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Here, we investigate the thermoelectric properties of the marcasite-type compounds MSb$_2$ (M = Ta, Nb) in the temperature range of 310-730 K. These compounds were synthesized by a solid-state reaction followed by the spark plasma sintering process. The Rietveld refinement method confirms the monoclinic phase with space group C2/m for both compounds. The observed values of Seebeck coefficients exhibit non-monotonic behaviour in the studied temperature range, with the maximum magnitude of -14.4 and -22.7 $\mu$V K$^{-1}$ for TaSb$_2$ and NbSb$_2$, respectively at ~444 K. The negative sign of S in the full temperature window signifies the n-type behaviour of these compounds. Both electrical and thermal conductivities show an increasing trend with temperature. The experimentally observed thermoelectric properties are understood through the first-principles DFT and Boltzmann transport equation. A pseudogap in the density of states around the Fermi level characterizes the semimetallic behaviour of these compounds. The multi-band electron and hole pockets were found to be mainly responsible for the temperature dependence of transport properties. The experimental power factors are found to be ~0.09 and ~0.42 mW m$^{-1}$ K$^{-2}$ at 310 K for TaSb2 and NbSb2, respectively. From the DFT-based calculations, the maximum possible power factors for p-type conduction are predicted as ~1.14 and ~1.74 mW m$^{-1}$ K$^{-2}$, while these values are found to be ~1.16 and ~1.80 mW m$^{-1}$ K$^{-2}$ for n-type TaSb$_2$ and NbSb$_2$, respectively at 300 K with the corresponding doping concentrations. The present study suggests that the combined DFT and Boltzmann transport theory are found to be reasonably good at explaining the experimental transport properties, and moderate power factors are predicted.

The inverse scattering problem is applied to 2-dimensional partial differential equations called soliton equations such as the KdV equation and so on. It is also used to integrate the Einstein equations with axial symmetry. These inverse scattering problems look different. We show that they can be understood in a unified way. As an application to the Einstein equation, we find solutions of the Einstein-Maxwell equations with a magnetic charge., Comment: 2v:25 pages, 2 figures, typos corrected, some comments added in sections 1,3,4 and references added

We give an explicit formula for the $p$-Frobenius number of triples associated with Diophantine equations $x^2+y^2=z^r$, that is, the largest positive integer that can only be represented in $p$ ways by combining the three integers of the solutions of Diophantine equations $x^2+y^2=z^r$. When $r=2$, the Frobenius number has already been given.

In this paper, we study the Johnson homomorphisms of basis-conjugating automorphism groups of free groups. We construct obstructions for the surjectivity of the Johnson homomorphisms. By using it, we determine its cokernels of degree up to four, and give further observations for degree greater than four. As applications, we give the affirmative answer for the Andreadakis problem for degree four. We show that the cup product map of the first cohomology groups of the basis-conjugating automorphism group of a free group into the second cohomology group is surjective. Finally, we calculate the twisted first cohomology groups of the braid-permutation automorphism groups of a free group.

Integrating topology optimization and additive manufacturing (AM) technology can facilitate innovative product development. However, laser powder bed fusion, which is the predominant method in metal AM, can lead to issues such as residual stress and deformation. Recently, topology optimization methods considering these stresses and deformations have been proposed; however, they suffer from challenges caused by an increased computational cost. In this study, we propose a method for reducing computational cost in topology optimization considering the deformation in AM. An inherent strain method-based analytical model is presented for simulating the residual stress and deformation in the AM process. Subsequently, a constraint condition to suppress the deformation is formulated, and a method to reduce the computational cost of the adjoint analysis in deriving sensitivity is proposed. The minimum mean compliance problem considering AM deformation and self-support constraints can then be incorporated into the level set-based topology optimization framework. Finally, numerical examples are presented for validating the effectiveness of the proposed topology optimization method., Comment: 26 pages, 15 figures

We introduce a novel model to spectroscopically constrain the mid-infrared (MIR) extinction/attenuation curve from 3--17 um, using Polycyclic Aromatic Hydrocarbon (PAH) emission drawn from an AKARI-Spitzer extragalactic cross-archival dataset. Currently proposed MIR extinction curves vary significantly in their slopes toward the near-infrared, and the variation of the strengths and shapes of the 9.7 um and 18 um silicate absorption features make MIR spectral modeling and interpretation challenging, particularly for heavily obscured galaxies. By adopting the basic premise that PAH bands have relatively consistent intrinsic ratios within dusty starbursting galaxies, we can, for the first time, empirically determine the overall shape of the MIR attenuation curve by measuring the differential attenuation at specific PAH wavelengths. Our attenuation model shows PAH emission in most (U)LIRGs is unambiguously subjected to attenuation, and we find strong evidence that PAH bands undergo differential attenuation as obscuration increases. Compared to pre-existing results, the MIR attenuation curve derived from the model favors relatively gray continuum absorption from 3-8 $\mu$m and silicate features with intermediate strength at 9.7 um but with stronger than typical 18 um opacity., Comment: 15 pages, 5 figures. Paper re-submitted to ApJ after addressing the first round of comments by the referee

