We obtain new lower and upper bounds for probabilities of unions of events. These bounds are sharp. They are stronger than earlier ones. General bounds may be applied in arbitrary measurable spaces. We have improved the method that has been introduced in previous papers. We derive new generalizations of the first and second parts of the Borel-Cantelli lemma.
Fifty years ago P. Erdős and A. Rényi published their famous paper on the new law of large numbers. In this survey, we describe numerous results and achievements which are related with this paper or motivated by it during these years.
Host plant-derived semiochemicals are becoming the most promising attractants to lure corn borers to traps in the field. Following success with the European corn borer (Ostrinia nubilalis), a two-component blend bisexual lure (phenylacetaldehyde and 2-(4-methoxyphenyl)ethanol) of the host plant odor was tested in wind tunnel and field trapping experiments on the Asian corn borer (Ostrinia furnacalis) (ACB). To be able to compare the lure's performance with synthetic pheromone, a new route for the sex pheromone components (Z)-12-tetradecenyl acetate and (E)-12-tetradecenyl acetate was also developed, and the biological activity of the products was confirmed. The bisexual lure attracted both males and females of ACB in laboratory wind tunnel, and also in the field. Field trapping results indicated that traps with the bisexual lure attracted somewhat more ACB (both sexes) than pheromone baited traps, but this indication needs further confirmation. Traps baited with the bisexual lure may offer a new tool for monitoring ACB for practical purposes.