A model of a hyperelliptic curve is called an imaginary or real model if it has one or two points at infinity, respectively. In this paper, we propose an algorithm to count points on hyperelliptic curves of genus 2 with real models defined over finite fields of large characteristics. We also estimate the complexity of our algorithm and prove that it has the same order as that of a previously known algorithm for imaginary models.

The Sinc approximation is known as an efficient function approximation formula for functions that decay exponentially and are defined over the entire infinite interval. Even for functions that do not satisfy such conditions, Stenger constructed an approximation formula based on the Sinc approximation combining with the Single-Exponential (SE) transformation and introducing auxiliary basis functions. In this study, we improve the approximation formula by replacing the SE transformation and the auxiliary basis functions. Two kinds of error bounds for the modified formula are also given.

We give two algorithms to compute linear determinantal representations of smooth plane curves of any degree over any field. As particular examples, we explicitly give representatives of all equivalence classes of linear determinantal representations of two special quartics over the field $\Q$ of rational numbers, the Klein quartic and the Fermat quartic.

We apply the shifted minimum residual method to a shifted linear system $(A+i\sigma I){\bf x}={\bf b}$ arising from quantum-mechanical wave packet simulation and discuss its advantages and disadvantages, comparing it with the widely used COCG method. Although the method requires more vector operations per iteration than the COCG method, it enjoys such nice properties as being free from breakdown, monotonic decrease of the residual norm and applicability to Hermitian-plus-shift systems, and can be a method of choice in some cases. Application of the method to the case of multiple shifts is also discussed.

A three-dimensional model of cellular electrophysiology, the 3D cable model, is numerically studied. Our numerical scheme is constructed based on the method of fundamental solutions, which is a meshfree numerical solver for homogeneous linear partial differential equations. We numerically show the existence of pulse-like traveling wave solutions for the model.

We propose a method of analyzing the time evolution of constraint equations of the Einstein's equation on the nonflat background by adding constraint terms to the evolution equations. In past studies, the eigenvalues of the coefficient matrix of the constraint equations was mostly obtained on the flat background. Since simulations do not always perform near the flat background, we need to calculate the eigenvalues on the appropriate background. We analyze eigenvalues numerically and predict the stability in the appropriate background. We also perform some numerical simulations and show consistency between the results of the eigenvalue analysis and the numerical stability.

In this paper, an explicit solution to a continuous-time mean-variance portfolio selection problem in a continuous semimartingale model is provided through the Lagrange multiplier method and results of a mean-variance hedging problem. Without reformulation of the problem which is usually employed in the literature, we get a more straightforward method of solution than earlier studies.

This paper presents a novel method for solving magnetoencephalography (MEG) inverse problems using the CANDECOMP/PARAFAC decomposition of a tensor in which Hankel matrices composed of the multipole moments of the observed data are aligned. The proposed method can reconstruct the positions and moments of the current dipoles in the human brain projected on the $xy$-plane more stably than the conventional direct method using Prony's algorithm. A novel spherical-spline-based method for the computation of the multipole moments is also proposed.

In this article, we propose a credit scoring method using purchase order information on target borrower firms. First, we introduce a time-series model which captures purchase order volume transitions of a target firm. Then, we execute credit scoring based on estimated financial statements reflecting expected values of future purchase orders obtained from the purchase order models. We demonstrate the applicability of our method to practical credit risk monitoring with a case study. One of the advantages of our method is its abilities to capture changes of credit risk timely reflecting the firms' business conditions.

In this paper, an identification procedure for the order of singularity near the interface edge of bonded structures is shown based on the finite element method using singular elements and the adjoint variable method in three dimensions. In this study, the three-dimensional Akin's singular element is introduced for discretization of the governing equation, and the formulation for the parameter identification analysis is carried out based on the adjoint variable method. A simple rectangular bonded structure model is employed in numerical analysis, and several numerical experiments are performed.

Nemec et al. analyzed secret key structure in the RSA cryptosystem used in smartcards manufactured by Infineon Technologies. In 2017, they estimated a form of prime numbers used for secret keys and proposed the prime factorization method in the context of composite numbers used in public keys. The purpose of this paper is to implement, and explore the applicability of, the prime factorization algorithm by Nemec et al.. We provide some notes on parameters used in the algorithm and conduct a numerical experiment under the parameter values we set.

