Palindromes in starlike trees

In this note, we obtain an upper bound on the maximum number of distinct non-empty palindromes in starlike trees. This bound implies, in particular, that there are at most 4 n distinct non-empty palindromes in a starlike tree with three branches each of length n. For such starlike trees labelled with a binary alphabet, we sharpen the upper bound to 4 n − 1 and conjecture that the actual maximum is 4 n − 2. It is intriguing that this simple conjecture seems difficult to prove, in contrast to the proof of the bound

Immediate replacement of fishing with dairying by the earliest farmers of the NE Atlantic archipelagos

The appearance of farming, from its inception in the Near East around 12 000 years ago, finally reached the northwestern extremes of Europe by the fourth millennium BC or shortly thereafter. Various models have been invoked to explain the Neolithization of northern Europe; however, resolving these different scenarios has proved problematic due to poor faunal preservation and the lack of specificity achievable for commonly applied proxies. Here, we present new multi-proxy evidence, which qualitatively and quantitatively maps subsistence change in the northeast Atlantic archipelagos from the Late Mesolithic into the Neolithic and beyond. A model involving significant retention of hunter–gatherer–fisher influences was tested against one of the dominant adoptions of farming using a novel suite of lipid biomarkers, including dihydroxy fatty acids, ω-(o-alkylphenyl)alkanoic acids and stable carbon isotope signatures of individual fatty acids preserved in cooking vessels. These new findings, together with archaeozoological and human skeletal collagen bulk stable carbon isotope proxies, unequivocally confirm rejection of marine resources by early farmers coinciding with the adoption of intensive dairy farming. This pattern of Neolithization contrasts markedly to that occurring contemporaneously in the Baltic, suggesting that geographically distinct ecological and cultural influences dictated the evolution of subsistence practices at this critical phase of European prehistory

Interação de micorriza vesicular-arbuscular com leguminosas em solos ácidos.

Este trabalho apresenta uma abordagem para MVA e acidez do solo; Simbiose MVA ? Rhizobium-leguminosa; Dependência de MVA e Micorrizas e pesquisa na região amazônica.bitstream/item/60903/1/Doc55-micorrizaarbuscular.pd