共查询到20条相似文献,搜索用时 234 毫秒
1.
Given a partially ordered setP=(X, ), a collection of linear extensions {L
1,L
2,...,L
r
} is arealizer if, for every incomparable pair of elementsx andy, we havex<y in someL
i
(andy<x in someL
j
). For a positive integerk, we call a multiset {L
1,L
2,...,L
t
} ak-fold realizer if for every incomparable pairx andy we havex<y in at leastk of theL
i
's. Lett(k) be the size of a smallestk-fold realizer ofP; we define thefractional dimension ofP, denoted fdim(P), to be the limit oft(k)/k ask. We prove various results about the fractional dimension of a poset.Research supported in part by the Office of Naval Research. 相似文献
2.
Ming-Chu Chou 《代数通讯》2013,41(2):898-911
Let R be a prime ring, L a noncentral Lie ideal of R, and a ∈ R. Set [x, y]1 = [x, y] = xy ? yx for x, y ∈ R and inductively [x, y]k = [[x, y]k?1, y] for k > 1. Suppose that δ is a nonzero σ-derivation of R such that a[δ(x), x]k = 0 for all x ∈ L, where σ is an automorphism of R and k is a fixed positive integer. Then a = 0 except when char R = 2 and R ? M2(F), the 2 × 2 matrix ring over a field F. 相似文献
3.
K. -H. Küfer 《Journal of Complexity》1996,12(4):339-357
Leta1, . . . ,ambe independent random points in
nthat are independent and identically distributed spherically symmetrical in
n. Moreover, letXbe the random polytope generated as the convex hull ofa1, . . . ,amand letLkbe an arbitraryk-dimensional subspace of
nwith 2 ≤k≤n− 1. LetXkbe the orthogonal projection image ofXinLk. We call those vertices ofXwhose projection images inLkare vertices ofXkshadow vertices ofXwith respect to the subspaceLk. We derive a distribution independent sharp upper bound for the expected number of shadow vertices ofXinLk. 相似文献
4.
Turán's problem is to determine the maximum numberT(n,k,t) oft-element subsets of ann-set without a complete sub-hypergraph onk vertices, i.e., allt-subsets of ak-set. It is proved that fora≥1 fixed andt sufficiently largeT(n, t+a,t)>(1-a(a+4+o(1))logt/(
a
t
)(
t
n
holds 相似文献
5.
Jishan Hu 《Studies in Applied Mathematics》1998,101(2):99-126
In this article, for the symmetric pendulum equation and the symmetric bisuperlinear equation respectively, we show that there are two one-parameter families of solutions, ys and ya, so that one is adiabatically symmetric, ys(?t)=ys(t)+o(εk) for all k≥0, and the other adiabatically antisymmetric, ya(?t)=?ya(t)+o(εk) for all k≥0. By using the techniques of exponential asymptotics to calculate y′s(0) and ya(0), we demonstrate that, in general, they are not genuinely symmetric or antisymmetric, because these quantities are in fact exponentially small. Finally, after establishing a relationship between the total change in the leading-order adiabatic invariant and the quantity y′s(0) for the family of solutions ys of the bisuperlinear equation, we are able to reveal explicitly how the behavior of the adiabatic invariant depends on the complex singularities of the equation. 相似文献
6.
巫世权 《高校应用数学学报(英文版)》1993,8(2):175-181
Let Cdenote the set of all k-subests of an n-set.Assume Alohtain in Ca,and A lohtain in (A,B) is called a cross-2-intersecting family if |A B≥2 for and A∈A,B∈B.In this paper,the best upper bounds of the cardinalities for non-empty cross-2-intersecting familles of a-and b-subsets are obtained for some a and b,A new proof for a Frankl-Tokushige theorem[6] is also given. 相似文献
7.
In the case of existence the smallest numberN=Rakis called a Rado number if it is guaranteed that anyk-coloring of the numbers 1, 2, …, Ncontains a monochromatic solution of a given system of linear equations. We will determine Rak(a, b) for the equationa(x+y)=bzifb=2 andb=a+1. Also, the case of monochromatic sequences {xn} generated bya(xn+xn+1)=bxn+2 is discussed. 相似文献
8.
Very Asymmetric Marking Games 总被引:1,自引:0,他引:1
We investigate a competitive version of the coloring number of a graph G = (V, E). For a fixed linear ordering L of V let s (L) be one more than the maximum outdegree of G when G is oriented so that x ← y if x <
L
y. The coloring number of G is the minimum of s (L) over all such orderings. The (a, b)-marking game is played on a graph G = (V, E) as follows. At the start all vertices are unmarked. The players, Alice and Bob, take turns playing. A play consists of Alice
marking a unmarked vertices or Bob marking b unmarked vertices. The game ends when there are no remaining unmarked vertices. Together the players create a linear ordering
L of V defined by x < y if x is marked before y. The score of the game is s (L). The (a, b)-game coloring number of G is the minimum score that Alice can obtain regardless of Bob’s strategy. The usual (1, 1)-marking game is well studied and
there are many interesting results. Our main result is that if G has an orientation with maximum outdegree k then the (k, 1)-game coloring number of G is at most 2k + 2. This extends a fundamental result on the (1, 1)-game coloring number of trees. We also construct examples to show that
this bound is tight for many classes of graphs. Finally we prove bounds on the (a, 1)-game coloring number when a < k. 相似文献
9.
