The present paper describes a numerical solution to shape optimization problems of contacting elastic bodies for controlling contact pressure. The contacting elastic problem is formulated as the minimization of potential energy with a constraint for penetration based on the large deformation theory. The contact pressure is defined as a Lagrange multiplier for the constraint of penetration in the minimization problem. An error norm of the contact pressure to a desired distribution is chosen as an objective functional. The shape derivative of the functional is theoretically evaluated. Numerical solutions are constructed by the traction method.

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In 1990, the present authors proposed the first ID-based non-interacrive key sharing scheme (ID-NIKS) based on the discrete logarithm problem (DLP) over a composite number $n$. With a rapid progress of computer system for the last two decades, ID-NIKS based on DLP over $n$ would have more chance to be applied practically. However, there existed no secure ID-NIKS based on DLP over $n$ against the square-root attack when $n$ is a product of three prime numbers. In this paper, we propose an ID-NIKS based on DLP over a product of three prime numbers which can circumvent the square-root attack.

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Inner angle of triangle made of consecutive three points on unit circle is investigated. We use two methods to plot points. One is plotting random numbers whose distribution is uniform. Another is plotting consecutive numbers obtained by a map which generates complex chaotic sequences with constant power. We focus on an inner angle at the middle point in consecutive three points. An angle for chaotic sequence is found to be different from one for uniform random sequence.

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The tanh rule and the double-exponential (DE) formula are known as efficient quadrature rules for \emph{definite integrals} over a finite interval $(a, b)$. In this note we consider a numerical method for \emph{indefinite integrals} obtained by applying the tanh rule or the DE formula to the integration over the interval $(a, x)$ for each $x$. For these methods the conventional error analyses yield error estimates depending on $x$, which are impractical. We here present error estimates that do not depend on $x$, and furthermore, with explicit constants.

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The Hasse-Witt matrix of a hyperelliptic curve gives partial information for the order of the Jacobian of the curve, therefore the Hasse-Witt matrices can be used for point counting of hyperelliptic curves. Bostan, Gaudry and Schost improved the Chudnovsky-Chudnovsky algorithm and computed the Hasse-Witt matrices by using their improved algorithm for constructing hyperelliptic cryptosystems. The both algorithms need $p$-adic integers with finite precision as the base operations. This paper shows improvements in the computation of the Hasse-Witt matrix that reduces the required precision of the $p$-adic integers.

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In this paper, we investigate the convergence of the V-type hyperplane constrained method for singular value decomposition. The V-type method involves employing the Newton type iteration to solve the nonlinear systems with the searching range of right singular vectors constrained on a hyperplane. First, we discuss the nonsingularity of the Jacobian matrix appearing in the Newton type iteration. Next, we clarify the convergence of the Newton type iteration. Finally, we prove that singular value decomposition is computable by the V-type method.

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In this paper, we design a mixed double-multiple precision version of the hyperplane constrained method for singular value decomposition (SVD), which is based on solving nonlinear systems with the solutions constrained on hyperplanes. We also propose its hybrid method in order to shorten the running time. Through some numerical examples for matrices with small singular values, it is shown that, by new versions, the SVD is computable with high relative accuracy.

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It is required to invent the public-key cryptosystem (PKC) that is based on an {\it NP\/}-hard problem so that the quantum computer might be realized. The knapsack PKC is based on the subset sum problem which is {\it NP\/}-hard. In this paper, we propose a knapsack PKC with a cyclic code over $GF(2)$ using the Chinese remainder theorem. The proposed scheme is secure against Shamir's attack and Adleman's attack and invulnerable to the low-density attack. Furthermore, the proposed scheme can reduce the size of public key by almost $25\% \sim 50\%$ of the conventional scheme using a linear code.

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In this paper, we discuss the apportionment problem of distributing seats in a legislature, based proportionally on the population of electoral districts or on the vote totals of political parties. If an apportionment method can be defined via discrete optimization, then its continuous relaxation should have an ideally proportional solution (i.e., the quota) at optimality. First, we propose a new class of reasonable methods of apportionment satisfying such a property. Then we study symmetries of five apportionment methods in the new class. Finally, we estimate how often the five methods stay within the quota.

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The present paper describes a numerical solution of shape optimization problems for non-stationary Navier-Stokes problems. As a concrete example, we consider the problem of finding the shape of an obstacle in a flow field in order to minimize the energy loss integral for an assigned time interval. The primary goal of the present paper is to demonstrate the evaluation of the shape derivative of the energy loss. The traction method is used for the reshaping algorithm. Numerical results show that the shapes of the circle obstacle converge to wedge shapes for the cases of Reynolds numbers of 100 and 250.

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We present an approach to preconditioning for large, relatively dense linear systems and verify the validity of our method. We restrict the target of our method to Molecular Orbital (MO) calculations. Sparse Approximate Inverse (SAI) is typically less effective at accelerating the convergence and requires a huge computational cost in its construction when a large number of nonzero entries are kept in the approximate inverse matrix. We explain a construction of Block SAI and a cutoff strategy to reduce the number of nonzero elements, and investigate the efficiency of a cutoff strategy and Block SAI.

