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One-dimensional model of interacting-step fluctuations on vicinal surfaces:Analytical formulas and kinetic Monte Carlo simulations
One-dimensional model interacting-step fluctuations vicinal surfaces Analytical formulas kinetic Monte Carlo simulations
2015/10/16
We study analytically and numerically a one-dimensional model of interacting line defects steps fluctuating on a vicinal crystal. Our goal is to formulate and validate analytical techniques for appr...
q-Hook Length Formulas for Signed Labeled Forests
statistic forest q-hook length formula Coxeter groups of types B and D (P w)-partition
2014/6/3
A signed labeled forest is defined as a (plane) forest labeled by {1, 2,..., n} along with minus signs associated to some vertices. Signed labeled forests can be viewed as an extension of signed permu...
On Han's Hook Length Formulas for Trees
hook length formula k-ary tree bijection staircase labeling
2014/6/3
Recently, Han obtained two hook length formulas for binary trees and asked for combinatorial proofs. One of Han’s formulas has been generalized to k-ary trees by Yang. Sagan has found a probabilistic ...
Weighted Koppelman formulas and the $\dbar$-equation on an analytic space
Weighted Koppelman formulas $\dbar$-equation analytic space
2011/2/23
Let X be an analytic space of pure dimension. We intro-duce a formalism to generate intrinsic weighted Koppelman formulas on X that provide solutions to the ¯@-equation. We obtain new existence r...
Applications of operational calculus: trigonometric interpolating equation for the nine-point prism and robust center point formulas
operational equations prismatic array central tendency
2010/9/26
The derivation of a trigonometric equation for the nine-point, rectangular prismatic array is illustrated. In many cases, the equation can be used to reproduce a ninth datum at an arbitrary point near...
Hook Length Formulas for Trees by Han's Expansion
hook length formulas for trees k-ary trees planes trees labeled trees
2014/6/3
Recently Han obtained a general formula for the weight function corresponding to the expansion of a series in terms of hook lengths of binary trees. In this paper, we present weight function formulas ...
Formulas for the number of spanning trees in a fan
Graph theory spanning trees enumeration
2010/9/10
Let Pn be a simple path on n vertices. An n-fan is a simple graph G formed from a path Pn by adding a vertex adjacent to every vertex of Pn. In this work we denote n-fan by Fn+1 and derive the explici...
Hyers-Ulam stability of the Generalized Trigonometric Formulas
Locally compact group Functional equation Hyers-Ulam stability Superstability
2008/7/1
Hyers-Ulam stability of the Generalized Trigonometric Formulas.