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An instability framework of Hopf–Turing–Turing singularity in 2-component reaction–diffusion systems 双分量反应扩散系统中霍普夫-图灵-图灵奇点的不稳定性框架
IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED Pub Date : 2024-09-04 DOI: 10.1007/s13160-024-00668-0
Hirofumi Izuhara, Shunusuke Kobayashi

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.

本文研究了具有线性扩散和局部反应项的双分量反应扩散系统中的模式形成。我们提出了一种新的不稳定性框架,其特征是双分量反应扩散系统中的 0 模式霍普夫不稳定性、(textit{m})和(textit{m})+ 1 模式图灵不稳定性。通过中心流形还原,我们推导出了子维度 3 分岔的正常形式,这是本文的主要成果之一。此外,我们还给出了某些反应扩散系统分岔的数值结果以及正常形式的混沌行为。
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引用次数: 0
Comprehensive and practical optimal delivery planning system for replacing liquefied petroleum gas cylinders 用于替换液化石油气钢瓶的全面实用的最佳交付规划系统
IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED Pub Date : 2024-09-03 DOI: 10.1007/s13160-024-00664-4
Akihiro Yoshida, Haruki Sato, Shiori Uchiumi, Nariaki Tateiwa, Daisuke Kataoka, Akira Tanaka, Nozomi Hata, Yousuke Yatsushiro, Ayano Ide, Hiroki Ishikura, Shingo Egi, Miyu Fuji, Hiroki Kai, Katsuki Fujisawa

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.

在液化石油气服务的日常运营中,气体供应商会拜访客户,并在气体即将耗尽时更换钢瓶。计划既要防止燃气短缺,又要实现最短工作时间。现有研究有两个局限性:缺乏全面系统和难以解决大规模问题。就前者而言,现有研究只解决了制定气瓶更换计划的局部问题,如根据用气量预测规划送气路线,或在未获得路线的情况下确定要拜访的客户。即使结合单个最优方法,也无法持续实现预防气荒和缩短工作时间的目标。在后一种限制中,如果客户较多,大多数现有研究都难以在合理时间内解决问题。这是因为他们通过编制代表客户间旅行的二进制变量来同时确定访问客户和路线规划。在本研究中,我们从燃气消耗量预测出发,构建了一个全面实用的系统,以确定大规模客户钢瓶更换的交付路线。为了应对这些挑战,我们的方法分为两个步骤:确定几天内要拜访的客户和单日路线。此外,我们还通过考虑用气量预测的不确定性,缓解了预测结果不佳客户的用气短缺问题。在日本对 1000 多家用户进行的实地测试证实,该系统在操作上是可行的,能够防止天然气短缺并实现短工作时间。
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引用次数: 0
Mathematical analysis of a norm-conservative numerical scheme for the Ostrovsky equation 奥斯特洛夫斯基方程的规范保守数值方案的数学分析
IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED Pub Date : 2024-09-02 DOI: 10.1007/s13160-024-00669-z
Shuto Kawai, Shun Sato, Takayasu Matsuo

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.

本研究的目标是奥斯特洛夫斯基方程的规范保守方案,因为其数学分析尚未涉及。首先,证明了其数值解的存在性和唯一性。随后,建立了二规范的收敛估计。这反过来又意味着使用补充的超规范有界性论证在一阶 Sobolev 空间中的收敛性。最后,这种保守方案可以微分形式实现,在计算成本效益方面大大优于积分形式。
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引用次数: 0
A new preconditioned Gauss-Seidel method for solving $${mathcal {M}}$$ -tensor multi-linear system 用于求解 $${mathcal {M}}$ 张量多线性系统的新型预处理高斯-赛德尔方法
IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED Pub Date : 2024-08-23 DOI: 10.1007/s13160-024-00670-6
Xuan-Le An, Xin-Mei Lv, Shu-Xin Miao

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.

通过利用与系数张量相关的大化矩阵每行的一些元素,我们提出了一种预处理方法,并给出了相应的预处理高斯-赛德尔方法,用于求解({mathcal {M}})张量多线性系统。从理论上,我们给出了所提出的预条件高斯-赛德尔方法的收敛性和比较定理。在数值上,我们通过一些例子证明了理论结果的正确性和所提预处理方法的高效性。
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引用次数: 0
Convergence error analysis of reflected gradient Langevin dynamics for non-convex constrained optimization 非凸约束优化的反射梯度朗格文动力学收敛误差分析
IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED Pub Date : 2024-08-20 DOI: 10.1007/s13160-024-00667-1
Kanji Sato, Akiko Takeda, Reiichiro Kawai, Taiji Suzuki

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.

梯度朗格文动力学及其各种变体因其向全局最优解的收敛性而受到越来越多的关注,最初是在无约束凸框架中,最近甚至在凸约束非凸问题中。在本研究中,我们将这些框架扩展到非凸可行区域上的非凸问题,并使用基于反射梯度朗格文动力学的全局优化算法,推导出其收敛率。通过有效利用其在边界上的反射,并结合具有诺伊曼边界条件的泊松方程的概率表示,我们提出了具有前景的收敛速率,尤其是比现有的凸约束非凸问题收敛速率更快。
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引用次数: 0
Four extremal solutions of discrete-time algebraic Riccati equations: existence theorems and computation 离散时间代数里卡提方程的四个极值解:存在定理与计算
IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED Pub Date : 2024-08-07 DOI: 10.1007/s13160-024-00663-5
Chun-Yueh Chiang, Hung-Yuan Fan

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.

