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## Uma representação construtiva global para sistemas ordenados de segunda ordem em espaços coerentes intervalares bi-estruturados, com aplicação em matemática intervalar; A global constructive representation of second order ordered systems using bi-structured interval coherence spaces, with an application in interval mathematics

Dimuro, Gracaliz Pereira
Tipo: Tese de Doutorado Formato: application/pdf
Português
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## Aperfeiçoamento de precondicionadores para solução de sistemas lineares dos métodos de pontos interiores; Improving the preconditioning of linear systems from interior point methods

Luciana Casacio
Fonte: Biblioteca Digital da Unicamp Publicador: Biblioteca Digital da Unicamp
Tipo: Tese de Doutorado Formato: application/pdf
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A solução de problemas de otimização linear através de métodos de pontos interiores envolve a solução de sistemas lineares. Esses sistemas quase sempre possuem dimensões elevadas e alto grau de esparsidade em aplicações reais. Para solução, tipicamente são realizadas operações algébricas que os reduzem a duas formulações mais simples: uma delas, conhecida por "sistema aumentado", envolve matrizes simétricas indefinidas e geralmente esparsas; a outra, denominada "sistema de equações normais", usa matrizes de menor dimensão, simétricas e definidas positivas. A solução dos sistemas lineares é a fase que requer a maior parte do tempo de processamento dos métodos de pontos interiores. Consequentemente, a escolha dos métodos de solução é de extrema importância para que se tenha uma implementação eficiente. Normalmente, aplicam-se métodos diretos para a solução como, por exemplo, a fatoração de Bunch-Parllett ou a fatoração de Cholesky. No entanto, em problemas de grande porte, o uso de métodos diretos torna-se desaconselhável, por limitações de tempo e memória. Nesses casos, abordagens iterativas se tornam mais atraentes. O sucesso da implementação de métodos iterativos depende do uso de bons precondicionadores...

## Optimal and suboptimal filtering for Toeplitz systems

Fonte: Laboratory for Information and Decision Systems, Massachusetts Institute of Technology Publicador: Laboratory for Information and Decision Systems, Massachusetts Institute of Technology
Formato: 26, [1] leaves; application/pdf
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by Joseph E. Wall, Jr., Alan S. Willsky, Nils R. Sandell, Jr.; Bibliography: leaf [27]; Department of Energy Contract ERDA-E-(49-18)-2087

## Resonance in dispersive wave systems

Amundsen, David Embury, 1972-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 112 p.; 5968284 bytes; 5968039 bytes; application/pdf; application/pdf
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by David Embury Amundsen.; Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1999.; Includes bibliographical references (p. 110-112).

## Model order reduction for nonlinear systems

Chen, Yong, 1979-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 70 p.; 3421366 bytes; 3421123 bytes; application/pdf; application/pdf
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by Yong Chen.; Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Mathematics, 1999.; Includes bibliographical references (p. 69-70).

## Model reduction of large linear systems via low rank system gramians

Li, Jing-Rebecca, 1973-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 104 p.; 7474818 bytes; 7474580 bytes; application/pdf; application/pdf
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by Jing-Rebecca Li.; Thesis (Ph.D.)--Massachusetts Institute of Technology, Dept. of Mathematics, 2000.; Includes bibliographical references (p. 100-104).

## Propositional proof systems : efficiency and automatizability

Alekhnovitch, Mikhail, 1978-
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 143 p.; 5200175 bytes; 5199983 bytes; application/pdf; application/pdf
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The thesis considers two fundamental questions in propositional proof complexity: lower bounds on the size of the shortest proof and automatizability of propositional proof systems. With respect to the first part, we develop a new paradigm for proving lower bounds in propositional calculus. Our method is based on the purely computational concept of pseudorandom generator. Namely, we call a pseudorandom generator Gn: [0, 1 ] - [0, 1]m hard for a propositional proof system P if P cannot efficiently prove the (properly encoded) statement G (xl,...,xn) f b for any string b [0, 1]m. We consider a variety of "combinatorial" pseudorandom generators inspired by the Nisan-Wigderson generator on the one hand, and by the construction of Tseitin tautologies on the other. We prove that under certain circumstances these generators are hard for such proof systems as Resolution, Polynomial Calculus and Polynomial Calculus with Resolution (PCR). As to the second part, we prove that the problem of approximating the size of the shortest proof within factor 2log1-o(1) is NP-hard. This result is very robust in that it holds for almost all natural proof systems, including: Frege systems, extended Frege systems, resolution, Horn resolution, the sequent calculus...