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Computational results are presented on micro-hologram diffraction for optical data storage using a finite element method. Retrieval of object light from a micro-hologram is formulated as an optical scattering problem in an infinite region. In order to overcome the difficulty of dealing with the infinite region a Dirichlet to Neumann (DtN) map is employed on an artificial boundary. By virtue of the DtN map reflection from the artificial boundary is effectively alleviated and non-reflecting boundary is obtained. Retrieval of the object light is computed for two different models.

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Recently, the discontinuous Galerkin FEM's (DGFEM) are widely studied. They use discontinuous approximate functions, where the discontinuity is dealt with by the Lagrange multiplier and/or interior penalty techniques. Such methods has a merit that various types of approximate functions can be used besides the usual continuous piecewise polynomials, although the band-widths of arising matrices are often much larger than the conventional ones. We here propose a hybrid displacement type DGFEM for the 2D Poisson equation with some mathematical and numerical results. In particular, we can use element matrices and vectors similar to those in the classical FEM.

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We propose a numerical method for conformally mapping unbounded multiply connected domains onto a canonical domain with a mixture of circular and radial slits. It expresses an analytic function by a linear combination of complex logarithmic functions based on the charge simulation method, and gives a simple form of approximate mapping function with high accuracy. A numerical example shows the effectiveness of our method.

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In this paper, principal component analysis (PCA) is applied to three different parametrization of interest rates: zero rates, yield curve, and forward rates. This comparative study is complementary to Akahori, Aoki, and Nagata \cite{AAN06} where they claimed that, under the no-arbitrage principle, yield curve cannot be a random walk. Conversely the forward curve could be a random walk. In our result of PCA, however, we observed that of the general beliefs. Our empirical results on the number of factors for the zero rates and the yield curve align with the general beliefs. This is a puzzle.

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We have introduced excluded volume effect, which is an important factor to model a realistic pedestrian queue, into queueing theory. The probability distributions of pedestrian number and pedestrian waiting time in a queue have been calculated exactly. Due to time needed to close up the queue, the mean number of pedestrians increases as pedestrian arrival probability ($\lambda$) and leaving probability ($\mu$) increase even if the ratio between them (i.e., $\rho=\lambda/\mu$) remains constant. Furthermore, at a given $\rho$, the mean waiting time does not increase monotonically with the service time (which is inverse to $\mu$), a minimum could be reached instead.

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In this paper, we use a multivariate affine jump process to model the downgrade intensities for several categories of business sector in credit portfolios. Since multivariate affine jump structure enables us to consider self-exciting effects as well as mutually exciting effects, the model can explain the downgrade clusters observed in the Japanese market. Also, we propose a new credit derivative named multi-downgrade protection (MDP) as an application of our model and discuss its fair pricing.

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We propose an approach for introducing the origin shift into the multiple dqd algorithm for computing the eigenvalues of a totally nonnegative matrix. Numerical experiments show that the shift speeds up the convergence while retaining the accuracy of the computed eigenvalue.

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The purpose of this paper is to obtain general solutions of Sakaki-Kakei equations of type 3, 5 and 6. We first obtain general solution of two dimensional discrete dynamical system associated with arithmetic and harmonic mean through a conjugacy of the iteration map. We next show that the arithmetic and harmonic mean system is semiconjugate to Sakaki-Kakei equations of type 3, 5 and 6 under some conditions. From those results, we obtain their general solutions. We finally clarify behaviors of the solutions.

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It has been clarified by numerical experiments that a variable preconditioned GCR($m$) method using the SOR method is efficient for solving a sparse linear system. However there are cases that the residual norm of variable preconditioned GCR method stagnates. Then the inner iteration counts increase, and more computation time is required. Therefore, we propose a strategy to reduce the inner iteration counts in case of stagnation of the residual norm by using a certain parameter related to convergence behavior. Numerical experiments show that our strategy is indeed effective.

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In \cite{QPKC}, a knapsack based cryptosystem is proposed using number fields as a scheme of quantum public key cryptosystems. We studied on key generation of this scheme in the case of imaginary quadratic fields \cite{Nishi}. In this paper, we study the cases of real quadratic fields and cubic fields. We first give some propositions for practical key generation. We then estimate various densities of the generated knapsack problems for these cases and for the imaginary quadratic case. We further generate explicit public keys and knapsack problems for several special cases and test the resistance against low-density attacks.

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In 2008, Hashimoto and Sakurai proposed a new efficient signature scheme, which is a non-commutative version of Shamir's birational permutation signature scheme. Shamir's scheme is a generalization of the Ong-Schnorr-Shamir scheme and was broken by Coppersmith et al. using its linearity and commutativity. The HS (Hashimoto-Sakurai) scheme is expected to be secure against the attack from its non-commutative structure. In this paper, we propose an attack against the HS scheme, which is practical under the condition that its step size and the number of steps are small. We discuss its efficiency by using some experimental results.

