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An application of linear analysis to initial value problemsLaw, Alan Greenwell January 1961 (has links)
Certain properties of an unknown element u in a Hilbert space are investigated. For u satisfying certain linear constraints, it is shown that approximations to u and error bounds for the approximations may be obtained in terms of functional representers.
The general approximation method is applied to homogeneous systems of ordinary linear differential equations and various formulae are derived. An Alwac III-E digital computer was used to compute optimal approximations and error bounds with the aid of these formulae.
Numerous applications to particular systems are mentioned. On the basis of the numerical results, certain remarks are given as a guide for the numerical application of the method, at least in the framework of ordinary differential equations. From the cases studied it is seen that this can be a practicable method for the numerical solution of differential equations. / Science, Faculty of / Mathematics, Department of / Graduate
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Função de Hilbert para uma k-algebra homogeneaBastos, Jefferson Luiz Rocha 20 December 1993 (has links)
Orientador : Paulo Roberto Brumatti / Dissertação (mestrado) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-07-18T21:36:19Z (GMT). No. of bitstreams: 1
Bastos_JeffersonLuizRocha_M.pdf: 1263797 bytes, checksum: dd5c506daab09f6eebe89e0057759684 (MD5)
Previous issue date: 1993 / Resumo: Não informado. / Abstract: Not informed. / Mestrado / Mestre em Matemática
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The Theory of Involutive Divisions and an Application to Hilbert Function ComputationsApel, Joachim 04 October 2018 (has links)
Generalising the divisibility relation of terms we introduce the lattice of so-called involutive divisions and define the admissibility of such an involutive division for a given set of terms. Based on this theory we present a new approach for building up a general theory of involutive bases of polynomial ideals. In particular, we give algorithms for checking the involutive basis property and for completing an arbitrary basis to an involutive one. It turns out that our theory is more constructive and more exible than the axiomatic approach to general involutive bases due to Gerdt and Blinkov. Finally, we show that an involutive basis contains more structural information about the ideal of leading terms than a Gröbner basis and that it is straight forward to compute the (affine) Hilbert function of an ideal I from an arbitrary involutive basis of I.
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Μελέτη εξισώσεων διαφορών σε χώρους Hilbert και Banach και εφαρμογές αυτώνΠετροπούλου, Ευγενία 30 September 2009 (has links)
- / -
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Hilbert and Hardy type inequalitiesHandley, G. D. Unknown Date (has links) (PDF)
I use novel splittings of conjugate exponents in Holder’s inequality and other techniques to obtain new inequalities of Hilbert, Hilbert-Pachpatte and Hardy type for series and integrals. The Thesis gives far reaching generalisations of the work of Dragomir-Kim (2003), Pachpatte (1987, 1990, 1992),Handley-Koliha-Pecaric (2000), Hwang-Yang (1990), Hwang(1996), Love-Pecaric (1995) and Mohapatra-Russell (1985) and inequalities for fractional derivatives of integrable functions. (For complete abstract open document)
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[en] DECOMPOSITION OF HILBERT-SPACE CONTRACTIONS / [pt] DECOMPOSIÇÃO DE CONTRAÇÕES EM ESPAÇOS DE HILBERTDENISE DE OLIVEIRA 19 April 2006 (has links)
[pt] O problema de decomposição de contrações em espaços de
Hilbert é motivado pelo problema do subespaço invariante,
o qual é um famoso problema em aberto em Teoria de
Operadores. Se T (pertence) B [H] é uma contração, define-
se o operador A como o limite forte da seqüência { T* n
Tn (pertence) B [H]; n > ou = 1}. Este operador
caracteriza as isometrias, uma vez que T é uma isometria
se e somente se A = I. A decomposição de Von Neumann-Wold
para isometrias estabelece que toda isometria é a soma
direta ortogonal de um Shift unilateral com um operador
unitário. O presente trabalho estende a decomposição de
Von Neumann-Wold para contrações tais que o operador A é
uma projeção ortogonal arbitrária. Através desta
decomposição, conclui-se que se uma contração não possui
subespaço invariante próprio, então T (pertence) C00 U
C01 U C10. uma análise abrangente do efeito dessa nova
decomposição é desenvolvida, interceptando a classe de
contrações em questão com as classes dos operadores
compactos, normais, quasinormais, subnormais, hiponormais
e normalóides. Como se conclui que o operador A é uma
projeção ortogonal apenas até a classe das contrações
quasinormais, também é analisado o quanto o operador A
referente a uma contração subnormal não-quasinormal pode
se afastar de uma projeção ortogonal. Além disso,
estabelece-se para contrações hipornormais o subespaço
onde A é uma projeção ortogonal. / [en] Decomposition of Hilbert-space contractions is motivated
the invariant subspace problem, which is a famous open
problem in Operator Theory. If T (pertenc) B [H] is a
contraction, {T*n Tn (pertenc) B [H]; n > = 1} converger
strongly. Let the operator A be its (strongly) limit. T is
a isometry if and only if A = I. The von Neumann-Wold
decomposition for isometries says that a isometry is the
direct orthogonal sum of a unilateral shift and a unitary
operator. The present work extends the von Neumann-Wold
decomposition to a contrataction for wich A is an
orthogonal projection. According to such a decomposition
it is established that a contractin with no nontrivial
invariant subspace is such that T (pertenc) C00 U C01 U
C10. it follows a detailed investigation n the impact of
such a new decomposition on several classes of operators;
viz. compact, normal, quasinormal, subnormal, hyponormal
and normaloid. It is verified that the operator A is an
orthogonal projection up to the class of all quasinormal
contraction T, but not for every subnormal contraction.
