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Summary We present a (semilocal) Kantorovich-type analysis for Newton-like methods for singular operator equations using outer inverses. We establish sharp generalizations of the Kantorovich theory and the Mysovskii theory for operator equations when the derivative is not necessarily invertible. The results reduce in the case of an invertible derivative to well-known theorems of Kantorovich and Mysovskii with no additional assumptions, unlike earlier theorems which impose strong conditions. The strategy of the analysis is based on Banach-type lemmas and perturbation bounds for outer inverses which show that the set of outer inverses (to a given bounded linear operator) admits selections that behave like bounded linear inverses, in contrast to inner inverses or generalized inverses which do not depend continuously on perturbations of the operator. We give two examples to illustrate our results and compare them with earlier results, and another numerical example to relate our results to computational issues.The research of the first author was partially supported by the National Science Foundation under grant DMS-901526. The research of the second author was supported by an Australian Research Council grant  相似文献
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While performing biomolecular interaction analysis (BIA), scientistsoften use surface plasmon resonance (SPR) to measure rate constantsof the associated reactions. A mathematical model of a BIAcoreTM,a common SPR device, consists of a convection-diffusion equationin a channel with a reacting surface at the channel ceiling.Asymptotic and singular perturbation techniques are used toanalyse the concentration of the reacting species in two cases:when the reaction occurs much more slowly than diffusion, andwhen the reaction occurs on the same time-scale as diffusion.Linear and nonlinear integral equations result from the analysis;explicit and asymptotic solutions are constructed for physicallyrealizable cases. These expressions provide a direct way toestimate the rate constants from raw data.  相似文献
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Uniqueness Theorems for the Inverse Problem of Acoustic Scattering   总被引:2,自引:0,他引:2  
Uniqueness theorems are obtained for the problem of determiningthe shape of a sound-soft or sound-hard obstacle from a knowledgeof (1) the far-field pattern at a fixed value of the wave numberand a finite number of distinct incident fields, or (2) thetotal scattering cross section for an interval of wave numbersand the incident field propagating in an arbitrary direction.  相似文献
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A Variational Approach to Upper and Lower Solutions   总被引:2,自引:0,他引:2  
Traditional proofs of the upper and lower solution existenceresults for nonlinear elliptic equations use monotone iterationschemes based on the maximum principle. In this paper, a directvariational method is employed which characterizes the solutionas the global minimum of a functional on a closed convex set.  相似文献
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Combining results on quadrics in projective geometries withan algebraic interplay between finite fields and Galois rings,the first known family of partial difference sets with negativeLatin square type parameters is constructed in nonelementaryabelian groups, the groups x for all k when is odd andfor all k < when is even. Similarly, partial differencesets with Latin square type parameters are constructed in thesame groups for all k when is even and for all k< when is odd. These constructions provide the first example wherethe non-homomorphic bijection approach outlined by Hagita andSchmidt can produce difference sets in groups that previouslyhad no known constructions. Computer computations indicate thatthe strongly regular graphs associated to the partial differencesets are not isomorphic to the known graphs, and it is conjecturedthat the family of strongly regular graphs will be new.  相似文献
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In this paper, we give a formal derivation of several systems of equations for injection moulding. This is done starting from the basic equations for nonisothermal, non-Newtonian flows in a three-dimensional domain. We derive systems for both (T0, p0) and (T1, p1) in the presence of body forces and sources. We find that body forces and sources have a nonlinear effect on the systems. We also derive a nonlinear “Darcy law”. Our formulation includes not only the pressure gradient, but also body forces and sources, which play the role of a nonlinearity. Later, we prove the existence of weak solutions to certain boundary value problems and initial-boundary value problems associated with the resulting equations for (T0,p0) but in a more general mathematical setting.  相似文献
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Growth and zero sets of analytic families of Cauchy-Stieltjes integrals   总被引:2,自引:0,他引:2  
The research of the first author was partially completed while on sabbatical leave from the University of Delaware.  相似文献
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