4,269 research outputs found
A Relation between the Protocol Partition Number and the Quasi-Additive Bound
In this note, we show that the linear programming for computing the
quasi-additive bound of the formula size of a Boolean function presented by
Ueno [MFCS'10] is equivalent to the dual problem of the linear programming
relaxation of an integer programming for computing the protocol partition
number. Together with the result of Ueno [MFCS'10], our results imply that
there exists no gap between our integer programming for computing the protocol
partition number and its linear programming relaxation
Spaces of real polynomials with common roots
Let RX_{k,n}^l be the space consisting of all (n+1)-tuples
(p_0(z),...,p_n(z)) of monic polynomials over R of degree k and such that there
are at most l roots common to all p_i(z). In this paper, we prove a stable
splitting of RX_{k,n}^l.Comment: This is the version published by Geometry & Topology Monographs on 29
January 200
The homology of spaces of polynomials with roots of bounded multiplicity
Let P_{k, n}^l be the space consisting of monic complex polynomials f(z) of
degree k and such that the number of n-fold roots of f(z) is at most l. In this
paper, we determine the integral homology groups of P_{k, n}^l.Comment: This is the version published by Geometry & Topology Monographs on 25
February 200
Toric degenerations of integrable systems on Grassmannians and polygon spaces
We introduce a completely integrable system on the Grassmannian of 2-planes
in an n-space associated with any triangulation of a polygon with n sides, and
compute the potential function for its Lagrangian torus fiber. The moment
polytopes of this system for different triangulations are related by an
integral piecewise-linear transformation, and the corresponding potential
functions are related by its geometric lift in the sense of Berenstein and
Zelevinsky.Comment: 35 pages, 10 figures; v2: corrected an error pointed out by Harada
and Escoba
Configurations, and parallelograms associated to centers of mass
The purpose of this article is to
\begin{enumerate}
\item define the -fold center of mass arrangement for points
in the plane,
\item give elementary properties of and
\item give consequences concerning the space of distinct points
in the plane, no four of which are the vertices of a parallelogram.
\end{enumerate}
The main result proven in this article is that the classical unordered
configuration of points in the plane is not a retract up to homotopy of the
space of unordered distinct points in the plane, no four of which are the
vertices of a parallelogram. The proof below is homotopy theoretic without an
explicit computation of the homology of these spaces.
In addition, a second, speculative part of this article arises from the
failure of these methods in the case of odd primes . This failure gives rise
to a candidate for the localization at odd primes of the double loop space
of an odd sphere obtained from the -fold center of mass arrangement.
Potential consequences are listed.Comment: 11 page
A statistical model describing temperature dependent gettering of Cu in p-type Si
A model is proposed describing quantitatively the temperature dependent gettering of Cu atoms in p-type Si wafers by taking into account the densities and the binding energies of all types of occupying sites, including the gettering ones. Binding energy in this context is defined as the decrease of the formation energy from the reference energy of the Cu atom when it is located at the T-site through which Cu atoms wander through the silicon lattice. By using a statistical approach, the model allows to predict the thermal equilibrium concentration of Cu atoms in each part of a wafer structure. The calculated results show good agreement with reported experimental observations. This model can also be applied to calculate thermal equilibrium concentrations of any contaminant
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