Integral Field Spectroscopy (IFS) is an observational method to obtain spatially resolved spectra over a specific field of view (FoV) in a single exposure. In recent years, near-infrared IFS has gained importance in observing objects with strong dust attenuation or at high redshift. One limitation of existing near-infrared IFS instruments is their relatively small FoV, less than 100 arcsec$^2$, compared to optical instruments. Therefore, we have developed a near-infrared (0.9-2.5 $\mathrm{\mu}$m) image-slicer type integral field unit (IFU) with a larger FoV of 13.5 $\times$ 10.4 arcsec$^2$ by matching a slice width to a typical seeing size of 0.4 arcsec. The IFU has a compact optical design utilizing off-axis ellipsoidal mirrors to reduce aberrations. Complex optical elements were fabricated using an ultra-precision cutting machine to achieve RMS surface roughness of less than 10 nm and a P-V shape error of less than 300 nm. The ultra-precision machining can also simplify alignment procedures. The on-sky performance evaluation confirmed that the image quality and the throughput of the IFU were as designed. In conclusion, we have successfully developed a compact IFU utilizing an ultra-precision cutting technique, almost fulfilling the requirements., Comment: 24 pages, 18 figures, 7 tables. Accepted for publication in JATIS

Ferroelectric domain walls, recognized as distinct from the bulk in terms of symmetry, structure, and electronic properties, host exotic phenomena including conductive walls, ferroelectric vortices, novel topologies, and negative capacitance. Contrary to conventional understanding, our study reveals that the structure of domain walls in HfO2 closely resembles its bulk. First, our first-principles simulations unveil that the robust ferroelectricity is supported by bosonic pairing of all the anionic phonons in bulk HfO2. Strikingly, the paired phonons strongly bond with each other and successfully reach the center of the domain wall without losing their integrity and produce bulk-like domain walls. We then confirmed preservation of the bulk phonon displacements and consequently full revival of the bulk structure at domain walls via aberration-corrected STEM. The newly found duality between the bulk and the domain wall sheds light on previously enigmatic properties such as zero-energy domain walls, perfect Ising-type polar ordering, and exceptionally robust ferroelectricity at the sub-nm scales. The phonon-pairing discovered here is robust against physical boundaries such as domain walls and enables zero momentum and zero-energy cost local ferroelectric switching. This phenomenon demonstrated in Si-compatible ferroelectrics provides a novel technological platform where data storage on domain walls is as feasible as that within the domains, thereby expanding the potential for high-density data storage and advanced ferroelectric applications., Comment: 24 pages, 4 figures

Data assimilation (DA) methods use priors arising from differential equations to robustly interpolate and extrapolate data. Popular techniques such as ensemble methods that handle high-dimensional, nonlinear PDE priors focus mostly on state estimation, however can have difficulty learning the parameters accurately. On the other hand, machine learning based approaches can naturally learn the state and parameters, but their applicability can be limited, or produce uncertainties that are hard to interpret. Inspired by the Integrated Nested Laplace Approximation (INLA) method in spatial statistics, we propose an alternative approach to DA based on iteratively linearising the dynamical model. This produces a Gaussian Markov random field at each iteration, enabling one to use INLA to infer the state and parameters. Our approach can be used for arbitrary nonlinear systems, while retaining interpretability, and is furthermore demonstrated to outperform existing methods on the DA task. By providing a more nuanced approach to handling nonlinear PDE priors, our methodology offers improved accuracy and robustness in predictions, especially where data sparsity is prevalent.

We present a combined experimental and theoretical study on the quasi-one-dimensional organic conductor (TMTTF)$_2$PF$_6$, and elucidate the variation of its physical properties under pressure. We fully resolve the crystal structure by single crystal x-ray diffraction measurements using a diamond anvil cell up to 8 GPa, and based on the structural data, we perform first-principles density-functional theory calculations and derive the $ab$ $initio$ extended Hubbard-type Hamiltonians. Furthermore, we compare the behavior of the resistivity measured up to 3 GPa using a BeCu clamp-type cell and the ground state properties of the obtained model numerically calculated by the many-variable variational Monte Carlo method. Our main findings are as follows: i) The crystal was rapidly compressed up to about 3 GPa where the volume drops to 80% and gradually varies down to 70% at 8 GPa. The transfer integrals increase following such behavior whereas the screened Coulomb interactions decrease, resulting in a drastic reduction of correlation effect. ii) The degree of dimerization in the intrachain transfer integrals, as the result of the decrease in structural dimerization together with the change in the intermolecular configuration, almost disappears above 4 GPa; the interchain transfer integrals also show characteristic variations under pressure. iii) The results of identifying the characteristic temperatures in the resistivity and the charge and spin orderings in the calculations show an overall agreement: The charge ordering sensitively becomes unstable above 1 GPa, while the spin ordering survives up to higher pressures. These results shed light on the similarities and differences between applying external pressure and substituting the chemical species (chemical pressure)., Comment: 13 pages, 10 figures

