Article
Mathematics, Applied
Douglas D. Novaes
Summary: This paper focuses on the problem of existence of periodic solutions for perturbative Caratheodory differential equations. The main result provides sufficient conditions on the averaged equation that guarantee the existence of periodic solutions. Additional conditions are also provided to ensure the uniform convergence of a periodic solution to a constant function. The proof of the main theorem is mainly based on an abstract continuation result for operator equations.
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
(2022)
Article
Mathematics, Applied
Elizabeth Gross, Cvetelina Hill
Summary: The paper provides an upper bound estimate for the steady-state degree of a chemical reaction network by utilizing polyhedral geometry, focusing on three cases of infinite families of networks generated by joining smaller networks. Formulas for the steady-state degree and mixed volume of the corresponding polynomial system are given for each family. Published by Elsevier Inc.
ADVANCES IN APPLIED MATHEMATICS
(2021)
Article
Mathematics, Applied
Sohail Ahmed, Hang Xu, Qiang Sun
Summary: This paper investigates the natural convection of a complex fluid containing nanoparticles and gyrotactic microorganisms in a heated square cavity. The behavior of the nanofluid is described using the Buongiorno model. The non-dimensional governing equations are obtained and solved using the Coiflet wavelet homotopy analysis method. The effects of various physics parameters on the convection are examined.
ADVANCES IN APPLIED MATHEMATICS AND MECHANICS
(2023)
Article
Mathematics, Applied
Praveen Agarwal, Muhammad Akbar, Rashid Nawaz, Mohamed Jleli
Summary: This paper introduces a powerful semi-analytical method called the optimal homotopy asymptotic method (OHAM) for solving systems of Volterra integro-differential equations. The effectiveness of the proposed technique is verified through numerical problems in the literature and compared with the Sinc-collocation method, demonstrating its reliability and efficiency. The OHAM method does not require discretization, allows easy control of the convergence region, and is simple and straightforward to use.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2021)
Article
Engineering, Electrical & Electronic
Mazhar Ali, Muhammad Hamza Ali, Elena Gryazina, Vladimir Terzija
Summary: Calculating loadability margins is crucial for the secure and stable operations of power grids. However, estimating these limits is challenging due to the non-convex structure of the power flow solution space and complex grid topology. To accurately estimate loadability margins, a two-stage algorithmic framework is proposed to identify all isolated loadability points within the power flow solution space. Numerical results from various test cases validate the computational performance of the proposed framework and demonstrate the convoluted structure of the power flow solution space.
INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS
(2023)
Article
Mathematics, Applied
Piotr Knosalla
Summary: The steady-state system of aerotaxis equations in higher dimensions is studied. It is found that the existence and multiplicity of solutions depend on the total mass of the colony of bacteria, the energy function, and the boundary conditions.
MATHEMATICAL METHODS IN THE APPLIED SCIENCES
(2023)
Article
Mathematics, Applied
Yao Huang, Wenrui Hao, Guang Lin
Summary: This paper introduces a new deep learning framework, HomPINNs, which combines PINNs with the homotopy continuation method to solve multiple solutions of nonlinear elliptic differential equations. The HomPINNs method trains a neural network in multiple steps to gradually optimize the model's performance.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2022)
Article
Mathematics
S. M. Afonso, E. M. Bonotto, Marcia R. da Silva
Summary: This article investigates the existence of periodic solutions for measure functional differential equations, utilizing a topological transversality theorem to derive the main result and presenting examples to illustrate the developed theory. Furthermore, the results obtained are applied to establish the existence of periodic solutions for impulsive functional differential equations.
JOURNAL OF DIFFERENTIAL EQUATIONS
(2022)
Article
Mechanics
Abiodun O. Ajibade, Ayuba M. Umar
Summary: This paper theoretically studies the effects of wall conduction and viscous dissipation on steady natural convection Couette flow in a vertical channel with thickness of the bounding slabs. The results show changes in velocity and temperature distributions of the working fluid under different thickness of the plates.
