For any k ∈ N, the k−distance graph DG has the same vertex set of G, and two vertices of DG are adjacent if they are exactly distance k apart in the original graph G. In this paper, we consider the connectivity of DG and state the conditions for graph G and integer k such that the graph DG is connected.

In this paper we obtain the Cartier duality for k-schemes of commutative monoids functorially without providing the vector spaces of functions with a topology (as in [DGr, Exposé VIIB by P. Gabriel, 2.2.1]), generalizing a result for finite commutative algebraic groups by M. Demazure & P. Gabriel ([DG, II, §1, 2.10]). All functors we consider are functors defined over the category of commutativ...

Given a smooth projective toric variety X, we construct an A∞ category of Lagrangians with boundary on a level set of the Landau-Ginzburg mirror of X. We prove that this category is quasi-equivalent to the DG category of line bundles on X.

in this paper, we use petrov-galerkin elements such as continuous and discontinuous lagrange-type k-0 elements and hermite-type 3-1 elements to find an approximate solution for linear fredholm integro-differential equations on $[0,1]$. also we show the efficiency of this method by some numerical examples

This work presents a computational model for discontinuous fibre composite manufacturing process. The alignment mechanism of this novel process, called the High Performance Discontinuous Fibre (H...

The embedded discontinuous Galerkin methods are obtained from hybridizable discontinuous Galerkin methods by a simple change of the space of the hybrid unknown. In this paper, we consider embedded methods for second-order elliptic problems obtained from hybridizable discontinuous methods by changing the space of the hybrid unknown from discontinuous to continuous functions. This change results ...

The dependence of the grain boundary character distribution for a Cu-4 at. % Ti polycrystal alloy (average grain size: 100 µm) on the nucleation of cellular discontinuous precipitates was systematically investigated. In an alloy over-aged at 723 K, cellular discontinuous precipitates consisted of a terminal Cu solid solution and a stable β-Cu₄Ti lamellae nucleated at grain boundaries. Electron ...

This paper is a short essay on discontinuous Galerkin methods intended for a very wide audience.We present the discontinuous Galerkin methods and describe and discuss their main features. Since the methods use completely discontinuous approximations, they produce mass matrices that are block-diagonal. This renders the methods highly parallelizable when applied to hyperbolic problems. Another co...