Mathematics and Computers in Simulation最新文献

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Influence of price elasticity of demand on monopoly games under different returns to scale

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-01-28 DOI: 10.1016/j.matcom.2025.01.017

Xiaoliang Li , Jing Yang , Ally Quan Zhang

This paper examines a monopoly market featured by a general isoelastic demand function. With a quadratic cost function for the monopolist, we explore how the price elasticity of demand influences monopolistic behavior under different (decreasing, constant, and increasing) returns to scale. The combination of the general isoelastic demand and quadratic cost functions leads to a transcendental equilibrium equation, making closed-form solutions unattainable. To address this challenge, we develop an innovative approach that leverages the specific structure of marginal revenue and cost to conduct a comprehensive comparative static and stability analysis. Additionally, we introduce two dynamic models based on distinct adjustment mechanisms: gradient and local monopolistic approximation (LMA). Our findings reveal that the LMA model is more stable in both parameter and state spaces compared to the gradient model. Notably, we prove that the unique non-vanishing equilibrium of the LMA model is globally asymptotically stable.

引用次数: 0

News of IMACS

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-01-28 DOI: 10.1016/S0378-4754(25)00027-8

引用次数: 0

IMACS Calendar of Events

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-01-28 DOI: 10.1016/S0378-4754(25)00028-X

引用次数: 0

Asymptotic expansions beyond the tQSSA for the double phosphorylation mechanism

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-01-27 DOI: 10.1016/j.matcom.2025.01.019

Alberto M. Bersani , Alessandro Borri , Giovanna Tomassetti , Pierluigi Vellucci

In this paper we study the asymptotic properties of the mathematical model of the double phosphorylation (dephosphorylation) enzymatic reaction, or futile cycle. Starting from the total quasi-steady state approximation (tQSSA), and applying singular perturbation techniques, we determine the inner and outer solutions and the corresponding matched expansions, up to the first order, in terms of an appropriate perturbation parameter

ϵ

(related to the kinetic constants and initial conditions of the model). Some numerical results are discussed.

引用次数: 0

A nonconservative macroscopic traffic flow model in a two-dimensional urban-porous city

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-01-25 DOI: 10.1016/j.matcom.2025.01.016

Néstor García-Chan , Lino J. Alvarez-Vázquez , Aurea Martínez , Miguel E. Vázquez-Méndez

In this paper we propose a novel traffic flow model based on understanding the city as a porous media, this is, streets and building-blocks characterizing the urban landscape are seen now as the fluid-phase and the solid-phase of a porous media, respectively. Moreover, based in the interchange of mass in the porous media models, we can model the interchange of cars between streets and off-street parking-spaces. Therefore, our model is not a standard conservation law, being formulated as the coupling of a non-stationary convection–diffusion–reaction PDE with a Darcy–Brinkman–Forchheimer PDE system. To solve this model, the classical Galerkin

P_{1}

finite element method combined with an explicit time marching scheme of strong stability preserving type was enough to stabilize our numerical solutions. Numerical experiences on an urban-porous domain inspired by the city of Guadalajara (Mexico) allow us to simulate the influence of the porosity terms on the traffic speed, the traffic flow at rush-valley hours, and traffic congestion due to the lack of parking spaces.

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引用次数: 0

Globally exponentially convergent observer for systems evolving on matrix Lie groups

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-01-23 DOI: 10.1016/j.matcom.2025.01.013

Soham Shanbhag, Dong Eui Chang

The estimate of a system state, arrived at using measurements, is often used in design of state controllers in robotics. These measurements are often biased and contain noise. Many such systems usually evolve on matrix Lie groups. In this paper, we propose a globally exponentially convergent observer for systems evolving on matrix Lie groups with bounded velocity. The design of observers on the Lie group prohibits continuous globally convergent observers, which we sidestep by designing the observer in the ambient Euclidean space of the group and show exponential convergence of the observer to the state of the system. The performance of the observer is shown using an example of the rigid body rotation and translation system evolving on the special Euclidean group. We also compare the proposed observer with an observer present in the literature and show the improvements afforded by our observer.

