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An outer-totalistic cellular automaton is a generalization of the totalistic cellular automaton. Totalistic rules are a proper superset of outer-totalistic rules. In ...

Bubbles can meet only at angles of 120 degrees (for three bubbles) and cos^(-1)(-1/3) approx 109 degrees28^'16^('') (for four bubbles), where cos^(-1)(-1/3) is the ...

In its original form, the Poincaré conjecture states that every simply connected closed three-manifold is homeomorphic to the three-sphere (in a topologist's sense) S^3, ...

Dirac (1952) proved that if the minimum vertex degree delta(G)>=n/2 for a graph G on n>=3 nodes, then G contains a Hamiltonian cycle (Bollobás 1978, Komlós et al. 1996). In ...

Let a!=b, A, and B denote positive integers satisfying (a,b)=1 (A,B)=1, (i.e., both pairs are relatively prime), and suppose every prime p=B (mod A) with (p,2ab)=1 is ...

A quasi-regular graph is a graph such that degree of every vertex is the same delta except for a single vertex whose degree is Delta=delta+1 (Bozóki et al. 2020). ...

A regular skew polyhedron is a polyhedron whose faces and vertex figures are regular skew polygons. There are only three regular skew polyhedra in Euclidean three-space ...

The term "rhombicosidodecahedron" is most commonly used (e.g., Wenninger 1989, p. 28; Maeder 1997. Model 27) to refer to the 62-faced Archimedean solid with faces ...

The term "rhombicuboctahedron" is most commonly used (e.g., Wenninger 1989, p. 27; Maeder 1997) to refer to the 26-faced Archimedean solid with faces 8{3}+18{4}. Cundy and ...

A set of 15 open problems on Schrödinger operators proposed by mathematical physicist Barry Simon (2000). This set of problems follows up a 1984 list of open problems in ...