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《Indagationes Mathematicae》2022,33(6):1312-1325
The Central Sets Theorem was introduced by H. Furstenberg and then afterwards several mathematicians have provided various versions and extensions of this theorem. All of these theorems deal with central sets, and its origin from the algebra of Stone–?ech compactification of arbitrary semigroup, say . It can be proved that every closed subsemigroup of is generated by a filter. We will show that, under some restrictions, one can derive the Central Sets Theorem for any closed subsemigroup of . We will derive this theorem using the corresponding filter and its algebra. Later we will also deal with how the notions of largeness along filters are preserved under some well behaved homomorphisms and give some consequences. 相似文献
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The stored energy functional of a homogeneous isotropic elastic body is invariant with respect to translation and rotation
of a reference configuration. One can use Noether's Theorem to derive the conservation laws corresponding to these invariant
transformations. These conservation laws provide an alternative way of formulating the system of equations governing equilibrium
of a homogeneous isotropic body. The resulting system is mathematically identical to the system of equilibrium equations and
constitutive relations, generally, of another material. This implies that each solution of the system of equilibrium equations
gives rise to another solution, which describes the reciprocal deformation and solves the system of equilibrium equations
of another material. In this paper we derive conservation laws and prove the theorem on conjugate solutions for two models
of elastic homogeneous isotropic bodies – the model of a simple material and the model of a material with couple stress (Cosserat
continuum).
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
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The aim of this study is to develop a model for the determination of the superficial velocities in horizontal and slightly inclined oil–water pipe flow conditions by using pressure gradient and mixture density information. In this article an inverse model is suggested for a dispersion of oil in water and of water in oil. This approach permits to select dispersed flow conditions from a set of experimental data, and uses a new hybrid model for the effective viscosity. A set of 310 oil–water experimental data points collected on an experimental set-up of length L = 15 m and diameter D = 8.28 cm at various (slight) orientations is used to validate the inverse method. The comparison between model reconstructions and measured flow velocities show a reasonable agreement. 相似文献
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