Related papers: Injective hulls of odd cycles
We investigate the combinatorics and geometry of permutation polytopes associated to cyclic permutation groups, i.e., the convex hulls of cyclic groups of permutation matrices. We give formulas for their dimension and vertex degree. In the…
The convex hulls of face-vertex incident vectors of 3-face-colorable convex polytopes are computed. It is found that every such convex hull is a $d$-polytope with $d+2$ or $d+3$ vertices. Utilizing Gale transform and Gale diagram, we…
In this article we survey recent results of joint work with Lutz Hille on exceptional sequences of invertible sheaves on rational surfaces and give examples.
As the dual notion of projective modules over trusses, injective modules over trusses are introduced. The Schanuel Lemmas on projective and injective modules over trusses are exhibited in this paper.
In this note a general result is proved that can be used to evaluate exactly a class of highly oscillatory integrals.
A new approach for the supercavitating hull optimization was proposed, which combines the CFD simulation and analytical methods. The high-speed penetration into water at the velocity 1 km/s was considered with the fixed body mass and…
We construct infinitely many complete, immersed self-shrinkers with rotational symmetry for each of the following topological types: the sphere, the plane, the cylinder, and the torus.
Irreducible cyclic codes are an interesting type of codes and have applications in space communications. They have been studied for decades and a lot of progress has been made. The objectives of this paper are to survey and extend earlier…
We introduce the tautological rings of moduli stacks of twisted curves and establish some basic properties.
Christodoulou and Rovelli have remarked on the large interiors possessed by static black holes. We amplify their remarks, and extend them to the spinning case.
We study the convex hull of $SO(n)$, thought of as the set of $n\times n$ orthogonal matrices with unit determinant, from the point of view of semidefinite programming. We show that the convex hull of $SO(n)$ is doubly spectrahedral, i.e.…
Manifolds all of whose geodesics are closed have been studied a lot, but there are only few examples known. The situation is different if one allows in addition for orbifold singularities. We show, nevertheless, that the abundance of new…
The relevant physics for the possible formation of black holes in the LHC is discussed.
Some properties of non-orientable 3-manifolds are shown. The semi-group of cobordism of immersions of surfaces in such manifolds is computed and proven actually to be a group. Explicit invariants are provided.
We introduce an invariant linked to some foundational questions in geometric measure theory and provide bounds on this invariant by decomposing an arbitrary cycle into uniformly rectifiable pieces. Our invariant measures the difficulty of…
Number Decision Diagrams (NDD) provide a natural finite symbolic representation for regular set of integer vectors encoded as strings of digit vectors (least or most significant digit first). The convex hull of the set of vectors…
We study the interior of distorted static axisymmetric black holes. We obtain a general interior solution and study its asymptotics both near the horizon and singularity. As a special example, we apply the obtained results to the case of…
Injectives in several classes of structures associated with logic are characterized. Among the classes considered are residuated lattices, MTL-algebras, IMTL-algebras, BL-algebras, NM-algebras and bounded hoops.
We describe and to some extent characterize a new family of K\"ahler spin manifolds admitting non-trivial imaginary K\"ahlerian Killing spinors.
We present a characterization, in terms of projective biduality, for the hypersurfaces appearing in the boundary of the convex hull of a compact real algebraic variety.