12,084 research outputs found
Unsymmetric Lanczos model reduction and linear state function observer for flexible structures
This report summarizes part of the research work accomplished during the second year of a two-year grant. The research, entitled 'Application of Lanczos Vectors to Control Design of Flexible Structures' concerns various ways to use Lanczos vectors and Krylov vectors to obtain reduced-order mathematical models for use in the dynamic response analyses and in control design studies. This report presents a one-sided, unsymmetric block Lanczos algorithm for model reduction of structural dynamics systems with unsymmetric damping matrix, and a control design procedure based on the theory of linear state function observers to design low-order controllers for flexible structures
Some Preconditioning Techniques for Saddle Point Problems
Saddle point problems arise frequently in many applications in science and engineering, including constrained optimization, mixed finite element formulations of partial differential equations, circuit analysis, and so forth. Indeed the formulation of most problems with constraints gives rise to saddle point systems. This paper provides a concise overview of iterative approaches for the solution of such systems which are of particular importance in the context of large scale computation. In particular we describe some of the most useful preconditioning techniques for Krylov subspace solvers applied to saddle point problems, including block and constrained preconditioners.\ud
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The work of Michele Benzi was supported in part by the National Science Foundation grant DMS-0511336
Pfaffian Stochastic Dynamics of Strict Partitions
We study a family of continuous time Markov jump processes on strict
partitions (partitions with distinct parts) preserving the distributions
introduced by Borodin (1997) in connection with projective representations of
the infinite symmetric group. The one-dimensional distributions of the
processes (i.e., the Borodin's measures) have determinantal structure. We
express the dynamical correlation functions of the processes in terms of
certain Pfaffians and give explicit formulas for both the static and dynamical
correlation kernels using the Gauss hypergeometric function. Moreover, we are
able to express our correlation kernels (both static and dynamical) through
those of the z-measures on partitions obtained previously by Borodin and
Olshanski in a series of papers.
The results about the fixed time case were announced in the author's note
arXiv:1002.2714. A part of the present paper contains proofs of those results.Comment: AMS-LaTeX, 59 pages. v2: Added new results about connections with the
z-measures and orthogonal spectral projection operators. Investigated
asymptotic behaviour of the dynamical Pfaffian correlation kernel. Removed
double contour integral expressions for correlation kernels to shorten the
tex
Cut-and-join structure and integrability for spin Hurwitz numbers
Spin Hurwitz numbers are related to characters of the Sergeev group, which
are the expansion coefficients of the Q Schur functions, depending on odd times
and on a subset of all Young diagrams. These characters involve two dual
subsets: the odd partitions (OP) and the strict partitions (SP). The Q Schur
functions Q_R with R\in SP are common eigenfunctions of cut-and-join operators
W_\Delta with \Delta\in OP. The eigenvalues of these operators are the
generalized Sergeev characters, their algebra is isomorphic to the algebra of Q
Schur functions. Similarly to the case of the ordinary Hurwitz numbers, the
generating function of spin Hurwitz numbers is a \tau-function of an integrable
hierarchy, that is, of the BKP type. At last, we discuss relations of the
Sergeev characters with matrix models.Comment: 22 page
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