1.
Two applications of matrix volume - CHEN, Qinghua; ZHOU, Zhenqiang; ZHANG, Jinzhou; CHEN, Rongqun
This paper puts forward two applications of matrix volume. First, we present a new method to determine whether a matrix is orthogonal; second, a new way is given to indicate whether a linear system is consistent.

2.
K-theory for the group C^{*}-algebras of certain solvable discrete groups - SUDO, Takahiro
We compute the K-theory groups for the group C^{*}-algebras of certain solvable discrete groups. The solvable discrete groups considered are the discrete elementary ax + b group and the generalized discrete elementary ax + b groups and their proper versions, and also the generalized discrete elementary Mautner groups and products of the generalized discrete elementary ax + b groups and their proper versions.

3.
A remark on the Navier-Stokes flow with bounded initial data having a special structure - SAWADA, Okihiro
The Navier-Stokes equations with bounded initial data admit unique local-in-time smooth mild solutions. It is shown that the solution can be extended globally-in-time, if the initial velocity has a special structure. Thanks to the structure, the annihilation of the pressure occurs, and then the mild solution is a solution to the viscous Burgers equations.
By the maximum principle, it is derived an a priori bound for velocity, uniformly in time and space.

4.
A construction of special Lagrangian 3-folds via the generalized Weierstrass representation - OKUHARA, Saki
We show that certain holomorphic loop algebra-valued 1-forms over Riemann surfaces yield minimal Lagrangian immersions into the complex 2-dimensional projective space via the Weierstrass type representation, hence 3-dimensional special Lagrangian submanifolds of ℂ^{3}. A particular family of 1-forms on ℂ corresponds to solutions of the third Painlevé equation which are smooth on (0, +∞).

5.
Cohomological equations and invariant distributions on a compact Lie group - EL KACIMI ALAOUI, Aziz; HMILI, Hadda
This paper deals with two analytic questions on a
connected compact Lie group G. i) Let a ∈ G
and denote by γ the diffeomorphism of G given by γ (x) = ax (left translation by a). We give necessary and sufficient conditions for the existence of solutions of the cohomological equation f - f ∘ γ = g on the Fréchet space C^{∞} (G) of complex C^{∞} functions on G. ii) When G is the torus ${\Bbb T}^n$, we compute explicitly the distributions on ${\Bbb T}^n$ invariant by an affine automorphism γ, that is, γ (x) = A (x + a)...

6.
Congruence classes of minimal ruled real hypersurfaces in a nonflat complex space form - ADACHI, Toshiaki; BAO, Tuya; MAEDA, Sadahiro
In this paper we study congruency of minimal ruled real hypersurfaces in a nonflat complex space form with respect to the action of its isometry group. We show that those in a complex hyperbolic space are classified into 3 classes and show that those in a complex projective space are congruent to each other hence form just one class.

7.
Biharmonic maps into symmetric spaces and integrable systems - URAKAWA, Hajime
In this paper, the formulation of the biharmonic map equation in terms of the Maurer-Cartan form for all smooth maps of a compact Riemannian manifold into a Riemannian symmetric space (G/K,h) induced from the bi-invariant Riemannian metric h on G is obtained. Using this, all the biharmonic curves into symmetric spaces are determined, and all the biharmonic maps of an open domain of ℝ^{2} with the standard Riemannian metric into (G/K,h) are characterized exactly.

8.
Biharmonic maps into compact Lie groups and integrable systems - URAKAWA, Hajime
In this paper, the formulation of the biharmonic map equation in terms of the Maurer-Cartan form for all smooth maps of a compact Riemannian manifold into a compact Lie group (G,h) with the bi-invariant Riemannian metric h is obtained. Using this, all biharmonic curves into compact Lie groups are determined exactly, and all the biharmonic maps of an open domain of ℝ^{2} equipped with a Riemannian metric conformal to the standard Euclidean metric into (G,h) are determined.

9.
On the character table of 2-groups - ABE, Shousaku
We shall show that there are infinite pairs of non-direct product 2-groups with the same character. They are not pairs of the generalized quaternion group and dihedral group.

10.
Quasi-invariance of measures of analytic type on locally compact abelian groups - YAMAGUCHI, Hiroshi
Asmar, Montgomery-Smith and Saeki gave a generalization of a theorem of Bochner for a locally compact abelian group with certain direction. We show that a strong version of their result holds for a σ-compact, connected locally compact abelian group with certain direction. We also give several conditions for quasi-invariance of analytic measures and another proof of a theorem of deLeeuw and Glicksberg.

