Chvátal’s conjecture in extremal combinatorics asserts that for any decreasing family F of subsets of a finite set S, there is a largest intersecting subfamily of F consisting of all members of F that include a particular x ∈ S. In this paper we reformulate the conjecture in terms of influences of variables on Boolean functions and correlation inequalities, and study special cases and variants ...

In this paper, we investigate the structures of extremal trees which have the minimal number of subtrees in the set of all trees with a given degree sequence. In particular, the extremal trees must be caterpillar and but in general not unique. Moreover, all extremal trees with a given degree sequence π = (d1, . . . , d5, 1, . . . , 1) have been characterized.

In this note, we study the covering radii of extremal doubly even self-dual codes. We give slightly improved lower bounds on the covering radii of extremal doubly even self-dual codes of lengths 64, 80 and 96. The covering radii of some known extremal doubly even self-dual [64, 32, 12] codes are determined.

background: low compliance with drugs regimens in diabetic patients is one of the greatest challenges in the treatment of diabetes. the aim of this study was to evaluate compliance with medical orders in diabetic patients referred to the endocrinology clinic of afzalipour hospital, kerman, iran. methods: in this cross sectional study 345 of the 3000 patients, who referred to the endocrinology c...

The existence of extremal functions for the Sobolev trace inequalities is studied using the concentration compactness theorem. The conjectured extremal, the function of conformal factor, is considered and is proved to be an actual extremal function with extra symmetry condition on functions. One of the limiting cases of the Sobolev trace inequalities is investigated and the best constant for th...

The extremal characteristics of random structures, including trees, graphs, and networks, are discussed. A statistical physics approach is employed in which extremal properties are obtained through suitably defined rate equations. A variety of unusual time dependences and system-size dependences for basic extremal properties are obtained.

We construct non-extremal fractional D-brane solutions of type-II string theory at the Z 2 orbifold point of K3. These solutions generalize known extremal fractional-brane solutions and provide further insights into N = 2 supersymmetric gauge theories and dual descriptions thereof. In particular, we find that for these solutions the horizon radius cannot exceed the non-extremal enhançon radius....

Let W (̟k) be the finite-dimensional irreducible module over a quantized affine algebra U ′ q(g) with the fundamental weight ̟k as an extremal weight. We show that its crystal B(W (̟k)) is isomorphic to the Demazure crystal B −(−Λ0 +̟k). This is derived from the following general result: for a dominant integral weight λ and an integral weight μ, there exists a unique homomorphism Uq(g)(uλ⊗ uμ) → V ...