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.
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, wh
ere they show that two groups with the same group determinant are isomorphic. The derived condition leads to a generalization of this result.
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 $1.72times 10^{-10}eV.m$ 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.
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 us
ing 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 Dedekinds theorem.
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 distri
butions 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.
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.
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 irredu
cible 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.
We give a further extension and generalization of Dedekinds 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.
