Let $\pi$ be a discrete group, and let $G$ be a compact-connected Lie group. Then, there is a map $\Theta \colon \mathrm {Hom}(\pi,G)_0\to \mathrm {map}_*(B\pi,BG)_0$ between the null components of the spaces of homomorphisms and based maps, which sends a homomorphism to the induced map between classifying spaces. Atiyah and Bott studied this map for $\pi$ a surface group, and showed that it is surjective in rational cohomology. In this paper, we prove that the map $\Theta$ is surjective in rational cohomology for $\pi =\mathbb {Z}^m$ and the classical group $G$ except for $SO(2n)$, and that it is not surjective for $\pi =\mathbb {Z}^m$ with $m\ge 3$ and $G=SO(2n)$ with $n\ge 4$. As an application, we consider the surjectivity of the map $\Theta$ in rational cohomology for $\pi$ a finitely generated nilpotent group. We also consider the dimension of the cokernel of the map $\Theta$ in rational homotopy groups for $\pi =\mathbb {Z}^m$ and the classical groups $G$ except for $SO(2n)$.

Let G be a compact connected Lie group, and let $\operatorname {Hom}({\mathbb {Z}}^m,G)$ be the space of pairwise commuting m-tuples in G. We study the problem of which primes $p \operatorname {Hom}({\mathbb {Z}}^m,G)_1$, the connected component of $\operatorname {Hom}({\mathbb {Z}}^m,G)$ containing the element $(1,\ldots ,1)$, has p-torsion in homology. We will prove that $\operatorname {Hom}({\mathbb {Z}}^m,G)_1$ for $m\ge 2$ has p-torsion in homology if and only if p divides the order of the Weyl group of G for $G=SU(n)$ and some exceptional groups. We will also compute the top homology of $\operatorname {Hom}({\mathbb {Z}}^m,G)_1$ and show that $\operatorname {Hom}({\mathbb {Z}}^m,G)_1$ always has 2-torsion in homology whenever G is simply-connected and simple. Our computation is based on a new homotopy decomposition of $\operatorname {Hom}({\mathbb {Z}}^m,G)_1$, which is of independent interest and enables us to connect torsion in homology to the combinatorics of the Weyl group.

Ganea proved that the loop space of $\mathbb{C} P^n$ is homotopy commutative if and only if $n=3$ . We generalize this result to that the loop spaces of all irreducible Hermitian symmetric spaces but $\mathbb{C} P^3$ are not homotopy commutative. The computation also applies to determining the homotopy nilpotency class of the loop spaces of generalized flag manifolds $G/T$ for a maximal torus T of a compact, connected Lie group G.

We determine the (non-)triviality of Samelson products of inclusions of factors of the mod p decomposition of $G_{(p)}$ for $(G,p)=(E_7,5),(E_7,7),(E_8,7)$. This completes the determination of the (non-)triviality of those Samelson products in p-localized exceptional Lie groups when G has p-torsion-free homology.

Integrated safety assessment methodology that analyzes radionuclide migration reflecting the spatial and temporal changes of disposal systems was developed for a geological disposal site with uplift and denudation, and then some case analyses for an assumed site were carried out. The combination of uniform uplift and denudation has the largest effect on the radionuclide migration because the ground water flow velocity increases with decreasing depth from the ground surface. In the case without denudation, tilted uplift has more effect than uniform uplift because flow velocity in tilted uplift increases with increasing hydraulic gradient. The long-term change of the geological structures including the uplift and denudation, the hydraulic conditions, and the recharge and outlet of the ground water around a candidate site should be carefully investigated to determine the appropriate the place, depth and layout of the repository.

F2 excimer laser (157 nm) irradiation was applied to modify sol–gel-derived amorphous Al2O3 thin films at ambient temperature. The surface morphology and density of the film were significantly altered by the laser irradiation (power: 2 mW/cm2/pulse). The surface properties of the film were also changed from hydrophilic to hydrophobic. These alterations were not observed when using ArF excimer laser (193 nm) irradiation at the same laser power as that of the F2 laser. It was found that the changes induced by F2 laser irradiation mainly arose from the direct photoexcitation of C = O groups in ethylacetoacetate, which was added as a chelating agent of aluminum-alkoxides. Consequently, photochemical reactions of the Norrish-type occur, resulting in the formation of hydrocarbon or olefin and the elimination of carbon monoxide (CO) or decomposition products. The elimination of CO is considered to cause the marked change in structure and surface properties of the film. Patterning of the gel films was successfully performed by using these findings.

There are four cattle beef breeds in Japan: Japanese Black, Japanese Brawn, Japanese Poll and Japanese Shorthorn. These breeds were crossed with European breeds in the early 1900's. As a result of introducing European blood, Japanese beef cattle have an expanded and more diverse gene pool. Furthermore, both the breed used for crossing and the selection criteria employed varied significantly from prefecture to prefecture Consequently, a number of distinct strains have been established. At present, however, the genetic diversity is becoming increasingly concentrated around a limited number of strains noted for their superior meat quality. From the genetic conservation view point, it is necessary to stock minor strains by frozen semen and embryos for future domands of genetic resources. This paper discusses the conservation and current utilization of beef cattle genetic resources in Japan.