arXiv subjects
Publications and source records attributed to Kazuki Sato.
In this paper, we study the solution structures of Serrin-type overdetermined problems with Kirchhoff-type nonlocal terms. We prove that the exact number of solutions is the same as those of some transcendental equations defined by the nonlocal terms. We also obtain the explicit form of solutions by using the unique solutions of the overdetermined problems without the nonlocal terms.
We study whether the norm one torus associated with a finite separable non-Galois field extension $K/k$ is $p$-retract rational over $k$ for a prime $p$, focusing on the case where the Galois group of the Galois closure of $K/k$ is either the symmetric or the alternating group.
In this paper, we study an overdetermined problem with Kirchhoff type nonlocal terms related to the celebrated work by Serrin. We obtain the precise number of solutions according to the value of the bifurcation parameter and study asymptotics of bifurcation curves of solutions when the bifurcation parameter is large in some cases.
In this paper, we study one-dimensional boundary blow up problems with Kirchhoff type nonlocal terms on an interval. We perform a bifurcation analysis on the problems and obtain the precise number of solutions according to the value of the bifurcation parameter. We also obtain the precise asymptotic formula for solutions for special cases.
We show that the holomorph of a cyclic group of order $n$ is isomorphic to its own automophism group when $n$ is twice of a power of an odd prime.
We showcase a study on the physical properties of the Circumnuclear Disk surrounding the Sgr A* of the Galactic Center, emphasizing the role of magnetic field (B field) with 0.47 pc spatial resolution, based on the sensitive λ = 850 μm polarization data taken with the JCMT. The B field within the CND exhibits a coherent spiral pattern. Applying the model described by Wardle and Ko\ddot{o}nigl 1990 (WK model) to the observed B field pattern, it favors gas-pressure-dominant models without dismissing a gas-and-B field comparable model, leading us to estimate the B-field strength in the ionized cavity around Sgr A* as 0.24 + 0.05 mG. Analysis -0.04 based on the WK model further allows us to derive representative B-field strengths for the radial, azimuthal, and vertical components as (Br,Bϕ,Bz) = (0.4 \pm 0.1,-0.7 \pm 0.2,0.2 \pm 0.05) mG, respectively. A key finding is that the |ϕ| component is dominant over Br and Bz components, consistent with the spiral morphology, indicating that the CND' s B-field is predominantly toroidal, possibly shaped by accretion dynamics. Considering the turbulent pressure, estimated plasma \{beta} values indicate the effective gas pressure should surpass the magnetic pressure. Assessing the CND of our MWG in the toroidal-and-vertical stability parameter space, we propose that such an "effective" magnetoro-tational instability (MRI) may likely be active. The estimated maximum unstable wavelength, λmax = 0.1 \pm 0.1 pc, is smaller than the CND' s scale height (0.2 \pm 0.1 pc), which indicates the potential for the effective MRI intermittent cycles of \sim 10^{6} years, which should profoundly affect the CND's evolution, considering the estimated mass accretion rate of 10^{-2}M_{\odot} yr^{-1} to the Sgr A*.
Complexity of quantum phases of matter is often understood by the underlying gauge structures, as was recognized by the $\mathbb{Z}_2$ and U(1) gauge theory description of spin liquid in frustrated magnets. Anomalous Hall effect of conducting electrons can intrisically arise from U(1) gauges expressing the spatial modulation of ferromagnetic moments or from SU(2) gauges representing the spin-orbit coupling effect. Similarly, in insulating ferro and antiferromagnets, the magnon excitations can contribute to anomalous transports by feeling the U(1) and SU(2) gauges arising from the features of ordered moments or interactions. In this work, we report the emergent higher rank SU(3) gauge structure in the magnon transport based on the thermal conductivity measurements of MnSc$_2$S$_4$ in an applied field up to 14\,T. The thermal Hall coefficient takes a substantial value when the material enters a three-sublattice antiferromagnetic skyrmion phase, which is confirmed by the large-scale spin wave theory. The excited magnons are dressed with SU(3) gauge field, which is a mixture of three species of U(1) gauge fields originating from the slowly varying magnetic moments on these sublattices.
