arXiv subjects

Hiroyuki Ogawa

Publications and source records attributed to Hiroyuki Ogawa.

5 recordsLinked to original sources

arXiv2025

Leaf as a Poincaré convex domain associated with an endomorphism on a real inner product space

We define a subset of the closure of the upper half plane associated with an endomorphism on a real inner product space, which is called the leaf. When the dimension of the space is at least 3, the leaf is a convex with respect to the Poincaré metric, and contains all eigenvalues with nonnegative imaginary part. Moreover, the leaf of a normal endomorphism is the minimum Poincaré convex domain containing all eigenvalues with nonnegative imaginary part. The most commonly studied convex domain containing eigenvalues is number range. Numerical range is convex with respect to the Euclidean metric on $\mathbb C$, so numerical range has less information than leaf about real eigenvalues. We provide a new visual approach to endomorphisms.

math.FA↗

arXiv2022

Thermal Control System to Easily Cool the GAPS Balloon-borne Instrument on the Ground

This study developed a novel thermal control system to cool detectors of the General AntiParticle Spectrometer (GAPS) before its flights. GAPS is a balloon-borne cosmic-ray observation experiment. In its payload, GAPS contains over 1000 silicon detectors that must be cooled below $-40^{\circ}\mbox{C}$. All detectors are thermally coupled to a unique heat-pipe system (HPS) that transfers heat from the detectors to a radiator. The radiator is designed to be cooled below $-50^{\circ}\mbox{C}$ during the flight by exposure to space. The pre-flight state of the detectors is checked on the ground at 1 atm and ambient room temperature, but the radiator cannot be similarly cooled. The authors have developed a ground cooling system (GCS) to chill the detectors for ground testing. The GCS consists of a cold plate, a chiller, and insulating foam. The cold plate is designed to be attached to the radiator and cooled by a coolant pumped by the chiller. The payload configuration, including the HPS, can be the same as that of the flight. The GCS design was validated by thermal tests using a scale model. The GCS design is simple and provides a practical guideline, including a simple estimation of appropriate thermal insulation thickness, which can be easily adapted to other applications.

astro-ph.IM↗

arXiv2021

Lissajous 3-braids

We classify 3-braids arising from collision-free choreographic motions of 3 bodies on Lissajous plane curves, and present a parametrization in terms of levels and (Christoffel) slopes. Each of these Lissajous 3-braids represents a pseudo-Anosov mapping class whose dilatation increases when the level ascends in the natural numbers or when the slope descends in the Stern-Brocot tree. We also discuss 4-symbol frieze patterns that encode cutting sequences of geodesics along the Farey tessellation in relation to odd continued fractions of quadratic surds for the Lissajous 3-braids.

math.GT↗

arXiv2020

On generalized median triangles and tracing orbits

We study generalization of median triangles on the plane with two complex parameters. By specialization of the parameters, we produce periodical motion of a triangle whose vertices trace each other on a common closed orbit.

math.MG↗

arXiv2019

A family of geometric operators on triangles with two complex variables

Given a plane triangle $Δ$, one can construct a new triangle $Δ'$ whose vertices are intersections of two cevian triples of $Δ$. We extend the family of operators $Δ\mapstoΔ'$ by complexifying the defining two cevian parameters and study its rich structure from arithmetic-geometric viewpoints. We also find another useful parametrization of the operator family via finite Fourier analysis and apply it to investigate area-preserving operators on triangles.

math.MG↗