arXiv subjects
Publications and source records attributed to Takashi Sato.
We determine the $T$-equivariant integral cohomology of $F_4/T$ combinatorially by the GKM theory, where T is a maximal torus of the exceptional Lie group $F_4$ and acts on $F_4/T$ by the left multiplication.
We prove the equivariant Leray-Hirsch theorem combinatorially for sufficiently good torus equivariant fiber bundles consisting of homogeneous spaces of Lie groups. We apply this theorem to determining the equivariant integral cohomology ring of the flag manifold of type $E_6$ and express it explicitly as a quotient ring of a polynomial ring.
Presented is a successful two week lab involving real sky observations of the Moon in which students make telescopic observations and analyze their own images. Originally developed around the 35 mm film camera as a common household object adapted for astronomical work, the lab transitioned to use the webcam as film photography evolved into an obscure specialty technology and increasing numbers of students had little familiarity with it. The printed circuit board with the CCD is harvested from a retail webcam and affixed to a tube to mount on a telescope in place of an eyepiece. Image frames are compiled to form a lunar mosaic and crater sizes are measured. Students also work through the logistical steps of telescope time assignment and scheduling, keeping to schedule and working with uncertainties of weather, in ways paralleling research observations. Because there is no need for a campus observatory, this lab can be replicated at a wide variety of institutions.
Both classical and quantum version of two models of price competition in duopoly market, the one is realistic and the other is idealized, are investigated. The pure strategy Nash equilibria of the realistic model exists under stricter condition than that of the idealized one in the classical form game. This is the problem known as Edgeworth paradox in economics. In the quantum form game, however, the former converges to the latter as the measure of entanglement goes to infinity.
A quantum Cournot game of which classical form game has multiple Nash equilibria is examined. Although the classical equilibria fail to be Pareto optimal, the quantum equilibrium exhibits the following two properties, (i) if the measurement of entanglement between strategic variables chosen by the competing firms is sufficiently large, the multiplicity of equilibria vanishes, and, (ii) the more strongly the strategic variables are entangled, the more closely the unique equilibrium approaches to the optimal one.
Electric conduction in thin graphite film was tuned by two gate electrodes to clarify how the gate electric field induces electric carriers in thin graphite. The graphite was sandwiched between two gate electrodes arranged in a top and bottom gate configuration. A scan of the top gate voltage generates a resistance peak in ambiploar response. The ambipolar peak is shifted by the bottom gate voltage, where the shift rate depends on the graphite thickness. The thickness-dependent peak shift was clarified in terms of the inter-layer screening length to the electric field in the double-gated graphite film. The screening length of 1.2 nm was experimentally obtained.