1.
On the classical limit of self-interacting quantum field Hamiltonians with cutoffs - AMMARI, Zied; ZERZERI, Maher
We study, using Hepp's method, the propagation of coherent states for a general class of self interacting bosonic quantum field theories with spatial cutoffs. This includes models with non-polynomial interactions in the field variables. We show indeed that the time evolution of coherent states, in the classical limit, is well approximated by time-dependent affine Bogoliubov unitary transformations. Our analysis relies on a non-polynomial Wick quantization and a specific hypercontractive estimate.

2.
Ulam's cellular automaton and Rule 150 - KAWAHARADA, Akane
In this paper we study Ulam's cellular automaton, a nonlinear almost equicontinuous two-dimensional cell-model of crystalline growths. We prove that Ulam's automaton contains a linear chaotic elementary cellular automaton (Rule 150) as a subsystem. We also study the application of the inverse ultradiscretization, a method for deriving partial differential equations from a given cellular automaton, to Ulam's automaton. It is shown that the partial differential equation obtained by the inverse ultradiscretization preserves the self-organizing pattern of Ulam's automaton.

3.
Fold maps with singular value sets of concentric spheres - KITAZAWA, Naoki
In this paper, we study fold maps from C^{∞} closed manifolds into Euclidean spaces whose singular value sets are disjoint unions of spheres embedded concentrically. We mainly study homology and homotopy groups of manifolds admitting such maps.

4.
Radiation condition at infinity for the high-frequency Helmholtz equation: optimality of a non-refocusing criterion - CASTELLA, François; KLAK, Aurélien
We consider the high frequency Helmholtz equation with a variable refraction index n^{2}(x) (x ∈ ℝ^{d}), supplemented with a given high frequency source term supported near the origin x = 0. A small absorption parameter α_{ε} > 0 is added, which prescribes a radiation condition at infinity for the considered Helmholtz equation. The semi-classical parameter is ε > 0. We let ε and α_{ε} go to zero simultaneously. We study the question whether the prescribed radiation condition at infinity is satisfied uniformly along the asymptotic process ε Ⅺ 0.
¶ This question has been previously studied by the first autor in...

5.
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.

6.
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.

7.
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.

8.
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, +∞).

9.
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)...

10.
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.

11.
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.

12.
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.

13.
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.

14.
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.

15.
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.

17.
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.

19.
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).

20.
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.