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A Wolstenholme prime is a prime number $p \geq 5$ that divides the numerator of the Bernoulli number $B_{p-3}$. A number of equivalent definitions for Wolstenholme primes are known, mostly related to congruences of harmonic sums or binomial coefficients. In this paper, we introduce an equivalent definition of Wolstelholme primes related the number of terms in the group determinant of cyclic groups, and equivalently, the cardinality of certain sets of restricted partitions.

We give a necessary and sufficient condition for a prime to be an integer group determinant for an arbitrary abelian $p$-group of the form ${\rm C}_{p} \times H$, where ${\rm C}_{p}$ is the cyclic group of order $p$. Also, we show that under certain conditions, the integer group determinant of a finite group $G$ that is prime is the integer group determinant of the abelianization of $G$. As a result, we know that the integer group determinant of a $p$-group that is prime is the integer group determinant of its abelianization.

It is important for daily life support robots to detect changes in their environment and perform tasks. In the field of anomaly detection in computer vision, probabilistic and deep learning methods have been used to calculate the image distance. These methods calculate distances by focusing on image pixels. In contrast, this study aims to detect semantic changes in the daily life environment using the current development of large-scale vision-language models. Using its Visual Question Answering (VQA) model, we propose a method to detect semantic changes by applying multiple questions to a reference image and a current image and obtaining answers in the form of sentences. Unlike deep learning-based methods in anomaly detection, this method does not require any training or fine-tuning, is not affected by noise, and is sensitive to semantic state changes in the real world. In our experiments, we demonstrated the effectiveness of this method by applying it to a patrol task in a real-life environment using a mobile robot, Fetch Mobile Manipulator. In the future, it may be possible to add explanatory power to changes in the daily life environment through spoken language., Comment: Accepted to 2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2023)

We have performed first-principles calculations using density functional theory on a kagome lattice model with a chiral spin state, as a representative example demonstrating significant longitudinal and transverse thermoelectric properties. The results revealed that the saddle-point-type van Hove singularity (VHS) enhances thermoelectric effects. The longitudinal thermoelectric conductivity $\alpha_{xx}$ was large at the chemical potentials tuned close to the band at the symmetry points, K (lower band edge), $\Gamma$ (upper band edge), and M (saddle point), where the VHSs of the density of states (DOS) were at the corresponding band energies. The transverse thermoelectric conductivity $\alpha_{xy}$ was large at the chemical potential of saddle-point-type VHS. A large anomalous Nernst coefficient of about 10 $\mu$V/K at 50 K was expected.

Let ${\rm C}_{4}$ be the cyclic group of order $4$. We determine all possible values of the integer group determinant of ${\rm C}_{4} \rtimes {\rm C}_{4}$., Comment: arXiv admin note: text overlap with arXiv:2303.08489

We assume that the forecast error follows a probability distribution which is symmetric and monotonically non-increasing on non-negative real numbers, and if there is a mismatch between observed and predicted value, then we suffer a loss. Under the assumptions, we solve a minimization problem with an asymmetric loss function. In addition, we give an inequality for the variance of the loss.

For any positive integer $n$, let ${\rm C}_{n}$ be the cyclic group of order $n$. We determine all possible values of the integer group determinant of ${\rm C}_{4} \times {\rm C}_{2}^{2}$, which is the only unsolved abelian group of order $16$.

We determine all possible values of the integer group determinant of ${\rm C}_{4}^{2}$, where ${\rm C}_{4}$ is the cyclic group of order $4$.