引用次数: 0

Uncertain stochastic linear quadratic control subject to forward and backward multi-stage systems

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-01-20 DOI: 10.1016/j.matcom.2025.01.015

Xin Chen, Zeyu Zhang, Peiqi Huang

This paper investigates linear quadratic (LQ) optimal control problems of forward uncertain and backward stochastic multi-stage systems. First, leveraging dynamic programming, we derive stochastic recursive equations tailored to address an LQ optimal control problem for backward stochastic multi-stage systems within a probabilistic framework. Subsequently, we extend our analysis to an equivalent LQ optimal control problem formulated under chance theory, incorporating both forward uncertain and backward stochastic dynamics. From this, we derive uncertain stochastic recursive equations to solve the equivalent problem and provide explicit analytical expressions for the optimal control strategies and corresponding optimal values. Additionally, we explore the effects of variable separability within uncertain random variables, demonstrating that under chance theory, the optimal solutions of LQ optimal control problems remain consistent when uncertain and random variables are separable. Finally, a numerical example is provided to validate our results.

引用次数: 0

Quenching phenomenon in the Caputo–Hadamard time-fractional Kawarada problem: Analysis and computation

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-01-18 DOI: 10.1016/j.matcom.2025.01.014

Dingding Cao, Changpin Li

In this study, the analysis and computation for quenching phenomenon in the Caputo–Hadamard time-fractional Kawarada problem is investigated. Initial findings confirm that its classical solution exhibits non-negativity and quenching in a finite time. Then the numerical method is established to detect the quenching phenomenon in the considered problem. Numerical simulations are provided to show the effectiveness of the theoretical analysis and computation.

引用次数: 0

Wavelet thresholding on independent subspace factorizations of spatially indexed wide functional data for robust estimation of cortical activity

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-01-17 DOI: 10.1016/j.matcom.2025.01.012

Marc Vidal , Ana M. Aguilera

We address the mathematical and statistical formalism that underpins optimal estimation of brain activity in artifact-corrupted electroencephalographic (EEG) signals. We argue the reconstruction of artifacts relates to approximating a function in a Hilbert basis that is a realization of a spatio-temporal random variable taking values in a Hilbert space. A model for sparse optimization based on a fixed-point iteration over the spatial domain and posterior enhancement in the temporal domain via wavelet thresholding is discussed under the paradigm of “wide functional data”. Two criteria are introduced for selecting wavelet expansion coefficients in scenarios where noise lacks a precise parametric specification: one based on multiplicative scaling and the other on the entropic NID (ENID), as introduced in Bruni et al. (2020). Through comprehensive numerical simulations and real data analyses of EEG data, we showcase the effectiveness of the proposed methods.

引用次数: 0

Image encryption algorithm based on butterfly module and chaos

IF 4.4 2区数学 Q1 COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS

Mathematics and Computers in Simulation

Pub Date : 2025-01-17 DOI: 10.1016/j.matcom.2025.01.011

Yong Zhang

Image information security is a hot research area in cryptography after text encryption research. To effectively secure digital images, a practical and graceful new image encryption algorithm was proposed in this paper. Firstly, four substitution boxes (S-boxes) are constructed based on the method of generating S-box of AES. Secondly, a chaotic system with uniform probability density function is created by fusing piecewise linear map (PWLM) and Arnold cat map. The resulting system is used to produce an equivalent-key sequence of the same size as the plain image using an external secret key of length 256 bits. Thirdly, a butterfly encoding module based on the butterfly node algorithm is presented. Finally, the basic image cryptosystem based on the butterfly encoding module, the enhanced image cryptosystem with cipher-text sensitivity, and the unified image cryptosystem with identical encryption and decryption processes are sequentially studied. The performance analysis shows that the proposed image encryption systems have a time complexity of 3 and a spatial complexity of approximately 3.03, the generated cipher images are similar to noise images, and the secret key, the equivalent key, and the plain image are all extremely sensitive. Thus, the proposed cryptographies are high-speed and secure image encryption algorithms.

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引用次数: 0

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