arXiv subjects

Shoichi Hasegawa

Publications and source records attributed to Shoichi Hasegawa.

23 records · Page 2Linked to original sources

arXiv2021

On weak solutions to a fractional Hardy-Hénon equation: Part II: Existence

This paper and [29] treat the existence and nonexistence of stable weak solutions to a fractional Hardy--Hénon equation $(-Δ)^s u = |x|^\ell |u|^{p-1} u$ in $\mathbb{R}^N$, where $0 < s < 1$, $\ell > -2s$, $p>1$, $N \geq 1$ and $N > 2s$. In this paper, when $p$ is critical or supercritical in the sense of the Joseph--Lundgren, we prove the existence of a family of positive radial stable solutions, which satisfies the separation property. We also show the multiple existence of the Joseph--Lundgren critical exponent for some $\ell \in (0,\infty)$ and $s \in (0,1)$, and this property does not hold in the case $s=1$.

math.AP↗

arXiv2021

On weak solutions to a fractional Hardy--Hénon equation: Part I: Nonexistence

This paper and [17] treat the existence and nonexistence of stable (resp. outside stable) weak solutions to a fractional Hardy--Hénon equation $(-Δ)^s u = |x|^\ell |u|^{p-1} u$ in $\mathbb{R}^N$ where $0 < s < 1$, $\ell > -2s$, $p>1$, $N \geq 1$ and $N > 2s$. In this paper, the nonexistence part is proved for the Joseph--Lundgren subcritical case.

math.AP↗

arXiv2020

Sensitivity to Haptic-Audio Envelope Asynchrony

We want to understand the human capabilities to perceive amplitude similarities between a haptic and an audio signal. So, four psychophysical experiments were performed. Three of them measured the asynchrony JND (Just Noticeable Difference) at the signals' attack, release and decay, while the forth experiment measured the amplitude decrease on the middle of the signal. All the experiments used a combination of the constant stimulus and staircase methods to present two stimuli, while the participants' (N=12) task was to identify which of the two stimuli was synchronized. The audiotactile stimulus was defined using an stereo audio signal with an ADSR (Attack Decay Sustain Release) envelope. The partial results reveal JNDs for temporal asynchrony of: 54ms for attack, 265ms for decay and 57ms for release. Also the results reveal an amplitude decrease JND of 25\%. Although for decay the results were to disperse, therefore we suspect that the participants were not able to the changes on the haptic signal.

cs.HC↗

arXiv2014

Observation of the "$K^-pp$"-like structure in the $d(π^+, K^+)$ reaction at 1.69 GeV/$c$

We have observed a "$K^-pp$"-like structure in the $d(π^+,K^+)$ reaction at 1.69 GeV/$c$. In this reaction $Λ(1405)$ hyperon resonance is expected to be produced as a doorway to form the $K^-pp$ through the $Λ^*p\rightarrow K^-pp$ process. However, most of the produced $Λ(1405)$'s would escape from deuteron without secondary reactions. Therefore, coincidence of high-momentum ($>$ 250~MeV/$c$) proton(s) in large emission angles ($39^\circ<θ_{lab.}<122^\circ$) was requested to enhance the signal-to-background ratio. A broad enhancement in the proton coincidence spectra are observed around the missing-mass of 2.27 GeV/$c^2$, which corresponds to the $K^-pp$ binding energy of 95 $^{+18}_{-17}$ (stat.) $^{+30}_{-21}$ (syst.) MeV and the width of 162 $^{+87}_{-45}$ (stat.) $^{+66}_{-78}$ (syst.) MeV.

nucl-ex↗

arXiv2014

Inclusive spectrum of the $d(π^+, K^+)$ reaction at 1.69 GeV/c

We have measured an inclusive missing-mass spectrum of the $d(π^+, K^+)$ reaction at the pion incident momentum of 1.69 GeV/$c$ at the laboratory scattering angles between 2$^\circ$ and 16$^\circ$ with the missing-mass resolution of 2.7 $\pm$ 0.1 MeV/$c^2$ (FWHM) at the missing mass of 2.27 GeV/$c^{2}$. In this Letter, we first try to understand the spectrum as a simple quasi-free picture based on several known elementary cross sections, considering the neutron/proton Fermi motion in deuteron. While gross spectrum structures are well understood in this picture, we have observed two distinct deviations; one peculiar enhancement at 2.13 GeV/$c^2$ is due to the $ΣN$ cusp, and the other notable feature is a shift of a broad bump structure, mainly originating from hyperon resonance productions of $Λ(1405)$ and $Σ(1385)^{+/0}$, by about 22.4 $\pm$ 0.4 (stat.) $^{+2.7}_{-1.7}$ (syst.) MeV/$c^2$ toward the low-mass side, which is calculated in the kinematics of a proton at rest as the target.

nucl-ex↗