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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...
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...
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...
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...
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...
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...
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...
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 ...
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...
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...
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...
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...
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...
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...

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