We propose a type of admissible-region analysis for track initiation in multisatellite problems when angles are the primary observable. For a specified rectangular partition in the space of orbital elements, we present explicit upper and lower bounds, and other constraints, for the values of range and range rate that will lead to initial orbit hypotheses (data association hypotheses) associated...

A k-partition Π = {S1,S2, . . . ,Sk} of V (G) is resolving if for every two distinct vertices u and v of a connected graph G, there is a set Si in Π so that the minimum distance between u and a vertex of Si is different from the minimum distance between v and a vertex of Si. A resolving partition Π is said to be connected if each subgraph < Si > induced by Si (1 ≤ i ≤ k) is connected in G. In t...

A Roman dominating function (RDF) on a digraph $D$ is a function $f: V(D)rightarrow {0,1,2}$ satisfying the condition that every vertex $v$ with $f(v)=0$ has an in-neighbor $u$ with $f(u)=2$. The weight of an RDF $f$ is the value $sum_{vin V(D)}f(v)$. The Roman domination number of a digraph $D$ is the minimum weight of an RDF on $D$. A set ${f_1,f_2,dots,f_d}$ of Roman dominating functions on ...

The partition function Q(n), which denotes the number of partitions of a positive integer n into distinct parts, has been the subject of a dozen papers. In this paper, we study this kind of partition with the additional constraint that the parts are bounded by a fixed integer. We denote the number of partitions of an integer n into distinct parts, each ≤ k, by Qk(n). We find a sharp upper bound...

We consider a natural generalization of the Partial Vertex Cover problem. Here an instance consists of a graph G = (V,E), a cost function c : V → Z, a partition P1, . . . , Pr of the edge set E, and a parameter ki for each partition Pi. The goal is to find a minimum cost set of vertices which cover at least ki edges from the partition Pi. We call this the Partition-VC problem. In this paper, we...

Studies have shown that random testing can be an effective testing strategy. One of tbe goals of testing is to estimate the reliability of tbe program from tbe test outcomes. In tbis paper we extend tbe Tbayer-Lipow-Nelson reliability model to account for tbe cost of errors. Also we compare random with partition testing by looking at upper confidence bounds for the cost weighted performance of ...

It was shown by V. Bergelson that any set B ⊆ N with positive upper multiplicative density contains nicely intertwined arithmetic and geometric progressions: For each k ∈ N there exist a, b, d ∈ N such that ̆ b(a + id) : i, j ∈ {1, 2, . . . , k} ̄ ⊆ B. In particular one cell of each finite partition of N contains such configurations. We prove a Hales-Jewett type extension of this partition theorem.

A systematic procedure is presented for connecting short to long scales in LGT. Approximate decimations are used which can provide both upper and lower bounds on the partition function. Its exact value is then obtained by interpolation between the bounds. By iterating the procedure representations of the partition function as well as other physical quantities can be obtained on progressively co...

We outline the steps in a derivation of the statement that the SU(2) gauge theory is in a confining phase for all values of the coupling, 0 < β < ∞, defined at lattice spacing a. The approach employed is to obtain both upper and lower bounds for the partition function and the ‘twisted’ partition function in terms of approximate decimation transformations. The behavior of the exact quantities is...