Let f,(n, k) denote the maximum number of k-subsets of an n-set satisfying the condition in the title . It is proved that f,(n,r(t-1)+1+d)-(n t dl/ u lk t dl for n sufficiently large whenever d = 0,1 or d < r/2 t 2 withJh equality holding iff there exists a Steiner system S(t, r(t 1) + l, n d). The determination of f,(n, 2r) led us to a new generalization of BIRD (Definition 2 .4). Exponential ...

We continue the exploration of various aspects divisibility ultrafilters, adding one more relation to picture: multiplicative finite embeddability. show that it lies between relations $$\mid _M$$ and $${\widetilde{\mid }}$$ . The set its minimal elements proves be very rich, -hierarchy is used get a better intuition this richness. find place -maximal ultrafilters among some known families ultra...

The existence, public availability, and widespread acceptance of a standard benchmark for a given information retrieval (IR) task are beneficial to research on this task, since they allow different researchers to experimentally compare their own systems by comparing the results they have obtained on this benchmark. The Reuters-21578 test collection, together with its earlier variants, has been ...

The existence, public availability, and widespread acceptance of a standard benchmark for a given information retrieval (IR) task are beneficial to research on this task, since they allow different researchers to experimentally compare their own systems by comparing the results they have obtained on this benchmark. The Reuters-21578 test collection, together with its earlier variants, has been ...

For biological arrays, performing multiple experimental repeats is a common way to improve certainty of gene identification. But this is offset by the high cost of each experiment. In a typical experiment, n independent measurements (e.g., data from n separate gene expression arrays (Affymetrix, 2002; Lipshutz et al., 1999) are combined to yield a single estimation per assay (e.g., per gene). T...

Let [n] denote the set {1, 2, ..., n}, 2 the collection of all subsets of [n] and F ⊂ 2 be a family. The maximum of |F| is studied if any r subsets have an at least s-element intersection and there are no ` subsets containing t+1 common elements. We show that |F| ≤ Pt−s i=0 n−s i + t+`−s t+2−s n−s t+1−s + `− 2 and this bound is asymptotically the best possible as n →∞ and t ≥ 2s ≥ 2, r, ` ≥ 2 a...

The Turing degrees 3d were introduced by Kleene and Post ([9], 1954) to isolate and study those properties of the subsets of the natural numbers N which are expressed purely in terms of relative computability. Intuitively, we form 3d by identifying any pair of subsets of N which are mutually computable and ordering the resulting equivalence classes by relative computability. The natural hierarc...

Pseudo-random subsets of the set {1, 2, . . . , N} have many applications in the fields of network security, cryptography and other security issues. Recently, Dartyge and Sárközy investigated the measures–the well distribution measure and the correlation measure of order k–of pseudorandomness of subsets of the set {1, 2, . . . , N}, and they presented several constructive examples for subsets w...

Maize (Zea mays L.) production requires large amounts of nitrogen (N) thatdirectly affect production cost. Poultry litter can be used as an alternative source ofN. To optimize its use, poultry litter requires technical and economic feasibilityanalyses. Crop simulation models have proven to be efficient tools to support thistype of research. The objectives of this study were to determine yield a...