The expected node-independence number of random trees

AbstractWe shall derive a formula for the expected value μ(n) of the node-independence number of a random tree with n labelled nodes and we shall determine the asymptotic behaviour of μ(n) as n tends to infinity

Hereditarily finite sets and identity trees

AbstractSome asymptotic results about the sizes of certain sets of hereditarily finite sets, identity trees, and finite games are proven

Numerical study on run-up heights of solitary wave with hydrodynamic pressure model

For many shallow water flows, it is sufficient to consider the depth-averaged equations, referred as the shallow water equations, which are two-dimensional in the horizontal plane, since the length scale of the vertical direction is much smaller than that of the horizontal directions. Assuming that the pressure distribution is hydrostatic, the mathematical formulation and its numerical implementation are considerably simplified. In this study, a numerical model is newly developed to investigate various free surface fl ow problems. The governing equations are the Navier???Stokes equations with the pressure decomposed into the sum of a hydrostatic and a hydrodynamic components. The equation for the free surface movement is a depth???averaged continuity equation which is a free surface equation. These governing equations are simultaneously solved by using a finite difference method with a semi???implicit method and fractional step method. At the first step, the vertical momentum equations are discretized by using an implicit method over the vertical direction. In the second step, the discrete horizontal momentum equations are projected on to the free surface equation. Finally, the hydrodynamic pressure and final velocity field are calculated. To verify the accuracy and stability, the present numerical model is applied to move practical problems such as the run???up process of solitary waves attacking a circular island. The numerically obtained maximum run???up heights around a circular island are compared with available laboratory measurements. A very reasonable agreement is observed

Fast algorithms for min independent dominating set

We first devise a branching algorithm that computes a minimum independent dominating set on any graph with running time O*(2^0.424n) and polynomial space. This improves the O*(2^0.441n) result by (S. Gaspers and M. Liedloff, A branch-and-reduce algorithm for finding a minimum independent dominating set in graphs, Proc. WG'06). We then show that, for every r>3, it is possible to compute an r-((r-1)/r)log_2(r)-approximate solution for min independent dominating set within time O*(2^(nlog_2(r)/r))

A Central Partition of Molecular Conformational Space.III. Combinatorial Determination of the Volume Spanned by a Molecular System

In the first work of this series [physics/0204035] it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the espace into a hierarchical set of cells that can be encoded by the face lattice poset of the arrangement. The model however, lacked explicit rotational symmetry which made impossible to distinguish rotated structures in conformational space. This problem was solved in a second work [physics/0404052] by sorting the elementary 3D components of the molecular system into a set of morphological classes that can be properly oriented in a standard 3D reference frame. This also made possible to find a solution to the problem that is being adressed in the present work: for a molecular system immersed in a heat bath we want to enumerate the subset of cells in conformational space that are visited by the molecule in its thermal wandering. If each visited cell is a vertex on a graph with edges to the adjacent cells, here it is explained how such graph can be built

REMOVED: Preparation of Nanofiltration Membranes using Sol–gel Transition of Organic Molecular Networks in their Phase–separating Mixtures with Linear Polymers

This article has been removed: please see Elsevier Policy on Article Withdrawal (http://www.elsevier.com/locate/withdrawalpolicy).This article has been removed at the request of the Executive Publisher.This article has been removed because it was published without the permission of the author(s)

Constitutive modeling of deformation behavior of high-entropy alloys with face-centered cubic crystal structure

A constitutive model based on the dislocation glide and deformation twinning is adapted to face-centered cubic high-entropy alloys (HEAs) as exemplified by the CrMnFeCoNi system. In this model, the total dislocation density is considered as the only internal variable, while the evolution equation describing its variation during plastic deformation is governed by the volume fraction of twinned material. The suitability of the model for describing the strain hardening behavior of HEAs was verified experimentally through compression tests on alloy CrMnFeCoNi and its microstructure characterization by electron backscatter diffraction and X-ray diffraction using synchrotron radiation. ? 2017 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group.1111Ysciescopu

On the topological classification of binary trees using the Horton-Strahler index

The Horton-Strahler (HS) index $r=\max{(i,j)}+\delta_{i,j}$ has been shown to be relevant to a number of physical (such at diffusion limited aggregation) geological (river networks), biological (pulmonary arteries, blood vessels, various species of trees) and computational (use of registers) applications. Here we revisit the enumeration problem of the HS index on the rooted, unlabeled, plane binary set of trees, and enumerate the same index on the ambilateral set of rooted, plane binary set of trees of $n$ leaves. The ambilateral set is a set of trees whose elements cannot be obtained from each other via an arbitrary number of reflections with respect to vertical axes passing through any of the nodes on the tree. For the unlabeled set we give an alternate derivation to the existing exact solution. Extending this technique for the ambilateral set, which is described by an infinite series of non-linear functional equations, we are able to give a double-exponentially converging approximant to the generating functions in a neighborhood of their convergence circle, and derive an explicit asymptotic form for the number of such trees.Comment: 14 pages, 7 embedded postscript figures, some minor changes and typos correcte

Feedback Vertex Sets in Tournaments

We study combinatorial and algorithmic questions around minimal feedback vertex sets in tournament graphs. On the combinatorial side, we derive strong upper and lower bounds on the maximum number of minimal feedback vertex sets in an n-vertex tournament. We prove that every tournament on n vertices has at most 1.6740^n minimal feedback vertex sets, and that there is an infinite family of tournaments, all having at least 1.5448^n minimal feedback vertex sets. This improves and extends the bounds of Moon (1971). On the algorithmic side, we design the first polynomial space algorithm that enumerates the minimal feedback vertex sets of a tournament with polynomial delay. The combination of our results yields the fastest known algorithm for finding a minimum size feedback vertex set in a tournament

A dc voltage step-up transformer based on a bi-layer \nu=1 quantum Hall system

A bilayer electron system in a strong magnetic field at low temperatures, with total Landau level filling factor nu =1, can enter a strongly coupled phase, known as the (111) phase or the quantum Hall pseudospin-ferromagnet. In this phase there is a large quantized Hall drag resistivity between the layers. We consider here structures where regions of (111) phase are separated by regions in which one of the layers is depleted by means of a gate, and various of the regions are connected together by wired contacts. We note that with suitable designs, one can create a DC step-up transformer where the output voltage is larger than the input, and we show how to analyze the current flows and voltages in such devices