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As the American political landscape becomes increasingly divided along urban–rural lines, it raises the prospect of deepening social identities that are tied to one's community-type. As community-type becomes an important social identity, it can lead to favoritism of one's community in-group, or denigration of one's community out-group. We explore the extent to which urban and rural identities exist above and beyond other factors like party and race, and whether they are consequential for the ways in which people evaluate the political and non-political world. Using national survey data, we demonstrate that people in both urban and rural locations hold beliefs that are consistent with a community-type social identity that is independent of other factors which are correlated with the urban–rural divide. We use two different experiments to assess the consequences of this identity, finding that there are distinct effects in the political arena when allocating government resources, and in the non-political world when judging hypothetical job applications. These effects are generally smaller in magnitude than other factors, such as partisanship, but suggest that community-type identities are important in politics. [ABSTRACT FROM AUTHOR]

In this paper, we employ Krasnoseľskii’s fixed point theorem to show the existence of positive solutions to three different two point fractional boundary value problems with fractional boundary conditions. Also, nonexistence results are given. [ABSTRACT FROM AUTHOR]

Drawing on the sizable literature on polarization in the American public, we consider the link between discussion network composition and perceptions of polarization. Participants in the 2008-2009 ANES panel study were asked to complete an innovative battery; they interactively moved histograms to rate other groups' positions on several prominent issues. These novel exercises provide data on individuals' projections of the average attitudes of others, but critically, they also provide data on the variability of such attitudes. Thus, we use these 'response-distributions' to thoroughly assess (1) the relationship between network characteristics and perceptions of the distance between party opinions, and (2) the relationship between network characteristics and perceptions of the homogeneity of opinions within parties. We find evidence that discussion networks track with individual perceptions of the parties in the electorate: exposure to interpersonal disagreement predicts the perception of less distance between (the mean opinions of) the parties, and the reporting of more heterogeneity of opinion within the parties. We conclude by discussing the implications of these findings for democratic functioning more generally. [ABSTRACT FROM AUTHOR]