9,941 research outputs found
Imaginary Projections: Complex Versus Real Coefficients
Given a multivariate complex polynomial ,
the imaginary projection of is defined as the projection
of the variety onto its imaginary part. We focus on studying
the imaginary projection of complex polynomials and we state explicit results
for certain families of them with arbitrarily large degree or dimension. Then,
we restrict to complex conic sections and give a full characterization of their
imaginary projections, which generalizes a classification for the case of real
conics. That is, given a bivariate complex polynomial
of total degree two, we describe the number and the boundedness of the
components in the complement of as well as their boundary
curves and the spectrahedral structure of the components. We further show a
realizability result for strictly convex complement components which is in
sharp contrast to the case of real polynomials.Comment: 24 pages; Revised versio
Matter as Spectrum of Spacetime Representations
Bound and scattering state Schr\"odinger functions of nonrelativistic quantum
mechanics as representation matrix elements of space and time are embedded into
residual representations of spacetime as generalizations of Feynman
propagators. The representation invariants arise as singularities of rational
representation functions in the complex energy and complex momentum plane. The
homogeneous space with rank 2, the orientation manifold of the
unitary hypercharge-isospin group, is taken as model of nonlinear spacetime.
Its representations are characterized by two continuous invariants whose ratio
will be related to gauge field coupling constants as residues of the related
representation functions. Invariants of product representations define unitary
Poincar\'e group representations with masses for free particles in tangent
Minkowski spacetime.Comment: 37 pages, latex, macros include
The inverse moment problem for convex polytopes: implementation aspects
We give a detailed technical report on the implementation of the algorithm
presented in Gravin et al. (Discrete & Computational Geometry'12) for
reconstructing an -vertex convex polytope in from the
knowledge of of its moments
Non intrusive polynomial chaos-based stochastic macromodeling of multiport systems
We present a novel technique to efficiently perform the variability analysis of electromagnetic systems. The proposed method calculates a Polynomial Chaos-based macromodel of the system transfer function that includes its statistical properties. The combination of a non-intrusive Polynomial Chaos approach with the Vector Fitting algorithm allows to describe the system variability features with accuracy and efficiency. The results of the variability analysis performed with the proposed method are verified by means of comparison with respect to the standard Monte Carlo analysis
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