New features of the first eigenvalue on negatively curved spaces

The paper is devoted to the study of fine properties of the first eigenvalue on negatively curved spaces. First, depending on the parity of the space dimension, we provide asymptotically sharp harmonic-type expansions of the first eigenvalue for large geodesic balls in the model n-dimensional hyperbolic space, complementing the results of Borisov and Freitas (2017), Hurtado, Markvorsen and Palmer (2016) and Savo (2008); in odd dimensions, such eigenvalues appear as roots of an inductively constructed transcendental equation. We then give a synthetic proof of Cheng’s sharp eigenvalue comparison theorem in metric measure spaces satisfying a Bishop–Gromov-type volume monotonicity hypothesis. As a byproduct, we provide an example of simply connected, non-compact Finsler manifold with constant negative flag curvature whose first eigenvalue is zero; this result is in a sharp contrast with its celebrated Riemannian counterpart due to McKean (1970). Our proofs are based on specific properties of the Gaussian hypergeometric function combined with intrinsic aspects of the negatively curved smooth/non-smooth spaces.

Traditional institutions and female labor force participation

Purpose In general, the return from participation in MNREGA will be highest for those women whose mobility and social interaction is least impeded by conservative social norms. However, if any intervention enhances knowledge base, or challenges traditional norms of gender, then return from that intervention may be highest for those women impede most by conservative social norms. It may be interpreted as non-monotonic effect of restrictedness across caste and religion. The purpose of this paper is to examine non-monotonicity hypothesis of social restrictedness for the intervention MNREGA. Design/methodology/approach Using primary data from three districts of West Bengal, the paper has tried to see whether there exists any non-monotonic effect of restrictedness on household’s “expenditure on consumption,” “expenditure on temptation good,” “expenditure on women’s health” and “expenditure on children’s education and health” across castes and religion. The sample is relatively homogeneous in terms of socio economic status, but differs in affiliation to castes and religion. Findings As a result of participating the labor force through MNREGA, the contribution of women to household earnings increases, which may potentially increase their bargaining power within the household. The conventional notion is that women who are least fettered by social norms should get maximum benefits of participation in MNREGA. However, the analysis shows that women of upper caste (UC) community have been able to exercise the highest level of agency in allocating household resources compared to the women of scheduled caste community. It substantiates the non-monotonicity of restrictedness of social norms across castes and religions. Agency of Muslim women has not increased significantly compared to the UC women. Research limitations/implications The study suffers from usual limitations of sampling. Originality/value There is hardly any study deciphering MNREGA from the perspective of caste, religion and gender.

Insurance Mortality Rates, Performance Indicators, and Possibly Monotonic Population Proportions

Two applications are described of a probability model that can express uncertainty regarding a pre-specified monotonicity hypothesis for binomial proportions. The model also yields a random effects overdispersion formulation where the population proportions definitely satisfy a monotonicity specification. One application concerns an insurance data set recording mortalities of clients from ages 35 to 64. Two new actuarial graduation procedures are developed. The other application derives from a Veterans' administration hospital quality monitor and concerns the failure to return rates for psychiatric patients attending substance abuse clinics. While smoothed performance indicators are proposed, measures of their extra-binomial variation highlight problems experienced by evidence-based approaches when the data are uncontrolled.