Related papers: The Extended Exterior Sphere Condition

The transform under study is defined by integration of functions over spheres centered on a sphere. Such transform is of interest due to its applications in analysis and (thermoacoustic) tomography. The range of this transform has been…

Applying the definition of the turnaround radius and the fact that the best agreement with observational data on extragalactic scales is currently provided by general relativity with the cosmological constant we consider the behaviour of…

The (full) extended plus closure was developed as a replacement for tight closure in mixed characteristic rings. Here it is shown by adapting Andr\'{e}'s perfectoid algebra techniques that, for complete local rings that have F-finite…

The Rolling Ball Theorem asserts that given a convex body K in Euclidean space and having a smooth surface bd(K) with all principal curvatures not exceeding c>0 at all boundary points, K necessarily has the property that to each boundary…

For functions of two quaternionic variables that are regular in the sense of Fueter, we establish a result similar in spirit to the Hanges and Tr\`eves theorem. Namely, we show that a ball contained in the boundary of a domain is a…

This paper discusses a more general contractive condition for a class of extended cyclic self-mappings on the union of a finite number of subsets of a metric space which are allowed to have a finite number of successive images in the same…

In [16], a theory of universal extensions in abelian categories is developed; in particular, the notion of Ext-universal object is presented. In the present paper, we show that an Ab3 abelian category which is Ext-small satisfies the Ab4…

We prove a complex polynomial plank covering theorem for not necessarily homogeneous polynomials. As the consequence of this result, we extend the complex plank theorem of Ball to the case of planks that are not necessarily centrally…

Writing the boundary integral equation for an exterior problem of elasticity is subordinate so far to hypotheses on the asymptotical behaviour at infinity of solutions. The sufficient conditions met in the literature are too restrictive and…

Let M be a smooth strictly convex closed surface in space and denote by H the set of points x in the exterior of M such that all the tangent segments from x to M have equal lengths. In this note we prove that if H is either a closed surface…

Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.

We consider the covering of a ball in certain normed spaces by its congruent subsets and show that if the finite number of sets is not greater than the dimensionality of the space, then the centre of the ball either belongs to the interior…

Let $E$ be a vector bundle over a suitable differential manifold $M$ and let $\wedge^p E$ denote $p$-exterior product of $E$. Given sections $\omega_1,\dots,\omega_k$ of $E$ and a section $\eta$ of $\wedge^p E$, we consider the problem if…

We establish spectral rigidity for spherically symmetric manifolds with boundary and interior interfaces determined by discontinuities in the metric under certain conditions. Rather than a single metric, we allow two distinct metrics in…

In this paper, we prove an extension theorem for spheres of square radii in $\mathbb{F}_q^d$, which improves a result obtained by Iosevich and Koh (2010). Our main tool is a new point-hyperplane incidence bound which will be derived via a…

We introduce the class of outerspatial 2-complexes as the natural generalisation of the class of outerplanar graphs to three dimensions. Answering a question of O-joung Kwon, we prove that a locally 2-connected 2-complex is outerspatial if…

In the context of extended Teleparallel gravity theories, we address the issue of junction conditions required to guarantee the correct matching of different regions of spacetime. In the absence of shells/branes, these conditions turn out…

In this paper, we study the non-singular extension problem of horizontal stable fold maps. This problem asks what conditions ensure the existence of a submersion whose restriction to the boundary coincides with a given map, called a…

We give the optimal conditions for the existence of a club consisting of former regular over an inaccessible and a measurable. The foricing construction based on iteration of distributive posets.

In this brief note, we show that there exist smooth 4-manifolds (with nonempty boundary) containing pairs of exotically knotted 2-spheres that remain exotic after one (either external or internal) stabilization. It follows that the ``one is…