In-context learning has emerged as a groundbreaking ability of Large Language Models (LLMs) and revolutionized various fields by providing a few task-relevant demonstrations in the prompt. However, trustworthy issues with LLM's response, such as hallucination, have also been actively discussed. Existing works have been devoted to quantifying the uncertainty in LLM's response, but they often overlook the complex nature of LLMs and the uniqueness of in-context learning. In this work, we delve into the predictive uncertainty of LLMs associated with in-context learning, highlighting that such uncertainties may stem from both the provided demonstrations (aleatoric uncertainty) and ambiguities tied to the model's configurations (epistemic uncertainty). We propose a novel formulation and corresponding estimation method to quantify both types of uncertainties. The proposed method offers an unsupervised way to understand the prediction of in-context learning in a plug-and-play fashion. Extensive experiments are conducted to demonstrate the effectiveness of the decomposition. The code and data are available at: https://github.com/lingchen0331/UQ_ICL., Comment: Accepted to the main conference of NAACL 2024

On March 8, 1995, was found the following nontrivial single axiom-schema characteristic of Le\'{s}niewski-Ishimoto's propositional ontology $\bf L_1$ (refer to Takao Inou\'{e}, A single axiom-schema of March 8th, Bulletin of the Section of Logic (L\'{o}d\'{z}, Poland), Vol. 24 (1995), p. 115). ($\mathrm{A_{M8}}$) $\enspace$ $\epsilon ab \wedge \epsilon cd . \supset . \epsilon aa \wedge \epsilon cc \wedge (\epsilon bc \supset . \epsilon ad \wedge \epsilon ba)$. In this paper, we shall present the progress about the above axiom-schema from 1995 and conjectures about it. Here we shall give two criteria nontiriviality and quasi-nontriviality in order to distinguish two axiom-schemata. As main results, among others, in \S 6 - \S 8, we shall give the simplified axiom-schemata ($\rm A_{S1}$), ($\rm A_{S2}$) and ($\rm A_{S3N}$) based on ($\mathrm{A_{M8}}$), their nontriviality and quasi-nontriviality., Comment: 31 pages, mainly revised in Abstract and Introduction

We give two criteria for diagrams of Heegaard splittings of 3-manifolds. Weaker one of them guarantees that the splitting is strongly irreducible, and the stronger one guarantees in addition that the Goeritz group is finite. They are generalizations of the criteria introduced by Casson-Gordon and Lustig-Moriah. Their original ones require as input the diagram formed by a pair of maximal disk systems. Our present ones accept as input that of arbitrary disk systems, including minimal disk systems. In other words, our criteria accept Heegaard diagrams., Comment: 21 pages, 14 figures, v2: minor corrections throughout the paper

We study the Gauss and Jacobi sums from a viewpoint of motives. We exhibit isomorphisms between Chow motives arising from the Artin-Schreier curve and the Fermat varieties over a finite field, that can be regarded as (and yield a new proof of) classically known relations among Gauss and Jacobi sums such as Davenport-Hasse's multiplication formula. As a key step, we define motivic analogues of the Gauss and Jacobi sums as algebraic correspondences, and show that they represent the Frobenius endomorphisms of such motives. This generalizes Coleman's result for curves. These results are applied to investigate the group of invertible Chow motives with coefficients in a cyclotomic field., Comment: 30 pages. Remark 6.7 was added

We report on X-ray polarization measurements of the extra-galactic Crab-like PSR B0540-69 and its Pulsar Wind Nebula (PWN) in the Large Magellanic Cloud (LMC), using a ~850 ks Imaging X-ray Polarimetry Explorer (IXPE) exposure. The PWN is unresolved by IXPE. No statistically significant polarization is detected for the image-averaged data, giving a 99% confidence polarization upper limit (MDP99) of 5.3% in 2-8 keV energy range. However, a phase-resolved analysis detects polarization for both the nebula and pulsar in the 4-6 keV energy range. For the PWN defined as the off-pulse phases, the polarization degree (PD) of (24.5 ${\pm}$ 5.3)% and polarization angle (PA) of (78.1 ${\pm}$ 6.2){\deg} is detected at 4.6${\sigma}$ significance level, consistent with the PA observed in the optical band. In a single on-pulse window, a hint of polarization is measured at 3.8${\sigma}$ with polarization degree of (50.0 ${\pm}$ 13.1)% and polarization angle of (6.2 ${\pm}$ 7.4){\deg}. A 'simultaneous' PSR/PWN analysis finds two bins at the edges of the pulse exceeding 3${\sigma}$ PD significance, with PD of (68 ${\pm}$ 20)% and (62 ${\pm}$ 20)%; intervening bins at 2-3${\sigma}$ significance have lower PD, hinting at additional polarization structure., Comment: 10 pages, 7 figures, 4 tables, author's version of the paper accepted for publication in ApJ