Weak finitely regular relations and applications

In this note, we introduce the concepts of weak finitely regular relations and weak hypercontinuous posets. It is proved that when a binary relation $$\rho :X/\rightarrow Y$$ satisfies a certain condition, $$\rho $$ is weak finitely regular if and only if $$(\varphi _{\rho }(X,Y),\subseteq )$$ is a weak hypercontinuous poset. For a poset P, we get that the relation $$\not \le $$ on P is weak finitely regular if and only if P is weak hypercontinuous.     

q-Deformed character theory for infinite-dimensional symplectic and orthogonal groups

Selecta Mathematica - We show that every finitely generated conical refinement monoid can be represented as the monoid $$\mathcal V (R)$$ of isomorphism classes of finitely generated projective...     

Convergence Towards the End Space for Random Walks on Schreier Graphs

Journal of Theoretical Probability - We consider a transitive action of a finitely generated group G and the Schreier graph $$\varGamma $$ defined by this action for some fixed generating set. For...     

Dedekind $$\sigma $$ σ -complete $$\ell $$ ℓ -groups and Riesz spaces as varieties

Positivity - We prove that the category of Dedekind $$\sigma $$ -complete Riesz spaces is an infinitary variety, and we provide an explicit equational axiomatization. In fact, we show that finitely...     

Some bounds for the annihilators of local cohomology and Ext modules

Czechoslovak Mathematical Journal - Let $$\mathfrak{a}$$ be an ideal of a commutative Noetherian ring R and t be a nonnegative integer. Let M and N be two finitely generated R-modules. In certain...     

Quantum Graphs with Summable Matrix Potentials

Doklady Mathematics - Let $$\mathcal{G}$$ be a metric, finite, noncompact, and connected graph with finitely many edges and vertices. Assume that the length of at least one of the edges is...     

Cayley graphs with few automorphisms

Journal of Algebraic Combinatorics - We show that every finitely generated group G with an element of order at least $$\bigl (5{{\,\mathrm{rank}\,}}(G)\bigr )^{12}$$ admits a locally finite...     

One-cusped congruence subgroups of Bianchi groups

We show that there are only finitely many maximal congruence subgroups of the Bianchi groups such that the quotient by has only one cusp.     

Subgroup separability in residually free groups

We prove that the finitely presentable subgroups of residually free groups are separable and that the subgroups of type are virtual retracts. We describe a uniform solution to the membership problem for finitely presentable subgroups of residually free groups.     

Isometric Embeddings of Subsets of Boundaries of Teichmüller Spaces of Compact Hyperbolic Riemann Surfaces

It is known that every finitely unbranched holomorphic covering π:S→S of a compact Riemann surface S with genus g≥2 induces an isometric embedding Φπ:Teich(S)→Teich(S).By the mutual relations between Strebel rays in Teich(S)and their embeddings in Teich(S),we show that the 1 st-strata space of the augmented Teichmüller space Teich(S)can be embedded in the augmented Teichmüller space Teich(S)isometrically.Furthermore,we show that Φπ induces an isometric embedding from the set Teich(S)B(∞)consisting of Busemann points in the horofunction boundary of Teich(S)into Teich(S)B(∞)with the detour metric.     

Some Finiteness Results for Local Cohomology Modules with Respect to a Pair of Ideals

Mathematical Notes - Suppose that $$R$$ is a commutative Noetherian ring with identity, $$I$$ , $$J$$ are ideals of $$R$$ , and let $$M$$ be a finitely generated $$R$$ -module. Let $$H^i_{I,J}(-)$$...     

Equimorphy in varieties of distributive double p-algebras

Any finitely generated regular variety V of distributive double p-algebras is finitely determined, meaning that for some finite cardinal n(V), any subclass S V of algebras with isomorphic endomorphism monoids has fewer than n(V) pairwise non-isomorphic members. This result follows from our structural characterization of those finitely generated almost regular varieties which are finitely determined. We conjecture that any finitely generated, finitely determined variety of distributive double p-algebras must be almost regular.     

Embedding some Riemann surfaces into $${\mathbb {C}^2}$$ with interpolation

We prove that several types of open Riemann surfaces, including the finitely connected planar domains, embed properly into such that the values on any given discrete sequence can be arbitrarily prescribed. Kutzschebauch supported by Schweizerische Nationalfonds grant 200021-107477/1.     

Periodic maximal surfaces in the Lorentz–Minkowski space $${\mathbb{L}^3}$$

A maximal surface with isolated singularities in a complete flat Lorentzian 3-manifold

Rings of algebraic numbers in infinite extensions of $${\mathbb {Q}}$$ and elliptic curves retaining their rank

We show that elliptic curves whose Mordell–Weil groups are finitely generated over some infinite extensions of , can be used to show the Diophantine undecidability of the rings of integers and bigger rings contained in some infinite extensions of rational numbers.      

A discrete carleson theorem along the primes with a restricted supremum

Mathematische Zeitschrift - Consider the discrete maximal function acting on finitely supported functions on the integers, $$\begin{aligned} \mathcal {C}_\Lambda f(n) := \sup _{\lambda \in \Lambda...     

On hyperelliptic modular curves over function fields

We prove that there are only finitely many modular curves of -elliptic sheaves over which are hyperelliptic. In odd characteristic we give a complete classification of such curves. The author was supported in part by NSF grant DMS-0801208 and Humboldt Research Fellowship.     

Fourth order approximation of harmonic maps from surfaces

Let be a compact Riemannian surface and let be a compact Riemannian manifold, both without boundary, and assume that N is isometrically embedded into some ℝ ^l . We consider a sequence of critical points of the functional with uniformly bounded energy. We show that this sequence converges weakly in and strongly away from finitely many points to a smooth harmonic map. One can perform a blow-up to show that there separate at most finitely many non-trivial harmonic two-spheres at these finitely many points. Finally we prove the so called energy identity for this approximation in the case that ↪ ℝ ^l . Mathematics Subject Classification (2000) 58E20, 35J60, 53C43     

The Critical Value of the Contact Process with Added and Removed Edges

We show that the critical value for the contact process on a vertex-transitive graph with finitely many edges added and/or removed is the same as the critical value for the contact process on . This gives a partial answer to a conjecture of Pemantle and Stacey.