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Research on the influence of spontaneous commercial space on the commercial vitality of historical and cultural districts. [PDF]
Sci RepWang R, Shang W, Zhang G.
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Covering convex bodies by translates of convex bodies
Mathematika, 1997A number of known estimates of the number of translates, or lattice translates, of a convex body H required to cover a convex body K are obtained as consequences of two simple results.
C. A. Rogers, Chuanming Zong
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Convex bodies with non‐convex cross‐section bodies
Mathematika, 1999It is shown that the regular n -dimensional simplex has a non-convex cross-section body for all n ≥ 4.
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1988
We shall now exploit the ellipsoid method (the central-cut and the shallow-cut version) described in Chapter 3. In Sections 4.2, 4.3, and 4.4 we study the algorithmic relations between problems (2.1.10),..., (2.1.14), and we will prove that — under certain assumptions — these problems are equivalent with respect to polynomial time solvability.
Martin Grötschel +4 more
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We shall now exploit the ellipsoid method (the central-cut and the shallow-cut version) described in Chapter 3. In Sections 4.2, 4.3, and 4.4 we study the algorithmic relations between problems (2.1.10),..., (2.1.14), and we will prove that — under certain assumptions — these problems are equivalent with respect to polynomial time solvability.
Martin Grötschel +4 more
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A Characterization of Convex Bodies
The American Mathematical Monthly, 1962(1962). A Characterization of Convex Bodies. The American Mathematical Monthly: Vol. 69, No. 1, pp. 25-31.
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Completions of convex families of convex bodies
Mathematical Notes, 2012The paper discusses the existence of a continuous extension of functions that are defined on subsets of ℝ n and whose values are convex bodies in ℝ n . This problem arose in convex geometry in connection with the notion, recently introduced in algebraic geometry, of convex Newton ...
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On the Minimal Convex Shell of a Convex Body
Canadian Mathematical Bulletin, 1993AbstractFor any convex body C in ℝd we introduce the notion of the convex shell and we prove that there exists a unique "minimal" convex shell, extending the notion of the minimal spherical shell of C. Then we prove that a "typical" convex body touches the boundary of its minimal convex shell in precisely d + 2 points.
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