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171.
It is shown that for certain classes of infinite block Toeplitz matricesT(a)=[a
j-k
]
0
the Moore-Penrose inverses of the finite sectionT
n
(a)=[a
j-k
]
0
n–1
converge to the Moore-Penrose inverse ofT(a). Furthermore the convergence for modified finite section methods and the finite section method for Wiener-Hopf integral and related operators are studied. 相似文献
172.
Summary It is shown that every convex set-valued function defined on a cone with a cone-basis in a real linear space with compact values in a real locally convex space has an affine selection. Similar results can be obtained for midconvex set-valued functions. 相似文献
173.
Let {S
1
(n)}
n0and {S
2
(n)}
n0be independent simple random walks in Z
4 starting at the origin, and let % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabfc6aqnaaBaaaleaacaqGPbaabeaatCvAUfKttLearyqr1ngB% Prgaiuaakiab-HcaOiaadggacaGGSaGaamOyaiab-LcaPiabg2da9i% ab-Tha7Hqbciab+Hha4jabgIGiolab+PfaAnaaCaaaleqabaGaaGin% aaaakiaacQdaieGacaqFtbWaaSbaaSqaaiaabMgaaeqaaOGae8hkaG% Iaa0xBaiab-LcaPiabg2da9iab+Hha4baa!5761!\[\Pi _{\rm{i}} (a,b) = \{ x \in Z^4 :S_{\rm{i}} (m) = x\]for the some % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaGqaciaa-1gacqGHiiIZtCvAUfKttLearyqr1ngBPrgaiuaacqGF% OaakcaWGHbGaaiilaiaadkgacqGFPaqkcqGF9bqFaaa!4936!\[m \in (a,b)\} \]. Let two integervalued sequences {a
n}n0and {b
n}n0be given, such that the limit limn a
nexists and lim
n
b
n=+. In this paper, it is shown that the probability of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabfc6aqnaaBaaaleaacaaIXaaabeaatCvAUfKttLearyqr1ngB% Prgaiuaakiab-HcaOiab-bdaWiab-XcaSiabg6HiLkab-LcaPiabgM% Iihlabfc6aqnaaBaaaleaacaaIYaaabeaakiab-HcaOiaadggadaWg% aaWcbaGaamOBaiaacYcaaeqaaOGaamyyamaaBaaaleaacaWGUbaabe% aakiabgUcaRiaadkgadaWgaaWcbaGaamOBaaqabaGccqWFPaqkcqGH% GjsUieaacaGFydaaaa!5904!\[\Pi _1 (0,\infty ) \cap \Pi _2 (a_{n,} a_n + b_n ) \ne \O \] is asymptotic to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaamaalaaabaGaaGymaaqaaiaaikdaaaGaciiBaiaac+gacaGGNbWe% xLMBb50ujbqeguuDJXwAKbacfaGae8hkaGIae8xmaeJae83kaSIaam% OyamaaBaaaleaacaWGUbaabeaakiaac+cacaWGHbWaaSbaaSqaaiaa% d6gaaeqaaOGae8xkaKIae83la8IaciiBaiaac+gacaGGNbGaamOyam% aaBaaaleaacaWGUbaabeaaaaa!5364!\[\frac{1}{2}\log (1 + b_n /a_n )/\log b_n \] if it tends to zero as n, and the probability of % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% qaaiabfc6aqnaaBaaaleaacaaIXaaabeaatCvAUfKttLearyqr1ngB% Prgaiuaakiab-HcaOiab-bdaWiab-XcaSiabg6HiLkab-LcaPiabgM% Iihlabfc6aqnaaBaaaleaacaaIYaaabeaakiab-HcaOiaadggadaWg% aaWcbaGaamOBaaqabaGccaGGSaGaamyyamaaBaaaleaacaWGUbaabe% aakiabgUcaRiaadkgadaWgaaWcbaGaamOBaaqabaGccqWFPaqkcqWF% 9aqpieaacaGFydaaaa!583C!\[\Pi _1 (0,\infty ) \cap \Pi _2 (a_n ,a_n + b_n ) = \O \]is asymptotic to % MathType!MTEF!2!1!+-% feaafeart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXafv3ySLgzGmvETj2BSbqefm0B1jxALjhiov2D% aebbfv3ySLgzGueE0jxyaibaiGc9yrFr0xXdbba91rFfpec8Eeeu0x% Xdbba9frFj0-OqFfea0dXdd9vqaq-JfrVkFHe9pgea0dXdar-Jb9hs% 0dXdbPYxe9vr0-vr0-vqpWqaaeaabiGaciaacaqabeaadaqaaqGaaO% abaeqabaaabaGaam4yaiaacUfaciGGSbGaai4BaiaacEgatCvAUfKt% tLearyqr1ngBPrgaiuaacqWFOaakcaWGHbWaaSbaaSqaaiaad6gaae% qaaOGaey4kaSIaamOyamaaBaaaleaacaWGUbaabeaakiab-LcaPiab% -9caViab-XgaSjab-9gaVjab-DgaNjab-HcaOiaadggadaWgaaWcba% GaamOBaaqabaGccqGHRaWkcaaIYaGae8xkaKIae8xxa01aaWbaaSqa% beaacqWFTaqlcqWFXaqmcqWFVaWlcqWFYaGmaaaaaaa!5BAC!\[\begin{array}{l} \Pi _1 (0,\infty ) \cap \Pi _2 (a_n ,a_n + b_n ) = \O \\ c[\log (a_n + b_n )/log(a_n + 2)]^{ - 1/2} \\ \end{array}\], for some constant c, if it tends to a finite constant (1) as n. These results extend some results obtained by G. F. Lawler about the intersection properties of simple random walks in Z
4. By using similar arguments, we also get corresponding results for the intersections of Wiener sausages in four dimensions. In particular, a conjecture suggested by M. Aizenman, which describes nonintersection of independent Wiener sausages in R
4, is proven.Partly supported by AvH Foundation. 相似文献
174.
