Given a set R, hypergraph is R-uniform if the size of every hyperedge belongs to R. A H called covering vertex pair contained in some H. In this note, we show that [3]-uniform on n≥6 vertices contains Berge cycle Cs for any 3≤s≤n. As an application, determine maximum Lagrangian k-uniform Berge-Ct-free hypergraphs and Berge-Pt-free hypergraphs.

We show that a recent spectral flow approach proposed by Berkolaiko–Cox–Marzuola for analyzing the nodal deficiency of partition associated to an eigenfunction can be extended more general partitions. To precise, we work with equipartitions satisfy pair compatible condition. Nodal partitions and minimal are examples such Along way, discuss different approaches Dirichlet-to-Neumann operators: vi...

We present the first nucleobase analog fluorescence resonance energy transfer (FRET)-pair. The pair consists of tC(O), 1,3-diaza-2-oxophenoxazine, as an energy donor and the newly developed tC(nitro), 7-nitro-1,3-diaza-2-oxophenothiazine, as an energy acceptor. The FRET-pair successfully monitors distances covering up to more than one turn of the DNA duplex. Importantly, we show that the rigid ...

There has been a good deal of research on covering arrays over the last 20 years. Most of this work has focused on constructions, applications and generalizations of covering arrays. The main focus of this thesis is a generalization of covering arrays, covering arrays on graphs. The original motivation for this generalization was to improve applications of covering arrays to testing systems and...

in this paper, we develop a capacitated location-covering model considering interval values for demand and service parameters. we also consider flexibility on distance standard for covering demand nodes by the servers. we use the satisfaction degree to represent the constraint of service capacity. the proposed model belongs to the class of mixed integer programming models. our model can be redu...

We point out that there are compact 4-manifolds which do not admit metrics of positive scalar curvature, but nonetheless have finite covering spaces which do carry such metrics. Moreover, passing from a 4-manifold to a covering space sometimes actually changes the sign of the Yamabe invariant. As was first pointed out by Bérard Bergery [1], there exist, in dimensions ≡ 1 or 2 mod 8, n ≥ 9, cert...

In this article we focus on constructing an algorithm that automatizes the generation of LPN solving algorithms from the considered parameters. When searching for an algorithm to solve an LPN instance, we make use of the existing techniques and optimize their use. We formalize an LPN algorithm as a path in a graph G and our algorithm is searching for the optimal paths in this graph. The results...

Spaces with radially symmetric curvature at base point p are shown to be diffeomorphic to space forms. Furthermore, they are either isometric to Rn or Sn under a radially symmetric metric, to RPn with Riemannian universal covering of Sn equipped with a radially symmetric metric, or else have constant curvature outside a metric ball of radius equal to the injectivity

If g(t) is a three-dimensional Ricci flow solution, with sectional curvatures that are O(t) and diameter that is O(t 1 2 ), then the pullback Ricci flow solution on the universal cover approaches a homogeneous expanding soliton.