119712961
On ideal-function-like functions
The aim of this paper is to extend the considerations of the first and the third authors and others to the setting of Suetuna, i.e. we consider some important sums of multiplicative ideal-functions in relative extensions of number fields. This contains most of the earlier work on those sums related to the divisor and the circle problems.
8028128
Maximal Sets of Integers with Distinct Divisors
A set of positive integers is said to have the distinct divisor property if there is an injective map that sends every integer in the set to one of its proper divisors. In 1983, P. Erdős and C. Pomerance showed that for every $c>1$, a largest subset of $[N,cN]$ with the distinct divisor property has cardinality $\sim \delta(c)N$, for some constant $\delta(c)>0$. They conjectured that $\delta(c)\sim c/2$ as $c \to \infty$. We prove their conjecture. In fact we show that there exist positive absolute constants $D_1,D_2$ such that $D_1\le c^{\beta}(c/2-\delta(c))\le D_2$ where $\beta = \log 2/\log (3/2)$.
5346923
Finding Scores in Tournaments
A tournamentTnis an orientation of the complete graph onnvertices. We continue the algorithmic study initiated by10of recognizing various directed trees in tournaments. Hell and Rosenfeld studied the complexity of finding various oriented paths in tournaments by probing edge directions. Here, we investigate the complexity of finding a vertex of prescribed outdegree (or indegree) in the same model. We show that the complexity of finding a vertex of outdegreek(?(n?1)/2) inTnis ?(nk). This bound is in sharp contrast to the ?(n) bound for selection in the case of transitive tournaments. We also establish tight bounds for finding vertices of prescribed degree from the adjacency matrix of general directed/undirected graphs. These bounds generalize the classical bound of11for finding a sink (a vertex of outdegree 0 and indegreen?1) in a directed graph.
30972999
Perfect Power Testing
Bach and Sorenson present two algorithms for testing whether a number n is a perfect power, with average running time O(log2 n) under the assumption that n is chosen uniformly from an interval of length at least (log n)3 log log log n. We modify their algorithms to reduce the interval to polynomial size.
27625864
Path Balance Heuristic for Self-Adjusting Binary Search Trees
In (A. Subramanian, An Explanation of Splaying, Proceedings of the 14th Foundations of Software Technology and Theoretical Computer Science, LNCS Springer Verlag 880 354–365), D. Sleator suggested the following heuristic for self adjusting binary search trees: Every time an access is made, restructure the entire path from the root of the search tree to the accessed node into a balanced binary search tree on those nodes, and place all other subtrees rooted at the children of the nodes in the access path in their proper positions. We show that the method has an O(log n log log n/ log log log n) amortized complexity.
13457273
A new Contrast Based Image Fusion using Wavelet Packets
Image Fusion, a technique which combines complimentary information from different images of the same scene so that the fused image is more suitable for segmentation, feature extraction, object recognition and Human Visual System. In this paper, a simple yet efficient algorithm is presented based on contrast using wavelet packet decomposition. First, all the source images are decomposed into low and high frequency sub-bands and then fusion of high frequency sub-bands is done by the means of Directive Contrast. Now, inverse wavelet packet transform is performed to reconstruct the fused image. The performance of the algorithm is carried out by the comparison made between proposed and existing algorithm.
95165110
A comparison of techniques for nondestructive composition measurements in CdZnTe substrates
We report an overview and a comparison of nondestructive optical techniques for determining alloy composition x in Cd1-xZnxTe substrates for HgCdTe epitaxy. The methods for single-point measurements include a new x-ray diffraction technique for precision lattice parameter measurements using a standard highresolution diffractometer, room-temperature photoreflectance, and low-temperature photoluminescence. We compare measurements on the same set of samples by all three techniques. Comparisons of precision and accuracy, with a discussion of the strengths and weaknesses of different techniques, are presented. In addition, a new photoluminescence excitation technique for full-wafer imaging of composition variations is described.