Todd genera of complex torus manifolds

In this paper, we prove that the Todd genus of a compact complex manifold $X$ of complex dimension $n$ with vanishing odd degree cohomology is one if the automorphism group of $X$ contains a compact $n$-dimensional torus \Tn as a subgroup. This implies that if a quasitoric manifold admits an invariant complex structure, then it is equivariantly homeomorphic to a compact smooth toric variety, which gives a negative answer to a problem posed by Buchstaber-Panov.Comment: 12 pages, Remark 1.2 is adde

Leakage of Mildly Flammable Refrigerants into a Room

The use of chlorofluorocarbons (CFCs) and hydrochlorofluorocarbons (HCFCs) has been widely restricted. They have been replaced with hydrofluorocarbons (HFCs) in order to protect the ozone layer. However, the leakage of refrigerant into air from active or end-of-life air conditioners has been a serious environmental issue owing to the high global warming potential (GWP). It has therefore been widely recognized that the replacement of HFCs with low-GWP refrigerants is a reasonable solution of the problem. In Japan, the low-GWP refrigerants such as R1234yf, R1234ze, and R32 are considered as candidate alternatives for conventional HFC refrigerants. However, these low-GWP refrigerants are often flammable. When refrigerants leak into a space, they tend to accumulate at the floor if they are heavier than air and ventilation is inadequate. If the refrigerant concentration is higher than the lower flammable limit (LFL), there is an ignition source, and the air velocity is lower than the burning velocity, the refrigerant may ignite. When leakage occurs from an air conditioner, there is always a region where the refrigerant concentration is higher than the LFL because the refrigerant concentration is about 100% near the outlet from the air conditioner. Thus, it is important to understand the diffusion phenomena of the low-GWP refrigerants when acquiring sufficient information for the safety standards to assess the risks in the usage of these refrigerants. Numerical analysis is an effective tool because it is very difficult to measure the diffusion of a refrigerant in a large space. In this study, diffusion phenomena were numerically analyzed when a refrigerant leaked from a room air conditioner (RAC), a package air conditioner (PAC) or a chiller into a large space where these were equipped. From the calculation results, the refrigerant concentration distributions, the volumes and positions of the flammable regions, and their changes in time were discussed