11.
On the univalence conditions for certain class of analytic functions - KUROKI, Kazuo; OWA, Shigeyoshi
A univalence condition for certain class of analytic functions was discussed by D. Yang and S. Owa (Hokkaido Math. J. 32 (2003), 127-136). In the present paper, by discussing some subordination relation, a new univalence condition is deduced.

13.
Algebraic independence of infinite products generated by Fibonacci and Lucas numbers - LUCA, Florian; TACHIYA, Yohei
The aim of this paper is to give an algebraic independence result for the two infinite products involving the Lucas sequences of the first and second kind. As a consequence, we derive that the two infinite products ∏_{k=1}^{∞}(1+1/F_{2k}) and ∏_{k=1}^{∞}(1+1/L_{2k}) are algebraically independent over ℚ, where {F_{n}}_{n≥0} and {L_{n}}_{n≥0} are the Fibonacci sequence and its Lucas companion, respectively.

15.
Classification of polarized manifolds by the second sectional Betti number - Fukuma, Yoshiaki
Let X be an n-dimensional smooth projective variety defined over the field of complex numbers, let L be an ample and spanned line bundle on X. Then we classify (X,L) with b_{2}(X,L) = h^{2}(X,ℂ)+1, where b_{2}(X,L) is the second sectional Betti number of (X,L).

16.
An estimate of the spread of trajectories for Kähler magnetic fields - BAI, Pengfei; ADACHI, Toshiaki
On a Kähler manifold we consider trajectories under the influence of Kähler magnetic fields. They are smooth curves which are parameterized by their arclengths and whose velocities and normal vectors form complex lines. In this paper we study how trajectories spread, and give an estimate of norms of magnetic Jacobi fields from below and an estimate of area elements of trajectory-spheres.

17.
Integral identities for Bi-Laplacian problems and their application to vibrating plates - LEI, Guang-Tsai; PAN, Guang-Wen (George)
In this paper we derive boundary integral identities for the bi-Laplacian eigenvalue problems under Dirichlet, Navier and simply-supported boundary conditions. By using these integral identities, we prove that the first eigenvalue of the eigenvalue problem under the simply-supported boundary conditions strictly increases with Poisson's ratio. In addition, we establish the boundary integral expressions for the strain energy calculation of the vibrating plates under the three types of boundary conditions.

18.
A normal family of operator monotone functions - MOSLEHIAN, Mohammad Sal; NAJAFI, Hamed; UCHIYAMA, Mitsuru
We show that the family of all operator monotone functions f on (-1,1) such that f(0) = 0 and f′(0) = 1 is a normal family and investigate some properties of odd operator monotone functions. We also characterize the odd operator monotone functions and even operator convex functions on (-1,1). As a consequence, we show that if f is an odd operator monotone function on (-1,1), then f is concave on (-1,0) and convex on (0,1).

19.
The Lie algebra of rooted planar trees - ISHIDA, Tomohiko; KAWAZUMI, Nariya
We study a natural Lie algebra structure on the free vector space generated by all rooted planar trees as the associated Lie algebra of the nonsymmetric operad (non-Σ operad, preoperad) of rooted planar trees. We determine whether the Lie algebra and some related Lie algebras are finitely generated or not, and prove that a natural surjection called the augmentation homomorphism onto the Lie algebra of polynomial vector fields on the line has no splitting preserving the units.

20.
Continuity of Julia sets and its Hausdorff dimension of P_{
c
}(z) = z^{
d
} + c - ZHUANG, Wei
Given d ≥ 2 consider the family of monic polynomials P_{c}(z) = z^{d} + c, for c ∈ ℂ. Denote by J_{c} and HD(J_{c}) the Julia set of P_{c} and the Hausdorff dimension of J_{c} respectively, and let $\mathcal{M}$_{d} = {c|J_{c} is connected} be the connectedness locus; for d = 2 it is called the Mandelbrot set. We study semihyperbolic parameters c_{0} ∈ ∂ $\mathcal{M}$_{d}: those for which the critical point is not recurrent by P_{c0}, 0 ∈ J_{c0}, and without parabolic cycles. We prove that if P_{cn} Ⅺ P_{c0} algebraically, then for some C > 0,
d_{H}(J_{cn}, J_{c0}) ≤ C|c_{n}...