Cominimum Additive Operators

This paper proposes a class of weak additivity concepts for an operator on the set of real valued functions on a finite state space \omega, which include additivity and comonotonic additivity as extreme cases. Let \epsilon be a collection of subsets of \omega. Two functions x and y on \omega are \epsilon-cominimum if, for each E \subseteq \epsilon, the set of minimizers of x restricted on E and that of y have a common element. An operator I on the set of functions on is E- cominimum additive if I(x+y) = I(x)+I(y) whenever x and y are \epsilon-cominimum. The main result characterizes homogeneous E-cominimum additive operators in terms of the Choquet integrals and the corresponding non-additive signed measures. As applications, this paper gives an alternative proof for the characterization of the E-capacity expected utility model of Eichberger and Kelsey (1999) and that of the multi-period decision model of Gilboa (1989).Choquet integral; comonotonicity; non-additive probabilities; capacities; cooperative games

Preliminary study of the transition of sea ice during the melting process

In order to understand the transition in sea ice, snow transformation, and temperature variations, we carried out tank experiments in a cold room. In the melting experiment of bare ice, the transition of the condition of the ice surface was observed through visual observations and reflectance measurements. The first change was manifested in the surface becoming wet and acquiring a rough texture. Subsequently, a porous layer was formed under the ice surface. Since this layer scattered the incident light, it appeared as a bright surface. The reflectance of this surface was high as compared with that measured during the initial stages of melting. However, this thin scattering layer disappeared as the melting progressed. As a result, the reflectance was reduced to its value during the initial stage of melting. In the melting experiments on snow covered sea ice, the structure of snow-ice became porous and mechanically weak before the thickness reduction commenced. The temperature gradients of bare ice and snow covered ice were small during the melting process compared to those during the growth period

Thermoluminescence studies of ordinary chondrites in the Japanese Antarctic meteorite collection, IV: Asuka ordinary chondrites

We measured TL properties of ninety Asuka (A) ordinary chondrites (LL: 16, L: 27, H: 47) from Japanese Antarctic meteorite collection. Most of the chondrites had TL sensitivities over 0.1, corresponding to petrologic subtype 3.5-3.9. Eight chondrites, A-881244 (L3), A-881607 (LL3), A-881328 (LL3), A-881408 (LL3), A-881397 (LL3), A-881522 (L3), A-881357 (LL3 or L3), and A-881199 (LL3) were revealed to be primitive ordinary chondrites under petrologic subtype 3.4, and therefore they are particularly significant in understanding the nature of primitive material in the solar system. Twenty-one chondrites with low TL sensitivities below 0.1 (Dhajala=1) had suffered remarkable shock and/or terrestrial weathering. Samples were mainly from three different dirt bands south of the Sr Rondane Mountains at D1, D2, and D3 sites. LT/HT distribution at D1 site suggested that chondrites at D1 site had shorter terrestrial ages than those at D2 and D3. A-880709, A-88710, A-88774, A-881324 which had extremely low LT/HT ratio under 0.1, and A-881484 and A-881546 which might be heated over 400°C were presumed to have small perihelia. We found 26 TL potential paired fragments, and 9 groups. A group of H3 at D1 site comprises a chain of paired fragments. A H3 chondrite might shower near the Asuka

A Primary Study about Imperial Admonition by Emperor Yong le (永楽) of Ming Dynasty on 1st November 1418

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CHIKU Kakugyo, The Books that Changed the World (Graphic-sha, 2017)

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