The Green's function of the discrete Schödinger operator on a finite graph is considered. This setting reproduces Laplacian and signless Laplacian by adjusting the appropriate potentials. We show two ways of the expression for the Green's function by using graph structures. The first way is based on the factor of the graph by subtrees which have uni-self-loops; the second way is based on that by odd unicycle graphs.
The uneven distribution of universities across regions has been argued to create educational inequalities based on place of residence. While studies have shown positive associations between college proximity, measured by distance to nearest college or its presence, and enrolment among local residents, regional availability has often been measured insufficiently, and longitudinal evidence on the relationship is limited. Using multiple social survey datasets combined with population census data from Japan, a country that has experienced significant policy shifts regarding university locations, we examine how longitudinal changes in regional university availability in an individual's residential and neighbouring prefectures are associated with their likelihood of university enrolment and how these associations differ by parental class and education. Our results show that increased university availability in both residential and neighbouring prefectures is positively associated with enrolment. While the strength of the association does not differ significantly by parental class, individuals with tertiary-educated parents are more responsive to increased availability. These findings suggest that increased university availability in underserved areas could reduce spatial inequality in enrolment, though may have a limited role in reducing, or may even be positively associated with, inequality based on social origin.
Recent research shows that gender ideology may not be stable among individuals over time. However, there is little evidence on the changes in gender and family attitudes in non-Western contexts. Using data from 11 waves (2011-2021) of the Japanese Panel Survey of Consumers (JPSC), we construct fixed-effects models that reveal how women's gender attitudes, together with life eventssuch as parenthood and women's employment, shape unpaid work distribution in Japanese couples. Overall, our results show that shifts in wives' gender ideology do not consistently lead to increased husband participation in domestic labor. However, this relationship becomes more nuanced when we distinguish between weekdays and weekends. On weekdays, when work demands are highest, more egalitarian shifts in the wife's attitudes are associated with increased domestic involvement from husbands. Yet, the transition to parenthood significantly decreases men's participation during weekdays, suggesting that women continue to carry the bulk of weekday childcare responsibilities.
We study the S=12\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$S=\frac{1}{2}$$\end{document} quantum spin system on the d-dimensional hypercubic lattice with d >= 2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$d\ge 2$$\end{document} with uniform nearest-neighbor interaction of the XY or XYZ type and arbitrary uniform magnetic field. By extending the method recently developed for quantum spin chains, we prove that the model possesses no local conserved quantities except for the trivial ones, such as the Hamiltonian. This result strongly suggests that the model is nonintegrable. We note that our result applies to the XX model without a magnetic field, which is one of the easiest solvable models in one dimension.
Dekel et al. (1998) showed that standard state-space models preclude non-trivial unawareness. We argue that their introspection axioms may be too strong and instead explore two new axioms on unawareness, weak KU introspection and U-monotonicity. We show that even if we relax their axioms, when employing these new axioms, we arrive at the same conclusions as theirs. Results illustrate the relationships among various axioms that have not been previously explored. Based on them, we also discuss briefly about the possibility of representing non-trivial unawareness within the standard state-space approach.
