共查询到20条相似文献,搜索用时 15 毫秒
1.
James Zhijian Qiu 《Integral Equations and Operator Theory》1996,25(2):235-252
In this paper we proved that for a large class of compact subsetsK in the complex plane,R(K) is dense inL
q
() if and only if the set of analytic bounded point evaluations forR
q
(K, ) is empty. As a consequence, we showed that this result is true for allK ifR(K) is replaced byA(K). Our main result includes the corresponding result of James Thomson for polynomials approximation as such a special case thatK is a disk. 相似文献
2.
The problem of cancelling a specified part of the zeros of a completely general rational matrix function by multiplication with an appropriate invertible rational matrix function is investigated from different standpoints. Firstly, the class of all factors that dislocate the zeros and feature minimal McMillan degree are derived. Further, necessary and sufficient existence conditions together with the construction of solutions are given when the factor fulfills additional assumptions like being J-unitary, or J-inner, either with respect to the imaginary axis or to the unit circle. The main technical tool are centered realizations that deliver a sufficiently general conceptual support to cope with rational matrix functions which may be polynomial, proper or improper, rank deficient, with arbitrary poles and zeros including at infinity. A particular attention is paid to the numerically-sound construction of solutions by employing at each stage unitary transformations, reliable numerical algorithms for eigenvalue assignment and efficient Lyapunov equation solvers. 相似文献
3.
For sequences of rational functions, analytic in some domain, a theorem of Montel's type is proved. As an application, sequences of rational functions of the best L
p
-approximation with an unbounded number of finite poles are considered. 相似文献
4.
A number of explicit solutions for the heat equation with a polynomial non-linearity and for the Fisher equation is presented.
An extended class of non-linear heat equations admitting solitary wave solutions is described. The generalization of the Fisher
equation is proposed whose solutions propagate with arbitrary ad hoc fixed velocity. 相似文献
5.
João Lucas Barbosa Walterson Ferreira Keti Tenenblat 《Annals of Global Analysis and Geometry》1996,14(4):381-401
The generalized equation and the intrinsic generalized equation are considered. The solutions of the first one are shown to correspond to Riemannian submanifolds M
n
(K) of constant sectional curvature of psedo-Riemannian manifolds % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WGnbaaamaaDaaaleaaieGacaWFZbaabaGaaGOmaiaad6gacqGHsisl% caaIXaaaaOGaaiikamaanaaabaGaam4saaaacaGGPaaaaa!3D97!\[\overline M _s^{2n - 1} (\overline K )\] of index s, with % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saiabgc% Mi5oaanaaabaGaam4saaaaaaa!3965!\[K \ne \overline K \], flat normal bundle and such that the normal principal curvatures are different from % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4saiabgk% HiTmaanaaabaGaam4saaaaaaa!388B!\[K - \overline K \]. The solutions of the intrinsic generalized equation correspond to Riemannian metrics defined on open subsets of R
n
which have constant sectional curvature. The relation between solutions of those equations is given. Moreover, it is proven that the submanifolds M under consideration are determined, up to a rigid motion of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WGnbaaaaaa!36D0!\[\overline M \], by their first fundamental forms, as solutions of the intrinsic generalized equation. The geometric properties of the submanifolds M associated to the solutions of the intrinsic generalized equation, which are invariant under an (n – 1)-dimensional group of translations, are given. Among other results, it is shown that such submanifolds are foliated by (n – 1)-dimensional flat submanifolds which have constant mean curvature in M. Moreover, each leaf of the foliation is itself foliated by curves of % MathType!MTEF!2!1!+-% feaafiart1ev1aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn% hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr% 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9% vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x% fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaWaa0aaaeaaca% WGnbaaaaaa!36D0!\[\overline M \] which have constant curvatures. 相似文献
6.
Olga Martin 《Central European Journal of Mathematics》2004,2(2):191-198
In this paper we present a variational method for approximating solutions of the Dirichlet problem for the neutron transport
equation in the stationary case. Error estimates from numerical examples are used to evaluate an approximation of the solution
with respect to the steps of two grids. 相似文献
7.
Anthony J. Small 《Annals of Global Analysis and Geometry》1994,12(1):97-101
The collection of minimal herissons in
3 is endowed with a vector space structure. The existence of this structure is related to the fact that null curves inC
3 are described by a single map from the étalé space of the sheaf of germs of holomorphic sections of the line bundle of degree 2 over 1 to C3, which islinear on stalks. There is an analogous construction for null curves inC
4. This gives a similar class of minimal surfaces in 4. 相似文献
8.
In this paper, the authors present some new results for the oscillation of the second order nonlinear neutral differential
equations of the form
. Easily verifiable criteria are obtained that are also new for differential equations without neutral term i.e. for p(t)≡0. 相似文献
9.
Murray Michael K. Norbury Paul Singer Michael A. 《Annals of Global Analysis and Geometry》2003,23(2):101-128
We associate to an SU(2) hyperbolic monopole a holomorphicsphere embedded in projective space and use this to uncovervarious features of the monopole. 相似文献
10.