## Microstructure of bicontinuous phases in surfactant systems

Barnes, Ian
Tipo: Thesis (PhD); Doctor of Philosophy (PhD)
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A geometric approach to microemulsions and other phases in surfactant systems is presented. The basic premise is that the behaviour of these systems is dominated by geometric constraints on microstructure. The utility of this approach is first demonstrated for the one-dimensional fluid, for which the statistical mechanics can be solved analytically, before being applied to more realistic but complex systems. Small-angle X-ray and neutron scattering techniques are used to obtain structural information. A numerical method for calculating theoretical scattering curves from arbitrary models is presented. The importance of the real-space correlation function is emphasised, and it is used to obtain a plot of the scale dependence of the internal surface. A new technique is proposed for the division of two spectra from the same sample measured at different contrasts, which eliminates the underlying lattice and gives sensitive local information. Two new geometric models for microemulsions are presented: a structure of interconnected cylinders and one of folded connected lamellae. It is shown that these models succeed where all others fail, in explaining the behaviour of the isotropic liquid phases found in ternary systems containing the double-chained cationic surfactant didodecyldimethylammonium bromide. This approach is also applied to two nonionic polyoxyethylene surfactant binary systems. Similar methods are also applied to cubic liquid crystalline phases. It is shown by a simple calculation that the scattering from such structures is very sensitive to small changes. Certain of these structures are thought to follow periodic minimal surfaces. Approximations to these are investigated and in particular it is shown that periodic equipotential surfaces and periodic minimal surfaces with the same symmetry and topology are not necessarily identical.; yes

## A multidisciplinary approach to complex systems design.

Ryan, Alex J.
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The design and management of organised systems, comprised of dynamic interdependent collectives of autonomous agents, is the kind of problem that the discipline of complex systems is intended to address. Nevertheless, conventional model-based applications of complex systems may be of limited utility when the problem is also data-poor and soft. In this case, a quantitative model may be at best meaning-less; at worst harmful. Systems approaches, such as soft systems methodologies, have been developed that provide some guidance in this domain. However, these alternatives do not utilise the exact techniques of complex systems, preferring to abandon mathematical representations altogether. It is the aim of this thesis to advance a “conceptual analysis" approach to complex systems design that exploits deep insights from the mathematics of complex systems, without building explicit models of the underlying system. It is argued that this approach can extend the domain of applicability of the discipline of complex systems into situations where quantitative data is unavailable, and human and social factors are significant. Conceptual analysis of complex systems is inherently multidisciplinary, because it is broader than the foundations of any single conventional discipline. This is reflected in the structure of this thesis...

## Three-dimensional solitary waves in dispersive wave systems; 3D solitary waves in dispersive wave systems

Kim, Boguk, Ph. D. Massachusetts Institute of Technology
Fonte: Massachusetts Institute of Technology Publicador: Massachusetts Institute of Technology
Tipo: Tese de Doutorado Formato: 122 p.
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Fully localized three-dimensional solitary waves, commonly referred to as 'lumps', have received far less attention than two-dimensional solitary waves in dispersive wave systems. Prior studies have focused in the long-wave limit, where lumps exist if the long-wave speed is a minimum of the phase speed and are described by the Kadomtsev-Petviashvili (KP) equation. In the water-wave problem, in particular, lumps of the KP type are possible only in the strong-surface-tension regime (Bond number, B > 1/3), a condition that limits the water depth to a few mm. In the present thesis, a new class of lumps is found that is possible under less restrictive physical conditions. Rather than long waves, these lumps bifurcate from infinitesimal sinusoidal waves of finite wavenumber at an extremum of the phase speed. As the group and phase velocities are equal there, small-amplitude lumps resemble fully localized wavepackets with envelope and crests moving at the same speed, and the wave envelope along with the induced mean-flow component are governed by a coupled Davey-Stewartson equation system of elliptic-elliptic type. The lump profiles feature algebraically decaying tails at infinity owing to this mean flow. In the case of water waves, lumps of the wavepacket type are possible when both gravity and surface tension are present on water of finite or infinite depth for B < 1/3.; (cont.) The asymptotic analysis of these lumps in the vicinity of their bifurcation point at the minimum gravity-capillary phase speed...