代数里卡提方程(AREs)已被广泛应用于线性优化控制问题,并开发出许多高效的数值方法。在过去的研究中,闭环矩阵的所有特征值都包含在复平面的开放(或封闭)单位盘中的稳定(或近似稳定)解是所有 ARE 赫米解中最受关注的。尽管如此,寻找 ARE 的极值解仍是一个有趣且具有挑战性的问题,因为极值解在应用中发挥着重要作用。本文的贡献有两方面。首先,本文在定点迭代框架下确定了这些极值解的存在性。其次,本文基于半群性质开发了一种加速定点迭代(AFPI)方法,用于计算离散时间代数 Riccati 方程的四个极值解,这在现有文献中尚未出现。此外,我们还证明了在一些温和的假设条件下,AFPI 的收敛性至少是阶(r>1)为 R 的超线性。我们用数值示例说明了所提算法的可行性和准确性。
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引用次数: 0
Ex ante and ex post envy-freeness on polytope resources 多面体资源的事前无嫉妒和事后无嫉妒
IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED Pub Date : 2024-08-04 DOI: 10.1007/s13160-024-00665-3
Yoshio Sano, Ping Zhan

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.

根据顺序偏好在代理人之间分配商品是一个经过深入研究的问题。在这项研究中,每种商品都可能有多种配额,配额在多面体中各不相同。当商品不可分割时,很难做到完全公平,但也有人提出了各种近似方法。根据以往的研究,可以获得精确的事前无嫉妒(在实现随机化或分解之前)。本研究基于 "最近 "结构实现了最多两份商品的无嫉妒。这种公平性被称为 "Best-of-Both-Worlds (BoBW)",意思是它在事前和事后,或随机化之前和之后,都实现了可能的最佳公平性概念。这项工作的不同之处在于,我们处理的是多份商品和整数需求,即离散分配的每个条目可以是任意正整数,而不是二进制数。虽然我们的近似值是针对两份商品,而不是一份不可分割的商品,但当商品份数较多时,我们的近似值可能会更好。此外,这些分配在随机支配(帕累托最优)中也是有效的。我们通过构建箱整数网络给出了这一问题的解决方案。此外,当资源多面体是多面体时,通过计算所谓的独立流,可以在多项式时间内获得随机分配。
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引用次数: 0
Mathematical analysis of a freely falling slinky 自由落体的数学分析
IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED Pub Date : 2024-07-02 DOI: 10.1007/s13160-024-00662-6
Tetsuya Kazumi, Shinsuke Nishikawa

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.

如果将悬挂在半空中的弹弓从最初的静止位置松开,你会发现一个有趣的现象:弹弓的底部会在半空中静止一段时间。在物理学家中,这一现象已广为人知,并已从物理角度进行了讨论。在本文中,我们从纯数学的角度探讨了自由下落的弹弓问题。通过严格的数学计算过程,我们得到了一个描述自由落体运动的明确公式,并证明这是一个不均匀波方程的解。我们的工作为物理学家获得的结果提供了数学上的依据。
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引用次数: 0
Existence and stability of a quasi-periodic two-dimensional motion of a self-propelled particle 自走质点准周期二维运动的存在性和稳定性
IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED Pub Date : 2024-07-02 DOI: 10.1007/s13160-024-00661-7
Kota Ikeda, Hiroyuki Kitahata, Yuki Koyano

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.

自走质点运动的机理引起了人们对生物运动的数学和物理理解的极大兴趣。在自上而下的方法中,简单的时间演化方程适用于定性分析不同类型解之间的转换以及系统内在对称性的影响,尽管不能定量地再现现象。我们旨在严格证明旋转解、振荡解和准周期解的存在,并根据小矢野等人(J Chem Phys 143(1):014117, 2015)提出的抛物线势约束自走粒子的典型方程确定它们的稳定性。在证明过程中,通过应用 Fenichel 关于常双曲不变流形的持久性定理和平均法,原始方程被还原为一个低维动力系统。此外,由于原始方程是 O(2)- 对称的,因此平均化后的系统本质上与一维方程相同。
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引用次数: 0
Data-driven confidence bound for structural response using segmented least squares: a mixed-integer programming approach 使用分段最小二乘法的结构响应数据驱动置信度:一种混合整数编程方法
IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED Pub Date : 2024-07-02 DOI: 10.1007/s13160-024-00657-3
Yoshihiro Kanno

As one of data-driven approaches to computational mechanics in elasticity, this paper presents a method finding a bound for structural response, taking uncertainty in a material data set into account. For construction of an uncertainty set, we adopt the segmented least squares so that a data set that is not fitted well by the linear regression model can be dealt with. Since the obtained uncertainty set is nonconvex, the optimization problem solved for the uncertainty analysis is nonconvex. We recast this optimization problem as a mixed-integer programming problem to find a global optimal solution. This global optimality, together with a fundamental property of the order statistics, guarantees that the obtained bound for the structural response is conservative, in the sense that, at least a specified confidence level, probability that the structural response is in this bound is no smaller than a specified target value. We present numerical examples for three different types of skeletal structures.

作为弹性计算力学的数据驱动方法之一,本文提出了一种考虑到材料数据集不确定性的结构响应约束的方法。在构建不确定性集时,我们采用了分段最小二乘法,这样就可以处理线性回归模型拟合效果不佳的数据集。由于得到的不确定度集是非凸的,因此不确定度分析的优化问题也是非凸的。我们将这一优化问题重塑为混合整数编程问题,以找到全局最优解。这种全局最优性以及阶次统计的基本属性保证了所获得的结构响应约束是保守的,即至少在指定的置信水平下,结构响应在此约束内的概率不小于指定的目标值。我们给出了三种不同类型骨架结构的数值示例。
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引用次数: 0
期刊
Japan Journal of Industrial and Applied Mathematics
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