Related papers: On Bi-Lipschitz classification of fractal cubes po…

In this paper we determine a complete list of rational surface singularities which have metrically conical bilipschitz type of its inner metric. We achieve this by using the thick-thin decomposition of Birbrair, Neumann and Pichon.

We show that the three-qubit entanglement classes: (0) Null, (1) Separable A-B-C, (2a) Biseparable A-BC, (2b) Biseparable B-CA, (2c) Biseparable C-AB, (3) W and (4) GHZ correspond respectively to ranks 0, 1, 2a, 2b, 2c, 3 and 4 of a…

We show that for every $k\ge 3$ there exist complex algebraic cones of dimension $k$ with isolated singularities, which are bi-Lipschitz and semi-algebraically equivalent but they have different degrees. We also prove that homeomorphic…

Recent investigations on the bifurcations in switching circuits have shown that many atypical bifurcations can occur in piecewise smooth maps which can not be classified among the generic cases like saddle-node, pitchfork or Hopf…

There are six orientable, compact, flat 3-manifolds that can occur as cusp cross-sections of hyperbolic 4-manifolds. This paper provides criteria for exactly when a given commensurability class of arithmetic hyperbolic 4-manifolds contains…

A rigid isotopy of real algebraic curves of a certain class is a path in the space of curves of this class. The paper's study completes the rigid isotopic classification of nonsingular real algebraic curves of bidegree (4,3) on a…

We give a complete enumeration of all 2-neighborly 0/1-polytopes of dimension 7. There are 13 959 358 918 different 0/1-equivalence classes of such polytopes. They form 5 850 402 014 combinatorial classes and 1 274 089 different f-vectors.…

We classify, up to automorphisms, the elliptic fibrations on the singular K3 surface $X$ whose transcendental lattice is isometric to $\langle 6\rangle\oplus \langle 2\rangle$.

A famous configuration of 27 lines on a non-singular cubic surface in $\mathbb P^3$ contains remarkable subconfigurations, and in particular the ones formed by six pairwise disjoint lines. We study such six-line configurations in the case…

We list the elliptic curves defined over $Q(\sqrt 5)$ with good reduction away from 2. There are 368 isomorphism classes. We give a global minimal model for each class.

We define and study a class of fractal dendrites called triangular labyrinth fractals. For the construction, we use triangular labyrinth patterns systems that consist of two triangular patterns: a white and a yellow one. Correspondingly, we…

In this paper, we present complete classifications, up to isomorphism, of all two-element dimonoids, all commutative three-element dimonoids, and all abelian three-element dimonoids. We show that, up to isomorphism, there exist exactly 8…

In this paper, an effort is made to classify which prime character degree graphs having eight vertices occur for some finite solvable group. To approach this, we compile known results and constructions from the literature which are used to…

We obtain the bifurcation of some special curves on generic 1-parameter families of surfaces in the Minkowski 3-space. The curves treated here are the locus of points where the induced pseudo metric is degenerate, the discriminant of the…

We classify del Pezzo surfaces with 1/3(1,1) points in 29 qG-deformation families grouped into six unprojection cascades (this overlaps with work of Fujita and Yasutake), we tabulate their biregular invariants, we give good model…

We classify the topological types of surfaces in the 3-dimensional unit sphere that contain both a great and a small circle through each point. In particular, these surfaces are homeomorphic to one of five normal forms and are either the…

For every smooth (irreducible) cubic surface $S$ we give an explicit construction of a representative for each of the 72 equivalence classes of determinantal representations. Equivalence classes (under $\GL_3\times \GL_3$ action by left and…

Let X be a very general complete intersection in complex projective space and we denote by $F_r(X)$ the variety of r-planes in X, for $r\geq 1$. We show that the Picard number of $F_r(X)$ is 1, as soon as $\dim F_r(X)\geq 2$, except when X…

We investigate prime character degree graphs of solvable groups that have six vertices. There are one hundred twelve non-isomorphic connected graphs with six vertices, of which all except nine are classified in this paper. We also…

Let $A$ be an algebra over a commutative ring $k$. We compute the center of the category of $A$-bimodules. There are six isomorphic descriptions: the center equals the weak center, and can be described as categories of noncommutative…