A spectral analogue of the Meinardus theorem on asymptotics of the number of partitions

An asymptotic formula for the number of states of Boson gas whose Hamiltonian is given by a positive elliptic pseudo-differential operator of order one on a compact manifold is given under a integrality assumption on the spectrum of the Hamiltonian. This is regarded as an analogue of the Meinardus theorem on asymptotics of the number of partitions of a positive integer.Comment: Introduction has rewritten. In particular, the assumption in the main theorem has been changed. The assumption of main theorem in the old version is not suitable. Some mistakes are fixed. To appear in the journal Asymptotic Analysi

‘“A fit person to be Poet Laureate”: Tennyson, In Memoriam, and the Laureateship’

Tennyson Research Bulletin 9 (2009), 233-4

Facing an Epidemic: An Analysis of HIV/AIDS, Antiretroviral Drug, and International Response to the AIDS Pandemic

More than 33 million people are living with HIV/AIDS around the globe with 68% of all cases occurring in sub-Saharan Africa. The global prevalence rate is shocking considering that the disease was relatively unknown just 30 years ago. After reviewing medical, health policy, and health statistical journals, I will argue in this paper that international aid to nations struggling with AIDS needs to be redirected and refocused on supplying antiretroviral therapy to afflicted nations because ARV has been proven to be effective in managing the disease in countries that can afford the costs of treatment. International aid to countries that are ravished by the epidemic, and the United States is one of the top contributors to such efforts with its “President’s Emergency Plan For AIDS Relief (PEPFAR). The U.S. has realized the potential economic benefits of helping out such as becoming primary trade partners with the nations who have plenty of valuable natural resources despite their AIDS issues. In the U.S.’s efforts to combat terrorism, the nation has an interest in “stabilizing” certain countries, which are typically in Africa, so that they can resist potential terrorist threats or military coups. PEPFAR’s goal in fighting AIDS is part of the stabilization effort on the continent of Africa. Fortunately, major pharmaceutical companies have discovered compounds that are effective in attacking the HIV virus, and this has led to the production of “antiretroviral” drugs. Anti-retroviral therapy has proven to be a useful tool used by those suffering from HIV/AIDS to manage their disease better and obtain a higher quality life. Such medications are widely available in wealthy nations, but poor countries that have the highest HIV/AIDS prevalence have a harder time affording such therapy or managing the drug supplies. Potential solutions to this problem include selling antiretroviral drugs at a lower cost to developing nations or using generic versions of such drugs

CAROLINE LEVINE. Forms: Whole, Rhythm, Hierarchy, Network

Review of English Studies 66 (2015), 1001-

The Hamiltonians generating one-dimensional discrete-time quantum walks

An explicit formula of the Hamiltonians generating one-dimensional discrete-time quantum walks is given. The formula is deduced by using the algebraic structure introduced previously. The square of the Hamiltonian turns out to be an operator without, essentially, the `coin register', and hence it can be compared with the one-dimensional continuous-time quantum walk. It is shown that, under a limit with respect to a parameter, which expresses the magnitude of the diagonal components of the unitary matrix defining the discrete-time quantum walks, the one-dimensional continuous-time quantum walk is obtained from operators defined through the Hamiltonians of the one-dimensional discrete-time quantum walks. Thus, this result can be regarded, in one-dimension, as a partial answer to a problem proposed by Ambainis.Comment: 9 page

Complementarity and Identification

This paper examines the identification power of assumptions that formalize the notion of complementarity in the context of a nonparametric bounds analysis of treatment response. I extend the literature on partial identification via shape restrictions by exploiting cross-dimensional restrictions on treatment response when treatments are multidimensional; the assumption of supermodularity can strengthen bounds on average treatment effects in studies of policy complementarity. This restriction can be combined with a statistical independence assumption to derive improved bounds on treatment effect distributions, aiding in the evaluation of complex randomized controlled trials. Complementarities arising from treatment effect heterogeneity can be incorporated through supermodular instrumental variables to strengthen identification in studies with one or multiple treatments. An application examining the long-run impact of zoning on the evolution of urban spatial structure illustrates the value of the proposed identification methods.Comment: 46 page