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131.
Ioannis K. Argyros 《Journal of Mathematical Analysis and Applications》2004,298(2):374-397
We provide a local as well as a semilocal convergence analysis for two-point Newton-like methods in a Banach space setting under very general Lipschitz type conditions. Our equation contains a Fréchet differentiable operator F and another operator G whose differentiability is not assumed. Using more precise majorizing sequences than before we provide sufficient convergence conditions for Newton-like methods to a locally unique solution of equation F(x)+G(x)=0. In the semilocal case we show under weaker conditions that our error estimates on the distances involved are finer and the information on the location of the solution at least as precise as in earlier results. In the local case a larger radius of convergence is obtained. Several numerical examples are provided to show that our results compare favorably with earlier ones. As a special case we show that the famous Newton-Kantorovich hypothesis is weakened under the same hypotheses as the ones contained in the Newton-Kantorovich theorem. 相似文献
132.
Based on the previously developed technique using the Laplace transformation of distributions with compact support, we calculate the Hochschild cohomologies of the algebra of smooth functions on a finite-dimensional real vector space with coefficients in the adjoint representation. 相似文献
133.
A. N. Koryukin 《Algebra and Logic》2003,42(6):387-397
We generalize a well-known two-parameter quantization for the group GL
2(k) (over an arbitrary field k). Specifically, a certain class of Hopf algebras is constructed containing that quantization. The algebras are constructed given an arbitrary coalgebra and an arbitrary pair of its commuting anti-isomorphisms, and are defined by quadratic relations. They are densely linked to the compact quantum groups introduced by Woronowicz. We give examples of Hopf algebras that can be rowed up to the two-parameter quantization for GL
2(k). 相似文献
134.
Mathematical Notes - 相似文献
135.
Andrzej Skowronski Kunio Yamagata 《Proceedings of the American Mathematical Society》2004,132(3):659-667
We prove that a large class of self-injective algebras of tilted type is invariant under stable equivalences of module categories.
136.
Banach frames and atomic decompositions are sequences that have basis-like properties but which need not be bases. In particular, they allow elements of a Banach space to be written as linear combinations of the frame or atomic decomposition elements in a stable manner. In this paper we prove several functional — analytic properties of these decompositions, and show how these properties apply to Gabor and wavelet systems. We first prove that frames and atomic decompositions are stable under small perturbations. This is inspired by corresponding classical perturbation results for bases, including the Paley — Wiener basis stability criteria and the perturbation theorem el kato. We introduce new and weaker conditions which ensure the desired stability. We then prove quality properties of atomic decompositions and consider some consequences for Hilbert frames. Finally, we demonstrate how our results apply in the practical case of Gabor systems in weighted L2 spaces. Such systems can form atomic decompositions for L2w(IR), but cannot form Hilbert frames but L2w(IR) unless the weight is trivial. 相似文献
137.
138.
139.
Liang Kong 《Advances in Mathematics》2007,213(1):271-340
We study the operadic and categorical formulations of (conformal) full field algebras. In particular, we show that a grading-restricted R×R-graded full field algebra is equivalent to an algebra over a partial operad constructed from spheres with punctures and local coordinates. This result is generalized to conformal full field algebras over VL⊗VR, where VL and VR are two vertex operator algebras satisfying certain finiteness and reductivity conditions. We also study the geometry interpretation of conformal full field algebras over VL⊗VR equipped with a nondegenerate invariant bilinear form. By assuming slightly stronger conditions on VL and VR, we show that a conformal full field algebra over VL⊗VR equipped with a nondegenerate invariant bilinear form exactly corresponds to a commutative Frobenius algebra with a trivial twist in the category of VL⊗VR-modules. The so-called diagonal constructions [Y.-Z. Huang, L. Kong, Full field algebras, arXiv: math.QA/0511328] of conformal full field algebras are given in tensor-categorical language. 相似文献
140.
We prove that a finite unary algebra with at least two operation symbols is a homomorphic image of a (finite) subdirectly
irreducible algebra if and only if the intersection of all its subalgebras which have at least two elements is nonempty.
While working on this paper the first and the third authors were partially supported by the Grant Agency of the Czech Republic,
grant #201/02/0594, and by the institutional grant MSM0021620839; the second author was supported by the Ministry of Science,
Technologies and Development of Republic of Serbia, grant no. 1227. 相似文献