A combinatorial Fredholm module on self-similar sets built on nn-cubes

We construct a Fredholm module on self-similar sets such as the Cantor dust, the Sierpinski carpet and the Menger sponge. Our construction is a higher dimensional analogue of Connes' combinatorial construction of the Fredholm module on the Cantor set. We also calculate the Dixmier trace of two operators induced by the Fredholm module.Comment: 24 page

A combinatorial integration on the Cantor dust

In this paper, we generalize the Cantor function to 2-dimensional cubes and construct a cyclic 2-cocycle on the Cantor dust. This cocycle is non-trivial on the pullback of the smooth functions on the 2-dimensional torus with the generalized Cantor function while it vanishes on the Lipschitz functions on the Cantor dust. The cocycle is calculated through the integration of 2-forms on the torus by using a combinatorial Fredholm module

A combinatorial integration on the Cantor dust

In this paper, we generalize the Cantor function to $2$-dimensional cubes and construct a cyclic $2$-cocycle on the Cantor dust. This cocycle is non-trivial on the pullback of the smooth functions on the $2$-dimensional torus with the generalized Cantor function while it vanishes on the Lipschitz functions on the Cantor dust. The cocycle is calculated through the integration of $2$-forms on the torus by using a combinatorial Fredholm module.Comment: 8 page

Exit and Voice in a Marriage Market

In this paper, we present a model in which agents choose voice, exit, or stay options when their marital condition becomes bad. The voice option can be interpreted as a spouses e¤ort or investment in the household to resolve his/her dissatisfaction and improve the marital condition. If a spouse hopes to divorce, he/she chooses the exitoption. If a spouse does not hope to express his/her opinion and divorce, he/she chooses the stayoption. We focus on the role of exitand voicein a marriage and investigate the e¤ects of a divorce law that is based on fault or no-fault on divorce rates. Our study shows that divorce rates tend to be too high under a unilateral divorce law in the non-transferable utility case. On the other hand, mutual-consent divorce law generates multiple equilibria, and divorce rates are then ine ¢ cient even in the transferable utility case. In this multiple equilibrium case

Two Cleptoparasitic Ant Crickets (Orthoptera: Myrmecophilidae) That Share Similar Host Ant Species Differentiate Their Habitat Use in Areas of Sympatry in Japan

Myrmecophilus crickets (Myrmecophilidae, Orthoptera) are typical ant guests. In Japan, about 10 species are recognized on the basis of morphological and molecular phylogenetic frameworks. We focused on two of these species, M. kinomurai and M. kubotai, and compared their host and habitat use. Previous work based on a limited sampling effort suggested that these two species share some ant species as hosts, but that their habitat (open versus shaded) preferences differ. Here, on the basis of exhaustive sampling across Japan, we confirmed that M. kinomurai and M. kubotai do not differ in their host ant preferences: both prefer formicine ants as hosts. As for habitat preferences, M. kubotai occurred significantly more often in open habitats than in shaded ones (P < 0.05). In contrast, M. kinomurai showed no habitat preference in areas where M. kubotai did not occur. However, M. kinomurai showed an obvious preference for shaded environments in areas of sympatry with its potential competitor M. kubotai. This pattern suggests that interspecific competition between M. kinomurai and M. Kubotai is a factor causing habitat differentiation in areas of sympatry

A Proposal of Lean Design Integration Method for Hierarchical Architecture Type Product Systems (A Practical Lean Development Example in Domestic Refrigerator Energy Saving Design with a Combination of CAE, Real experiment and Humanistic collaboration)

In developing process for competitive commercial refrigerator/ air-conditioning system products, practical whole system integration method is very important to realize a compact product with high cost performance. These products are characterized by hierarchical architecture type module product systems. This paper proposes a practical lean development method which combines 1D and 3D-CAE analysis with human decision making process. A Model-based development method using product base platform is also proposed for realizing a practical product family series development. Finally, the effectiveness of this method is demonstrated quantitatively by applying to an energy saving type household refrigerator