## A Note on Surjective Inverse Systems

Tipo: Artigo de Revista Científica
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Given an upward directed set $I$ we consider surjective $I$-inverse systems $\{X_\al,f_{\al\be}:X_\be\lra X_\al| \al\leq\be\in I\}$, namely those inverse systems that have all $f_{\al\be}$ surjective. A number of properties of $I$-inverse systems have been investigated; such are the Mittag-Leffler condition, investigated by Grothendieck and flabby and semi-flabby $I$-inverse systems studied by Jensen. We note that flabby implies semi-flabby implies surjective implies Mittag-Leffler. Some of the results about surjective inverse systems have been known for some time. The aim of this note is to give a series of equivalent statements and implications involving surjective inverse systems and the systems satisfying the Mittag-Leffler condition, together with improvements of established results, as well as their relationships with the already known, but scattered facts. The most prominent results relate cardinalities of the index sets with right exactness of the inverse limit functor and the non-vanishing of the inverse limit -- connections related to cohomological dimensions.

## An excursion from enumerative goemetry to solving systems of polynomial equations with Macaulay 2

Sottile, Frank
Tipo: Artigo de Revista Científica
Português
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Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics has instead developed deep and powerful theories about the solutions to polynomial equations. Enumerative Geometry is concerned with counting the number of solutions when the polynomials come from a geometric situation and Intersection Theory gives methods to accomplish the enumeration. We use Macaulay 2 to investigate some problems from enumerative geometry, illustrating some applications of symbolic computation to this important problem of solving systems of polynomial equations. Besides enumerating solutions to the resulting polynomial systems, which include overdetermined, deficient, and improper systems, we address the important question of real solutions to these geometric problems. The text contains evaluated Macaulay 2 code to illuminate the discussion. This is a chapter in the forthcoming book "Computations in Algebraic Geometry with Macaulay 2", edited by D. Eisenbud, D. Grayson, M. Stillman, and B. Sturmfels. While this chapter is largely expository, the results in the last section concerning lines tangent to quadrics are new.; Comment: LaTeX 2e...

## Macaulay inverse systems revisited

Pommaret, Jean-François
Tipo: Artigo de Revista Científica
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Since its original publication in 1916 under the title "The Algebraic Theory of Modular Systems", the book by F. S. Macaulay has attracted a lot of scientists with a view towards pure mathematics (D. Eisenbud,...) or applications to control theory (U. Oberst,...).However, a carefull examination of the quotations clearly shows that people have hardly been looking at the last chapter dealing with the so-called "inverse systems", unless in very particular situations. The purpose of this paper is to provide for the first time the full explanation of this chapter within the framework of the formal theory of systems of partial differential equations (Spencer operator on sections, involution,...) and its algebraic counterpart now called "algebraic analysis" (commutative and homological algebra, differential modules,...). Many explicit examples are fully treated and hints are given towards the way to work out computer algebra packages.; Comment: From a lecture at the International Conference : Application of Computer Algebra (ACA 2008) july 2008, RISC, LINZ, AUSTRIA

## Lie systems: theory, generalisations, and applications

Cariñena, J. F.; de Lucas, J.
Tipo: Artigo de Revista Científica
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Lie systems form a class of systems of first-order ordinary differential equations whose general solutions can be described in terms of certain finite families of particular solutions and a set of constants, by means of a particular type of mapping: the so-called superposition rule. Apart from this fundamental property, Lie systems enjoy many other geometrical features and they appear in multiple branches of Mathematics and Physics, which strongly motivates their study. These facts, together with the authors' recent findings in the theory of Lie systems, led to the redaction of this essay, which aims to describe such new achievements within a self-contained guide to the whole theory of Lie systems, their generalisations, and applications.; Comment: 161 pages, 2 figures

