Japan Journal of Industrial and Applied Mathematics最新文献

This paper investigates pattern formation in 2-component reaction–diffusion systems with linear diffusion and local reaction terms. We propose a novel instability framework characterized by 0-mode Hopf instability, (textit{m}) and (textit{m}) + 1 mode Turing instabilities in 2-component reaction–diffusion systems. A normal form for the codimension 3 bifurcation is derived via the center manifold reduction, representing one of the main results in this paper. Additionally, we present numerical results on the bifurcation of certain reaction–diffusion systems and on the chaotic behavior of the normal form.

In the daily operation of liquefied petroleum gas service, gas providers visit customers and replace cylinders if the gas is about to run out. The plans should both prevent gas shortages and realize the minimum working time. Existing research has two limitations: the absence of a comprehensive system and the difficulty of solving large-scale problems. In the former limitation, existing research tackled the partial problems of making plans for cylinder replacement, such as planning delivery routes given gas consumption forecast or determining the customers for visiting without obtaining the route. It does not consistently achieve gas shortage prevention and short working hours even when combining individual optimal methods. In the latter limitation, most existing studies have difficulty solving the problem within a reasonable time if there are many customers. This is because they simultaneously determined the customers for visiting and route planning by preparing binary variables representing customer-to-customer travel. In this study, we construct a comprehensive and practical system from gas consumption forecast to determine delivery routes for cylinder replacement with large-scale customers. To address these challenges, our method takes two steps: determining which customers to visit within several days and a single-day route. Moreover, we mitigate gas shortages among customers with poor forecast performance by considering the uncertainty of the gas consumption forecast. A field test involving over 1000 customers in Japan confirmed that the system is operationally viable and capable of preventing gas shortages and realizing short working time.

The target of this study is a norm-conservative scheme for the Ostrovsky equation, as its mathematical analysis has not been addressed. First, the existence and uniqueness of its numerical solutions are demonstrated. Subsequently, a convergence estimate in the two-norm is established. This, in turn, implies a convergence in the first-order Sobolev space using a supplementary sup-norm boundedness argument. Finally, this conservative scheme can be implemented in a differential form, which is considerably better than the integral form in terms of computational cost-effectiveness.

By utilizing some elements of each row of the majorization matrix associated with the coefficient tensor, we propose a preconditioner, and present the corresponding preconditioned Gauss–Seidel method for solving ({mathcal {M}})-tensor multi-linear system. Theoretically, we give the convergence and comparison theorems of the proposed preconditioned Gauss–Seidel method. Numerically, we show the correctness of theoretical results and the efficiency of the proposed preconditioner by some examples.

Gradient Langevin dynamics and a variety of its variants have attracted increasing attention owing to their convergence towards the global optimal solution, initially in the unconstrained convex framework while recently even in convex constrained non-convex problems. In the present work, we extend those frameworks to non-convex problems on a non-convex feasible region with a global optimization algorithm built upon reflected gradient Langevin dynamics and derive its convergence rates. By effectively making use of its reflection at the boundary in combination with the probabilistic representation for the Poisson equation with the Neumann boundary condition, we present promising convergence rates, particularly faster than the existing one for convex constrained non-convex problems.

Algebraic Riccati equations (AREs) have been extensively applied in linear optimal control problems and many efficient numerical methods were developed. The stabilizing (or almost stabilizing) solution that all eigenvalues of its closed-loop matrix are contained in the open (or closed) unit disk of the complex plane has attracted the most attention among all Hermitian solutions of the ARE in the past works. Nevertheless, it is an interesting and challenging issue in finding the extremal solutions of AREs which play an important role in the applications. The contribution of this paper is twofold. Firstly, the existence of these extremal solutions is established under the framework of fixed-point iteration. Secondly, an accelerated fixed-point iteration (AFPI) based on the semigroup property is developed for computing four extremal solutions of the discrete-time algebraic Riccati equation, which has not appeared in the existing literature. In addition, we prove that the convergence of the AFPI is at least R-suplinear with order (r>1) under some mild assumptions. Numerical examples are shown to illustrate the feasibility and accuracy of the proposed algorithm.

Allocating goods among agents under ordinal preferences is a well-studied problem. In this study, each type of good may have multi-copies with quotas varying in a polytope. When goods are indivisible, it is difficult to achieve exact fairness, but various approximations have been suggested. An exact ex ante envy-freeness (before the randomization or decomposition is realized) can be obtained based on past research. This study achieves the envy-freeness for up to two copies of goods based on a “nearest” structure. The fairness is called “Best-of-Both-Worlds (BoBW),” meaning it achieves the best possible fairness notions in both the ex ante and ex post senses, or before and after randomization. What differentiates this work is that we deal with the multi-copies of goods and integer demands, i.e., each entry of a discrete allocation can be an arbitrary positive integer instead of a binary number. Although our approximation is for two copies of goods, instead of one indivisible good, this may lead to a much better approximation when the number of copies is larger. Additionally, these allocations are also efficient in stochastic dominance (a Pareto optimality). We give a solution to this problem by constructing box-integer networks. Moreover, the randomized allocations can be obtained in polynomial time when the resource polytope is a polymatroid through computing so-called independent flows.

If you release a slinky hung in midair from its initial stationary position, you can observe something interesting: the bottom of the slinky is at rest in midair for a while. Among physicists, this phenomenon is well known and has been discussed from the physical point of view. In this paper we deal with the problem of a freely falling slinky from the purely mathematical point of view. Through the rigorous mathematical process we obtained an explicit formula which describes the motion of the freely falling slinky and it turns out that this is a solution to an inhomogeneous wave equation. Our work gives the mathematical justification of the results obtained by physicists.

The mechanism of self-propelled particle motion has attracted much interest in mathematical and physical understanding of the locomotion of living organisms. In a top-down approach, simple time-evolution equations are suitable for qualitatively analyzing the transition between the different types of solutions and the influence of the intrinsic symmetry of systems despite failing to quantitatively reproduce the phenomena. We aim to rigorously show the existence of the rotational, oscillatory, and quasi-periodic solutions and determine their stabilities regarding a canonical equation proposed by Koyano et al. (J Chem Phys 143(1):014117, 2015) for a self-propelled particle confined by a parabolic potential. In the proof, the original equation is reduced to a lower dimensional dynamical system by applying Fenichel’s theorem on the persistence of normally hyperbolic invariant manifolds and the averaging method. Furthermore, the averaged system is identified with essentially a one-dimensional equation because the original equation is O(2)-symmetric.