Related papers: Cupping with random sets

We prove that the C*-algebra of a second-countable, \'etale, amenable groupoid is simple if and only if the groupoid is topologically principal and minimal. We also show that if G has totally disconnected unit space, then the associated…

Quantum electrodynamics is considered to be a trivial theory. This is based on a number of evidences, both numerical and analytical. One of the strong indications for triviality of QED is the existence of the Landau pole for the running…

Let $V$ be a smooth cubic surface over a $p$-adic field $k$ with good reduction. Swinnerton-Dyer (1981) proved that $R$-equivalence is trivial on $V(k)$ except perhaps if $V$ is one of three special types--those whose $R$-equivalence he…

Null Hypothesis Statistical Testing is a dominant framework for conducting statistical analysis across the sciences. There remains considerable debate as to whether, and under what circumstances, evidence can be said to be confirmatory of a…

Understanding how singularities behave under small perturbations is a central theme in singularity theory. In this paper we establish sufficient conditions for families of analytic function-germs on a germ of a complex analytic space to…

Let $G$ be a connected graph with minimum degree $\delta(G)$ and vertex-connectivity $\kappa(G)$. The graph $G$ is $k$-connected if $\kappa(G)\geq k$, maximally connected if $\kappa(G) = \delta(G)$, and super-connected (or super-$\kappa$)…

Motivated by situations in which the removal of a zero (a.k.a., an absorbing element) from a semigroup yields a subsemigroup with another zero, sets of quasi-zeros (a.k.a., quasi-absorbing elements) are introduced as well as primitive…

We initiate the study of simple games from the point of view of combinatorial topology. The starting premise is that the losing coalitions of a simple game can be identified with a simplicial complex. Various topological constructions and…

Essential $\aleph_0$-categoricity; i.e., $\aleph_0$-categoricity in some full countable language, is shown to be a robust notion for strongly minimal compact complex manifolds. Characterisations of triviality and essential…

We prove that each of the model structures for ($n$-trivial, saturated) comical sets on the category of marked cubical sets having only faces and degeneracies (without connections) is Quillen equivalent to the corresponding model structure…

We show that for a minimal system $(X,T)$, the set of saturated points along cubes with respect to its maximal $\infty$-step pro-nilfactor $X_\infty$ has a full measure. As an application, it is shown that if a minimal system $(X,T)$ has no…

The Andrews-Curtis conjecture claims that every balanced presentation of the trivial group can be reduced to the standard one by a sequence of ``elementary transformations" which are Nielsen transformations augmented by arbitrary…

Let $V$ be a finite relational vocabulary in which no symbol has arity greater than 2. Let $M$ be countable $V$-structure which is homogeneous, simple and 1-based. The first main result says that if $M$ is, in addition, primitive, then it…

We show that a separable C*-algebra is an inductive limits of projective C*-algebras if and only if it has trivial shape, that is, if it is shape equivalent to the zero C*-algebra. In particular, every contractible C*-algebra is an…

We study the complexity of the classification problem for countable models of set theory (ZFC). We prove that the classification of arbitrary countable models of ZFC is Borel complete, meaning that it is as complex as it can conceivably be.…

Regular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that…

In this paper we prove that the generalized version of the Minimal Resolution Conjecture stated by Mustata holds for certain general sets of points on a smooth cubic surface $X \subset \mathbb{P}^3$. The main tool used is Gorenstein liaison…

We prove that an element of the symplectic Steinberg group is trivial if and only if its image under any maximal localisation homomorphism is trivial.

We discuss the so-called "simplifying assumption" of conditional copulas in a general framework. We introduce several tests of the latter assumption for non- and semiparametric copula models. Some related test procedures based on…

We give a counterexample to a conjecture of D.H. Gottlieb and prove a strengthened version of it. The conjecture says that a map from a finite CW-complex X to an aspherical CW-complex Y with non-zero Euler characteristic can have…