## Recursos de colección

1. #### Yang-Mills connections with Weyl structure

Park, Joon-Sik
In this paper, we treat with an arbitrary given connection $D$ which is not necessarily \textit{metric} or \textit{torsion-free} in the tangent bundle $TM$ over an $n$-dimensional closed (compact and connected) Riemannian manifold $(M,g)$. We find the fact that if any connection $D$ with Weyl structure $(D,g,\omega)$ relative to a 1-form $\omega$ in the tangent bundle is a Yang-Mills connection, then $d\omega=0$. Moreover under the assumption $\sum_{i=1}^{n}[\alpha(e_{i}),R^{D}(e_{i},X)]=0$ $(X \in \mathfrak{X}(M))$, a necessary and sufficient condition for any connection $D$ with Weyl structure $(D,g,\omega)$ to be a Yang-Mills connection is $\delta_{\nabla}R^{D}=0$, where $\{e_{i}\}_{i=1}^{n}$ is an (locally defined) orthonormal frame on $(M,g)$ and...

2. #### Global solvability of the free-boundary problem for one-dimensional motion of a self-gravitating viscous radiative and reactive gas

Umehara, Morimichi; Tani, Atusi
In this paper we consider a system of equations describing the one-dimensional motion of a self-gravitating, radiative and chemically reactive gas having the free-boundary. For arbitrary large, smooth initial data we prove the unique existence, global in time, of a classical solution of the corresponding problem with fixed domain, obtained by the Lagrangian mass transformation.

3. #### Disconnected Julia sets of quartic polynomials and a new topology of the symbol space

Katagata, Koh
For a certain quartic polynomial, there exists a homeomorphism between the set of all components of the filled-in Julia set with the Hausdorff metric and some subset of the corresponding symbol space with the ordinary metric. But these sets are not compact with respect to each metric. We introduce a new topology with respect to which these sets are compact.

4. #### New proofs of the trace theorem of Sobolev spaces

Miyazaki, Yoichi
We present three new proofs of the trace theorem of $L_{p}$ Sobolev spaces, which do not rely on the theory of interpolation spaces. The first method originates in Morrey’s proof for the Sobolev embedding theorem concerning the Hölder-Zygmund space. The second method is based on Muramatu’s integral formula and the third method is based on an integral operator with Gauss kernel. These methods give unified viewpoints for the proofs of the trace theorem and the Sobolev embedding theorem.

5. #### Proper actions of $SL(2,\mathbf{C})$ on irreducible complex symmetric spaces

Teduka, Katsuki
We classify irreducible complex symmetric spaces that admit proper $SL(2,\mathbf{C})$-actions.$^{*}$

6. #### Relative versions of theorems of Bogomolov and Sukhanov over perfect fields

Bac, Dao Phuong; Thang, Nguyen Quoc
In this paper, we investigate some aspects of representation theory of reductive groups over non-algebraically closed fields. Namely, we state and prove relative versions of well-known theorems of Bogomolov and of Sukhanov, which are related to observable and quasi-parabolic subgroups of linear algebraic groups over non-algebraically closed perfect fields.

7. #### Corwin–Greenleaf multiplicity functions for Hermitian symmetric spaces

Nasrin, Salma
Kobayashi’s multiplicity-free theorem asserts that irreducible unitary highest weight representations $\pi$ are multiplicity-free when restricted to any symmetric pairs if $\pi$ is of scalar type. The Hua–Kostant–Schmid–Kobayashi branching laws embody this abstract theorem with explicit irreducible decomposition formulas of holomorphic discrete series representations with respect to symmetric pairs. In this paper, we study the ‘classical limit’ (geometry of coadjoint orbits) of a special case of these representation theoretic theorems in the spirit of the Kirillov–Kostant–Duflo orbit method. \\ First, we consider the Corwin–Greenleaf multiplicity function $n (\mathcal{O}^{G},\,\mathcal{O}^{K})$ for Hermitian symmetric spaces $G/K$. The first main theorem is that $n(\mathcal{O}^{G},\,\mathcal{O}^{K}) \le 1$...

8. #### The tropical resultant

Odagiri, Shinsuke
The resultant of two tropical polynomials satisfies the similar properties to the resultant of two polynomials over a field.

9. #### Dedekind sums in finite characteristic

Hamahata, Yoshinori
This paper is concerned with Dedekind sums in finite characteristic. We introduce Dedekind sums for lattices, and establish the reciprocity law for them.

10. #### On $p$-class group of an $A_{n}$-extension

Konomi, Yutaka
Let $p$ be a prime and $L$ an $A_{n}$-extension over a number field $K$. The aim of this paper is to estimate the ratio of the $p$-class number of $L$ to the ambiguous $p$-class number of $L$ with respect to $K$.

11. #### Duality of linking pairing in Arnold’s singularities

Hikami, Kazuhiro
As a new aspect of the Arnold strange duality among 14 unimodal singularities, we point out that there exists a duality in linking pairing on Seifert manifolds associated with singularities.

12. #### Sur la structure des espaces de Riemann dont le groupe d'holonomie fixe un plan à un nombre quelconque de dimensions

Yano, Kentaro; Sasaki, Shigeo

Honda, Kinya

16. #### Sur les propriétés de la famille des courbes intégrales d'un système différentiel ordinaire

Hukuhara, Masuo