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Computational Analysis of the Energetic Stability of High-Entropy Structures of a Prototypical Lanthanide-Based Metal-Organic Framework. [PDF]

J Phys Chem C Nanomater Interfaces
Kumar SKA, Sava Gallis DF, Sholl DS.
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Regular Convex Bodies

Journal of the London Mathematical Society, 1994
The authors consider two operations, \(\square\) and \(\diamondsuit\), on the class of convex bodies. The first one is product (or direct sum) with Euclidean metric (compare the reviewer's paper in Glasnik Mat. 27(47), 145-158 (1992)). The second is defined by the formula: \(A\diamondsuit B=\text{conv}(A\times \{b\}\cup \{a\}\times B)\), where \(a ...
Farran, H. R., Robertson, S. A.
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Covering convex bodies by translates of convex bodies

Mathematika, 1997
Hadwiger conjectured that the smallest number of translates of a convex body \(K\) required to cover \(K\) is \(2^n\). Here a number of known weaker estimates of the number of required translates, or lattice translates, are obtained as consequences of two simple results.
Rogers, C. A., Zong, C.
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Convex bodies with non‐convex cross‐section bodies

Mathematika, 1999
For \(K\) a convex body in \(\mathbb{R}^d\), the inner \((d-1)\)-quermass at direction \(u\in S^{d-1}\) is defined by \[ m_K(u)= \max_{t\in R}\lambda_{d-1} \bigl( K\cap (u^\perp+ tu)\bigr), \] where \(\lambda_{d-1}\) denotes the \((d-1)\)-dimensional Lebesgue measure. The cross-section body \(CK\) of \(K\), introduced by H.
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Intersections of Convex Bodies

Journal of Mathematical Sciences, 2001
For convex bodies \(K_0,K_1,\dots,K_m \subset\mathbb{R}^n\) and for \(\rho=(r_1, \dots,r_n) \in(\mathbb{R}^n)^m\), let \(\Phi(\rho): =K_0\cap \bigcup^m_{i =1} (K_1+r_i)\) and \(D:=\{\rho: \Phi(\rho) \neq\emptyset\}\). Then \(D\) is convex, and the family \(\{\Phi(\rho)\}_{\rho\in D}\) is concave.
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Convex bodies and convexity on grassmann cones (X): Projection functions of parallel convex bodies

Annali di Matematica Pura ed Applicata, 1965
It is shown that if K is a convex polyhedron or a smooth convex body, then for sufficiently large positive ρ, the body parallel to K at distance ρ has convex projection functions. An example is given of a convex body which does not have this property.
Busemann, H., Shephard, Geoffrey C.
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The cross-section body, plane sections of convex bodies and approximation of convex bodies, I

Geometriae Dedicata, 1996
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Makai, E. jun., Martini, H.
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