we study the limiting distribution of the degree of a given node in a scaled attachment random recursive tree, a generalized random recursive tree, which is introduced by devroye et. al (2011). in a scaled attachment random recursive tree, every node $i$ is attached to the node labeled $lfloor ix_i floor$ where $x_0$, $ldots$ , $x_n$ is a sequence of i.i.d. random variables, with support in [0,...

A tree of order n is said to be graceful if the vertices can be assigned the labels {0, . . . , n−1} such that the absolute value of the differences in vertex labels between adjacent vertices generate the set {1, . . . , n− 1}. The Graceful Tree Conjecture is the unproven claim that all trees are graceful. We present major results known on graceful trees from those dating from the problem’s ori...

If we took all of the single copy genes in all sequenced genomes, made phylogenetic trees from them individually, and then made the supertree of those trees, what would we get? Recently, David Pisani and colleagues did that experiment and their results are likely to spark much discussion. Their prokaryote tree looks very familiar, but the genome history of eukaryotes appears dominated by genes ...

We consider nearest-neighbor self-avoiding walk, bond percolation, lattice trees, and bond lattice animals on Z. The two-point functions of these models are respectively the generating function for self-avoiding walks from the origin to x ∈ Z, the probability of a connection from the origin to x, and the generating functions for lattice trees or lattice animals containing the origin and x. Usin...

In this study we have demonstrated the variations of carbohydrates and phenolic compounds present in the leaves and stems of ‘Kinnow’ mandarin (Citrus reticulata Blanco) trees in alternate bearing cycle and the possible involvement of these compounds to flower bud formation process. The amounts of these compounds were determined in the leaves and stems of “on” and “off” trees  monthly  from Nov...

Independently from its origin, trichloroacetic acid (TCA) as a phytotoxic substance affects coniferous trees. Its uptake, distribution and degradation were thus investigated in the Norway spruce/soil-system using 14C labeling. TCA is distributed in the tree mainly by the transpiration stream. As in soil, TCA seems to be degraded microbially, presumably by phyllosphere microorganisms in spruce n...

Białowieża Primeval Forest (BPF, approx. 1700 km2) is an important forest area in Europe from the point of view protection natural diversity. BPF covered with old mixed tree stands mostly origin. Norway spruce a species and covers 27% its area. Between 2012 2017 large outbreak bark beetle Ips typographus (Linnaeus, 1758) took place forest, which transformed left many dead standing trees. At tha...

selection cutting using skidding system often causes physical damage to residual stand through felling and skidding resulting decline of bole quality and tree value. this research evaluated logging damage using skidding system on residual trees and stand regeneration in uneven aged hardwood forest of asalem, were selection cutting was practiced. in this regard, systematic sampling method was us...