Related papers: Three-dimensional terminal toric flips
We take a categorical approach to describe ternary derivations and ternary automorphisms of triangular algebras. New classes of automorphisms and derivations of triangular algebras are also introduced and studied.
We study some topological properties of attractors.
We give a characterization of all complete smooth toric varieties whose rational homotopy is of elliptic type. All such toric varieties of complex dimension not more than three are explicitly described.
The paper describes and classifies hexagonal circular 3-webs on unit sphere such that the polar points of the web circles lie on a twisted cubic, thus completing classification of hexagonal circular 3-webs with algebraic polar curves of…
The paper continues a series of publications devoted to the 3D nonlinear localized coherent structures on the surface of vertically falling liquid films. The work is primarily focussed on experimental investigations. We study: (i)…
Two-, three- and four-dimensional representations of Penrose tilings of the plane are described. The vertices that occur in these representations lie on lattices. Symmetries and methods of visualizing these representations are discussed.…
Those maps of a closed surface to the three-dimensional torus that are homotopic to embeddings are characterized. Particular attention is paid to the somewhat intricate case when the surface is nonorientable.
We consider the dynamics of light rays in triangle tilings where triangles are transparent and adjacent triangles have equal but opposite indices of refraction. We find that the behavior of a trajectory on a triangle tiling is described by…
We study toric G-solid Fano threefolds that have at most terminal singularities, where G is an algebraic subgroup of the normalizer of a maximal torus in their automorphism groups.
We prove the existence of flips in dimension n, contingent on the termination of real flips in dimension n-1.
Topological insulators in three dimensions are nonmagnetic insulators that possess metallic surface states as a consequence of the nontrivial topology of electronic wavefunctions in the bulk of the material. They are the first known…
A \textit{domino} is a $2\times 1\times 1$ parallelepiped formed by the union of two unit cubes and a \textit{slab} is a $2\times 2\times 1$ parallelepiped formed by the union of four unit cubes. We are interested in tiling regions formed…
In this paper we study the (equivariant) topological types of a class of 3-dimensional closed manifolds (i.e., 3-dimensional small covers), each of which admits a locally standard $(\mathbb{Z}_2)^3$-action such that its orbit space is a…
The toric surfaces for octonions and related objects are discussed.
In this paper, we consider domino tilings of regions of the form $\mathcal{D} \times [0,n]$, where $\mathcal{D}$ is a simply connected planar region and $n \in \mathbb{N}$. It turns out that, in nontrivial examples, the set of such tilings…
The relation between fracture surface morphology and the three-dimensional structure of crack fronts is investigated through direct observation of brittle cracks in gels. A key notion in this investigation is the discontinuity of the crack…
We construct relatively bounded toroidal and toric models of relatively bounded fibrations over curves.
We obtain upper bounds on the number of singular points of factorial terminal Fano threefolds.
A three-dimensional (3D) nodal-loop semimetal phase is exploited to engineer a number of intriguing phases featuring different peculiar topological surface states. In particular, by introducing various two-dimensional gap terms to a 3D…
In linear transport theory, three-dimensional equations reduce to one-dimensional equations by means of rotated reference frames. In this paper, we illustrate how the technique works and three-dimensional transport theories are obtained.