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C^1-stably positively expansive maps

100%

Sakai K.

tom Vol. 52, nr 2

197-209

The notion of C^1-stably positively expansive differentiable maps on closed C^infinity manifolds is introduced, and it is proved that a differentiable map f is C^1-stably positively expansive if and only if f is expanding. Furthermore, for such maps, the [epsilon]-time dependent stability is shown. As a result, every expanding map is e-time dependent stable.

Environmental management of concrete and concrete structures - toward sustainable development in construction industry

100%

Sakai K.

Architecture Civil Engineering Environment

2008

tom Vol. 1, no. 3

67-80

Concrete and construction industries have consumed an enormous amount of resources and energy and generated a large amount of wastes. We need to properly manage them from the environmental point of view. In this paper, environmental aspects of concrete and some systems for environmental management in the design of concrete structures are discussed.

Przemysł betonowy i budowlany pochłonęły ogromną ilość zasobów naturalnych i energii wytwarzając wielkie ilości odpadów. Z punktu widzenia środowiska musimy odpowiednio tymi odpadami zarządzać. Artykuł omawia aspekty środowiskowe betonu oraz niektórych systemów zarządzania środowiskiem w procesie projektowania konstrukcji z betonu.

The spaces of closed convex sets in Euclidean spaces with the fell topology

63%

Sakai K. , Yang Z.

2007

tom Vol. 55, no 2

139-143

Let ConvF(Rn) be the space of all non-empty closed convex sets in Euclidean space Rn endowed with the Fell topology. We prove that ConvF(lRn) ≈ Rn x Q for every n > 1 whereas ConvF(R) ≈ R x I.

Open subsets of LF-spaces

63%

Mine K. , Sakai K.

2008

tom Vol. 56, no 1

25-37

Let F = ind lim Fn be an infinite-dimensional LF-space with density dens F = r ( ≥ ℵo) such that some Fn is infinite-dimensional and dens Fn = r. It is proved that every open subset of F is homeomorphic to the product of an l2(r)-manifold and R∞ = ind lim Rn (hence the product of an open subset of l2(r) and R∞). As a consequence, any two open sets in F are homeomorphic if they have the same homotopy type.

Hyperspaces of finite sets in universal spaces for absolute Borel classes

51%

Mine K. , Sakai K. , Yaguchi M.

2005

tom Vol. 53, no 4

409-419

By Fin(X) (resp. Fink (X)), we denote the hyperspace of all non-empty finite subsets of X (resp. consisting of at most k points) with the Vietoris topology. Let ℓ2 (τ) be the Hilbert space with weight τ and ℓf2 (τ) the linear span of the canonical orthonormal basis of ℓ2 (τ). It is shown that if E = ℓf2 (τ) or E is an absorbing set in ℓ2 (τ) for one of the absolute Borel classes aα (τ) and Mα (τ) of weight ≤ τ (α > 0) then Fin(E) and each Fink (E) are homeomorphic to E. More generally, if X is a connected E-manifold then Fin(X) is homeomorphic to E and each Fink (X) is a connected E-manifold.

Prevention of chronic fatigue among health care workers working long-hour shifts

51%

Kogi K. , Sakai K. , Matsumoto S. , Itani T.

tom 29

nr 3-4