Certain unified integral inequalities in connection with quantum fractional calculus

Some unified integral inequalities involving quantum fractional calculus are obtained via the functions having classical and relative convexity property

ITERATED FAILURE RATE MONOTONICITY AND ORDERING RELATIONS WITHIN GAMMA AND WEIBULL DISTRIBUTIONS

Stochastic ordering of random variables may be defined by the relative convexity of the tail functions. This has been extended to higher order stochastic orderings, by iteratively reassigning tail-weights. The actual verification of stochastic orderings is not simple, as this depends on inverting distribution functions for which there may be no explicit expression. The iterative definition of distributions, of course, contributes to make that verification even harder. We have a look at the stochastic ordering, introducing a method that allows for explicit usage, applying it to the Gamma and Weibull distributions, giving a complete description of the order of relations within each of these families.

Hardy-Littlewood-Polya theorem of majorization in the framework of generalized convexity

Based on a new concept of generalized relative convexity, a large extension of Hardy-Littlewood-Polya theorem ´ of majorization is obtained. Several applications escaping the classical framework of convexity are included.

Compaction-related deformation in Cambrian olenelloid trilobites and its implications for fossil morphometry

Morphometric analyses of silicified and nonsilicified (preserved in shale) specimens of the olenelloid trilobites Olenellus (Olenellus) gilberti Meek (in White, 1874) and Nephrolenellus geniculatus Palmer, 1998, from the Lower Cambrian C-Shale Member of the Pioche Formation show that even well-preserved specimens in shales have undergone significant changes in lateral as well as vertical dimensions as a result of compaction. Analyses of cephalic landmarks show that in both species compaction causes posteriordirected collapse of the anterior lobe of the glabella, adaxial deformation of the ocular lobes, and abaxial and anterior splaying of genal regions. These shape changes are explicable in terms of observed exoskeletal fracture patterns. Landmarks show an increase in scatter around their ontogenetic trajectories that is generally proportional to the degree of lateral shift each landmark has undergone. Interspecific differences in compactional response may depend on the relative convexity of the cephalon. Olenellus (Olenellus) gilberti is a low-convexity species and shows marked lateral shape change, particularly in the genal region. Nephrolenellus geniculatus is more convex and shows less severe lateral shape change. Landmarks of both species exhibit an average trebling of the degree of scatter around their average ontogenetic trajectories in compacted samples. Because even well-preserved specimens in shales differ in shape from their precompactional appearance, results of morphometric studies utilizing metric distances between landmarks in trilobites where compaction can be detected must be interpreted with caution.