Constructive sufficient conditions for univalent resolvability of a two-point boundary value problem for nonlinear Riccati
equation are obtained. An illustrative example is given. 相似文献
11.
Letg:U→ℝ (U open in ℝn) be an analytic and K-subanalytic (i. e. definable in ℝ
an
K
, whereK, the field of exponents, is any subfield ofℝ) function. Then the set of points, denoted Σ, whereg does not admit an analytic extension is K-subanalytic andg can be extended analytically to a neighbourhood of Ū\∑.
Partially supported by the European RTN Network RAAG (contract no. HPRN-CT-00271) 相似文献
12.
Ruishi Kuwabara 《Annals of Global Analysis and Geometry》1996,14(2):193-218
A one-parameter familyg(t) (0 t T) of Riemannian metric on a compact manifold is called an isospectral deformation of a metricg(0) if the Laplace-Beltrami operators associated to the metricsg(t) have the same spectra. Examples of non-trivial isospectral deformations were constructed on solvmanifolds for the first time by C.S. Gordon and E. Wilson on the basis of Kirillov theory. This paper considers the isospectral deformations on nilmanifolds from the dynamical point of view. First, we see for certain isospectral deformations that the associated Hamiltonian systems of geodesic flows are decomposed into a collection of reduced systems which are left invariant as Hamiltonian systems under the deformations. This fact is formulated by the classical Lax equations. Next, by using a quantization procedure, we attempt to obtain Lax equations for the reduced Laplacians from the classical Lax equations. As a result, we show that certain isospectral deformations by Gordon-Wilson are represented by the Lax equations. 相似文献
13.
Sufficient conditions which guarantee that certain linear integro-differential equation cannot have a positive solution are
established. 相似文献
14.
Critical points of a master function associated to a simple Lie algebra
come in families called the populations [11]. We prove that a population is isomorphic to the flag variety of the Langlands
dual Lie algebra
. The proof is based on the correspondence between critical points and differential operators called the Miura opers.
For a Miura oper D, associated with a critical point of a population, we show that all solutions of the differential equation DY=0 can be written explicitly in terms of critical points composing the population.
Supported in part by NSF grant DMS-0140460
Supported in part by NSF grant DMS-0244579 相似文献
15.
Following Ebin and Marsden the Navier-Stokes equation is viewed as a perturbation of a geodesic flow on the group of volume preserving diffeomorphisms on a compact Riemannian manifold. Existence and uniqueness of bounded solutions for all position time is shown by taking a higher order diffusion term.Partial y supported by Alexander von Humboldt Foundation 相似文献
16.
17.
Aaron Wootton 《Central European Journal of Mathematics》2005,3(2):260-272
A compact Riemann surface X of genus g≥2 which admits a cyclic group of automorphisms C
q of prime order q such that X/C
q has genus 0 is called a cyclic q-gonal surface. If a q-gonal surface X is also p-gonal for some prime p≠q, then X is called a multiple prime surface. In this paper, we classify all multiple prime surfaces. A consequence of this classification
is a proof of the fact that a cyclic q-gonal surface can be cyclic p-gonal for at most one other prime p. 相似文献
18.
We can consider the Riemann-Stieltjes integral dg as an integral of a point function f with respect to an interval function g. We could extend it to the Henstock-Stieltjes integral. In this paper, we extend it to a generalized Stieltjes integral dg of a point function f with respect to a function g of divisions of an interval. Then we prove for this integral the standard results in the theory of integration, including
the controlled convergence theorem.
相似文献
19.
Elmar Schrohe 《Annals of Global Analysis and Geometry》1992,10(3):237-254
The pseudodifferential operators with symbols in the Grushin classes \~S
inf0
sup,
, 0 < 1, of slowly varying symbols are shown to form spectrally invariant unital Frécher-*-algebras (*-algebras) in L(L
2(R
n
)) and in L(H
st
) for weighted Sobolev spaces H
inf
supst
defined via a weight d function . In all cases, the Fredholm property of an operator can be characterized by uniform ellipticity of the symbol. This gives a converse to theorems of Grushin and Kumano-Ta-Taniguchi. Both, the spectrum and the Fredholm spectrum of an operator turn out to be independent of the choices of s, t and .The characterization of the Fredholm property by uniform ellipticity leads to an index theorem for the Fredholm operators in these classes, extending results of Fedosov and Hörmander. 相似文献
20.
J. Liesen 《Constructive Approximation》2001,17(2):267-274
Faber polynomials corresponding to rational exterior mapping functions of degree (m, m − 1) are studied. It is shown that these polynomials always satisfy an (m + 1)-term recurrence. For the special case m = 2, it is shown that the Faber polynomials can be expressed in terms of the classical Chebyshev polynomials of the first
kind. In this case, explicit formulas for the Faber polynomials are derived. 相似文献