Article
Mathematics, Applied
Hawsar Ali Hama Rashid, Mudhafar Fattah Hama
Summary: This paper investigates the solvability of boundary value problems for a nonlinear integro-differential equation. A suitable transformation is used to convert the problem into an equivalent nonlinear Volterra-Fredholm integral equation (NVFIE). The existence and uniqueness of continuous solutions for the NVFIE are studied under certain given conditions using the Krasnoselskii fixed point theorem and Banach contraction principle. Finally, the NVFIE is numerically solved and the rate of convergence is studied using modified Adomian decomposition method and Liao's homotopy analysis method. Some examples are provided to support the findings.
Article
Mathematics, Applied
Muhammad Nadeem, Qura Tul Ain, Yahya Alsayaad
Summary: The paper introduces a new scheme called Laplace-Carson homotopy integral transform method (LcHITM) for the approximate solution of 1D, 2D, and 3D wave equations. Using Laplace-Carson integral transform (LcIT) and homotopy perturbation method (HPM), LcHITM provides a recurrence relation and successive iteration for solving the wave equations. The scheme is shown to have a high rate of convergence through numerical examples and graphical representation.
JOURNAL OF FUNCTION SPACES
(2023)
Article
Engineering, Multidisciplinary
Abiodun O. Ajibade, Tafida M. Kabir
Summary: This article investigates the effect of viscous dissipation on steady natural convection Couette flow under convective boundary condition. The solutions of the energy and momentum equations were obtained using the homotopy perturbation method. The impacts of the controlling parameters were analyzed graphically. It was found that increasing viscous dissipation leads to higher fluid temperature and lower fluid velocity. Heat generation decreases the rate of heat transfer on the heated plate and increases it on the cold plate. Additionally, an increase in Biot number results in an increase in the velocity boundary layer thickness.
INTERNATIONAL JOURNAL OF NONLINEAR SCIENCES AND NUMERICAL SIMULATION
(2023)
Article
Mathematics
Mikhail V. Korobkov, Konstantin Pileckas, Remigio Russo
Summary: This study proves that the classical Leray solution to the obstacle problem for the stationary Navier-Stokes system in a two-dimensional exterior domain is always nontrivial, without any additional conditions. This extends a classical result by Amick (1988) where nontriviality was proved under a symmetry assumption.
ADVANCES IN MATHEMATICS
(2021)
Article
Mathematics, Applied
Eleonora Amoroso, Gabriele Bonanno, Giuseppina D'Agui, Salvatore Foti
Summary: The paper aims to investigate a parameter-dependent nonlinear differential problem with Sturm-Liouville type equation and Dirichlet boundary conditions. By imposing a suitable behavior on the nonlinearity, an interval of parameter lambda is determined for which the problem has three or infinitely many solutions.
NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS
(2023)
Article
Engineering, Multidisciplinary
Xiangyuan Meng, Mei Huang, Boxue Wang, Yaodi Li, Yanting Cheng, Chihiro Morita
Summary: The half-boundary method (HBM) is developed for nonlinear convection-diffusion equations (CDEs) and shows excellent performance in simulating flow and heat transfer, especially for convection domination. The HBM reduces the maximum order of matrix and calculation memory storage by utilizing the variable relationship between the nodes inside the domain and the nodes on half of the boundaries. Moreover, it can directly solve discontinuous problems without adding continuity conditions due to the use of mixed variables.
