Adaptive Cartesian mesh methods have demonstrated unique abilities for automated mesh generation and dynamic mesh adaptation to flow solution and moving boundaries. However Navier-Stokes (NS) solvers with Cartesian mesh often produce large fluctuations of surface quantities (pressure, skin friction, and heat flux) at solid boundaries. We show that the Immersed Boundary Method (IBM) with adaptiv...

in this paper, we investigate a problem of finding natural condition to assure the product of two graphs to be hamilton-connected. we present some sufficient and necessary conditions for $gbox h$ being hamilton-connected when $g$ is a hamilton-connected graph and $h$ is a tree or $g$ is a hamiltonian graph and $h$ is $k_2$.

A graph is said to be S-prime if, whenever it is a subgraph of a nontrivial Cartesian product graph, it is a subgraph of one of the factors. A diagonalized Cartesian product is obtained from a Cartesian product graph by connecting two vertices of maximal distance by an additional edge. We show there that a diagonalized product of S-prime graphs is again S-prime. Klavžar et al. [Discr. Math. 244...

In this paper, we design an algorithm that, given a directed graph G and the Cartesian-product decomposition of its underlying undirected graph G̃, produces the directed Cartesian-product decomposition of G in linear time. This is the first time that the linear complexity is achieved for this problem, which has two major consequences. Firstly, it shows that the directed and undirected versions o...

A logic is developed in which function symbols are allowed to represent partial functions. It has the usual rules of logic (in the form of a sequent calculus) except that the substitution rule has to be modi ed. It is developed here in its minimal form, with equality and conjunction, as partial Horn logic . Various kinds of logical theory are equivalent: partial Horn theories, quasi-equational ...

Cartesian routing is a novel packet routing methodology in which a packet's route is determined by the position of the router relative to that of the destination. Cartesian routing di€ers from existing provider-based unicast routing in that routing tables are unnecessary since communications are topologically dependent, thereby potentially reducing router and network overheads. For example, rou...

The notion of a fractional Cartesian product and a subsequent notion of combinatorial dimension appeared first in a harmonic-analytic context in the course of filling ”analytic” gaps between successive (ordinary) Cartesian products of spectral sets [1, 2]. (Detailed accounts of this, and much more, appear in [4].) Combinatorial dimension is an index of interdependence: attached to a subset of a...

Graph bundles generalize the notion of covering graphs and graph products. In [8], authors constructed an algorithm that ÿnds a presentation as a nontrivial Cartesian graph bundle for all graphs that are Cartesian graph bundles over triangle-free simple base. In [21], the unique square property is deÿned and it is shown that any equivalence relation possessing the unique square property determi...