Weak law of large numbers for iterates of random-valued functions

Aequationes mathematicae - Given a probability space $$ (\Omega , {\mathcal {A}}, P) $$ , a complete and separable metric space X with the $$ \sigma $$ -algebra $$ {\mathcal {B}} $$ of all its...     

On toric ideals arising from signed graphs

Journal of Algebraic Combinatorics - A signed graph is a pair $$(G,\tau )$$ of a graph G and its sign $$\tau $$ , where a sign $$\tau $$ is a function from $$\{ (e,v)\mid e\in E(G),v\in V(G), v\in...     

On Finsler manifolds with hyperbolic geodesic flows

Archiv der Mathematik - Let (M, F) be a closed $$C^\infty $$ Finsler manifold and $$\varphi $$ its geodesic flow. In the case that $$\varphi $$ is Anosov, we extend to the Finsler setting...     

Asymptotic Behavior of the Fundamental Solutions for Critical Schrödinger Forms

Journal of Theoretical Probability - Let $$\{X_t\}_{t \ge 0}$$ be a transient $$\alpha $$ -stable process on $${\mathbb {R}}^d$$ and denote by H its generator. We consider the perturbation of the...     

Algebraic entropy of sign-stable mutation loops

Geometriae Dedicata - In the theory of cluster algebras, a mutation loop induces discrete dynamical systems via its actions on the cluster $${\mathcal {A}}$$ - and $${\mathcal {X}}$$ -varieties. In...     

Idempotent Completion of n-Angulated Categories

Applied Categorical Structures - Let $${\mathcal {C}}$$ be an n-angulated category. We prove that its idempotent completion $$\widetilde{{\mathcal {C}}}$$ admits a unique n-angulated structure such...     

The depth of a reflexive polytope

Given arbitrary integers d and r with $$d \ge 4$$ and $$1 \le r \le d + 1$$ , a reflexive polytope $${\mathscr {P}}\subset {\mathbb R}^d$$ of dimension d with $$\mathrm{depth}\,K[{\mathscr {P}}] = r$$ for which its dual polytope $${\mathscr {P}}^\vee $$ is normal will be constructed, where $$K[{\mathscr {P}}]$$ is the toric ring of $${\mathscr {P}}$$ .     

The Lawson number of a semitopological semilattice

Semigroup Forum - For a Hausdorff topologized semilattice X its Lawson number $$\bar{\Lambda }(X)$$ is the smallest cardinal $$\kappa $$ such that for any distinct points $$x,y\in X$$ there exists...     

Pro- $$\mathcal {C}$$ C congruence properties for groups of rooted tree automorphisms

We propose a generalisation of the congruence subgroup problem for groups acting on rooted trees. Instead of only comparing the profinite completion to that given by level stabilizers, we also compare pro- $$\mathcal {C}$$ completions of the group, where $$\mathcal {C}$$ is a pseudo-variety of finite groups. A group acting on a rooted, locally finite tree has the $$\mathcal {C}$$ -congruence subgroup property ( $$\mathcal {C}$$ -CSP) if its pro- $$\mathcal {C}$$ completion coincides with the completion with respect to level stabilizers. We give a sufficient condition for a weakly regular branch group to have the $$\mathcal {C}$$ -CSP. In the case where $$\mathcal {C}$$ is also closed under extensions (for instance the class of all finite p-groups for some prime p), our sufficient condition is also necessary. We apply the criterion to show that the Basilica group and the GGS-groups with constant defining vector (odd prime relatives of the Basilica group) have the p-CSP.     

Weighted Triangle-free 2-matching Problem with Edge-disjoint Forbidden Triangles

Mathematical Programming - The weighted $${\mathcal {T}}$$ -free 2-matching problem is the following problem: given an undirected graph G, a weight function on its edge set, and a set $${\mathcal...     

Quaternion lattices and quaternion fields

Archiv der Mathematik - Let $$Q_8$$ be the quaternion group of order 8 and $${\chi }$$ its faithful irreducible character. Then $${\chi }$$ can be realized over certain imaginary quadratic number...     

Algebraic invariants of weighted oriented graphs

Journal of Algebraic Combinatorics - Let $$\mathcal {D}$$ be a weighted oriented graph and let $$I(\mathcal {D})$$ be its edge ideal in a polynomial ring R. We give the formula of...     

Comparing symbolic powers of edge ideals of weighted oriented graphs

Journal of Algebraic Combinatorics - Let D be a weighted oriented graph and I(D) be its edge ideal. If D contains an induced odd cycle of length $$2n+1$$ , under certain condition, we show that $$...     

Steklov convexification and a trajectory method for global optimization of multivariate quartic polynomials

Mathematical Programming - The Steklov function $$\mu _f(\cdot ,t)$$ is defined to average a continuous function f at each point of its domain by using a window of size given by $$t>0$$ . It...     

Endomorphism of Abelian Groups as Modules over Their Endomorphism Rings

Mathematical Notes - For an Abelian group $$A$$ , viewed as a module over its endomorphism ring $$E(A)$$ , the near-ring $$\mathcal{M}_{E(A)}(A)$$ of homogeneous mappings is defined as the set of...     

Completely Decomposable Quotient Divisible Abelian Groups with Isomorphic Endomorphism Semigroups

Mathematical Notes - Let $$\Lambda$$ be a class of Abelian groups. A group $$A\in\Lambda$$ is said to be determined by its endomorphism semigroup $$E^\star(A)$$ in the class $$\Lambda$$ if every...     

Partitions of the complete hypergraph $$K_6^3$$ and a determinant-like function

Journal of Algebraic Combinatorics - In this paper, we introduce a determinant-like map $$\mathrm{det}^{S^3}$$ and study some of its properties. For this, we define a graded vector space $$\Lambda...     

A remark on the field of moduli of Riemann surfaces

Archiv der Mathematik - Let S be a closed Riemann surface of genus $$g\ge 2$$ and let $$\mathrm{Aut}(S)$$ be its group of conformal automorphisms. It is well known that if either: (i)...     

On the arithmetic mean of the size of cross-union families

Acta Mathematica Hungarica - Let $$n > k > 1$$ be integers, $$[n] = \{1, \ldots, n\}$$ the standard $$n$$ -element set and $${[n]\choose k}$$ the collection of all its $$k$$ -subsets....