## Recursos de colección

1. #### Reaction-diffusion system approximation to the cross-diffusion competition system

Izuhara, Hirofumi; Mimura, Masayasu
We study the stationary problem of a reaction-diffusion system with a small parameter $\varepsilon$, which approximates the cross-diffusion competition system proposed to study spatial segregation problem between two competing species. The convergence between two systems as $\varepsilon \downarrow 0$ is discussed from analytical and complementarily numerical point of views.

2. #### Dynamical approximation of internal transition layers in a bistable nonlocal reaction-diffusion equation via the averaged mean curvature flow

Okada, Koji
A singular perturbation problem for a scalar bistable nonlocal reaction-diffusion equation is treated. It is rigorously proved that the layer solutions of this nonlocal reaction-diffusion equation converge to solutions of the averaged mean curvature flow on a finite time interval as the singular perturbation parameter tends to zero.

3. #### Canonical filtrations and stability of direct images by Frobenius morphisms II

Kitadai, Yukinori; Sumihiro, Hideyasu
We study the stability of direct images by Frobenius morphisms. We prove that if the cotangent vector bundle of a nonsingular projective surface $X$ is semistable with respect to a numerically positive polarization divisor satisfying certain conditions, then the direct images of the cotangent vector bundle tensored with line bundles on $X$ by Frobenius morphisms are semistable with respect to the polarization. Hence we see that the de Rham complex of $X$ consists of semistable vector bundles if $X$ has the semistable cotangent vector bundle with respect to the polarization with certain mild conditions.

4. #### Isolated singularities, growth of spherical means and Riesz decomposition for superbiharmonic functions

Futamura, Toshihide; Kitaura, Keiji; Mizuta, Yoshihiro
We consider Riesz decomposition theorem for superbiharmonic functions in the punctured ball. In fact, we show that under certain growth condition on surface integrals, superbiharmonic functions are represented as a sum of potentials and biharmonic functions.

5. #### On strongly $1$-trivial Montesinos knot

Torisu, Ichiro
We present a certain family of strongly $1$-trivial Montesinos knots, and show that if a well-known conjecture on Seifert surgery is valid, then the family contains all strongly $1$-trivial Montesinos knots.

6. #### Partial primitives, polyprimitives and decompositions of the class of infinitely differentiable functions

Kurokawa, Takahide
We give two kinds of direct sum decompositions of the class of infinitely differentiabe functions. They are related to the kernel of the higher order partial derivative operator and the polynomial space.

7. #### John disks are local bilipschitz images of quasidisks

Broch, Ole Jacob
It is proved that all bounded John disks are local bilipschitz images of quasidisks. This makes it easy to prove many necessary conditions for John disks

8. #### Compact Toeplitz operators on parabolic Bergman spaces

Nishio, Masaharu; Suzuki, Noriaki; Yamada, Masahiro
Parabolic Bergman space $\berg[p]$ is a Banach space of all $p$-th integrable solutions of a parabolic equation $(\partial/\partial t + (-\Delta)^{\alpha})u = 0$ on the upper half space, where $0<\alpha\leq1$ and $1\leq p<\infty$. In this note, we consider the Toeplitz operator from $\berg[p]$ to $\berg[q]$ where $p\leq q$, and discuss the condition that it be compact.

9. #### Elliptic equations with nonstandard growth involving measures

Lukkari, T.
We show that given a positive and finite Radon measure $\mu$, there is a $\Apx$ -superharmonic function $u$ which satisfies $-\dive\A(x,Du)=\mu$ ¶ in the sense of distributions. Here $\A$ is an elliptic operator with $p(x)$-type nonstandard growth.

10. #### Floquet representations and asymptotic behavior of solutions to periodic linear difference equations

Naito, T.; Ngoc, P. H. A.; Shin, J. S.
We give new representations of solutions for the periodic linear difference equation of the type $x(n+1)=B(n)x(n)+b(n)$, where complex nonsingular matrices $B(n)$ and vectors $b(n)$ are $\rho$-periodic. These are based on the Floquet multipliers and the Floquet exponents, respectively. By using these representations, asymptotic behavior of solutions is characterized by initial values. In particular, we can characterize necessary and sufficient conditions that the equation has a bounded solution(or a $\rho$-periodic solution), and the Massera type theorem by initial values.

11. #### The genera of Galois closure curves for plane quartic curves

Watanabe, S.
Let $C$ be a smooth plane quartic curve defined over a field $k$ and $k(C)$ the rational function field of $C$. Let $\pi_P$ be the projection from $C$ to a line $\ell$ with a center $P\in C$. Then $\pi_P$ induces an extension of fields; $k(C)/k(\ell)$. Let $\widetilde C$ be a nonsingular model of the Galois closure of the extension, which we call the Galois closure curve of $k(C)/k(\ell)$. We give an answer to the problem for the genus of the Galois closure curve of quartic curve.

12. #### Large time behavior of solutions to the compressible Navier-Stokes equation in an infinite layer

Kagei, Y.
Large time behavior of solutions to the compressible Navier-Stokes equation around a given constant state is considered in an infinite layer ${\bf R}^{n-1}\times (0,a)$, $n\geq2$, under the no slip boundary condition for the velocity. The $L^p$ decay estimates of the solution are established for all $1\leq p\leq \infty$. It is also shown that the time-asymptotic leading part of the solution is given by a function satisfying the $n-1$ dimensional heat equation. The proof is given by combining a weighted energy method with time-weight functions and the decay estimates for the associated linearized semigroup

13. #### Renormalized solutions of Dirichlet problems for quasilinear elliptic equations with general measure data

Maeda, F.
We consider quasilinear elliptic equations with lower order term and general measure data. We define renormalized solutions of Dirichlet problems and show the existence of such solutions. We also give uniqueness in some special cases.

14. #### A Riesz decomposition theorem on harmonic spaces without positive potentials

Bajunaid, I.; Cohen, J. M.; Colonna, F.; Singman, D.
In this paper, we give a new definition of the flux of a superharmonic function defined outside a compact set in a Brelot space without positive potentials. We also give a new notion of potential in a BS space (that is, a harmonic space without positive potentials containing the constants) which leads to a Riesz decomposition theorem for the class of superharmonic functions that have a harmonic minorant outside a compact set. Furthermore, we give a characterization of the local axiom of proportionality in terms of a global condition on the space.

15. #### Maximally differential graded ideals in zero characteristic

Gaur, A.; Maloo, A. K.
A new proof, which is much simpler and which works in more generality, of a structure theorem on maximally differential graded ideals in a Noetherian graded ring containing a field of characteristic zero is given.

16. #### Norm estimates for the Bernardi integral transforms of functions defined by subordination

Parvatham, R.; Ponnusamy, S.; Sahoo, S. K.

18. #### On the oscillation of solutions of second order quasilinear ordinary differential equations

Kusano, Takaŝi; Ogata, Akio; Usami, Hiroyuki

Ilyas, Bilal

20. #### Kirillov-Kostant theory and Feynman path integrals on coadjoint orbits of a certain real semisimple Lie group

Hashimoto, Takashi

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