On integro‐differential inclusions with operator‐valued kernels

We study integro‐differential inclusions in Hilbert spaces with operator‐valued kernels and give sufficient conditions for the well‐posedness. We show that several types of integro‐differential equations and inclusions are covered by the class of evolutionary inclusions, and we therefore give criteria for the well‐posedness within this framework. As an example, we apply our results to the equations of visco‐elasticity and to a class of nonlinear integro‐differential inclusions describing phase transition phenomena in materials with memory. Copyright © 2014 John Wiley & Sons, Ltd.     

Discrete Approximation of Impulsive Differential Inclusions

The article deals with the approximation of the solution set and the reachable sets of an impulsive differential inclusion with variable times of impulses. It is strongly connected to [11 T. Donchev ( 2008 ). Approximation of the solution set of impulsive systems . In Lecture Notes in Comput. Sci . ( et al. . eds.). Vol. 4818 , Springer-Verlag , Berlin , pp. 309 – 316 . [Google Scholar]] and is its continuation. We achieve order of convergence 1 for the Euler approximation under Lipschitz assumptions on the set-valued right-hand side and on the functions describing the jump surfaces and jumps themselves. Another criterion prevents the beating phenomena and generalizes available conditions. Several test examples illustrate the conditions and the practical evaluation of the jump conditions.     

Existence and Controllability Results for First-and Second-Order Functional Semilinear Differential Inclusions with Nonlocal Conditions

In this paper, we prove existence and controllability results for first- and second-order semilinear differential inclusions in Banach spaces with nonlocal conditions.     

Characterisation of FXTAS related isolated intranuclear protein inclusions using laser tweezers Raman spectroscopy

We report the analysis of the vibrational modes of intranuclear protein inclusions isolated from the brain of human subjects with the Fragile X‐associated tremor/ataxia syndrome (FXTAS). In this preliminary study, Raman spectra of optically trapped inclusions were measured and analysed to determine protein composition and structure. Our main findings are as follows: (1) The spectra of protein inclusions are characteristic of H2A and H2B histones, which correlate with previous mass spectrometry (MS) studies; (2) Tyrosine is present in its OH form and exposed at the protein surface; (3) Zn and to a lesser extent Cu bound to histidine side chains are detected in the inclusions; (4) The tryptophan side‐chain torsion angle is calculated to be 102°; (5) Several potential spectroscopic markers for the inclusions of FXTAS are identified. These results show the capability of using laser tweezers Raman spectroscopy to identify protein inclusions in a non‐perturbative way and to gain further insight into the pathogenesis and progression of FXTAS in human subjects and in experimental models of this disorder. Copyright © 2009 John Wiley & Sons, Ltd.     

Normalizers of irreducible subfactors

We consider normalizers of an infinite index irreducible inclusion N⊆M of II₁ factors. Unlike the finite index setting, an inclusion uNu^∗⊆N can be strict, forcing us to also investigate the semigroup of one-sided normalizers. We relate these one-sided normalizers of N in M to projections in the basic construction and show that every trace one projection in the relative commutant N^′∩〈M,eN〉 is of the form u^∗eNu for some unitary u∈M with uNu^∗⊆N generalizing the finite index situation considered by Pimsner and Popa. We use this to show that each normalizer of a tensor product of irreducible subfactors is a tensor product of normalizers modulo a unitary. We also examine normalizers of infinite index irreducible subfactors arising from subgroup-group inclusions H⊆G. Here the one-sided normalizers arise from appropriate group elements modulo a unitary from L(H). We are also able to identify the finite trace L(H)-bimodules in ?²(G) as double cosets which are also finite unions of left cosets.     

On random variational inclusions with random fuzzy mappings and random relaxed cocoercive mappings

In this paper, we introduce and study the random variational inclusions with random fuzzy and random relaxed cocoercive mappings. We define an iterative algorithm for finding the approximate solutions of this class of variational inclusions and establish the convergence of iterative sequences generated by proposed algorithm. Our results improve and generalize many known corresponding results.     

An iterative algorithm based on -proximal mappings for a system of generalized implicit variational inclusions in Banach spaces

In this paper, we give the notion of M-proximal mapping, an extension of P-proximal mapping given in [X.P. Ding, F.Q. Xia, A new class of completely generalized quasi-variational inclusions in Banach spaces, J. Comput. Appl. Math. 147 (2002) 369–383], for a nonconvex, proper, lower semicontinuous and subdifferentiable functional on Banach space and prove its existence and Lipschitz continuity. Further, we consider a system of generalized implicit variational inclusions in Banach spaces and show its equivalence with a system of implicit Wiener–Hopf equations using the concept of M-proximal mappings. Using this equivalence, we propose a new iterative algorithm for the system of generalized implicit variational inclusions. Furthermore, we prove the existence of solution of the system of generalized implicit variational inclusions and discuss the convergence and stability analysis of the iterative algorithm.     

广义非线性含参隐拟变分包含解的灵敏性分析

引入并研究了一类新的广义非线性含参隐拟变分包含,用预解算子方法证明了其解的存在性,并在H ilbert空间中分析了这类变分包含解的灵敏性,这些结果改进和推广了近期文献的相关结果.