In this study, we implemented a finite-difference algorithm for computing anomalous Hall and Nernst conductivity. Based on the expression to evaluate the Berry curvature in an insulating system [J. Phys. Soc. Jpn. 74 1674(2005)], we extended the methods to a metallic system. We calculated anomalous Hall conductivity and Nernst conductivity in a two-dimensional ferromagnetic material FeCl$_2$ and three-dimensional ferromagnetic transition metals bcc-Fe, hcp-Co, and fcc-Ni. Our results are comparable to previously reported results computed by Kubo-formula or Wannier representation. To evaluate anomalous Nernst coefficients, the detailed Fermi-energy dependence of the anomalous Hall conductivity is required. Nonetheless, previous methods based on Wannier representation or Kubo-formula have numerical instability due to the ${\boldsymbol k}$-space Dirac monopole. The present method will open an efficient thermoelectric material design based on the high-throughput first-principles screening., Comment: 7 pages, 4 figures

We solve Olga Taussky-Todd's circulant problem in the case of order 16.

We give explicit expressions of some special values for the monomial symmetric polynomials as applications of symmetric functions and group determinants. We also prove some vanishing or non-vanishing properties of these special values.

In this paper, we give a refinement of a generalized Dedekind's theorem. In addition, we show that all possible values of integer group determinants of any group are also possible values of integer group determinants of its any abelian subgroup. By applying the refinement of a generalized Dedekind's theorem, we determine all possible values of integer group determinants of the direct product group of the cyclic group of order $8$ and the cyclic group of order $2$.

We propose a linear-combination-of-pseudo-atomic-orbitals scheme for a finite electric field method based on the modern theory of polarization. We derive the matrix elements of the effective potential for the field and the corresponding terms of the forces on atoms. In addition, we successfully evaluated the dielectric constants and Born effective charges of typical semiconducting and insulating materials. Our formalism will aid in the study of materials under electric fields., Comment: 16 pages, 1 figure; resolved typographical errors; additionally written

Olga Taussky-Todd suggested the problem of determining the possible values of integer circulant determinants. To solve a special case of the problem, Laquer gave a factorization of circulant determinants. In this paper, we give a modest generalization of Laquer's theorem. Also, we give an application of the generalization to integer group determinants.

The spin splitting driven by spin-orbit coupling in monolayer (ML) transition metal dichalcogenides (TMDCs) family has been widely studied only for the 1H-phase structure, while it is not profound for the 1T-phase structure due to the centrosymmetric of the crystal. Based on first-principles calculations, we show that significant spin splitting can be induced in the ML 1T-TMDCs by introducing the line defect. Taking the ML PtSe2 as a representative example, we considered the most stable form of the line defects, namely Se-vacancy line defect (Se-VLD). We find that large spin splitting is observed in the defect states of the Se-VLD, exhibiting a highly unidirectional spin configuration in the momentum space. This peculiar spin configuration may yield the so-called persistent spin textures (PST), a specific spin structure resulting in protection against spin-decoherence and supporting an extraordinarily long spin lifetime. Moreover, by using k.p perturbation theory supplemented with symmetry analysis, we clarified that the emerging of the spin splitting maintaining the PST in the defect states is originated from the inversion symmetry breaking together with one-dimensional nature of the Se-VLD engineered ML PtSe2. Our findings pave a possible way to induce the significant spin splitting in the ML 1T-TMDCs, which could be highly important for designing spintronic devices., Comment: 5 figures, under review

For some estimations and predictions, we solve minimization problems with asymmetric loss functions. Usually, we estimate the coefficient of regression for these problems. In this paper, we do not make such the estimation, but rather give a solution by correcting any predictions so that the prediction error follows a general normal distribution. In our method, we can not only minimize the expected value of the asymmetric loss, but also lower the variance of the loss.

For controlling the critical electric fields of the topological phase transition in single bilayer Bi(111), we investigated topological phases in a strained system through first-principles calculations. We found a quadratic band touching semimetallic state at tensile strain $\epsilon=0.5$%. Around this strain, the topological phase can be switched to a trivial insulator by an infinitesimal electric field. The positions at which Dirac cones appear in the electric-field-induced topological phase transition changed for the strain $\epsilon>0.5$% and $\epsilon<0.5$%. Our results indicate that this topological phase transition could be applied to novel spintronic devices.