Vladislav V. Kravchenko R. Michael Porter Sergii M. Torba 《Mathematical Methods in the Applied Sciences》2019,42(15):4902-4908
Let L be the n‐th order linear differential operator Ly=?0y(n)+?1y(n?1)+?+?ny with variable coefficients. A representation is given for n linearly independent solutions of Ly=λry as power series in λ, generalizing the SPPS (spectral parameter power series) solution that has been previously developed for n=2. The coefficient functions in these series are obtained by recursively iterating a simple integration process, beginning with a solution system for λ=0. It is shown how to obtain such an initializing system working upwards from equations of lower order. The values of the successive derivatives of the power series solutions at the basepoint of integration are given, which provides a technique for numerical solution of n‐th order initial value problems and spectral problems. 相似文献
10.
Let R
k,s
(n) denote the number of solutions of the equation n = x2 + y1k + y2k + ?+ ysk{n= x^2 + y_1^k + y_2^k + \cdots + y_s^k} in natural numbers x, y
1, . . . , y
s
. By a straightforward application of the circle method, an asymptotic formula for R
k,s
(n) is obtained when k ≥ 3 and s ≥ 2
k–1 + 2. When k ≥ 6, work of Heath-Brown and Boklan is applied to establish the asymptotic formula under the milder constraint s ≥ 7 · 2
k–4 + 3. Although the principal conclusions provided by Heath-Brown and Boklan are not available for smaller values of k, some of the underlying ideas are still applicable for k = 5, and the main objective of this article is to establish an asymptotic formula for R
5,17(n) by this strategy. 相似文献
11.
M. Thamban Nair 《Advances in Computational Mathematics》2012,36(2):315-329
Problem of solving integral equations of the first kind, òab k(s, t) x(t) dt = y(s), s ? [a, b]\int_a^b k(s, t) x(t)\, dt = y(s),\, s\in [a, b] arises in many of the inverse problems that appears in applications. The above problem is a prototype of an ill-posed problem.
Thus, for obtaining stable approximate solutions based on noisy data, one has to rely on regularization methods. In practice,
the noisy data may be based on a finite number of observations of y, say y(τ
1), y(τ
2), ..., y(τ
n
) for some τ
1, ..., τ
n
in [a, b]. In this paper, we consider approximations based on a collocation method when the nodes τ
1, ..., τ
n
are associated with a convergent quadrature rule. We shall also consider further regularization of the procedure and show
that the derived error estimates are of the same order as in the case of Tikhonov regularization when there is no approximation
of the integral operator is involved. 相似文献
12.
Given two integers n and k, n ≥ k > 1, a k-hypertournament T on n vertices is a pair (V, A), where V is a set of vertices, |V| = n and A is a set of k-tuples of vertices, called arcs, so that for any k-subset S of V, A$ contains exactly one of the k! k-tuples whose entries belong to S. A 2-hypertournament is merely an (ordinary) tournament. A path is a sequence v1a1v2v3···vt−1vt of distinct vertices v1, v2,⋖, vt and distinct arcs a1, ⋖, at−1 such that vi precedes vt−1 in a, 1 ≤ i ≤ t − 1. A cycle can be defined analogously. A path or cycle containing all vertices of T (as vi's) is Hamiltonian. T is strong if T has a path from x to y for every choice of distinct x, y ≡ V. We prove that every k-hypertournament on n (k) vertices has a Hamiltonian path (an extension of Redeis theorem on tournaments) and every strong k-hypertournament with n (k + 1) vertices has a Hamiltonian cycle (an extension of Camions theorem on tournaments). Despite the last result, it is shown that the Hamiltonian cycle problem remains polynomial time solvable only for k ≤ 3 and becomes NP-complete for every fixed integer k ≥ 4. © 1997 John Wiley & Sons, Inc. J Graph Theory 25: 277–286, 1997 相似文献
13.
Kirill A. Kopotun 《Journal of Approximation Theory》1998,94(3):481-493
It is shown that an algebraic polynomial of degree k−1 which interpolates ak-monotone functionfatkpoints, sufficiently approximates it, even if the points of interpolation are close to each other. It is well known that this result is not true in general for non-k-monotone functions. As an application, we prove a (positive) result on simultaneous approximation of ak-monotone function and its derivatives inLp, 0<p<1, metric, and also show that the rate of the best algebraic approximation ofk-monotone functions (with bounded (k−2)nd derivatives inLp, 1<p<∞, iso(n−k/p). 相似文献
14.
A finite group G is said to be a B(n, k) group if for any n-element subset {a 1,…, a n } of G, |{a i a j |1 ≤ i, j ≤ n}| ≤k. In this article, we give characterizations of the B(5, 19) 2-groups, and the B(6, k) 2-groups for 21 ≤ k ≤ 28. 相似文献
15.
In this paper, the authors study the asymptotic behavior of solutions of second-order neutral type difference equations of the form
Δ2(yn+pyn−k)+f(n,yn−ℓ)=0,n