UOV and Rainbow are multivariate signature schemes, which are known to be efficient and secure enough against known attacks under suitable parameter selections, and have been expected to be post-quantum cryptography. Recently, new variants of UOV and Rainbow, called Circulant UOV and Circulant Rainbow respectively, were proposed by Peng and Tang. In these variants, the signature generation is faster than the original schemes since circulant matrices appear in the process of signature generation. However, such circulant structures weaken the security. In this paper, we study the structures of these circulant variants and show that they are vulnerable against Kipnis-Shamir's attack.

We propose a new method for generating collocation points that give an accurate approximation in the method of fundamental solutions (MFS). It is known that collocation points that maximize the determinant of the coefficient matrix of the linear system in the MFS give an accurate approximation. However, the maximization problem is intractable. We design an efficient algorithm to automatically take collocation points that do not depend on a boundary condition. Numerical experiments show that the proposed collocation points give a better condition number and an accurate approximation when we use source points far from the boundary.

The quadratic Frobenius test is a primality test. Some composite numbers may pass the test and such numbers are called quadratic Frobenius pseudoprimes. No quadratic Frobenius pseudoprimes with respect to $x^{2}+5x+5$, which are congruent to 2 or 3 modulo 5, have been found. Shinohara studied a specific type of such a quadratic Frobenius pseudoprime, which is a product of distinct prime numbers $p$ and $q$. He showed experimentally that $p$ must be larger than $10^{9}$, if such a quadratic Frobenius pseudoprime exists. The present paper extends the lower bound of $p$ to $10^{11}$.

After the financial crisis, it has been widely recognized that counterparty default risks have serious consequences and that there are remarkably large differences in various interest rates. As a result, the methodology for pricing derivative securities has been modified: Currently, the price of a derivative security is expressed as the so-called XVA, which is the risk-neutral price plus total valuation adjustment. In this paper, we aim to provide a theoretical interpretation of XVA: Some valuation adjustments are interpreted as the ``$0$th-order'' approximation of XVA. Further, we describe a sufficient condition to ensure the arbitrage-free property of the $0$th-order price approximation.

Lyapunov exponent is commonly used as a measure of chaos. Chaos Degree is propsed as another measure of chaos based on information theory. The advantage of Chaos Degree is that it is calculable from data. However, there is a difference between Chaos Degree and Lyapunov exponent and determination of chaos requires caution by using Chaos Degree. In this paper, we find out information-theoretic interpretation of the difference between Chaos Degree and Lyapunov exponent for asymmetric tent maps.

The double exponential formula, or the DE formula, is a high-precision integration formula using a change of variables called a DE transformation. However, it has a disadvantage that it is sensitive to singularities of an integrand near the real axis, and Slevinsky and Olver (SIAM J. Sci. Comput., 2015) attempted to improve it by constructing conformal maps based on the locations of singularities. In this letter, we construct a new transformation formula based on their ideas. This can be regarded as a generalization of the DE transformations. We confirm the effectiveness of this by a numerical experiment.

In this paper, we describe the shape identification of a channel in incompressible viscous flow considering a rotational body. The purpose of this study is to obtain an optimal shape that will closely approach the target velocity in the target regions. The incompressible Navier Stokes equations are employed as the governing equations, and the adjoint variable method is applied to obtain the sensitivity for the optimal shape. The traction method is used to control the numerical oscillations of sensitivity for the shape update. Shape identification analysis is carried out using computed flow velocities in the target regions of target shape.

After characterizing the integrable discrete analogue of the Euler's elastica, we focus our attention on the problem of approximating a given discrete planar curve by an appropriate discrete Euler's elastica. We carry out the fairing process via a $L^2\!$-distance minimization to avoid the numerical instabilities. The optimization problem is solved via a gradient-driven optimization method (IPOPT). This problem is non-convex and the result strongly depends on the initial guess, so that we use a discrete analogue of the algorithm provided by Brander et al., which gives an initial guess to the optimization method.

We consider applying the Strang splitting to semilinear parabolic problems. The key ingredients of the Strang splitting are the decomposition of the equation into several parts and the computation of approximate solutions by combining the time evolution of each split equation. However, when the Dirichlet boundary condition is imposed, order reduction could occur due to the incompatibility of the split equations with the boundary condition. In this paper, to overcome the order reduction, a modified Strang splitting procedure is presented for the one-dimensional semilinear parabolic equation with first-order spatial derivatives, like the Burgers equation.