Kei Irie

Hofer–Zehnder capacity of unit disk cotangent bundles and the loop product

We prove the finiteness of the Hofer-Zehnder capacity of unit disk cotangent bundles of closed Riemannian manifolds, under some simple topological assumptions on the manifolds. The key ingredient of the proof is a computation of the pair-of-pants product on Floer homology of cotangent bundles. We reduce it to a simple computation of the loop product, making use of results of A.Abbondandolo- M.Schwarz.

A numerical study on the effect of shear resistance on the landslide by Discontinuous Deformation Analysis (DDA)

Japan is located in Circum-Pacific earthquake zone, which is one of the most seismologically active areas in the world. As a result, landslides have occurred frequently and often cause serious damage not only to human lives but also to the various important structures such as national roads, railway, electric power plans etc. From the engineering point of view, to investigate the mechanism of landslide due to earthquakes and estimate the damage caused by landslides are important issues. In this study, as the first step, to check the validity of DDA simulation for the seismic problems, a series of shaking table tests were carried out in the laboratory and simulated by DDA. Then, one of the largest landslides occurred in Aratozawa Area, Miyagi, Japan in 2008 caused by Iwate-Miyagi Nairiku Earthquake was simulated using DDA and discussed the mechanisms of the landslide. The 2-D DDA model for one of the survey lines was created based on the geological survey, and physical properties were determined from the laboratory tests using rock/soil samples obtained from the landslide site. In this study, to discuss the mechanism of the landslide, a series of parametric study in terms of shear resistance along the fractures was conducted.

VC Dimensions of Principal Component Analysis

Motivated by statistical learning theoretic treatment of principal component analysis, we are concerned with the set of points in ℝd that are within a certain distance from a k-dimensional affine subspace. We prove that the VC dimension of the class of such sets is within a constant factor of (k+1)(d−k+1), and then discuss the distribution of eigenvalues of a data covariance matrix by using our bounds of the VC dimensions and Vapnik’s statistical learning theory. In the course of the upper bound proof, we provide a simple proof of Warren’s bound of the number of sign sequences of real polynomials.

A {C^\infty} closing lemma for Hamiltonian diffeomorphisms of closed surfaces

We prove a

Periodic billiard trajectories and Morse theory on loop spaces

{C^\infty}

Polyamidoamine dendrimer-conjugated quantum dots for efficient labeling of primary cultured mesenchymal stem cells.

C∞ closing lemma for Hamiltonian diffeomorphisms of closed surfaces. This is a consequence of a

DENSE EXISTENCE OF PERIODIC REEB ORBITS AND ECH SPECTRAL INVARIANTS

{C^\infty}