We compute the motivic Donaldson-Thomas theory of the resolved conifold, in all chambers of the space of stability conditions of the corresponding quiver. The answer is a product formula whose terms depend on the position of the stability vector, generalizing known results for the corresponding numerical invariants. Our formulae imply in particular a motivic form of the DT/PT correspondence for the resolved conifold. The answer for the motivic PT series is in full agreement with the prediction of the refined topological vertex formalism.

We compute the motivic Donaldson-Thomas theory of a small crepant resolution of a toric Calabi-Yau 3-fold.Now we have computed all the dimensions T (π [a,b] , π [c,d] ) and B(π [a,b] , π [c,d] ). The next lemma combines corollaries 8.5 and 8.9 to compute their difference. We see that in most cases there is an exact cancellation.Lemma 8.10. We have [a,b] , π [c,d] ) aside from the following cases,if a = c and b = a − 1.Case 5: a ∈ I 3 , b ∈ I 2 , a − 1 ∈ [c, d], d = a − 1, b = d M ((π [a,b] ) ′ , π [c,b] ) − M (π [a,b] , π [c,b] ).

We provide a reduction formula for the motivic Donaldson-Thomas invariants associated to a quiver with superpotential. The method is valid provided the superpotential has a linear factor, it allows us to compute virtual motives in terms of ordinary motivic classes of simpler quiver varieties. We outline an application, giving explicit formulas for the motivic Donaldson-Thomas invariants of the orbifolds [C × C 2 /Zn].

We prove a formula, originally due to Feit and Fine, for the class of the commuting variety in the Grothendieck group of varieties. Our method, which uses a power structure on the Grothendieck group of stacks, allows us to prove several refinements and generalizations of the Feit-Fine formula. Our main application is to motivic Donaldson-Thomas theory.

strategy. The study demonstrated the need for higher concentration in known markets and revealed potential new markets. The study used existing dataparticularly the 1972 Census of Transportation and the 1974 and 1975 National Travel Surveys of the United States Travel Data Center-and combined these data with new attitudinal and behavioral data obtained by conducting a consumer survey in Michigan and the five adjacent states plus Ontario.From the consumer survey, a target market group was defined by combining measures of those who had vacationed in Michigan in the past year with those individuals who attitudinally showed some likelihood of vacationing in Michigan in the future. This target market group was then segmented by vacation activity preferences, using factor analysis and factor scoring of activity and recreational interests scales developed in the survey. By use of cross tabulations, plus data from the prior studies, the segments were identified by population size and proportions in various geographically defined market areas. The segments were then ranked according to their economic value on the basis of recent vacation spending by tourists from those areas and the relative potential of those travelers for vacationing in Michigan. Subsequently, strategies were developed for reaching these market segments most effectively through public relations and advertising campaigns.Study Purposes The Travel Bureau had multiple purposes for sponsoring a study of its market area. The first was to better define the market area and the segments within it which make the most contribution to tourism now and/or Barbara E Bryant is Group Vice President and Andrew J Morrison is Vice President for Consumer Research with Market Opinion Research in Detroit, Michigan have the most potential for growth. The second purpose was to determine the dollar, employment, and tax revenue impact of tourism on the present economy of Michigan. Tourism is an intangible product supplied by diversified businesses, most of which are small, and its actual contribution to a state's economy is hard to measure. The third purpose of the study was to evaluate advertising and promotion efforts being done by the Travel Bureau on a relatively limited budget.The study's overall purpose, of course, was to develop strategies for increasing tourism to Michigan in order to increase its contribution to the state's economy.