This paper addresses the natural question: “How should frames be compared?” We answer this question by quantifying the overcompleteness of all frames with the same index set. We introduce the concept of a frame measure function: a function which maps each frame to a continuous function. The comparison of these functions induces an equivalence and partial order that allows for a meaningful compa...

ABSTRACT Pepper plants can be used as ornamental ones due to the contrasting traits of plants, flowers, and especially fruits. This variability exploited in genetic improvement programs aiming at identifying superior genotypes obtaining hybrids. work aimed select parental hybrid individuals through diallel analysis for fruit Capsicum annuum. Seven pepper were crossed, eleven fruit-related quant...

SECTION 1 introduces a method for constructing a measure by inner approximation, starting from a set function defined on a lattice of sets. SECTION 2 defines a “tightness” property, which ensures that a set function has an extension to a finitely additive measure on a field determined by the class of approximating sets. SECTION 3 defines a “sigma-smoothness” property, which ensures that a tight...

in order to estimate heritability, heterosis, general and specific combining ability and relationships between them in traits of fruit number per plant, days to the first fruit harvest, yield per plant, average fruit weight and rind thickness, seven local populations of iranian melon (‘tashkandi’, ‘khatouni’, ‘garmak’, ‘aran1’, ‘mirpanji’, ‘suski-e-sabz’ and ‘golpaygan’) were crossed using a co...

combining ability effects were estimated for different agronomic characters in line × tester crossing program comprising 21 hybrids produced by crossing 7 lines and 3 testers. parents and hybrids differed significantly for general combining ability (gca) and specific combining ability (sca) effects, respectively. the variance due to gca and sca showed that gene action was predominantly additive...

In classical measure theory, the Radon-Nikodym theorem states in a concise condition, namely domination, how a measure can be factorized by another (bounded) measure through a density function. Several approaches have been undertaken to see under which conditions an exact factorization can be obtained with set functions that are not σ-additive (for instance finitely additive set functions or su...