Monotonicity properties of norms

Monotonicity of the maximum of inner product norms

Let K be the field of real or complex numbers. In this note we characterize all inner product norms p1, . . . , pm on K for which the norm x 7−→ max{p1(x), . . . , pm(x)} on K is monotonic.

Old and New Monotonicity Properties

Suppose that each ballot consists of a strict preference ranking of the alternatives, that alternative x has just won the election, and that a single voter now changes her ballot by moving x higher up in the ranking (without changing her relative preference among other alternatives). The standard monotonicity property of social choice theory asserts, in any such scenario, that x should remain t...

Monotonicity properties of certain Laplacian eigenvectors

Nath and Paul (Linear Algebra Appl., 460 (2014), 97-110) have shown that the largest distance Laplacian eigenvalue of a path is simple and the corresponding eigenvector has properties similar to the Fiedler vector. We given an alternative proof, establishing a more general result in the process. AMS Classification: 05C05, 05C50

Monotonicity and Aging Properties of Random Sums

In this paper, we discuss the distributional properties of random sums. We first derive conditions under which the distribution of a binomial sum is PF2 and then show under the same conditions the distribution of a Poisson sum is PF2 by approximating a Poisson sum by a sequence of binomial sums. The PF2 property reveals the monotonicity property of the reversed failure rates of certain compound...

Monotonicity Properties of Stochastic Inventory Systems