Results 1 
4 of
4
Inequalities Involving Gamma and Psi Functions
"... We prove that certain functions involving the gamma and qgamma function are monotone. We also prove that (x m /(x)) (m+1) is completely monotonic. We conjecture that (x m / (m\Gamma1 (x)) (m) is completely monotonic for m 2, we prove it, with help from Maple, for 2 m 16. We give a ve ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
We prove that certain functions involving the gamma and qgamma function are monotone. We also prove that (x m /(x)) (m+1) is completely monotonic. We conjecture that (x m / (m\Gamma1 (x)) (m) is completely monotonic for m 2, we prove it, with help from Maple, for 2 m 16. We give a very useful Maple proceedure to verify this for higher values of m. A stronger result is also formulated where we conjecture that the power series coefficients of a certain function are all positive. Running Title: Gamma Function Inequalities Mathematics Subject Classification. Primary 33B15. Secondary 26D07, 26D10. Key words and phrases. gamma function, digamma function, inequalities, complete monotonicity. 1. Introduction. Inequalities of functions involving gamma functions have been of interest since the 1950's when inequalities by Gautchi, Erber and Kershaw were established. For references and generalizations we refer the interested reader to [5], [13], [14], [15], [16], and to Alzer's p...
A Note on Hamilton Cycles in Kneser Graphs
 Bull. Inst. Combin. Appl
"... The Kneser graph K(n; k) has as vertices the ksubsets of f1; 2; :::; ng where two vertices are adjacent if the ksubsets are disjoint. In this paper we use a computational heuristic of Shields and Savage to extend previous results and show that all connected Kneser graphs (except the Petersen g ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
The Kneser graph K(n; k) has as vertices the ksubsets of f1; 2; :::; ng where two vertices are adjacent if the ksubsets are disjoint. In this paper we use a computational heuristic of Shields and Savage to extend previous results and show that all connected Kneser graphs (except the Petersen graph) have Hamilton cycles when n 27. A similar result is shown for bipartite Kneser graphs.
Hamilton Cycle Heuristics in Hard Graphs
, 2004
"... In this thesis, we use computer methods to investigate Hamilton cycles and paths in several families of graphs where general results are incomplete, including Kneser graphs, cubic Cayley graphs and the middle two levels graph. We describe a novel heuristic which has proven useful in finding Hamilton ..."
Abstract
 Add to MetaCart
In this thesis, we use computer methods to investigate Hamilton cycles and paths in several families of graphs where general results are incomplete, including Kneser graphs, cubic Cayley graphs and the middle two levels graph. We describe a novel heuristic which has proven useful in finding Hamilton cycles in these families and compare its performance to that of other algorithms and heuristics. We describe methods for handling very large graphs on personal computers. We also explore issues in reducing the possible number of generating sets for cubic Cayley graphs generated by three involutions.
New construction of errortolerant pooling designs
"... Abstract We present a new class of errortolerant pooling designs by constructing d z −disjunct matrices associated with subspaces of a finite vector space. ..."
Abstract
 Add to MetaCart
Abstract We present a new class of errortolerant pooling designs by constructing d z −disjunct matrices associated with subspaces of a finite vector space.