George Voronoi (1908, 1909) introduced two important reduction methods for positive quadratic forms: the reduction with perfect forms, and the reduction with Ltype domains, often called domains of Delaunay type. The first method is important in studies of dense lattice packings of spheres. The second method provides the key tools for finding the least dense lattice coverings with equal spheres ...

Until recently, the solution to the Kelvin problem of nding a partition of R 3 into equal-volume cells with the least surface area was believed to be tessellation by the truncated octahe-dron. In 1994, D. Weaire and R. Phelan described a partition that outperformed the truncated octahedron partition in this respect. In this paper, we show that the eeective normalized moment of inertia (NMI) of ...

SUMMARY A variable partition duplex scheme on packet reservation multiple access protocol (VPD-PRMA) is analyzed in this paper. We assume a four-state speech model for a conversational pair and successfully obtain performance measures by approximate Markovian analysis. Analytical results show that they quite fit simulation results; and VPD-PRMA can get higher statistical multiplexing gain than ...

We study the probability that two or more agents can attain common knowledge of nontrivial events when the size of the state space grows large. We adopt the standard epistemic model where the knowledge of an agent is represented by a partition of the state space. Each agent is endowed with a partition generated by a random scheme consistent with his cognitive capacity. Assuming that agents’ par...

The fundamental concept in the theory of fuzzy transform (F-transform) is that of fuzzy partition. The original definition assumes that each two fuzzy subsets overlap in such a way that sum of membership degrees in each point is equal to 1. However, this condition can be generalized to obtain a denser fuzzy partition that leads to improvement of approximation properties of Ftransform. However, ...

We construct curve counting invariants for a Calabi-Yau threefold Y equipped with a dominant birational morphism π : Y → X. Our invariants generalize the stable pair invariants of Pandharipande and Thomas which occur for the case when π : Y → Y is the identity. Our main result is a PT/DT-type formula relating the partition function of our invariants to the Donaldson-Thomas partition function in...

This paper focuses on updating a client’s beliefs about an event based on information about the different probabilities which various experts assess for that event. A substantial literature solves this problem when all experts assess their probabilities over the same partitioning of the possible outcomes of an event. But different experts often think about the same problem in quite different wa...

To enhance the utilization of the traffic channels of a network (instead of allocating radio channel to an individual user), a channel or a group of channels are allocated to a user group. The idea behind this is the statistical distribution of traffic arrival rates and the service time for an individual user or a group of users. In this paper, we derive the blocking probability and throughput ...

The problem of partitioning space into equal-volume cells, using the least interface area, was considered in 1887 by Sir William Thomson, Lord Kelvin [Kel]. His proposed solution yields a foam with cells of a single shape, tiling space by the translations of the body-centered cubic lattice. In 1993, Denis Weaire and Robert Phelan [WP] proposed a new equal-volume foam with two different cell sha...

The comparison of partition and random sampling methods for software testing has received considerable attention in the literature. A standard criterion for comparisons between random and partition testing based on their expected efficacy in program debugging is the probability of detecting at least one failure causing input in the program’s domain. We investigate the relative effectiveness of ...