英文版)》1999,42(11):1173-1183
Thek-dimensional Piatetski-Shapiro prime number problem fork⩾3 is studied. Let π(x
1
c
1,⋯,c
k
) denote the number of primesp withp⩽x,
, where 1<c
1<⋯<c
k
are fixed constants. It is proved that π(x;c
1,⋯,c
k
) has an asymptotic formula ifc
1
−1
+⋯+c
k
−1
>k−k/(4k
2+2).
Project supported by the National Natural Science Foundation of China (Grant No. 19801021) and the Natural Science Foundation
of Shandong Province (Grant No.Q98A02110). 相似文献
16.
Ben Juurlink Petr Kolman Friedhelm Meyer auf der Heide Ingo Rieping 《Journal of Discrete Algorithms》2003,1(2):151
In this paper matching upper and lower bounds for broadcast on general purpose parallel computation models that exploit network locality are proven. These models try to capture both the general purpose properties of models like the PRAM or BSP on the one hand, and to exploit network locality of special purpose models like meshes, hypercubes, etc., on the other hand. They do so by charging a cost l(|i−j|) for a communication between processors i and j, where l is a suitably chosen latency function.An upper bound T(p)=∑i=0loglogp2i·l(p1/2i) on the runtime of a broadcast on a p processor H-PRAM is given, for an arbitrary latency function l(k).The main contribution of the paper is a matching lower bound, holding for all latency functions in the range from l(k)=Ω(logk/loglogk) to l(k)=O(log2k). This is not a severe restriction since for latency functions l(k)=O(logk/log1+log(k)) with arbitrary >0, the runtime of the algorithm matches the trivial lower bound Ω(logp) and for l(k)=Θ(log1+k) or l(k)=Θ(k), the runtime matches the other trivial lower bound Ω(l(p)). Both upper and lower bounds apply for other parallel locality models like Y-PRAM, D-BSP and E-BSP, too. 相似文献
17.
Guizhen LIU 《Frontiers of Mathematics in China》2009,4(2):311-323
Let G be a digraph with vertex set V(G) and arc set E(G) and let g = (g
−, g
+) and ƒ = (ƒ
−, ƒ
+) be pairs of positive integer-valued functions defined on V(G) such that g
−(x) ⩽ ƒ
−(x) and g
+(x) ⩽ ƒ
+(x) for each x ∈ V(G). A (g, ƒ)-factor of G is a spanning subdigraph H of G such that g
−(x) ⩽ id
H
(x) ⩽ ƒ
−(x) and g
+(x) ⩽ od
H
(x) ⩽ ƒ
+(x) for each x ∈ V(H); a (g, ƒ)-factorization of G is a partition of E(G) into arc-disjoint (g, ƒ)-factors. Let
= {F
1, F
2,…, F
m} and H be a factorization and a subdigraph of G, respectively.
is called k-orthogonal to H if each F
i
, 1 ⩽ i ⩽ m, has exactly k arcs in common with H. In this paper it is proved that every (mg+m−1,mƒ−m+1)-digraph has a (g, f)-factorization k-orthogonal to any given subdigraph with km arcs if k ⩽ min{g
−(x), g
+(x)} for any x ∈ V(G) and that every (mg, mf)-digraph has a (g, f)-factorization orthogonal to any given directed m-star if 0 ⩽ g(x) ⩽ f(x) for any x ∈ V(G). The results in this paper are in some sense best possible.
相似文献
18.
Let (GA)
n
[k](a), A
n
(a), G
n
(a) be the third symmetric mean of k degree, the arithmetic and geometric means of a
1, …, a
n
(a
i
> 0, i = 1, …, n), respectively. By means of descending dimension method, we prove that the maximum of p is k−1/n−1 and the minimum of q is n/n−1(k−1/k)
k/n
so that the inequalities {fx505-1} hold. 相似文献
19.
Mathew Cropper Anthony J. W. Hilton Peter D. Johnson Jr. Jenö Lehel 《Journal of Graph Theory》2010,65(1):16-34
We show that the four‐cycle has a k‐fold list coloring if the lists of colors available at the vertices satisfy the necessary Hall's condition, and if each list has length at least ?5k/3?; furthermore, the same is not true with shorter list lengths. In terms of h(k)(G), the k ‐fold Hall number of a graph G, this result is stated as h(k)(C4)=2k??k/3?. For longer cycles it is known that h(k)(Cn)=2k, for n odd, and 2k??k/(n?1)?≤h(k)(Cn)≤2k, for n even. Here we show the lower bound for n even, and conjecture that this is the right value (just as for C4). We prove that if G is the diamond (a four‐cycle with a diagonal), then h(k)(G)=2k. Combining these results with those published earlier we obtain a characterization of graphs G with h(k)(G)=k. As a tool in the proofs we obtain and apply an elementary generalization of the classical Hall–Rado–Halmos–Vaughan theorem on pairwise disjoint subset representatives with prescribed cardinalities. © 2009 Wiley Periodicals, Inc. J Graph Theory 65: 16–34, 2010. 相似文献
20.
In this paper, k-blocking sets in PG(n, q), being of Rédei type, are investigated. A standard method to construct Rédei type k-blocking sets in PG(n, q) is to construct a cone having as base a Rédei type k-blocking set in a subspace of PG(n, q). But also other Rédei type k-blocking sets in PG(n, q), which are not cones, exist. We give in this article a condition on the parameters of a Rédei type k-blocking set of PG(n, q = p
h
), p a prime power, which guarantees that the Rédei type k-blocking set is a cone. This condition is sharp. We also show that small Rédei type k-blocking sets are linear. 相似文献