We consider approximation of L 1 functions by H 1 functions on proper subsets of the circle. We derive some properties of traces of Hardy classes on such subsets, and then turn to a generalization of classical extremal problems involving norm constraints on the complementary subset.

In this paper, we show that if a partially ordered set has 2n elements and has dimension n, then it is isosnorphic to the set of n-l element subsets and lelement subsets of a sef, ordered by inclusion, or else it has six elements and is isomorphic to a partially ordered b;i we call the chevron or to its dual.

The vertex arboricity $rho(G)$ of a graph $G$ is the minimum number of subsets into which the vertex set $V(G)$ can be partitioned so that each subset induces an acyclic graph‎. ‎A graph $G$ is called list vertex $k$-arborable if for any set $L(v)$ of cardinality at least $k$ at each vertex $v$ of $G$‎, ‎one can choose a color for each $v$ from its list $L(v)$ so that the subgraph induced by ev...

Let E be a separable Banach space not containing a copy of l. The complexity of the l(n)’s inside E may be measured by Bourgain’s l-index [3] or by locating so called lα-spreading models [8]. It is easy to see that the existence of l 1 α-spreading models implies a large l-index. In general, the implication is not reversible [7, Remark 6.6(i)]. However, suppose that T is the standard Tsirelson s...

In this paper, we construct two fuzzy sets using the notions of level subsets and strong level subsets of a given fuzzy set in a ring R. These fuzzy sets turn out to be identical and provide a universal construction of a fuzzy ideal generated by a given fuzzy set in a ring. Using this construction and employing the technique of strong level subsets, we provide the shortest and direct fuzzy set ...

Let X be an arbitrary nonempty set and L a lattice of subsets of X such that ∅, X ∈ L. A L denotes the algebra generated by L, andM L denotes those nonnegative, finite, finitely additive measures on A L . In addition, I L denotes the subset of M L which consists of the nontrivial zeroone valued measures. The paper gives detailed analysis of products of lattices, their associated Wallman spaces,...

If m(n,l) denotes the maximum number of subsets of an n-element set such that the intersection of any two of them has cardinality divisible by l, then a trivial construction shows that m(n,l) ≥ 2 [n / l]. For l = 2, this was known to be essentially best possible. For l ≥ 3, we show by construction that m(n,l) 2 − [n / l] grows exponentially in n, and we provide upper bounds.

Let p be a prime and let L = {l1, l2, . . . , ls} and K = {k1, k2, . . . , kr} be two subsets of {0, 1, 2, . . . , p − 1} satisfying max lj < min ki. We will prove the following results: If F = {F1, F2, . . . , Fm} is a family of subsets of [n] = {1, 2, . . . , n} such that |Fi ∩ Fj | (mod p) ∈ L for every pair i 6= j and |Fi| (mod p) ∈ K for every 1 ≤ i ≤ m, then |F| ≤ ( n− 1 s ) + ( n− 1 s− 1...

The knowledge about a planned system in engineering design applications is never complete. Often, a probabilistic quantification of the uncertainty arising from this missing information is warranted in order to efficiently incorporate our partial knowledge about the system and its environment into their respective models. This leads to a robust stochastic design framework where probabilistic mo...

in this note first we define the notions of fuzzy positive implicativehyper bck-ideals of types 1,2,3 and 4. then we prove some theorems whichcharacterize the above notions according to the level subsets. also we obtainthe relationships among these notions, fuzzy (strong, weak, reflexive) hyperbck-ideals and fuzzy positive implicative hyper bck-ideals of types 5,6,7and 8. then, we define the no...