Matematica数学
Matematica(英文缩写 MATEMATICA-US),ISSN 2730-9657,eISSN 2730-9657,中文译名:数学 是一本学术期刊。本页汇总该期刊的最新影响因子、分区信息以及最新收录于 PubMed 的文献,帮助您快速了解期刊全貌。
发文量统计区间：2025-10-01 至 2026-09-30，按本站收录文献的发表日期统计。
期刊介绍
Matematica 最新收录文献
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1. Influence of Magnetohydrodynamics and Viscosity Ratio on Modified Tetra-Hybrid Nanofluid Flow under a Threshold Non-Fourier Heat Flux Framework.
PMID:日期:2026-09-23This study examines the combined effects of magnetohydrodynamics (MHD), viscosity ratio, and thermal radiation on the flow and heat transfer of a water-based tetra-hybrid nanofluid containing Gold, Silver, Titanium dioxide, and Aluminium oxide nanoparticles over a stretching surface. The governing momentum and energy equations are reduced to ordinary differential equations via similarity transformations, and closed-form analytical solutions are obtained using Appell hypergeometric functions. Key parameters, including the viscosity ratio, nanoparticle volume fraction, and inverse Darcy number, are analysed and compared across di-, tri-, and tetra-hybrid nanofluids. The results show that stronger magnetic fields and higher nanoparticle loadings suppress the velocity field, while changes in the thermal parameters modify the temperature distribution and thermal boundary-layer thickness. Among the formulations considered, the di-hybrid nanofluid exhibits the largest normalized wall-temperature gradient, whereas the tetra-hybrid formulation exhibits higher temperature profiles under the parameter ranges studied.
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2. Body-Force Effects in Homogenised Models of Anisotropic Double Poroelastic Materials.
PMID:日期:2026-09-23We develop a rigorous multiscale homogenisation framework for determining the effective behaviour of materials composed of a poroelastic matrix containing embedded poroelastic subphases, each governed by fully anisotropic and heterogeneous Biot equations and subject to body forces. Starting from local balance laws for momentum, Darcy flow, and mass conservation, and assuming scale separation, periodic microstructure, and macroscopic uniformity, we derive a closed system of Biot-type equations at the macroscale. The resulting effective coefficients explicitly capture the influence of microstructural geometry, elastic and hydraulic heterogeneity, and mesoscale forcing. The framework yields well-posed cell problems for the effective elasticity tensor, hydraulic conductivity tensor, and Biot-type coupling coefficients, establishing a unified multiscale theory that extends and subsumes existing single-phase, composite, and double-poroelastic models. As an illustrative application, we specialise the theory to magnetic Lorentz forcing and show that body forces with gradient structure induce additional pressure-like terms in the effective Darcy law, rather than appearing solely as averaged source terms. The proposed framework sets the agenda for modelling complex poroelastic materials with interacting subphases, with applications in biomechanics, engineered composites, and geomechanics.
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3. Speaking of Opinions: Comparing Approaches to Modelling Opinion Manipulation.
PMID:日期:2026-09-09This review outlines the major approaches to modelling opinion formation and manipulation in mathematics and computer science. Key tools such as ordinary and partial differential equations, stochastic models, control theory, and interaction protocols are introduced and compared as methods for describing manipulation. The review is divided into models that use a continuous opinion space and those that use discrete opinions, with the advantages and disadvantages of each discussed. Particular emphasis is placed on bounded-confidence models in continuous opinion dynamics and on binary opinion models in the discrete setting. Finally, the authors provide an interdisciplinary perspective on opinion dynamics and its social significance.
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4. Community-Driven Data Science Practices.
PMID:日期:2026-09-06Mathematics researchers are becoming more involved with research questions at the interface of data science and social justice. This type of research needs to be grounded in the needs of the community in order to have significant impact. In this paper, we examine two examples of community-research partnerships in data science for social justice co-authored by both community members and mathematical researchers. The first, VECINA, is a place-based community-research partnership focused on environmental justice. VECINA introduces a framework for developing fruitful local collaborations. The second example, SToPA, originates in citizens' request for an analysis of their town's policing data, but focuses on how to scale this work beyond that place-based setting. SToPA's research helps us imagine how we can continue to actively collaborate with community members even when working to scale projects beyond a single community. In both of these case studies, we examine the harmonies between established principles of power, process, and perspective with our framework for research-community partnerships. We use a duoethnography approach, directly illustrating the experiences of researchers. We also offer a set of reflections on the impact of these research-community partnerships.
