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 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 ...

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...

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 murine model of Leishmania major infection has been an invaluable tool in understanding T helper differentiation in vivo. The initial evidence for a role of distinct CD4(+) T helper subsets in the outcome of infection was first obtained with this experimental model. The development of CD4(+) Th1 cells was associated with resolution of the lesion, control of parasite replication, and resista...

(1) For every right zeroed non empty RLS structure V holds every Affine subset M of V is parallel to M. (2) Let V be an add-associative right zeroed right complementable non empty RLS structure and M, N be Affine subsets of V . If M is parallel to N, then N is parallel to M. (3) Let V be an Abelian add-associative right zeroed right complementable non empty RLS structure and M, L, N be Affine s...