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We propose a divide-and-conquer algorithm with multiple division for singular value decomposition (SVD). The algorithm turns out to be efficient for reducing the execution time in the case that the deflation occurrence rate of the input matrix is low, which is exactly the case that the standard divide-and-conquer algorithm (DC2-SVD) with division number two requires $O(n^3)$ arithmetic operations. Here $n$ is the size of the input matrix. The comparison with DC2-SVD as well as another up-to-date algorithm I-SVD is made through numerical experiment.

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Ultradiscrete analogues of the nonautonomous discrete finite Toda lattice and its modified system are explicitly given. It is shown that these two systems can be seen as the box-ball system with size limits and one with speed limits, respectively. Particular solutions and the Lax forms of these ultradiscrete systems on the finite lattice are also discussed.

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In this paper, we propose a new hybridized discontinuous Galerkin method for the Poisson equation with homogeneous Dirichlet boundary condition. Our method has the advantage that the stability is better than the previous hybridized method. We derive $L^2$ and $H^1$ error estimates of optimal order. Some numerical results are presented to verify our analysis.

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This paper empirically shows that in the days near the last trading day of Nikkei 225 Futures the best bid/ask prices follows the highly negatively correlated first order Markov process, and has no trend up to four ticks based on the total $\rho$-variation. This is consistent with the model by Endo et al. and the empirical results therein by different approach. It also derives the theoretical asymptotic formula for the total $\rho$-variation when the process follows the first order random Markov walks, and shows that its fit is satisfactory for $\rho\le 4$.

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Understanding nonhyperbolicity in dynamical systems is important, yet, it is usually difficult to see whether a system is hyperbolic or not. In this letter, angles between stable and unstable directions on a point of a chaotic attractor of the Lorenz system with some sets of various parameter values are calculated through identifying Lyapunov vectors numerically. Then we estimate the parameter value where the system becomes nonhyperbolic in one parameter family.

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It is graphically observed that curves of mean breakdown points obtained by $\ell_1$ optimization for compressed sensing defined by underdetermined systems $y=Aw$ with uniformly distributed random matrices $A\in{\mathbb R}^{d\times m}$ and sparse $w$ almost coincide with the curves obtained by normally distributed random matrices, both with sparse vectors $w^+$ with nonnegative components and $w^\pm$ with components of either sign. Three-dimensional figures illustrate asymptotic phase transition cliffs. These and the standard deviation of the mean breakdown points can be used to define a level of sparseness of $w$ below which a unique solution is expected to a high probability.

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We consider a quadrature-based eigensolver to find eigenpairs of Hermitian matrices arising in lattice quantum chromodynamics. To reduce the computational cost for finding eigenpairs of such Hermitian matrices, we propose a new technique for solving shifted linear systems with complex shifts by means of the shifted CG method. Furthermore, by using integration paths along horizontal lines corresponding to the real axis of the complex plane, the number of iterations for the shifted CG method is also reduced. Some numerical experiments illustrate the accuracy and efficiency of the proposed method by comparison with a conventional method.

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We propose a novel algorithm to compute a Jordan basis (JB) for an arbitrarily given square matrix. The algorithm is based on the fact that a JB for a linear transformation $f$ is obtained by extending a JB for the restriction of $f$ to its range $R(f)$. The main ingredient of the algorithm is singular value decomposition, and that ensures backward-stability of the algorithm. To enhance the practical utility, we also introduce an automatic mechanism into the algorithm such that it outputs all possible Jordan structures close to the exact one of the input matrix.

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In this paper, the pass rate of the NIST SP800-22 statistical test suite for the ideally true random sequences is analyzed by the simulation of statistical tests, and derived by the theoretical analysis under the assumption that there are no correlation among tests. As examples of chaos based system, Vector Stream Cipher (VSC128S) and the encryption system using Arnold's cat map are tested. The test results are compared with the theoretical one for the true random sequences and validity of presented analysis is discussed.

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Some kinds of eigensolver for large sparse matrices require specification of parameters that are based on rough estimates of the desired eigenvalues. In this paper, we propose a stochastic estimation method of eigenvalue distribution using the combination of a stochastic estimator of the matrix trace and contour integrations. The proposed method can be easily parallelized and applied to matrices for which factorization is infeasible. Numerical experiments are executed to show that the method can perform rough estimates at a low computational cost.

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The finest simultaneous block-diagonalization for a given set of square matrices has been studied independently in the area of independent component analysis (ICA) and semidefinite programming. A new algorithm for this problem, which finds the finest decomposition with a capability of coping with numerical errors, has recently been proposed by the present authors. In this paper we indicate the use of the algorithm for ICA by describing its main features and comparing the method with the other existing methods.

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