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Structured Mapping Problems for Matrices Associated with Scalar Products Part I: Lie and Jordan Algebras
Get PDFGiven a class of structured matrices \Sb, we identify pairs of vectors
for which there exists a matrix A\in\Sb such that , and also
characterize the set of all matrices A\in\Sb mapping to . The
structured classes we consider are the Lie and Jordan algebras associated with
orthosymmetric scalar products. These include (skew-)symmetric,
(skew-)Hamiltonian, pseudo (skew-)Hermitian, persymmetric and perskew-symmetric
matrices. Structured mappings with extremal properties are also investigated. In
particular, structured mappings of minimal rank are identified and shown to be
unique when rank-1 is achieved. The structured mapping of minimal Frobenius norm
is always unique and explicit formulas for it and its norm are obtained. Finally
the set of all structured mappings of minimal 2-norm is characterized. Our
results generalize and unify existing work, answer a number of open questions,
and provide useful tools for structured backward error investigations
Isotropic Flow of Homeomorphisms on S^d with Respect to the Metric H^{(d+2)/2}
Get PDFIn this work, we shall deal with the critical Sobolev isotropic Brownian flows on the sphere S^d. Based on previous works by O. Raimond and LeJan-Raimond (see Ann. Inst. H. Poincare, 35 (1999), p. 313-354 and Ann. of Prob., 30 (2002), p. 826-873), we prove that the associated flow is a flow of homeomorphisms
Ranking the Importance of Boards of Directors
Get PDFWe measure the importance (centrality) of boards of directors using
the PageRank algorithm from computational graph theory. PageRank is
at the heart of the immensely successful Google web search engine and, we
argue, can be naturally extended to social network settings. In this view,
a board can be represented as part of an affiliation network or, in graph
theoretic-terms, an undirected bipartite graph. But PageRank operates
on directed graphs, so we develop a procedure to pass from an undirected
bipartite graph to appropriately weighted, directed pro jections. Finally,
we present the rankings of publicly traded US and UK firms using this
method
On the Value of Optimal Stopping Games
Get PDFWe show, under weaker assumptions than in the previous
literature, that a perpetual optimal stopping game always has a value.
We also show that there exists an optimal stopping time for the seller,
but not necessarily for the buyer. Moreover, conditions are provided
under which the existence of an optimal stopping time for the buyer is
guaranteed. The results are illustrated explicitly in two examples
Universal homotopy associative, homotopy commutative -spaces and the EHP spectral sequence
No full textAssume that all spaces and maps are localised at a fixed prime . We study the possibility of generating a universal space from a space which is universal in the category of homotopy associative, homotopy commutative -spaces in the sense that any map to a homotopy associative, homotopy commutative -space extends to a uniquely determined -map . Developing a method for recognising certain universal spaces, we show the existence of the universal space of a certain three-cell complex . Using this specific example, we derive some consequences for the calculation of the unstable homotopy groups of spheres, namely, we obtain a formula for the -differential of the EHP-spectral sequence valid in a certain range
Classifying thick subcategories of perfect complexes
Get PDFGiven a commutative coherent ring R, a bijective correspondence between the thick subcategories of perfect complexes D_{per}(R) and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set of (iso-classes for) indecomposable injective modules are essentially used
The American put is log-concave in the log-price
No full textWe show that the American put option price is log-concave as a function of the log-price of the underlying asset. Thus the elasticity of the price decreases with increasing stock value. We also consider related contracts of American type, and we provide an example showing that not all American option prices are log-concave in the stock log-price
Model-Updating for Symmetric Quadratic Eigenvalue Problems
Get PDFThis paper concerns quadratic matrix functions of the form L(λ) = Mλ² + Dλ +K where M, D, K are real and symmetric n × n matrices with M > 0. Given complete spectral information on L(λ), it is shown how new systems of the same type can be generated with updated eigenvalues and/or eigenvectors. A general purpose algorithm is formulated and illustrated with problems having no real eigenvalues, or a mixture of real and non-real eiegnvalues, or only real eigenvalues. The methods also apply for matrix polynomials of higher degree
Efficient order selection algorithms for integer valued ARMA processes
Get PDFWe consider the problem of model (order) selection for integer
valued autoregressive moving-average (INARMA) processes. A very
efficient Reversible Jump Markov chain Monte Carlo (RJMCMC)
algorithm is constructed for moving between INARMA processes of
different order. An alternative in the form of the EM algorithm is
given for determining the order of an integer valued autoregressive
(INAR) process. Both algorithms are successfully applied to both
simulated and real data sets
The problem of differentiation of an Abelian function over its parameters
Get PDFThe present work is devoted to the problem of differentiation of an Abelian function, defined by a family of plane algebraic curves, over the parameters of the family.
A precise formulation of the problem involves the language of Differential Geometry.
We give an effective solution, which is based on our theory of multivariate sigma-function. We obtain explicit expressions for the generators of the module of differentiations of a ring of Abelian functions. This result is equivalent, as we show, to an explicit construction of a Gauss-Manin connection and a Koszul connection in the appropriate vector bundles.
In the course of exposition we outline the key classic results relevant to the problem