This paper considers several approximate operators used in a particle method based on a Voronoi diagram. We introduce and study our approximate operators on gradient and Laplace operators. We derive error estimates for these approximate operators by applying our weight functions. The key idea of deriving our error estimates is to divide the integration region into a ring-shaped area and some areas. In the Appendix, we give an example application of the main results of this paper.
In image anomaly detection, Autoencoders are the popular methods that reconstruct the input image that might contain anomalies and output a clean image with no abnormalities. These Autoencoder-based methods usually calculate the anomaly score from the reconstruction error, the difference between the input image and the reconstructed image. On the other hand, the accuracy of the reconstruction is insufficient in many of these methods, so it leads to degraded accuracy of anomaly detection. To improve the accuracy of the reconstruction, we consider defining loss function in the frequency domain. In general, we know that natural images contain many low-frequency components and few high-frequency components. Hence, to improve the accuracy of the reconstruction of high-frequency components, we introduce a new loss function named weighted frequency domain loss(WFDL). WFDL provides a sharper reconstructed image, which contributes to improving the accuracy of anomaly detection. In this paper, we show our method's superiority over the conventional Autoencoder methods by comparing it with AUROC on the MVTec AD dataset.
New superconductors, Li$_x$(C$_n$H$_{2n+3}$N)$_y$Fe$_{1-z}$Se ($n$ = 6, 8, 18), have been synthesized via the co-intercalation of linear monoamines together with Li into FeSe. The distance between neighboring Fe layers expands up to 55.7 Å for n = 18, which is much larger than the previous record of 19 Å in the FeSe-based intercalation superconductors. Tc remains saturated at $\sim$42 K.
We have developed a method to make a spectral-line-based survey of hot cores, which represent an important stage of high-mass star formation, and applied the method to the data of the FUGIN (FOREST Unbiased Galactic plane Imaging survey with the Nobeyama 45-m telescope) survey. First, we select hot core candidates by searching the FUGIN data for the weak hot core tracer lines (HNCO and CH$_3$CN) by stacking, and then we conduct follow-up pointed observations on these candidates in C$^{34}$S, SO, OCS, HC$_3$N, HNCO, CH$_3$CN, and CH$_3$OH $J=2-1$ and $J=8-7$ lines to confirm and characterize them. We applied this method to the $l = 10^\circ-20^\circ$ portion of the FUGIN data and identified 22 "Hot Cores" (compact sources with more than two significant detection of the hot core tracer lines, i.e., SO, OCS, HC$_3$N, HNCO, CH$_3$CN, or CH$_3$OH $J=8-7$ lines) and 14 "Dense Clumps" (sources with more than two significant detection of C$^{34}$S, CH$_3$OH $J=2-1$, or the hot core tracer lines). The identified Hot Cores are found associated with signposts of high-mass star formation such as ATLASGAL clumps, WISE HII regions, and Class II methanol masers. For those associated with ATLASGAL clumps, their bolometric luminosity to clump mass ratios are consistent with the star formation stages centered at the hot core phase. The catalog of FUGIN Hot Cores provides a useful starting point for further statistical studies and detailed observations of high-mass star forming regions.
We have succeeded in synthesizing new intercalation superconductors Lix(C2H8N2)yMoSe2 and Lix(C6H16N2)yMoSe2 with Tc = 4.2 and 3.8-6.0 K, respectively, via the co-intercalation of lithium and ethylenediamine or hexamethylenediamine into semiconducting 2H-MoSe2. It has been found that the Tc values are related not to the interlayer spacing between MoSe2 layers so much but to the electronic density of states (EDOS) at the Fermi level. Moreover, only Li-intercalated LixMoSe2 with a small interlayer spacing has been found to be non-superconducting. Accordingly, it has been concluded that not only a sufficient amount of EDOS at the Fermi level due to the charge transfer from intercalated Li to MoSe2 layers but also the enhancement of the two-dimensionality of the crystal structure and/or electronic structure due to the expansion of the interlayer spacing between MoSe2 layers is necessary for the appearance of superconductivity in MoSe2-based intercalation superconductors. The pairing mechanism and the analogy to the superconductivity in the electric double-layer transistors of 2H-MoX2 (X = S, Se, Te) are discussed.
