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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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Frank Aurzada Alexander Iksanov Matthias Meiners 《Mathematische Nachrichten》2015,288(17-18):1921-1938
For a Lévy process on the real line, we provide complete criteria for the finiteness of exponential moments of the first passage time into the interval , the sojourn time in the interval , and the last exit time from . Moreover, whenever these quantities are finite, we derive their respective asymptotic behavior as . 相似文献
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A Trigger of Coupled Singularities 总被引:3,自引:0,他引:3
By using example of nonlinear dynamics of a pair of coupled gears, the phenomenon of appearance and disappearance of a trigger of coupled singularities and homoclinic orbits in the form of number eight in the phase portrait in the phase plane is investigated. That phenomenon is an accompanying phenomenon of loss of stability of the local unique equilibrium position. For a generalized case under certain conditions, a theorem of the appearance of a trigger of coupled singularities in a nonlinear dynamical conservative system, the first derivative of the system potential energy which is a product of two periodic functions with different periods, and one bifurcation parameter, which is the cause for the appearance of new roots of these two functions, is defined. 相似文献