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THE PUZZLE CONJECTURE FOR THE COHOMOLOGY OF TWO-STEP FLAG MANIFOLDS
PUZZLE CONJECTURE TWO-STEP FLAG MANIFOLDS
2015/12/17
We prove a conjecture of Knutson asserting that the Schubert
structure constants of the cohomology ring of a two-step flag variety are equal
to the number of puzzles with specified borde...
Unification of step bunching phenomena on vicinal surfaces
step bunching phenomena vicinal surfaces
2015/10/16
We unify step bunching SB instabilities occurring under various conditions on crystal surfaces below roughening. We show that when attachment-detachment of atoms at step edges is the rate-limiting p...
ANISOTROPIC STEP STIFFNESS FROM A KINETIC MODEL OF EPITAXIAL GROWTH
epitaxial growth island dynamics step edge adatoms edge-atoms surface diffusion step stiffness line tension step edge kinetics kinetic steady state Gibbs–Thomson formula Ehrlich–Schwoebel barrier step permeability
2015/10/16
Starting from a detailed model for the kinetics of a step edge or island boundary, we derive a Gibbs–Thomson-type formula and the associated step stiffness as a function of the step edge orientation a...
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...
CONNECTION OF KINETIC MONTE CARLO MODEL FOR SURFACES TO ONE-STEP FLOW THEORY IN 1+1 DIMENSIONS
kinetic Monte Carlo Burton–Cabrera–Frank theory low-density approximation near-equilibrium condition master equation maximum principle
2015/10/16
The Burton–Cabrera–Frank (BCF) theory of step flow has been recognized as a valuable tool for describing nanoscale evolution of crystal surfaces. We formally derive a single-step BCF-type model from a...
Island-dynamics model for mound formation:Effect of a step-edge barrier
Island-dynamics model mound formation step-edge barrier
2015/10/16
We formulate and implement a generalized island-dynamics model of epitaxial growth based on the level-set technique to include the effect of an additional energy barrier for the attachment and detachm...
Emergence of step flow from an atomistic scheme of epitaxial growth in 1+1 dimensions
step flow atomistic scheme epitaxial growth 1+1 dimensions
2015/10/16
The Burton-Cabrera-Frank (BCF) model for the flow of line defects (steps) on crystal surfaces has offered useful insights into nanostructure evolution. This model has rested on phenomenological ground...
Performance of a Practical Two-Step Detector for Non-Fluctuating Targets
Practical Two-Step Detector Non-Fluctuating Targets
2015/9/29
In this paper we analyze a two-step detection scheme for use in distributed sensor systems (e.g. statistical MIMO radar). The scheme arises when a data rate restriction forces each of the distributed ...
Cooperative Networked Radar:The Two-Step Detector
Cooperative Networked Radar Two-Step Detector
2015/9/29
Cooperative Networked Radar:The Two-Step Detector.
Lateral stability of the spring-mass hopper suggests a two-step control strategy for running
spring-mass hopper suggests control strategy
2015/8/25
This paper investigates the control of running gaits in the context of a spring loaded inverted
pendulum model in three dimensions. Specifically, it determines the minimal number of steps
required f...
Step-up Simultaneous Tests for Identifying Active Effects in Orthogonal Saturated Designs
Identifying Active Effects Orthogonal Saturated Designs
2015/3/18
A sequence of null hypotheses regarding the number of negligible
effects (zero effects) in orthogonal saturated designs is formulated. Two
step-up simultaneous testing procedures are proposed to ide...
ESTABLISHING STRONG CONTROL OF FAMILYWISE ERROR RATE FOR ITERATIVE STEP-DOWN TESTS
ESTABLISHING STRONG ITERATIVE STEP-DOWN TESTS
2015/3/18
A long-standing problem concerning the iterative analysis of orthogonal
saturated designs has b een resolved. Consider an unreplicated factorial design
yielding indep endent, normally distributed es...
Proof of hypothesis of twin primes (important step: choosing a suitable interval)
Twin primes supremum infimum
2015/6/2
1. Distributive law of primes: (x/㏒x)㏒e＜π(x)≤(x/㏒x) ㏒11330／113, (11≤x＜∞); 2. Shortest suitable interval, [11, 19]; 3. Expression of twin odd numbers, ︱2x－11,…,…,…,4x－27︱ ︱2x－ 9,…,…,…,4x－25︱, Number of...
Strong Convergence of a New Three Step Iterative Scheme in Banach Spaces
Fixed Point Various Iterative Schemes Rate of Convergence
2013/1/30
In this paper, we suggest a new type of three step iterative scheme called the CR iterative scheme and study the strong convergence of this iterative scheme for a certain class of quasi-contractive op...
On the existence of nilsolitons on 2-step nilpotent Lie groups
existence nilsolitons 2-step nilpotent Lie groups Differential Geometry
2012/4/16
A 2-step nilpotent Lie algebra n is said to be of type (p,q)if dim(n)=p+q and dim([n,n])=p. By considering a class of 2-step nilpotent Lie algebras naturally attached to graphs, we prove that there ex...