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Given a metric continuum X, we consider the following hyperspaces of X  : 2X2X, Cn(X)Cn(X) and Fn(X)Fn(X) (n∈NnN). Let F1(X)={{x}:x∈X}F1(X)={{x}:xX}. A hyperspace K(X)K(X) of X   is said to be rigid provided that for every homeomorphism h:K(X)→K(X)h:K(X)K(X) we have that h(F1(X))=F1(X)h(F1(X))=F1(X). In this paper we study under which conditions a continuum X   has a rigid hyperspace Fn(X)Fn(X).  相似文献   

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Simple inequalities for some integrals involving the modified Bessel functions Iν(x)Iν(x) and Kν(x)Kν(x) are established. We also obtain a monotonicity result for Kν(x)Kν(x) and a new lower bound, that involves gamma functions, for K0(x)K0(x).  相似文献   

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For almost all x>1x>1, (xn)(xn)(n=1,2,…)(n=1,2,) is equidistributed modulo 1, a classical result. What can be said on the exceptional set? It has Hausdorff dimension one. Much more: given an (bn)(bn) in [0,1[[0,1[ and ε>0ε>0, the x  -set such that |xn−bn|<ε|xnbn|<ε modulo 1 for n   large enough has dimension 1. However, its intersection with an interval [1,X][1,X] has a dimension <1, depending on ε and X. Some results are given and a question is proposed.  相似文献   

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Let K   be a hypergroup with a Haar measure. The purpose of the present paper is to initiate a systematic approach to the study of the class of invariant complemented subspaces of L(K)L(K) and C0(K)C0(K), the class of left translation invariant w?w?-subalgebras of L(K)L(K) and finally the class of non-zero left translation invariant C?C?-subalgebras of C0(K)C0(K) in the hypergroup context with the goal of finding some relations between these function spaces. Among other results, we construct two correspondences: one, between closed Weil subhypergroups and certain left translation invariant w?w?-subalgebras of L(K)L(K), and another, between compact subhypergroups and a specific subclass of the class of left translation invariant C?C?-subalgebras of C0(K)C0(K). By the help of these two characterizations, we extract some results about invariant complemented subspaces of L(K)L(K) and C0(K)C0(K).  相似文献   

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In this work, we are interested in the small time global null controllability for the viscous Burgers' equation ytyxx+yyx=u(t)ytyxx+yyx=u(t) on the line segment [0,1][0,1]. The right-hand side is a scalar control playing a role similar to that of a pressure. We set y(t,1)=0y(t,1)=0 and restrict ourselves to using only two controls (namely the interior one u(t)u(t) and the boundary one y(t,0)y(t,0)). In this setting, we show that small time global null controllability still holds by taking advantage of both hyperbolic and parabolic behaviors of our system. We use the Cole–Hopf transform and Fourier series to derive precise estimates for the creation and the dissipation of a boundary layer.  相似文献   

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