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1.
Let x=(x1,…,xn) be a sequence of positive integers. An x-parking function is a sequence (a1,…,an) of positive integers whose non-decreasing rearrangement b1bn satisfies bix1++xi. In this paper we give a combinatorial approach to the enumeration of (a,b,…,b)-parking functions by their leading terms, which covers the special cases x=(1,…,1), (a,1,…,1), and (b,…,b). The approach relies on bijections between the x-parking functions and labeled rooted forests. To serve this purpose, we present a simple method for establishing the required bijections. Some bijective results between certain sets of x-parking functions of distinct leading terms are also given. 相似文献
2.
Let X1, X2, …, Xn be random vectors that take values in a compact set in Rd, d ≥ 1. Let Y1, Y2, …, Yn be random variables (“the responses”) which conditionally on X1 = x1, …, Xn = xn are independent with densities f(y | xi, θ(xi)), i = 1, …, n. Assuming that θ lives in a sup-norm compact space Θq,d of real valued functions, an optimal L1-consistent estimator
of θ is constructed via empirical measures. The rate of convergence of the estimator to the true parameter θ depends on Kolmogorov's entropy of Θq,d. 相似文献
3.
There exist infinitely many finite sequences (a1, …, an) (ai {0, 1}) such that Φi = 1n − k aiai + k is odd for each k = 0, 1, …, n − 1. 相似文献
4.
Marco Buratti 《Journal of Combinatorial Theory, Series A》2000,90(2):353
A Z-cyclic triplewhist tournament for 4n+1 players, or briefly a TWh(4n+1), is equivalent to a n-set {(ai, bi, ci, di) | i=1, …, n} of quadruples partitioning Z4n+1−{0} with the property that ni=1 {±(ai−ci), ±(bi−di)}=ni=1 {±(ai−bi), ±(ci−di)}=ni=1 {±(ai−di), ±(bi−ci)}=Z4n+1−{0}. The existence problem for Z-cyclic TWh(p)'s with p a prime has been solved for p1 (mod 16). I. Anderson et al. (1995, Discrete Math.138, 31–41) treated the case of p≡5 (mod 8) while Y. S. Liaw (1996, J. Combin. Des.4, 219–233) and G. McNay (1996, Utilitas Math.49, 191–201) treated the case of p≡9 (mod 16). In this paper, besides giving easier proofs of these authors' results, we solve the problem also for primes p≡1 (mod 16). The final result is the existence of a Z-cyclic TWh(v) for any v whose prime factors are all≡1 (mod 4) and distinct from 5, 13, and 17. 相似文献
5.
E. Kimchi 《Journal of Approximation Theory》1978,24(4):350-360
Let {u0, u1,… un − 1} and {u0, u1,…, un} be Tchebycheff-systems of continuous functions on [a, b] and let f ε C[a, b] be generalized convex with respect to {u0, u1,…, un − 1}. In a series of papers ([1], [2], [3]) D. Amir and Z. Ziegler discuss some properties of elements of best approximation to f from the linear spans of {u0, u1,…, un − 1} and {u0, u1,…, un} in the Lp-norms, 1 p ∞, and show (under different conditions for different values of p) that these properties, when valid for all subintervals of [a, b], can characterize generalized convex functions. Their methods of proof rely on characterizations of elements of best approximation in the Lp-norms, specific for each value of p. This work extends the above results to approximation in a wider class of norms, called “sign-monotone,” [6], which can be defined by the property: ¦ f(x)¦ ¦ g(x)¦,f(x)g(x) 0, a x b, imply f g . For sign-monotone norms in general, there is neither uniqueness of an element of best approximation, nor theorems characterizing it. Nevertheless, it is possible to derive many common properties of best approximants to generalized convex functions in these norms, by means of the necessary condition proved in [6]. For {u0, u1,…, un} an Extended-Complete Tchebycheff-system and f ε C(n)[a, b] it is shown that the validity of any of these properties on all subintervals of [a, b], implies that f is generalized convex. In the special case of f monotone with respect to a positive function u0(x), a converse theorem is proved under less restrictive assumptions. 相似文献
6.
