Let be an ideal of over a -finite measure space and let be the Köthe dual of with . Let be a real Banach space, and the topological dual of . Let be a subspace of the space of equivalence classes of strongly measurable functions and consisting of all those for which the scalar function belongs to . For a subset of for which the set is -bounded the following statement is equivalent to conditional -compactness: the set is conditionally -compact and is a conditionally weakly compact subset of for each , with . Applications to Orlicz-Bochner spaces are given.
Let
be a real Banach space and let E be an ideal of L0 over a -finite measure space (, , ). Let (X) be the space of all strongly -measurable functions f: X such that the scalar function
, defined by
, belongs to E. The paper deals with strong topologies on E(X). In particular, the strong topology
the order continuous dual of E(X)) is examined. We generalize earlier results of [PC] and [FPS] concerning the strong topologies. 相似文献
We construct a generalization of the Conley index for flows. The new index preserves information which in the classical case is lost in the process of collapsing the exit set to a point. The new index has most of the properties of the classical index. As examples, we study a flow with a knotted orbit in , and the problem of continuing two periodic orbits which are not homotopic as loops.
The aim of this article was to show the effects of an electron radiation dose and presence of a compatibilizer on the oxidation of composites made of blends of low-density polyethylene (LDPE), high-density polyethylene (HDPE), polypropylene (PP), polystyrene (PS), and poly(ethylene terephthalate) (PET) as well as of blends of LDPE, HDPE, and PP. As the compatibilizers, the styrene-ethylene/butylene-styrene elastomer grafted with maleic anhydride (SEBS-g-MA) and trimethylol propane trimethylacrylate (TMPTA) were used; they were added in the amounts of 5, 10, and 15 wt% and 1, 2, and 3 wt%, respectively. The oxidation of the surface layer (SL) was investigated by the X-ray photoelectron spectroscopy (XPS) and Fourier transform infrared spectroscopy (FTIR). It was found that the extent of the composite oxidation increased with the increasing dose of the electron radiation. The addition of the compatibilizers enhanced the oxidation of the SL but hindered the oxidation of the bulk of the material. 相似文献
This paper is devoted to the study of a nonlinear evolution eddy current model of the type δtB(H) + △↓× ( △↓ × H) =0 subject to homogeneous Dirichlet boundary conditions H × v = 0 and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by B(H). We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of B(H). 相似文献
Mathematical assessment of homogenisation progress of the granular material mixing process is presented. The mixing process
was realised using a vessel in the form of two partly penetrating horizontal cylinders equipped with two multi-ribbon agitators.
The experimental system consisted of three sets of particles of different colour. Random states of the mixed granular material
were characterised by the sampling procedure at different moments of the mixing process. Informational entropy as well as
the flow of quantum of information were applied to describe the progress of the homogenisation process. Analysis of this process
was based on experimental investigations in the form of informational entropy patterns and described by means of the average
informational entropy or the quantum of information.
Presented at the 34th International Conference of the Slovak Society of Chemical Engineering, Tatranské Matliare, 21–25 May
2007. 相似文献
Summary. We prove an abstract convergence estimate for the Algebraic Multigrid Method with prolongator defined by a disaggregation
followed by a smoothing. The method input is the problem matrix and a matrix of the zero energy modes of the same problem
but with natural boundary conditions. The construction is described in the case of a general elliptic system. The condition
number bound increases only as a polynomial of the number of levels, and requires only a uniform weak approximation property
for the aggregation operators. This property can be a-priori verified computationally once the aggregates are known. For illustration,
it is also verified here for a uniformly elliptic diffusion equations discretized by linear conforming quasiuniform finite
elements. Only very weak and natural assumptions on the hierarchy of aggregates are needed.
Received March 1, 1998 / Revised version received January 28, 2000 / Published online: December 19, 2000 相似文献