Place elements in the form of an inverted triangle, and color them from top to bottom by row according to some rule. When doing so, is it possible to predict the color of the element that becomes the triangle's botttom vertex? It turns out that when you begin with a triangle of 4,10,28, ... elements in its top row, knowing the colors of that row's leftmost and rightmost elements in sufficient to predict the color of that bottom vertex, and this article presents an elegant proof of this surprising result. Coloring triangles is simple even for children, but this problem provides a springboard to learning about some advanced mathematics, including Abelian groups, the superposition principle, and fractal structures.
The remote island economies heavily depend on the public work budgets. The Japanese government has cut spending for public work projectsd; therefore they are suffering from establishing an additional source of income. The Ie Island launched a kind of community based tourism lodging at the house of a private citizen. In 2012, the Ie Island where only 5,000 people living in it attracts 50,000 school trip visitors a year, and 13% of total households participate in the lodging business. This paper intends to show the distinctive futures of the community based tourism and the assessment of its territorial economic impacts useing input-output analysis. The features that can be found are (1) utilizing inherent living culture and lifestyle of local people, (2) critical role of the intermediate organization between the costumers and the local people offering accommodation, (3) necessity of the participation and corporate identity of the local people, and (4) considering inter-industrial linkage in the territorial economy. The tourism output multiplier on the local economy is estimated at 1.4. The lodging business utilizing private house is extremely labor-intensive. Consequently, the majority of the receipt from visitors is left as incom in the local economy, and the expenditures from teh income induce a large size of ripple economic effect in the local economy. The territorial income generated by the tourism is estimated at about 500 million yen a year, which is just about equivalent to the territorial incom generated by the public work projects. We can conclude that the community based tourism presents potentialities for the autonomous development of the remote island economies.
The English instrumental intransitive constructions with a generic reading, which have been regarded as pseudo-middles cannot be treated as middles, because the intransitive construction allows object insertion. Rather, they should be understood as the intransitive counterparts of the instrumental generic transitive (IGT) construction, that is, the instrumental generic intransitive (IGI). IGIs and IGTs share a basic syntactic structure and are differentiated by phonological specification rules after syntax. Their instrumental subjects are introduced by a light verb (LV) without lexical information, vFUNCTOR (vF). In contrast, the subject of a middle is derived by the object movement. Fuuthermore, the generic properties of the IGI, IGT, and middle can be uniformly accounted for by a fine-grained event structure analysis os the Logical Form (LF). In the IGT and IGI, θ-role assignment can be captured derivationally by means of the LF representations based on our derivational structures. Therefore, θ-role assignment rules and principles at the lexicon-syntax interface can be discarded. This study rationalizes the organization of a possible grammatical model by reducing the lexical burden. Thus, our proposal enables the capturing of the English instrumental constructions in a more comprehensive and elegant manner.