Raffaele Giancarlo Roberto Grossi 《Journal of Algorithms in Cognition, Informatics and Logic》1997,24(2):223-265
We introduce a new multidimensional pattern matching problem that is a natural generalization of string matching, a well studied problem[1]. The motivation for its algorithmic study is mainly theoretical. LetA[1:n1,…,1:nd] be a text matrix withN = n1…ndentries andB[1:m1,…,1:mr] be a pattern matrix withM = m1…mrentries, whered ≥ r ≥ 1 (the matrix entries are taken from an ordered alphabet Σ). We study the problem of checking whether somer-dimensional submatrix ofAis equal toB(i.e., adecisionquery).Acan be preprocessed andBis given on-line. We define a new data structure for preprocessingAand propose CRCW-PRAM algorithms that build it inO(log N) time withN2/nmaxprocessors, wherenmax = max(n1,…,nd), such that the decision query forBtakesO(M) work andO(log M) time. By using known techniques, we would get the same preprocessing bounds but anO((dr)M) work bound for the decision query. The latter bound is undesirable since it can depend exponentially ond; our bound, in contrast, is independent ofdand optimal. We can also answer, in optimal work, two further types of queries: (a) anenumerationquery retrieving all ther-dimensional submatrices ofAthat are equal toBand (b) anoccurrencequery retrieving only the distinct positions inAthat correspond to all of these submatrices. As a byproduct, we also derive the first efficient sequential algorithms for the new problem. 相似文献
7.
M Boshernitzan A.S Fraenkel 《Journal of Algorithms in Cognition, Informatics and Logic》1984,5(2):187-198
Given a sequence of integers [ai]i=1n, an O(n) iterative algorithm is presented which decides whether there exist real numbers α and β such that ai = [iα + β] (1 ? i ? n). In fact, the linear algorithm computes the partial quotients of the continued fraction expansions of and such that if and only if ai = [iα + β] (1 ? i ? n) for suitable β = β(α). 相似文献
8.
We give a direct formulation of the invariant polynomials μGq(n)(, Δi,;, xi,i + 1,) characterizing U(n) tensor operators p, q, …, q, 0, …, 0 in terms of the symmetric functions Sλ known as Schur functions. To this end, we show after the change of variables Δi = γi − δi and xi, i + 1 = δi − δi + 1 thatμGq(n)(,Δi;, xi, i + 1,) becomes an integral linear combination of products of Schur functions Sα(, γi,) · Sβ(, δi,) in the variables {γ1,…, γn} and {δ1,…, δn}, respectively. That is, we give a direct proof that μGq(n)(,Δi,;, xi, i + 1,) is a bisymmetric polynomial with integer coefficients in the variables {γ1,…, γn} and {δ1,…, δn}. By making further use of basic properties of Schur functions such as the Littlewood-Richardson rule, we prove several remarkable new symmetries for the yet more general bisymmetric polynomials μmGq(n)(γ1,…, γn; δ1,…, δm). These new symmetries enable us to give an explicit formula for both μmG1(n)(γ; δ) and 1G2(n)(γ; δ). In addition, we describe both algebraic and numerical integration methods for deriving general polynomial formulas for μmGq(n)(γ; δ). 相似文献
9.
In a symmetrizable Kac–Moody algebra g(A), let α=∑i=1nkiαi be an imaginary root satisfying ki>0 and α,αi<0 for i=1,2,…,n. In this paper, it is proved that for any xαgα{0}, satisfying [xα,fn]≠0 and [xα,fi]=0 for i=1,2,…,n−1, there exists a vector y such that the subalgebra generated by xα and y contains g′(A), the derived subalgebra of g(A). 相似文献
10.
Ying Guang Shi 《Journal of Approximation Theory》1998,92(3):463-471
This paper shows that under certain conditions a solution of the minimax problem mina<x1<…<xn<b max1in+1 fi(x1, …, xn) admits the equioscillation characterizations of Bernstein and Erd
s and has strong uniqueness. This problem includes as a particular example the optimal Lagrange interpolation problem. 相似文献
11.
Persistence, contractivity and global stability in logistic equations with piecewise constant delays
Yoshiaki Muroya 《Journal of Mathematical Analysis and Applications》2002,270(2):1532-635
We establish sufficient conditions for the persistence and the contractivity of solutions and the global asymptotic stability for the positive equilibrium N*=1/(a+∑i=0mbi) of the following differential equation with piecewise constant arguments: where r(t) is a nonnegative continuous function on [0,+∞), r(t)0, ∑i=0mbi>0, bi0, i=0,1,2,…,m, and a+∑i=0mbi>0. These new conditions depend on a,b0 and ∑i=1mbi, and hence these are other type conditions than those given by So and Yu (Hokkaido Math. J. 24 (1995) 269–286) and others. In particular, in the case m=0 and r(t)≡r>0, we offer necessary and sufficient conditions for the persistence and contractivity of solutions. We also investigate the following differential equation with nonlinear delay terms: where r(t) is a nonnegative continuous function on [0,+∞), r(t)0, 1−ax−g(x,x,…,x)=0 has a unique solution x*>0 and g(x0,x1,…,xm)C1[(0,+∞)×(0,+∞)××(0,+∞)]. 相似文献
12.
For all integers m3 and all natural numbers a1,a2,…,am−1, let n=R(a1,a2,…,am−1) represent the least integer such that for every 2-coloring of the set {1,2,…,n} there exists a monochromatic solution to
a1x1+a2x2++am−1xm−1=xm.