A range assignment to the nodes in a wireless ad hoc network induces a topology in which there is an edge between two nodes if and only if both of them are within each other’s transmission range. The critical transmission radius for -connectivity is the smallest such that if all nodes have the transmission radius , the induced topology is -connected. In this paper, we study the asymptotic criti...

In Takemura and Kuriki (1999b) we have established that the tube formula and the Euler characteristic method give identical and valid asymptotic expansion of tail probability of the maximum of Gaussian random field when the random field has finite Karhunen-Loève expansion and the index set has positive critical radius. The purpose of this paper is to show that the positiveness of the critical r...

All known results on covering radius are presented, as well as some new results. There are a number of upper and lower bounds, including asymptotic results, a few exact determinations of covering radius, some extensive relations with other aspects of coding theory through the Reed-Muller codes, and new results on the least covering radius of any linear [II, k] code. There is also a recent resul...

In this paper, we study properties of rank metric codes in general and maximum rank distance (MRD) codes in particular. For codes with the rank metric, we first establish Gilbert and sphere-packing bounds, and then obtain the asymptotic forms of these two bounds and the Singleton bound. Based on the asymptotic bounds, we observe that asymptotically Gilbert-Varsharmov bound is exceeded by MRD co...

We investigate the use of asymptotically null slices combined with stretching or compactification of the radial coordinate for the numerical simulation of asymptotically flat spacetimes. We consider a 1-parameter family of coordinates characterised by the asymptotic relation r ∼ R between the physical radius R and coordinate radius r, and the asymptotic relation K ∼ R for the extrinsic curvatur...

It is nontrivial whether the average size of a ring polymer should become smaller or larger under a topological constraint. Making use of some knot invariants, we numerically evaluate the mean-square radius of gyration for ring polymers having a fixed knot type, where the ring polymers are given by self-avoiding polygons consisting of freely jointed hard cylinders. We obtain plots of the gyrati...

Abstract. Dirichlet density extends global asymptotic density in an additive number system A whose generating series A(x) diverges at its radius of convergence (see [1], p. 50). This note shows that the parallel result holds for a multiplicative number system A, namely if the abcissa of convergence α of the generating series A(x) is finite and A(α) = ∞ then Dirichlet density extends global asym...

We investigate the uplink of a power-controlled multi-user distributed antenna system (DAS) with antennas deployed on a circle. Applying results from random matrix theory, we prove that for such a DAS, the per-user sum rate and the total transmit power both converge as user number and antenna number go to infinity with a constant ratio. The relationship between the asymptotic per-user sum rate ...

Asymptotically locally conical (ALC) metric of exceptional holonomy has an asymptotic circle bundle structure that accommodates the M theory circle in type IIA reduction. Taking Spin(7) metrics of cohomogeneity one as explicit examples, we investigate deformations of ALC metrics, in particular that change the asymptotic S radius related to the type IIA string coupling constant. When the canonic...

We construct a two-parameter family of models for self-collimated, magnetized outflows from accretion disks. As in previous magnetocentrifugal wind solutions, a flow at zero initial poloidal speed leaves the surface of a disk in Kepler rotation about a central star, and is accelerated and redirected toward the pole by rotating, helical magnetic fields which thread the disk. At large distances f...