Alon and Roichman (1994) proved that for every ε > 0 there is a finite c(ε) such that for any sufficiently large group G, the expected value of the second largest (in absolute value) eigenvalue of the normalized adjacency matrix of the Cayley graph with respect to c(ε) log |G| random elements is less than ε. We reduce the number of elements to c(ε) logD(G) (for the same c), where D(G) is the su...

Techniques for query expansion from top retrieved documents have been recently used by many groups at TREC, often on a purely empirical ground. In this paper we present a novel method for ranking and weighting expansion terms. The method is based on the concept of relative entropy, or Kullback-Lieber distance, developed in Information Theory, from which we derive a computationally simple and th...

Techniques for query expansion from top retrieved documents have been recently used by many groups at TREC, often on a purely empirical ground. In this paper we present a novel method for ranking and weighting expansion terms. The method is based on the concept of relative entropy, or Kullback-Lieber distance, developed in Information Theory, from which we derive a computationally simple and th...

We show that for a given holomorphic noncharacteristic surface S ∈ C, and a given holomorphic function on S, there exists a unique meromorphic solution of Burgers’ equation which blows up on S. This proves the convergence of the formal Laurent series expansion found by the Painlevé test. The method used is an adaptation of Nirenberg’s iterative proof of the abstract Cauchy-Kowalevski theorem. A...

In the present article, we construct the exact traveling wave solutions of nonlinear PDEs in mathematical physics via the (1 + 1) dimensional modified Kawahara equation by using the following two methods: (i) A further improved ( ′ G )expansion method, where G = G(ξ) satisfies the auxiliary ordinary differential equation [G′(ξ)]2 = aG2(ξ) + bG4(ξ) + cG6(ξ), where ξ = x − V t while a, b, c and V...

OBJECTIVE Non-supermarket food retailers can be a promising channel for increasing the availability of healthy foods in underserved communities. The present paper reports on retailer practices, attitudes and beliefs about the supply of healthy foods before and after the introduction of new subsidies for healthy foods by the US Special Supplemental Nutrition Program for Women, Infants, and Child...

In 1993, National Car Rental faced liquidation. General Motors Corporation (National's parent) took a $744 million charge against earnings related to its ownership of National Car Rental Systems. National faced liquidation, with the loss of 7,500 jobs, unless it could show a profit in the short term. National initiated a comprehensive revenue management program whose core is a suite of analytic...

Successful information retrieval requires effective matching between the user’s search request and the contents of relevant documents. Often the request entered by a user may not use the same topic relevant terms as the authors’ of the documents. One potential approach to address problems of query-document term mismatch is document expansion to include additional topically relevant indexing ter...

We study the critical set C of the nonlinear differential operator F (u) = −u′′+f(u) defined on a Sobolev space of periodic functions Hp(S1), p ≥ 1. Let Rxy ⊂ R3 be the plane z = 0 and, for n > 0, let ⊲⊳n be the cone x2 + y2 = tan2 z, |z − 2πn| < π/2; also set Σ = Rxy ∪ ⋃ n>0 ⊲⊳n. For a generic smooth nonlinearity f : R → R with surjective derivative, we show that there is a diffeomorphism betw...