in this paper, using generalized {polya} urn models we find the expected value of the size of a branch in recursive $k$-ary trees. we also find the expectation of the number of nodes of a given outdegree in a branch of such trees.

Combining ability in forage sorghum [Sorghum bicolor (L.) Moench] was not as much investigated as in grain sorghum. In the present study, 4 local stocks (Testers) and 7 exotic stocks in A3 cytoplasm were crossed in line x tester fashion to investigate combining ability in forage sorghum. The hybrids and their parents were evaluated across two years (2002 2003) and at two locations in Khartoum S...

One approach to improving efficiency of protein and nitrogen use for optimal productivity in dairy heifers is to provide adequate levels of protein with differing rumen degradabilities. The objective of this experiment was to determine effects of manipulating RDP in diets of dairy heifers precision fed low- and high-quality forage. Eight rumen-cannulated Holstein heifers (448 ± 19 kg BW) were r...

Information about forage productivity and its interactions with cultural practices or climatic variation is necessary to plan livestock management and to increase production without damaging the environment. Remote sensing provides a valuable data source to achieve these goals. Here we characterize forage production over a large region (92 million hectares) by analyzing spatial, seasonal, and i...

Forage legumes have a relatively high biomass yield and crude protein content, but their grazed and harvested biomass lacks the high-energy carbohydrates required to meet the productivity potential of modern livestock breeds. Because of their low carbohydrate content, forage legume diets are typically supplemented with starch rich cereal grains or maize (Zea mays), leading to the disruption of ...

This paper reviews P´olya urn models and their connection to random trees. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology: • P´olya-Eggenberger’s urn • Bernard Friedman’s urn • Generalized P´olya urns • Extended urn schemes • Invertible urn schemes ...

Female hairy-faced hover wasps forage for the young of a dominant breeder, but some forage more than others. New research shows that helpers decide how much to help by looking to the future.

forage is the main product of rangelands. so, determining its economic value as one of the main important nonmonetary functions can help managers to improve planning and optimal utilization management of rangelands. the main purpose of this study is to estimate the economic valuation of the forage of summer rangelands in nour-roud watershed basin in mazandaran province. consequently, total fora...

The spatial and temporal distribution of forage quality is among the most central factors affecting herbivore habitat selection. Yet, for high latitude areas, forage quantity has been found to be more important than quality. Studies on large ungulate foraging patterns are faced with methodological challenges in both assessing animal movements at the scale of forage distribution, and in assessin...

Forage quality in grassland-savanna ecosystems support high biomass of both wild ungulates and domestic livestock. Forage quality is however variable in both space and time. In this study findings from ecological and laboratory studies, focused on assessing forage quality, are combined to evaluate the feasibility of a remote sensing approach for predicting the spatial and temporal variations in...