Related papers: Extraction Theorems With Small Extraction Numbers
We prove the conjecture that higher Verlinde categories are geometrically reductive. This is one of the two properties required in order for recent results on algebraic geometry in tensor categories to apply to these categories. We also…
String theory suggests modifications of our spacetime such as extra dimensions and the existence of a mininal length scale. In models with addidional dimensions, the Planck scale can be lowered to values accessible by future colliders.…
By nonstandard analysis, a very short and elementary proof of the Spectral Theorem for unbounded self-adjoint operators is given.
Polynomial series approximations are a central theme in approximation theory due to their utility in an abundance of numerical applications. The two types of series, which are featured most prominently, are Taylor series expansions and…
In this paper we study the right differentiability of a parametric infimum function over a parametric set defined by equality constraints. We present a new theorem with sufficient conditions for the right differentiability with respect to…
We develop a method that we call \emph{omission of intervals}, for establishing topological properties of subsets of the real line based on their combinatorial structure. Using this method, we obtain conceptual proofs of the fundamental…
According to their strength, the tracing properties of a code can be categorized as frameproof, separating, IPP and TA. It is known that if the minimum distance of the code is larger than a certain threshold then the TA property implies the…
Developing data-efficient instance detection models that can handle rare object categories remains a key challenge in computer vision. However, existing research often overlooks data collection strategies and evaluation metrics tailored to…
We state and prove some counting formulas relating to cliques in the distant graphs of projective lines over finite rings. As a preliminary to this, we prove a decomposition theorem for the graphs in terms of the direct-product…
We analyse a class of quantum field theory models illustrating some of the possibilities that have emerged in the general study of the short distance properties of superselection sectors, performed in a previous paper (together with R.…
We establish maximal trees and graphs for the difference of average distance and proximity proving thus the corresponding conjecture posed in [4]. We also establish maximal trees for the difference of average eccentricity and remoteness and…
Fractons and other subdimensional particles are an exotic class of emergent quasi-particle excitations with severely restricted mobility. A wide class of models featuring these quasi-particles have a natural description in the language of…
We introduce the basic elements of the theory of parametrized $\infty$-categories and functors between them. These notions are defined as suitable fibrations of $\infty$-categories and functors between them. We give as many examples as we…
We show connections between a special type of addition formulas and a theorem of Stieltjes and Rogers. We use different techniques to derive the desirable addition formulas. We apply our approach to derive special addition theorems for…
We segment moving objects in videos by ranking spatio-temporal segment proposals according to "moving objectness": how likely they are to contain a moving object. In each video frame, we compute segment proposals using multiple…
Let K be an Abstract Elementary Class. Under the asusmptions that K has a nicely behaved forking-like notion, regular types and existence of some prime models we establish a decomposition theorem for such classes. The decomposition implies…
Objects $T$ whose exponential functor $(-)^T$ admits a right adjoint $(-)_T$ are known under different names. The fact that they exist, yet that the only set that satisfies this in the category of sets is the singleton made Lawvere suggest…
We argue that there exists an excellent `physics case' motivating the search for axions, WIMPs, WISPs and other phenomena testable at low energies. This physics case arises from both experimental and observational evidence as well as the…
Using an elementary argument, we prove new fixed point theorems for classical elliptic complexes. We obtain new results for conformal relations and coisotropic intersections. We obtain theorems for the average intersections of families of…
This is the continuation of the article by the author that proves a broader class of families admitting the theorem of restriction of sections other than Abelian varieties and gives new examples of pseudo-N\'eron models. In this work, we…