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5. Rescaling and Asymptotic Acceleration in Unconstrained Quadratic Optimisation.
PMID:日期:2026-06-12We investigate the properties of a class of piecewise-fractional maps arising from the introduction of an invariance under rescaling into convex quadratic maps. The subsequent maps are quasiconvex, and pseudoconvex on specific convex cones; they can be optimised via exact line search along admissible directions. We study the minimisation of such relaxed maps via coordinate descents with gradient-based rules, placing a special emphasis on coordinate directions verifying a maximum-alignment property in the reproducing kernel Hilbert spaces related to the underlying positive-semidefinite matrices. In this setting, we illustrate theoretically and empirically that accounting for the optimal rescaling of the iterates can in certain situations substantially accelerate the unconstrained minimisation of convex quadratic maps.
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6. Convergence of the Immersed Interface Method in Linear Elasticity.
PMID:日期:2026-05-12We consider an open, bounded, simply connected (Lipschitz) domain in , which contains a closed polyhedral surface or polygonal contour, referred to as the interface. From this interface, forces are exerted in the normal direction. The forces are continuously distributed over the interface, resulting in an integral expression. This features an important characteristic of the immersed interface method. Since the integral cannot be resolved exactly, one relies on numerical quadrature rules to approximate the integral. Therefore, we consider two different linear elasticity problems with forces over a curve or surface (interface) that is located within the (open) domain of computation: (1) The force is defined by an integral over the interface; (2) The force is defined by a quadrature approximation of the integral over the interface. We prove that the -norm of the difference between the solutions from the two elasticity problems is of the same order as the error of quadrature. The results are demonstrated for both bounded and unbounded domains. The proof that we establish relies on the use of: (i) fundamental solutions for linear elasticity, exhibiting singular behaviors (in particular around points of action) and not being in , and (ii) on the use of singularity removal principle and the Extended Trace Theorem. Convergence is demonstrated in the -norm on curves and manifolds. We show some numerical experiments on the basis of fundamental solutions with a Midpoint quadrature rule in an unbounded and a bounded domain. The numerical experiments confirm our theoretical results. We note that the difference between the interface integral and the quadrature rule over the interface holds for the exact solution in the bulk and not for any discretization carried out in the bulk. Hence, in the numerical finite element-based simulations, the numerical results contain an additional error due to the finite element approach.
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7. Impact of Vascular Network Structure Heterogeneity on Retinal Tissue Oxygenation.
PMID:日期:2025-06-05A theoretical model of the human retina is simulated using two distinct vascular network geometries to predict the impact of heterogeneity in vascular network structure on retinal tissue oxygenation. Each vascular network is modeled as a combined heterogeneous representation of retinal arterioles and compartmental representation of capillaries, small venules, and large venules. A Green's function method is used to model oxygen transport in the arterioles, and a Krogh cylinder model is used in the capillaries and venules. Identical input arterial blood saturation (0.92), arteriolar pressure drop (16 mmHg), and arteriolar diameters by vessel order ( ) are assumed for both networks. The model shows that 12% of the arteriolar tissue in Branch 1 has a PO less than 25 mmHg, while only 1% of the arteriolar tissue in Branch 2 has a PO less than 25 mmHg. However, downstream of the capillaries, Branch 2 was predicted to exhibit lower tissue PO than Branch 1. The model also predicted increased oxygen extraction fraction as oxygen demand increased or capillary density decreased. Even with identical initial conditions for saturation, pressure drop, and diameter, variations in network geometry led to significantly different regions of low PO, indicating a wide range of potential oxygenation outcomes for individual patients. This study therefore demonstrates that regional heterogeneity in vessel branching architecture may significantly impact oxygen saturation and ultimately retinal ganglion cell functionality, motivating the need for creating patient-specific vascular networks.
