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1.
目的是研究Banach空间中无限族非扩张映象和非扩张半群的强收敛问题.为此提出一个改进的迭代序列,在适当条件下,某些强收敛定理被证明.结果改进和推广了一些人的最新结果.  相似文献   
2.
The spreading of a liquid drop over liquid subphase can be driven by change in interfacial tension mediated through a surfactant, volatile solvent or photoinduced reaction. In contrast to the spreading dynamics of a liquid drop, a liquid crystal drop with anisotropic structure can lead to interesting behaviour due to its viscoelasticity and anchoring at the interfaces. Recently, we have reported studies on unusual spreading and retraction dynamics of a smectic domain doped with a fluorescent dye in the collapsed state of a Langmuir monolayer. Under epifluorescence microscope, during excitation, a stack of layers of the dye-doped smectic domain gets sheared causing the domain to spread asymmetrically. Further, due to line tension, the domain transforms into a circular shape. We also find the domain size to be about twice that of the initial size. Interestingly, in the absence of excitation, the domain retracts to a smaller area. During retraction of the domain, successive generation of edge dislocation loops arising from a nucleus results in an increase in the domain thickness. The dynamics of spreading and retraction of the domain can be understood by invoking changes in the spreading coefficient due to photoinduced modification of the interfacial tension.  相似文献   
3.
The free retraction of vulcanised strips of natural rubber released from simple uniaxial deformation is studied using high speed cinematography in the context of a simple momentum theory. Good agreement between the theory and experiment is observed when vulcanisates are released from stresses below 1 MPa, which corresponds to tensile strains rates below 1 × 103 s−1. Above this critical stress and corresponding strain rate value, an increasing dispersion is observed in the form of slowing down of the characteristic retraction pulse, and also by a relaxation of strain ahead of the pulse front (a dispersion of the pulse). Holding samples at high strains for an extended period of time prior to releasing results in a further, significant retardation of the retraction pulse velocity. These effects are related to the increasing non-linearity of high strain rate retraction stress–strain behaviour. Energy balance arguments show that the dispersion of the retraction pulse is a prerequisite for pulse propagation, and that its magnitude underpins the deviation from the momentum model outlined in this paper.  相似文献   
4.
带有正交约束的矩阵优化问题在材料计算、统计及数据分析等领域中有着广泛的应用.由于正交约束的可行域是Stiefel流形,一直以来流形上的优化方法是求解这一问题的主要方法.近年来,随着实际应用问题所要求的变量规模的扩大,传统的流形优化方法在计算上的劣势显现出来,而一些迭代简单、收敛快的新算法逐渐被提出.通过收缩方法、非收缩可行方法、不可行方法三个类别分别来介绍求解带有正交约束的矩阵优化问题的最新算法.通过分析这些方法的主要特性,以及应用问题的要求,对这类问题算法设计的研究进行了展望.  相似文献   
5.
Suppose K is a closed convex nonexpansive retract of a real uniformly smooth Banach space E with P as the nonexpansive retraction. Suppose T : KE is an asymptotically d-weakly contractive map with sequence {kn }, kn ≥ 1, lim kn = 1 and with F(T) n int (K) ≠ ø F(T):= {xK: Tx = x}. Suppose {x n } is iteratively defined by x n+1 = P((l ? knαn )x n +k n α n T(PT) n?l xn ), n = 1,2,...,x 1K, where αn (0,l) satisfies lim αn = 0 and Σαn = ∞. It is proved that {x n } converges strongly to some x *F(T)∩ int K. Furthermore, if K is a closed convex subset of an arbitrary real Banach space and T is, in addition uniformly continuous, with F(T) ≠ ø, it is proved that {xn } converges strongly to some x *F(T).  相似文献   
6.
Let E be a real reflexive Banach space having a weakly continuous duality mapping Jφ with a gauge function φ, and let K be a nonempty closed convex subset of E. Suppose that T is a non‐expansive mapping from K into itself such that F (T) ≠ ??. For an arbitrary initial value x0K and fixed anchor uK, define iteratively a sequence {xn } as follows: xn +1 = αn u + βn xn + γn Txn , n ≥ 0, where {αn }, {βn }, {γn } ? (0, 1) satisfies αn +βn + γn = 1, (C 1) limn →∞ αn = 0, (C 2) ∑n =1 αn = ∞ and (B) 0 < lim infn →∞ βn ≤ lim supn →∞ βn < 1. We prove that {xn } converges strongly to Pu as n → ∞, where P is the unique sunny non‐expansive retraction of K onto F (T). We also prove that the same conclusions still hold in a uniformly convex Banach space with a uniformly Gâteaux differentiable norm or in a uniformly smooth Banach space. Our results extend and improve the corresponding ones by C. E. Chidume and C. O. Chidume [Iterative approximation of fixed points of non‐expansive mappings, J. Math. Anal. Appl. 318 , 288–295 (2006)], and develop and complement Theorem 1 of T. H. Kim and H. K. Xu [Strong convergence of modified Mann iterations, Nonlinear Anal. 61 , 51–60 (2005)]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   
7.
The poset retraction problem for a poset P is whether a given poset Q containing P as a subposet admits a retraction onto P, that is, whether there is a homomorphism from Q onto P which fixes every element of P. We study this problem for finite series-parallel posets P. We present equivalent combinatorial, algebraic, and topological charaterisations of posets for which the problem is tractable, and, for such a poset P, we describe posets admitting a retraction onto P.  相似文献   
8.
Given any morphism, we construct extensions of the original category in which this morphism admits certain factorizations, in particular a (retraction, section)-factorization. To this end, we solve the word problem for a certain type of systems of generators and relations for categories. This also enables us to prove preservation properties for the said extensions, e.g. preservation of a pair of diagonalizing classes of epimorphisms and monomorphisms.Iterating such extension processes, we obtain factorizable extensions of categories; in particular, we construct a free proper factorization structure on a given category, which leads to a characterization of preimages of proper factorization structures under full embeddings. As a further application, we characterize an absoluteness property regarding factorizations of functorial images of a morphism.  相似文献   
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