Kevin McLeod Albert Milani 《NoDEA : Nonlinear Differential Equations and Applications》1996,3(1):79-114
We prove that the quasilinear parabolic initial-boundary value problem (1.1) below is globally well-posed in a class of high order Sobolev solutions, and that these solutions possess compact, regular attractors ast+. 相似文献
175.
Set-valued mappings from a topological space into subsets of a Banach space which satisfy a restricted form of weak upper semi-continuity, have particularly noteworthy properties. We establish a selection theorem for certain set-valued mappings from a (-) unfavourable topological space into subsets of a Banach space and as a consequence derive the property that restricted weak upper semi-continuous set-valued mappings which satisfy a minimality condition, from a (-) unfavourable topological space into subsets of a Banach space are single-valued and norm upper semi-continuous at the points of a residual subset of their domain. 相似文献
176.
Zhen-Qing Chen 《Potential Analysis》1996,5(4):383-401
Let D be an open set in d and E be a relatively closed subset of D having zero Lebesgue measure. A necessary and sufficient integral condition is given for the Sobolev spaces W
1,2 (D) and W
1,2(D\E) to be the same. The latter is equivalent to (normally) reflecting Brownian motion (RBM) on
being indistinguishable (in distribution) from RBM on
. This integral condition is satisfied, for example, when E has zero (d–1)-dimensional Hausdorff measure. Therefore it is possible to delete from D a relatively closed subset E having positive capacity but nevertheless the RBM on
is indistinguishable from the RBM on
, or equivalently, W
1,2(D\E)=W1,2(D). An example of such kind is: D=2 and E is the Cantor set. In the proof of above mentioned results, a detailed study of RBMs on general open sets is given. In particular, a semimartingale decomposition and approximation result previously proved in [3] for RBMs on bounded open sets is extended to the case of unbounded open sets.Research supported in part by NSF Grant DMS 86-57483. 相似文献
177.
Lurdes Sousa 《Applied Categorical Structures》1996,4(1):87-95
Each ordinal equipped with the upper topology is a T
0-space. It is well known that for =2 the reflective hull of in Top0 is the subcategory of sober spaces. Here, we define -sober space for each 2 in such a way that the reflective hull of in Top0 is the subcategory of -sober spaces. Moreover, we obtain an order-preserving bijective correspondence between a proper class of ordinals and the corresponding (epi)reflective hulls. Our main tool is the concept of orthogonal closure operator, first introduced in [12].The author acknowledges financial support from Instituto Politécnico de Viseu and from Centro de Matemática da Universidade de Coimbra. 相似文献
178.
Ryszard Rudnicki 《Integral Equations and Operator Theory》1996,24(3):320-327
A class of Markov operators appearing in biomathematics is investigated. It is proved that these operators are asymptotic stable inL
1, i.e. lim
n
P
n f=0 forfL
1 and f(x) dx=0. 相似文献
179.
We realize the
current algebra at an arbitrary level in terms of one deformed free bosonic field and a pair of deformed parafermionic fields. It is shown that the operator product expansions of these parafermionic fields involve an infinite number of simple poles and simple zeros, which then condensate to form a branch cut in the classical limitq1. Our realization coincides with those of Frenkel-Jing and Bernard when the levelk takes the values 1 and 2, respectively. 相似文献
180.
Approximation by translates of refinable functions 总被引:23,自引:0,他引:23
Summary.
The functions
are
refinable if they are
combinations of the rescaled and translated functions
.
This is very common in scientific computing on a regular mesh.
The space of approximating functions with meshwidth
is a
subspace of with meshwidth
.
These refinable spaces have refinable basis functions.
The accuracy of the computations
depends on , the
order of approximation, which is determined by the degree of
polynomials
that lie in .
Most refinable functions (such as scaling functions in the theory
of wavelets) have no simple formulas.
The functions
are known only through the coefficients
in the refinement equation – scalars in the traditional case,
matrices for multiwavelets.
The scalar "sum rules" that determine
are well known.
We find the conditions on the matrices
that
yield approximation of order
from .
These are equivalent to the Strang–Fix conditions on the Fourier
transforms
, but for refinable
functions they can be explicitly verified from
the .
Received
August 31, 1994 / Revised version received May 2, 1995 相似文献