ENGINEERING ANALYSIS WITH BOUNDARY ELEMENTS
(2023)
Article
Food Science & Technology
Esau Bojorquez-Velazquez, Aida Jimena Velarde-Salcedo, Antonio De Leon-Rodriguez, Hugo Jimenez-Islas, Jose Luis Perez-Torres, Alfredo Herrera-Estrella, Eduardo Espitia-Rangel, Ana Paulina Barba de la Rosa
JOURNAL OF CEREAL SCIENCE
(2018)
Article
Chemistry, Applied
J. A. Torres-Ochoa, N. R. Osornio-Rubio, H. Jimenez-Islas, J. L. Navarrete-Bolanos, G. M. Martinez-Gonzalez
REVISTA MEXICANA DE INGENIERIA QUIMICA
(2019)
Article
Chemistry, Applied
J. L. Navarrete-Bolanos, I Gonzalez-Torres, V. H. Vargas-Bermudez, H. Jimenez-Islas
REVISTA MEXICANA DE INGENIERIA QUIMICA
(2020)
Article
Thermodynamics
L. I. Quemada-Villagomez, F. I. Molina-Herrera, M. Carrera-Rodriguez, M. Calderon-Ramirez, G. M. Martinez-Gonzalez, J. L. Navarrete-Bolanos, H. Jimenez-Islas
INTERNATIONAL JOURNAL OF THERMOPHYSICS
(2020)
Article
Food Science & Technology
F. J. Vicente-Magueyal, A. Bautista-Mendez, H. D. Villanueva-Tierrablanca, J. L. Garcia-Ruiz, H. Jimenez-Islas, J. L. Navarrete-Bolanos
LWT-FOOD SCIENCE AND TECHNOLOGY
(2020)
Article
Biotechnology & Applied Microbiology
J. Manuel Oliveros-Munoz, Jose A. Martinez-Villalba, Hugo Jimenez-Islas, Mayra Y. Luna-Porres, Carlos Escamilla-Alvarado, Francisco Javier Rios-Franquez
Summary: The study employed mathematical modeling and computer simulation to determine the microaeration initiation time of biodigesters treating cow manure, minimizing hydrogen sulfide production while maintaining competitive methane production levels. Experimental validation showed high statistical significance for optimized parameters in a non-perfectly mixed batch bioreactor, providing a deeper explanation of the microaeration effect through microbial consortia evolution simulation.
BIOCHEMICAL ENGINEERING JOURNAL
(2021)
Article
Biotechnology & Applied Microbiology
J. L. Navarrete-Bolanos, O. Serrato-Joya, H. Chavez-Mireles, F. J. Vicente-Magueyal, H. Jimenez-Islas
Summary: This study presents a guideline for designing efficient fermentation-industrial processes for agave distilled production, starting from laboratory experiments and optimizing the process variables using the evolutionary operation method. The results show that different levels of production require specific process variables to achieve similar performance values. Both laboratory and pilot-plant processes produced fermented products with pleasant fruity and ethereal aromatic notes.
BIOPROCESS AND BIOSYSTEMS ENGINEERING
(2021)
Article
Construction & Building Technology
L. I. Quemada-Villagomez, R. Miranda-Lopez, M. Calderon-Ramirez, J. L. Navarrete-Bolanos, G. M. Martinez-Gonzalez, H. Jimenez-Islas
Summary: The study proposes two environmental temperature prediction models: a Gaussian model and a cosenoidal model. The Gaussian model calculates temperature based on maximum and minimum temperatures and relative time, while the cosenoidal model predicts continuous temperature within a day.
BUILDING AND ENVIRONMENT
(2021)
Article
Multidisciplinary Sciences
Cynthia Teresa Lara-Garcia, Hugo Jimenez-Islas, Rita Miranda-Lopez
Summary: This study compared the phytochemistry of creole avocado with commercial varieties, revealing unique VOC profiles in creole avocado leaves and distinctive chemical components in the Drymifolia variety associated with anticancer, anti-inflammatory, and antioxidant activities. These findings have implications for promoting the use of creole avocado as an ingredient, additive, or phytopharmaceutical in the food or biotechnology industry.
Article
Thermodynamics
Marcelino Carrera-Rodriguez, Jose Francisco Villegas-Alcaraz, Carmen Salazar-Hernandez, Juan Manuel Mendoza-Miranda, Hugo Jimenez-Islas, Juan Gabriel Segovia Hernandez, Juan de Dios Ortiz-Alvarado, Higinio Juarez-Rios
Summary: This study investigates the impact of high mileage vehicles on oil degradation, lubrication efficiency, CO2 emissions, and fuel consumption. The findings reveal significant negative effects, with an annual excess of fuel consumption, CO2 emissions, and costs. The methodology used can be applied to different car brands and oils in countries with similar vehicle fleets, contributing to monitoring and proper use of automotive oil and the formulation of low pollution policies.