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8. Parity Property of Hexagonal Sliding Puzzles.
PMID:日期:2025-05-07We study the puzzle graphs of hexagonal sliding puzzles of various shapes, and with various numbers of holes. The puzzle graph is a combinatorial model which captures the solvability and the complexity of sequential mechanical puzzles. Questions relating to the puzzle graph have been previously studied and resolved for the 15 Puzzle, which is the most famous-and unsolvable-square sliding puzzle of all time. It is known that for square puzzles such as the 15 Puzzle, solvability depends on a parity property that splits the puzzle graph into two components. In the case of hexagonal sliding puzzles, we get more interesting parity properties that depend on the shape of the boards and on the missing tiles or holes on the board. We show that for large-enough hexagonal, triangular, or parallelogram-shaped boards with hexagonal tiles, all puzzles with three or more holes are solvable. For puzzles with two or more holes, we give a solvability criterion involving both a parity property, and the placement of tiles in of the board. The puzzle graph is a discrete model for the configuration space of hard tiles (hexagons or squares) moving on different tessellation-based domains. Understanding the combinatorics of the puzzle graph could lead to understanding some aspects of the topology of these configuration spaces.
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9. Retinal Venous Vulnerability in Primary Open Angle Glaucoma: The Combined Effects of Intraocular Pressure and Blood Pressure with Application to the Thessaloniki Eye Study.
PMID:日期:2024-12-23Primary open angle glaucoma (POAG) is a leading cause of irreversible blindness with risk factors including elevated intraocular pressure (IOP), and both high and low blood pressure (BP). This study investigates the joint influence of IOP and BP on retinal hemodynamics, emphasizing venous circulation. A synthetic dataset comprising 2500 eyes with varied IOP [5-45] mmHg, systolic BP (SBP) [90-200] mmHg and diastolic BP (DBP) [40-120] mmHg was created. Mean pressure , mean flow , and mean resistance , were estimated using a validated mathematical model. The values of these hemodynamic output variables were then analyzed in relation to different values of IOP and mean arterial pressure (MAP; MAP = 1/3 SBP + 2/3 DBP). Clinical data from a population-based Greek study were similarly analyzed. Differences in the simulated hemodynamic output variables and clinical markers between healthy and POAG eyes were then measured. Synthetic dataset analysis revealed that and vary significantly depending on different IOP-MAP combinations. Notably, eyes with low MAP and high IOP demonstrated a drastic increase in in the venules accompanied with a dramatic decrease in in the central retinal vein (CRV). Clinical data indicated that venules in POAG eyes had significantly higher than healthy eyes ( < 0.01), along with decreased in the CRV of POAG eyes compared to healthy eyes ( = 0.01). The study highlights the increased susceptibility to venous collapse in POAG eyes and the importance of considering the venous side of retinal circulation in the combined impact of risk factors in POAG.
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10. {"_":"Analysis of Waveform Parameters in the Retinal Vasculature Mathematical Modeling and Data Analytics Methods.","i":["via"]}
PMID:日期:2024-09-11Patient-specific mathematical modeling combined with data analytics methods presents a promising approach for analyzing retinal hemodynamics. In this study, we build upon previous developments in retinal blood flow modeling, integrating clinical measurements and physiological insights to reconstruct parameters such as the central retinal artery velocity (CRA) Doppler profile and pressure wave. By leveraging personalized input data, including CRA velocity profile, systemic blood pressure, heart rate, and intraocular pressure, we evaluate the performance of our approach. Our investigation highlights the significance of methodological considerations in combining automatic image processing and mathematical modeling, particularly concerning the selection of appropriate strategies and the inclusion of personalized supplementary data. Through extensive validation and comparison with prior works, we demonstrate the impact of different assessment methods on clinically meaningful quantities, particularly biomarkers related to blood flow. Furthermore, our study introduces a novel metric based on the Wasserstein distance for monitoring temporal changes in retinal blood flow dynamics, providing valuable insights into the evolution of vascular function. Overall, our findings underscore the importance of patient-specific input data, automatic image processing, and personalized mathematical modeling to ensure robust and clinically relevant outcomes in retinal vasculature analysis.