We generalize the concept of the group determinant and prove a necessary and sufficient novel condition for a subset to be a subgroup. This development is based on the group determinant work by Edward Formanek, David Sibley, and Richard Mansfield, where they show that two groups with the same group determinant are isomorphic. The derived condition leads to a generalization of this result., Comment: 6 pages

At interfaces with inversion symmetry breaking, Rashba effect couples the motion of electrons to their spin; as a result, spin-charge interconversion mechanism can occur. These interconversion mechanisms commonly exploit Rashba spin splitting at the Fermi level by spin pumping or spin torque ferromagnetic resonance. Here, we report evidence of significant photoinduced spin to charge conversion via Rashba spin splitting in an unoccupied state above the Fermi level at the Cu(111)/$\alpha$-Bi$_{2}$O$_{3}$ interface. We predict an average Rashba coefficient of $1.72\times 10^{-10}eV.m$ at 1.98 eV above the Fermi level, by fully relativistic first-principles analysis of the interfacial electronic structure with spin orbit interaction. We find agreement with our observation of helicity dependent photoinduced spin to charge conversion excited at 1.96 eV at room temperature, with spin current generation of $J_{s}=10^{6}A/m^{2}$. The present letter shows evidence of efficient spin-charge conversion exploiting Rashba spin splitting at excited states, harvesting light energy without magnetic materials or external magnetic fields., Comment: 7 pages, 4 figures in main text and 5 figures in appendix

We investigated the Rashba spin splittings in a compressive-strained SrTiO$_3$(001) ultra thin-film using first-principles calculations. The effect of the polarization due to the compressive strain leads to the 2DEG with large Rashba spin splittings, where the sheet carrier density is of the same order of magnitude as that of the heterostructure LaAlO$_3$/SrTiO$_3$ ($\sim10^{14}$ cm$^{-2}$). Some localized surface states (SSs) show the giant Rashba coefficient $\alpha_R$ larger than 100 meV$\cdot$\AA., Comment: 4 pages, 3 figures, Only the Authors field in metadata was corrected and the Journal-ref and DOI fields were added

In this paper, we define the concept of the Study-type determinant, and we present some properties of these determinants. These properties lead to some properties of the Study determinant. The properties of the Study-type determinants are obtained using a commutative diagram. This diagram leads not only to these properties, but also to an inequality for the degrees of representations and to an extension of Dedekind's theorem.

Large spin splitting at Rashba interface, giving rise to strong spin-momentum locking, is essential for efficient spin-to-charge conversion. Recently, a Cu/Bismuth oxide (Bi2O3) interface has been found to exhibit an efficient spin-to-charge conversion similar to a Ag/Bi interface with large Rashba spin splitting. However, the guiding principle of designing the metal/oxide interface for the efficient conversion has not been clarified yet. Here we report strong non-magnetic (NM) material dependence of spin splitting at NM/Bi2O3 interfaces. We employed spin pumping technique to inject spin current into the interface and evaluated the magnitude of interfacial spin-to-charge conversion. We observed large modulation and sign change in conversion coefficient which corresponds to the variation of spin splitting. Our experimental results together with first-principles calculations indicate that such large variation is caused by material dependent electron distribution near the interface. The results suggest that control of interfacial electron distribution by tuning the difference in work function across the interface may be an effective way to tune the magnitude and sign of spin-to-charge conversion and Rashba parameter at interface.

In this paper, we formulate a method for minimising the expectation value of the procurement cost of electricity in two popular spot markets: {\it day-ahead} and {\it intra-day}, under the assumption that expectation value of unit prices and the distributions of prediction errors for the electricity demand traded in two markets are known. The expectation value of the total electricity cost is minimised over two parameters that change the amounts of electricity. Two parameters depend only on the expected unit prices of electricity and the distributions of prediction errors for the electricity demand traded in two markets. That is, even if we do not know the predictions for the electricity demand, we can determine the values of two parameters that minimise the expectation value of the procurement cost of electricity in two popular spot markets. We demonstrate numerically that the estimate of two parameters often results in a small variance of the total electricity cost, and illustrate the usefulness of the proposed procurement method through the analysis of actual data.