Review
Food Science & Technology
L. Jarquin-Enriquez, P. Ibarra-Torres, H. Jimenez-Islas, N. L. Flores-Martinez
Summary: Recent studies have shown that essential oils from Pimenta dioica are rich in eugenol, which has a wide antimicrobial spectrum and is suitable for food preservation. However, their strong aroma may affect consumer acceptance, hence nanotechnology is used to encapsulate them in biodegradable materials for controlled release.
INTERNATIONAL FOOD RESEARCH JOURNAL
(2021)
Article
Mathematics, Applied
Junfeng Cao, Ke Chen, Huan Han
Summary: This paper proposes a two-stage image segmentation model based on structure tensor and fractional-order regularization. In the first stage, fractional-order regularization is used to approximate the Hausdorff measure of the MS model. The solution is found using the ADI scheme. In the second stage, thresholding is used for target segmentation. The proposed model demonstrates superior performance compared to state-of-the-art methods.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Dylan J. Oliver, Ian W. Turner, Elliot J. Carr
Summary: This paper discusses a projection-based framework for numerical computation of advection-diffusion-reaction (ADR) equations in heterogeneous media with multiple layers or complex geometric structures. By obtaining approximate solutions on a coarse grid and reconstructing solutions on a fine grid, the computational cost is significantly reduced while accurately approximating complex solutions.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Nathan V. Roberts, Sean T. Miller, Stephen D. Bond, Eric C. Cyr
Summary: In this study, the time-marching discontinuous Petrov-Galerkin (DPG) method is applied to the Vlasov equation for the first time, using backward Euler for a Vlasov-Poisson discretization. Adaptive mesh refinement is demonstrated on two problems: the two-stream instability problem and a cold diode problem.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Yizhi Sun, Zhilin Sun
Summary: This work investigates the convexity of a specific class of positive definite probability measures and demonstrates the preservation of convexity under multiplication and intertwining product. The study reveals that any integrable function on an interval with a polynomial expansion of fast absolute convergence can be decomposed into a pair of positive convex interval probabilities, simplifying the study of interval distributions and discontinuous probabilistic Galerkin schemes.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Bhagwan Singh, Komal Jangid, Santwana Mukhopadhyay
Summary: This paper examines the prediction of bending characteristics of nanoscale materials using the Moore-Gibson-Thompson thermoelasticity theory in conjunction with the nonlocal strain gradient theory. The study finds that the stiffness of the materials can be affected by nonlocal and length-scale parameters, and the aspect ratios of the beam structure play a significant role in bending simulations.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Guoliang Wang, Bo Zheng, Yueqiang Shang
Summary: This paper presents and analyzes a parallel finite element post-processing algorithm for the simulation of Stokes equations with a nonlinear damping term, which integrates the algorithmic advantages of the two-level approach, the partition of unity method, and the post-processing technique. The algorithm generates a global continuous approximate solution using the partition of unity method and improves the smoothness of the solution by adding an extra coarse grid correction step. It has good parallel performance and is validated through theoretical error estimates and numerical test examples.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Hao Xu, Zeng-Qi Wang
Summary: Fluid flow control problems are crucial in industrial applications, and solving the optimal control of Navier-Stokes equations is challenging. By using Oseen's approximation and matrix splitting preconditioners, we can efficiently solve the linear systems and improve convergence.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
Article
Mathematics, Applied
Zhengya Yang, Xuejuan Chen, Yanping Chen, Jing Wang
Summary: This paper focuses on the high-order stable numerical solutions of the time-space fractional diffusion equation. The Fourier spectral method is used for spatial discretization and the Spectral Deferred Correction (SDC) method is used for numerical solutions in time. As a result, a high-precision numerical discretization scheme for solving the fractional diffusion equation is obtained, and the convergence and stability of the scheme are proved. Several numerical examples are presented to demonstrate the effectiveness and feasibility of the proposed numerical scheme.
COMPUTERS & MATHEMATICS WITH APPLICATIONS
(2024)