Thus it is investigated how the operator A, for a
susbnormal contraction T, can distanciate from an
orthogonal projection, for hyponormal contraction T, is
exhibited as well
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[en] ON SPECTRAL RADIUS OF A CLASS OF OPERATORS TRANSFORMATIONS / [pt] SOBRE RAIOS ESPECTRAIS DE UMA CLASSE DE TRANSFORMAÇÕES DE OPERADORESGISELLE MARTINS DOS SANTOS FERREIRA 26 June 2006 (has links)
[pt] As transformações F e F(diferente) surgiram associados ao
problema de estabilidade em média-quadrática de sistemas
bilineares discretos de dimensão infinita evoluindo em
espaços de Hilbert separáveis, tendo sido originariamente
definidas através de séries infinitas na álgebra de Banach
dos operadores lineares e limitados no espaço de Hilbert
em que o sistema evolui. O presente trabalho parte de uma
condição suficiente para a estabilidade, condição esta
anteriormente determinada, que se traduz imposições sobre
os raios espectrais das transformações mencionadas ambos
estritamente menores que um- e do fato já conhecido de
que, a condição sendo parcialmente satisfeita, isto é, um
dos raios espectrais menor que um, não implica que ela o
seja por completo. Deste modo, coloca-se uma primeira
questão: em que casos tal implicação existe?
O estudo é então desenvolvido sobre a simplificação das
condições que originaram: as transformações F e F
(diferente) são tomadas simplificadamente como somas de
apenas dois termos, e a questão inicial se converte na
pesquisa de casos em que a igualdade entre raios
espectrais de F e F(diferente) ocorre. Mais precisamente,
os termos que compõem F e F(diferente) se constitui em
produtos de operadores pertencentes à álgebra de Banach
inicialmente referida, de modo que é feita uma análise do
comportamento dos raios espectrais de F e F(diferente)
situando-se esses operadores em classes específicas nessa
álgebra. Sob estas condições são apresentados resultados
relativos às classes dos operadores auto-adjuntos,
unitários, normais, isometrias e subnormais, assim como um
resultado referente aos shifts ponderados. Além disto, é
apresentado um resultado geral para o caso de espaços de
dimensão finita. / [en] The transformations f and F(different) appeared associated
to the mean-square stability problem for infinite
dimensional discrete bilinear systems evolving in a
separable Hilbert space, being originally defined as
infinite series in the Banach algebra of bounded linear
operators on the Hilbert space where the system evolves.
The present work starts with a previously defined
sufficient stability condition, expressed by assumptions
on the spectral radiuses of the mentioned transformations -
both strictly less than one- and from the already known
fact that the condition being partially fulfilled, that
is, one of the spectral radiuses less than one, does not
imply that it be so completely. Thus one poses a first
question: in which cases does one have such an implication?
The study is then developed on a simplification of the
conditions from which it arose: both F and F(different)
are taken as sums of only terms, and the initial question
becomes the search for cases in which the equality betweem
the spectral radiuses of F and F(different) occurs. More
precisely, the terms that compose F and F(different) are
products of operators in the above mentioned algebra, so
that the behaviour of the spectral radiuses of F and F
(different) is analysed by placing those operators in
specific classes in that algebra. Under these assumptions,
results related to the classes of self-adjoint, unitary,
normal, isometries and subnormal operators are presented,
as well as result referring to weighted shifts. Besides, a
general result related to finite-dimensional spaces is
also presented.
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Hilbert Polynomials of Projective SchemesMa, Hemming January 2022 (has links)
We introduce localization and sheaves to define projective schemes, and in particular the projective n-space. Afterwards, we define closed subschemes of projective space and show that they arise from quotients of graded rings by homogeneous ideals. We then define the Hilbert function and Hilbert polynomial to determine several invariants of closed subschemes of projective space: their degree, dimension, and arithmetic genus. Finally, we provide numerous examples with explicit computations, finding the invariants of hypersurfaces, curves, the twisted cubic and more.
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Subspace methods and informative experiments for system identificationChui, Nelson Loong Chik January 1997 (has links)
No description available.
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Asymptotics for the solution of the Schrödinger equationAl-Naggar, Ibtesam M. Abu-Sulayman January 1994 (has links)
No description available.
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