Using first-principles calculations, we found the topological phase transition induced by electric fields in one-bilayer Bi(111). The bandgap decreased with increasing electric field strength, and it is closed at 2.1 V/{\AA}. For fields exceeding 2.1 V/{\AA}, the bandgap increased with increasing electric field strength, reaching 0.34 eV at 4.0 V/{\AA}. We computed the $Z_{2}$ invariant that characterizes topological insulator phases. As results, one-bilayer Bi(111) showed a topological phase transition induced by the electric field, from the topological insulator phase to the trivial insulator phase through a Dirac semimetal. This topological phase transition could be applied to novel devices.

We investigated the effect of the tensile strain on the spin splitting at the n-type interface in LaAlO$_3$/SrTiO$_3$ in terms of the spin-orbit coupling coefficient $\alpha$ and spin texture in the momentum space using first-principles calculations. We found that the $\alpha$ could be controlled by the tensile strain and be enhanced up to 5 times for the tensile strain of 7%, and the effect of the tensile strain leads to a persistent spin helix, which has a long spin lifetime. These results support that the strain effect on LaAlO$_3$/SrTiO$_3$ is important for various applications such as spinFET and spin-to-charge conversion., Comment: 3 pages, 3 figures, corrected typographical errors and misleading expressions

Inspired by the Capelli identities for group determinants obtained by T\^oru Umeda, we give a basis of the center of the group algebra of any finite group by using Capelli identities for irreducible representations. The Capelli identities for irreducible representations are modifications of the Capelli identity. These identities lead to Capelli elements of the group algebra. These elements construct a basis of the center of the group algebra.

Frobenius built a representation theory of finite groups in the process of obtaining the irreducible factorization of the group determinant. Here, we give a generalization of Frobenius' theorem. The generalization leads to a corollary on irreducible representations of finite groups., Comment: arXiv admin note: substantial text overlap with arXiv:1610.06047

We give a further extension and generalization of Dedekind's theorem over those presented by Yamaguchi. In addition, we give two corollaries on irreducible representations of finite groups and a conjugation of the group algebra of the groups which have an index-two abelian subgroups.

We performed density functional calculations for ultra-thin bismuth surface alloys: surface alloys of bismuth and face-centered cubic metals Bi/$M$(111)-$(\sqrt{3}\times\sqrt{3})R30\deg$ ($M$=Cu, Ag, Au, Ni, Co, and Fe). Our calculated Rashba parameters for the Bi/Ag are consistent with the previous experimental and theoretical results. We predicted a trend in the Rashba coefficients $\alpha_R$ of bands around the Fermi energy for noble metals as follows: Bi/Ag > Bi/Cu > Bi/Au. As for the transition metals, there is a trend in $\alpha_R$: Bi/Ni > Bi/Co > Bi/Fe. Our finding may lead to design efficient spin-charge conversion materials., Comment: 4 pages, 3 figures

A transfer is a group homomorphism from a finite group to an abelian quotient group of a subgroup of the group. In this paper, we explain some of the properties of transfers by using noncommutative determinants. These properties enable us to understand transfers more naturally.

For any given finite abelian group, we give factorizations of the group determinant in the group algebra of any subgroup. The factorizations are an extension of Dedekind's theorem. The extension leads to a generalization of Dedekind's theorem and a simple expression for inverse elements in the group algebra.

For some monoids, we give a method of composing invertibility preserving maps associated to "partial involutions." Also, we define the notion of "determinants for finite dimensional algebras over a field." As examples, we give invertibility preserving maps for Clifford algebras into a field and determinants for Clifford algebras into a field, where we assume that the algebras are generated by less than or equal to 5 generators over the field. On the other hand, "determinant formulas for Clifford algebras" are known. We understand these formulas as an expression that connects invertibility preserving maps for Clifford algebras and determinants for Clifford algebras. As a result, we have a better sense of determinant formulas. In addition, we show that there is not such a determinant formula for Clifford algebras generated by greater than 5 generators.