This article proves strong lower bounds for distributed computing in the congest model, by presenting bit-gadget : a new technique constructing graphs with small cuts. The contribution of bit-gadgets is twofold. First, developing careful sparse graph constructions cuts extends known techniques to show near-linear bound diameter, result previously only dense graphs. Moreover, sparseness construc...

We consider the problem of finding a condition for univariate polynomial having given multiplicity structure when number distinct roots is given. It well known that such conditions can be written as conjunctions several equations and one inequation in coefficients, by using repeated parametric gcd's. In this paper, we give novel which not based on Furthermore, it shown polynomials optimal degre...

We study the problem of recognizing graph powers and computing roots of graphs. We provide a polynomial time recognition algorithm for r-th powers of graphs of girth at least 2r + 3, thus improving a bound conjectured by Farzad et al. (STACS 2009). Our algorithm also finds all r-th roots of a given graph that have girth at least 2r+3 and no degree one vertices, which is a step towards a recent ...

We tested the relation between below- and aboveground tree phenology, determining if beech oak have a greater fine-root lifespan smaller turnover rate than birch thinner fine-roots or born in spring shorter thicker another season. The bud burst, leaf senescence Belgian stands were monitored using minirhizotrons, visual observations, chlorophyll measurements, respectively. phenology estimated ge...

A three-dimensional numerical model is proposed for modeling the TP transport in the Horizontal Subsurface Flow (HSSF) and Wavy subsurface Flow (WSSF) constructed wetland in this article. Both numerical simulations and physical experiments indicate that the removal efficiency of WSSF is higher than that of HSSF. The difference of performance in removing pollutants, e.g., Total Phosphorus (TP), ...