Hopf Bifurcation Analysis in a Modified Price Differential Equation Model with Two Delays

The paper investigates the behavior of price differential equation model based on economic theory with two delays. The primary aim of this thesis is to provide a research method to explore the undeveloped areas of the price model with two delays. Firstly, we modify the traditional price model by considering demand function as a downward opening quadratic function, and supply and demand functions both depending on the price of the past and the present. Then the price model with two delays is established. Secondly, by considering the price model with one delay, we get the stable interval. Regarding another delay as a parameter, we studied the linear stability and local Hopf bifurcation. In addition, we pay attention to the direction and stability of the bifurcating periodic solutions which are derived by using the normal form theory and center manifold method. Afterwards, the study turns to simulate the results through numerical analysis, which shows that the provided method is valid

The mechanical properties of a three-dimensional stochastic fibrous network with cross-linking

Fibrous materials are promising for a wide range of engineering applications due to their low density and high stiffness and strength. Stochastic filamentous networks can be widely found in biomaterials at the micro- and nano-scales. The objective of this study is to investigate the mechanical properties of macro-sized, micro-sized and nano-sized stochastic fibrous networks with cross-linking. A continuum mechanics-based three-dimensional periodic beam model has been developed to describe stochastic fibrous materials by the Finite Element Method (FEM). Relative density is a key parameter to elucidate the mechanical properties of porous fibrous materials. The relative density of the beam model developed in this study can be adjusted by changing the concentration of the cross-linker, the fibre aspect ratio and the coefficient of overlap. In general, the non-dimensional Young’s moduli and shear moduli increase with increasing relative density. The simulation and analytical model have suggested that strut bending is the dominant deformation mechanism for stochastic fibrous materials. Based on the total strain energy density, scalar measures of characteristic stress and strain have been applied to reveal the yielding of stochastic fibrous materials. The effect of relative density on uniaxial yield strength of stochastic fibrous materials shows a quadratic function in the x direction and a cubic function in the z direction. When the dimensions of fibrous structures are reduced to the micro- or nano-scale, the stiffness is much different from that of their macro-sized counterparts. Strain gradient effects at the micro-meter scale, and the surface elasticity and initial stress effects at the nano-meter scale have been incorporated into the deformation mechanism of fibrous materials. For both of the micro- and nano-sized fibrous structure, the smaller the diameter, the larger the non-dimensional Young’s moduli and shear moduli. Generally speaking, the dimensionless stiffness of nano-sized stochastic fibrous structures is larger than their micro-sized counterparts. The size-dependent effects investigated in this study could provide good reference points for scientists in tissue engineering and serve as a guide in the design of MEMS and NEMS

The mechanical properties of a three-dimensional stochastic fibrous network with cross-linking

Fibrous materials are promising for a wide range of engineering applications due to their low density and high stiffness and strength. Stochastic filamentous networks can be widely found in biomaterials at the micro- and nano-scales. The objective of this study is to investigate the mechanical properties of macro-sized, micro-sized and nano-sized stochastic fibrous networks with cross-linking. A continuum mechanics-based three-dimensional periodic beam model has been developed to describe stochastic fibrous materials by the Finite Element Method (FEM). Relative density is a key parameter to elucidate the mechanical properties of porous fibrous materials. The relative density of the beam model developed in this study can be adjusted by changing the concentration of the cross-linker, the fibre aspect ratio and the coefficient of overlap. In general, the non-dimensional Young’s moduli and shear moduli increase with increasing relative density. The simulation and analytical model have suggested that strut bending is the dominant deformation mechanism for stochastic fibrous materials. Based on the total strain energy density, scalar measures of characteristic stress and strain have been applied to reveal the yielding of stochastic fibrous materials. The effect of relative density on uniaxial yield strength of stochastic fibrous materials shows a quadratic function in the x direction and a cubic function in the z direction. When the dimensions of fibrous structures are reduced to the micro- or nano-scale, the stiffness is much different from that of their macro-sized counterparts. Strain gradient effects at the micro-meter scale, and the surface elasticity and initial stress effects at the nano-meter scale have been incorporated into the deformation mechanism of fibrous materials. For both of the micro- and nano-sized fibrous structure, the smaller the diameter, the larger the non-dimensional Young’s moduli and shear moduli. Generally speaking, the dimensionless stiffness of nano-sized stochastic fibrous structures is larger than their micro-sized counterparts. The size-dependent effects investigated in this study could provide good reference points for scientists in tissue engineering and serve as a guide in the design of MEMS and NEMS

Ensuring the authenticity of the conservation and reuse of modern industrial heritage architecture: a case study of the large machine factory, China

The Large Machine Factory (LMF) was built in the complex historical context of the late Qing Dynasty (1840–1912). Its space and construction faithfully record the architectural and cultural fusion between Chinese and western traditions and mark the beginning of modern architectural techniques in China. Through historical data and empirical studies, the historical background and architectural characteristics of the LMF were analyzed, and interventions aimed at ensuring authenticity were established. The cultural significance and results of construction were considered two crucial elements in terms of outstanding characteristics. Comprehensive inspection and assessment strategies were discussed, with minimal intervention and interpretation principles. Preventive reinforcement of the foundation, complementary reinforcement of the main structures, restoration of the historic façade and environment, and adaptive spatial interventions were found to be effective ways to ensure authenticity. The principles of minimal intervention and interpretability, which include prevention, recognizability, invisibility, subsidiarity, and intertextuality, were proposed through a comparison with the literature and practical experience. This study provides an appropriate technical reference for ensuring authenticity in the conservation and reuse of modern historic buildings with complex contexts. We propose a new understanding of intervention principles and suggest a guiding intervention path that avoids the complexities arising from the generalized interpretations of authenticity.Postprint (published version

Causality-Aided Trade-off Analysis for Machine Learning Fairness

There has been an increasing interest in enhancing the fairness of machine learning (ML). Despite the growing number of fairness-improving methods, we lack a systematic understanding of the trade-offs among factors considered in the ML pipeline when fairness-improving methods are applied. This understanding is essential for developers to make informed decisions regarding the provision of fair ML services. Nonetheless, it is extremely difficult to analyze the trade-offs when there are multiple fairness parameters and other crucial metrics involved, coupled, and even in conflict with one another. This paper uses causality analysis as a principled method for analyzing trade-offs between fairness parameters and other crucial metrics in ML pipelines. To ractically and effectively conduct causality analysis, we propose a set of domain-specific optimizations to facilitate accurate causal discovery and a unified, novel interface for trade-off analysis based on well-established causal inference methods. We conduct a comprehensive empirical study using three real-world datasets on a collection of widelyused fairness-improving techniques. Our study obtains actionable suggestions for users and developers of fair ML. We further demonstrate the versatile usage of our approach in selecting the optimal fairness-improving method, paving the way for more ethical and socially responsible AI technologies