where {e1, · · · , en} (resp. {ξ1, · · · , ξm}) is an orthonormal basis of the tangent (resp. normal) bundle, and R (resp. R) is the curvature tensor for the tangent (resp. normal) bundle. In the study of submanifold theory, De Smet, Dillen, Verstraelen, and Vrancken [5] made the following normal scalar curvature conjecture: Conjecture 1. Let h be the second fundamental form, and let H = 1 n tr...

The reduction in distribution costs of digital products has renewed interest in strategies for pricing goods with low marginal costs. In this paper, we evaluate the concept of customized bundling in which consumers can choose up to a quantity M of goods drawn from a larger pool of N different goods (N>M) for a fixed price. We show that the complex mixed bundle problem can be reduced to the cust...

The emerging field of data analytics and the increasing importance of data and information in decision making has created a large market for buying and selling information and information-related services. In this market, for some types of information products, it is common for a consumer to purchase the same type of information product from multiple sources. In other situations, a consumer may...

We give a non-trivial class of valuation functions for which we give auctions that are efficient, truthful and envy-free. We give interesting classes of valuations for which one can design such auctions. Surprisingly, we also show that minor modifications to these valuations lead to impossibility results, the most surprising of which is that for a natural class of valuations, one cannot achieve...