In this paper, we present a comprehensive study of the monotonicity and log-concavity of the generalized Marcum and Nuttall -functions. More precisely, a simple probabilistic method is first given to prove the monotonicity of these two functions. Then, the log-concavity of the generalized Marcum -function and its deformations is established with respect to each of the three parameters. Since th...

In this paper, a new graph data structure for 2-D shape representation is proposed. The new structure is called a concavity graph, and is an evolution from the already known “concavity tree”. Even though a concavity graph bears a fundamental resemblance to a concavity tree, the former is able to describe the shape of multiple objects in an image and their spatial configuration, and is hence inh...

Digital Elevation Models (DEMs) are used to estimate different morphologies, analysis of river profile, delineating drainage basin and drainage pattern associated with lithological and structural changes. The study area is Maroon River located in Khuzestan Province, Iran. In this study geomorphometric analysis based on DEM carried out to understand Maroon river uplift rate and tectonic- erosion...

The marginal social value of income redistribution is understood to depend on both the concavity of individuals’ utility functions and the concavity of the social welfare function. In the pertinent literatures, notably on optimal income taxation and on normative inequality measurement, it seems to be accepted that the role of these two sources of concavity is symmetric with regard to the social...

Motivated by Schur-concavity, we introduce the notion of G-concavity where G is a closed subgroup of the orthogonal group O(V ) on a finite dimensional real inner product space V . The triple (V,G, F ) is an Eaton triple if F ⊂ V is a nonempty closed convex cone such that (A1) Gx ∩ F is nonempty for each x ∈ V . (A2) maxg∈G(x, gy) = (x, gy) for all x, y ∈ F . If W := spanF and H := {g|W : g ∈ G...

We prove that the following three conditions together imply the concavity of the sequence Pn iˆ0 aibi= Pn iˆ0 ai : concavity of fbng, log-concavity of fang and nonincreasing of f…bn ÿ bnÿ1†=…anÿ1=an ÿ anÿ2=anÿ1†g. As a consequence we get necessary and sufficient conditions for the concavity of the sequences fSnÿ1…x†=Sn…x†g and fSn…x†=Sn…x†g for any nonnegative x, where Sn…x† is the nth partial ...

Decomposing a 3D model into approximately convex components has gained more attention recently due to its ability to efficiently generate small decomposition with controllable concavity bound. However, current methods are computationally expensive and require many user parameters. These parameters are usually unintuitive and add unnecessary obstacles in processing a large number of meshes and m...

Sagan, B.E., Inductive proofs of q-log concavity, Discrete Mathematics 99 (1992) 289-306. We give inductive proofs of q-log concavity for the Gaussian polynomials and the q-Stirling numbers of both kinds. Similar techniques are applied to show that certain sequences of elementary and complete symmetric functions are q-log concave.