On a Lower Bound for the Multivariate Normal Mills' Ratio

A Lower Bound on the Competitive Ratio of Truthful Auctions

We study a class of single-round, sealed-bid auctions for a set of identical items. We adopt the worst case competitive framework defined by [1,2] that compares the profit of an auction to that of an optimal single price sale to at least two bidders. In this framework, we give a lower bound of 2.42 (an improvement from the bound of 2 given in [2]) on the competitive ratio of any truthful auctio...

Screening for a Multivariate Mixture Normal Distribution

The Tight Lower Bound for the Steiner Ratio in

A minimum Steiner tree for a given set X of points is a network interconnecting the points of X having minimum possible total length. The Steiner ratio for a metric space is the largest lower bound for the ratio of lengths between a minimum Steiner tree and a minimum spanning tree on the same set of points in the ,metric space. In this note, we show that for any Minkowski plane, the Steiner rat...

Lower bound theorem for normal pseudomanifolds

In this paper we present a self-contained combinatorial proof of the lower bound theorem for normal pseudomanifolds, including a treatment of the cases of equality in this theorem. We also discuss McMullen and Walkup’s generalised lower bound conjecture for triangulated spheres in the context of the lower bound theorem. Finally, we pose a new lower bound conjecture for non-simply connected tria...

A lower bound for ratio of power means

holds for r > 0 and n∈N. We call the left-hand side of this inequality Alzer’s inequality [1] and the right-hand side Martins’ inequality [8]. Let {ai}i∈N be a positive sequence. If ai+1ai−1 ≥ ai for i ≥ 2, we call {ai}i∈N a logarithmically convex sequence; if ai+1ai−1 ≤ ai for i≥ 2, we call {ai}i∈N a logarithmically concave sequence. In [2], Martins’ inequality was generalized as follows: let ...