## The Pseudospectrum of Systems of Semiclassical Operators

Dencker, Nils
Tipo: Artigo de Revista Científica
Português
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The pseudospectra (or spectral instability) of non-selfadjoint operators is a topic of current interest in applied mathematics. In fact, for non-selfadjoint operators the resolvent could be very large outside the spectrum, making the numerical computation of the complex eigenvalues very hard. This has importance, for example, in quantum mechanics, random matrix theory and fluid dynamics. The occurence of pseudospectra for non-selfadjoint semiclassical differential operators is due to the existence of quasimodes, i.e., approximate local solutions to the eigenvalue problem. For scalar operators, the quasimodes appear since the bracket condition is not satisfied for topological reasons, see the paper by Dencker, Sjostrand and Zworski in Comm. Pure Appl. Math. 57 (2004), 384-415. In this paper we shall investigate how these result can be generalized to square systems of semiclassical differential operators of principal type. These are the systems whose principal symbol vanishes of first order on its kernel. We show that the resolvent blows up as in the scalar case, except in a nowhere dense set of degenerate values. We also define quasi-symmetrizable systems and systems of subelliptic type for which we prove estimates on the resolvent.; Comment: Introduced the notion of quasi-symmetric systems and proved invariance properties for these systems. Changed the definition of the approximation property in Definition 5.10. Skipped erroneous Remark 3.5 and strengthened Proposition 3.7. Corrected an error in the proof of Proposition 6.1...

## Relative parametrization of linear multidimensional systems

Pommaret, Jean-François
Tipo: Artigo de Revista Científica
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In the last chapter of his book "The Algebraic Theory of Modular Systems " published in 1916, F. S. Macaulay developped specific techniques for dealing with " unmixed polynomial ideals " by introducing what he called " inverse systems ". The purpose of this paper is to extend such a point of view to differential modules defined by linear multidimensional systems, that is by linear systems of ordinary differential (OD) or partial differential (PD) equations of any order, with any number of independent variables, any number of unknowns and even with variable coefficients in a differential field. The first and main idea is to replace unmixed polynomial ideals by " pure differential modules ". The second idea is to notice that a module is 0-pure if and only if it is torsion-free and thus if and only if it admits an " absolute parametrization " by means of arbitrary potential like functions, or, equivalently, if it can be embedded into a free module by means of an " absolute localization ". The third idea is to refer to a difficult theorem of algebraic analysis saying that an r-pure module can be embedded into a module of projective dimension equal to r, that is a module admitting a projective resolution with exactly r operators. The fourth and final idea is to establish a link between the use of extension modules for such a purpose and specific formal properties of the underlying multidimensional system through the use of involution and a "relative localization " leading to a "relative parametrization "...

## Leibniz triple systems

Bremner, Murray R.; Sanchez-Ortega, Juana
Tipo: Artigo de Revista Científica
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We define Leibniz triple systems in a functorial manner using the algorithm of Kolesnikov and Pozhidaev which converts identities for algebras into identities for dialgebras. We verify that Leibniz triple systems are the natural analogues of Lie triple systems in the context of dialgebras by showing that both the iterated bracket in a Leibniz algebra and the permuted associator in a Jordan dialgebra satisfy the defining identities for Leibniz triple systems. We construct the universal Leibniz envelopes of Leibniz triple systems and prove that every identity satisfied by the iterated bracket in a Leibniz algebra is a consequence of the defining identities for Leibniz triple systems. To conclude, we present some examples of 2-dimensional Leibniz triple systems and their universal Leibniz envelopes.; Comment: 18 pages

## An Excursion-Theoretic Approach to Stability of Discrete-Time Stochastic Hybrid Systems

Chatterjee, Debasish; Pal, Soumik
Tipo: Artigo de Revista Científica
Português
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We address stability of a class of Markovian discrete-time stochastic hybrid systems. This class of systems is characterized by the state-space of the system being partitioned into a safe or target set and its exterior, and the dynamics of the system being different in each domain. We give conditions for $L_1$-boundedness of Lyapunov functions based on certain negative drift conditions outside the target set, together with some more minor assumptions. We then apply our results to a wide class of randomly switched systems (or iterated function systems), for which we give conditions for global asymptotic stability almost surely and in $L_1$. The systems need not be time-homogeneous, and our results apply to certain systems for which functional-analytic or martingale-based estimates are difficult or impossible to get.; Comment: Revised. 17 pages. To appear in Applied Mathematics & Optimization

## Control in an Information Rich World: Report of the Panel on Future Directions in Control, Dynamics, and Systems

Murray, Richard M.
Fonte: Society for Industrial and Applied Mathematics Publicador: Society for Industrial and Applied Mathematics
Tipo: Book; NonPeerReviewed Formato: application/pdf; application/pdf; application/pdf; application/pdf; application/pdf; application/pdf; application/pdf; application/pdf; application/pdf