New intercalation superconductors of Li$_x$(C$_2$H$_8$N$_2$)$_y$TiSe$_2$ and Li$_x$(C$_6$H$_{16}$N$_2$)$_y$TiSe$_2$ with $T_{\rm c}$ = 4.2 K have successfully been synthesized via the co-intercalation of lithium and ethylenediamine or hexamethylenediamine into 1T-TiSe$_2$. Moreover, it has been found that both intercalation compounds of Li$_x$TiSe$_2$ and (C$_2$H$_8$N$_2$)$_y$TiSe$_2$ also show superconductivity with $T_{\rm c}$ = 2.4 K and 2.8 K, respectively. These results indicate that both the electron doping due to the intercalation of lithium and the expansion of the interlayer spacing between TiSe2 layers due to the intercalation of diamines suppress the charge density wave in 1T-TiSe$_2$, leading to the appearance of superconductivity.
We consider the dominant equations for the motion of the non-Newtonian fluid in a domain from an energetic point of view. We apply our energetic variational approaches and the first law of thermodynamics to derive the generalized compressible non-Newtonian fluid system. We also derive the generalized incompressible non-Newtonian fluid system by using our energetic variational approaches.
New FeSe-based intercalation superconductors, $A_x$(C$_8$H$_{11}$N)$_y$Fe$_{1-z}$Se ($A$ = Li, Na), with $T_\mathrm{c}$ = 39-44 K have been successfully synthesized via the intercalation of alkali metals and 2-phenethylamine into FeSe. The interlayer spacings, namely, the distances between neighboring Fe layers, $d$, of $A_x$(C$_8$H$_{11}$N)$_y$Fe$_{1-z}$Se ($A$ = Li, Na) are 19.04(6) and 18.0(1) Å, respectively. These $d$ values are the largest among those of the FeSe-based intercalation compounds and are understood to be due to the intercalation of two molecules of 2-phenethylamine in series perpendicular to the FeSe layers. It appears that the relationship between $T_\mathrm{c}$ and $d$ in the FeSe-based intercalation superconductors is not domic but $T_\mathrm{c}$ is saturated at ~ 45 K, which is comparable to the $T_\mathrm{c}$ values of single-layer FeSe films, for $d$ $\geq$ 9 Å.
We show under the assumption that the Tate-Shafarevich group of any elliptic curve over the rational numbers is finite that the cubic surface $x_1^3 + p_1p_2x_2^3 + p_2p_3x_3^3 + p_3p_1x_4^3 = 0$ has a rational point, where $p_1, p_2$ and $p_3$ are rational primes congruent to $2$ or $5$ modulo $9$.
We show the observation of the coexistence of bulk superconductivity and ferromagnetism in CeO1-xFxBiS2(x = 0 - 1.0) prepared by annealing under high-pressure. In CeO1-xFxBiS2 system, both superconductivity and two types of ferromagnetism with respective magnetic transition temperatures of 4.5 K and 7.5 K are induced upon systematic F substitution. This fact suggests that carriers generated by the substitution of O by F are supplied to not only the BiS2 superconducting layers but also the CeO blocking layers. Furthermore, the highest superconducting transition temperature is observed when the ferromagnetism is also enhanced, which implies that superconductivity and ferromagnetism are linked to each other in the CeO1-xFxBiS2 system.
We give a sufficient condition for the injectivity of the global-to-local map of the relative Chow group of zero-cycles on a quadric fibration of dimension 2 or 3 defined over a number field.