The paper studies the weighted weak type inequalities for the Hardy operator as an operator from weighted L to weighted weak L in the case p = 1. It considers two different versions of the Hardy operator and characterizes their weighted weak type inequalities when p = 1. It proves that for the classical Hardy operator, the weak type inequality is generally weaker when q < p = 1. The best consta...

The inverse Schulze-Hardy rule was recently proposed based on experimental observations. This rule describes an interesting situation of the aggregation of charged colloidal particles in the presence of the multivalent coions. Specifically, it can be shown that the critical coagulation concentration is inversely proportional to the coion valence. Here the derivation of the inverse Schulze-Hardy...

let and be a sequence with non-negative entries. if , denote by the infimum of those satisfying the following inequality: whenever . the purpose of this paper is to give an upper bound for the norm of operator t on weighted sequence spaces d(w,p) and lp(w) and also e(w,?). we considered this problem for certain matrix operators such as norlund, weighted mean, ceasaro and copson matrices. th...

We establish Hardy-type inequalities for the Riemann-Liouville and Weyl transforms associated with the Jacobi operator by using Hardy-type inequalities for a class of integral operators.

We analyzed allelic associations (disequilibria) for four restriction fragment length polymorphisms (RFLPs) in the region of the 43-kb Apo B gene in a sample of 233 unrelated individuals from Montreal, Canada, sampled for health. This total sample (T) included 160 individuals of known French Canadian (FC) ancestry. We present a rigorous application of current methodology to these samples, inclu...

We developed a library of twelve polymorphic di- and tri-nucleotide microsatellite markers for Megalopta genalis, a facultatively eusocial sweat bee. We tested each locus in a panel of 23 unrelated females and found 7-20 alleles per locus. Observed and expected heterozygosities ranged from 0.65 to 0.96 and from 0.69 to 0.95 respectively. None of the loci deviated from Hardy-Weinberg equilibrium...