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This study aims to assess the use of variational quantum imaginary time evolution for solving partial differential equations using real-amplitude ansätze with full circular entangling layers. A graphical mapping technique for encoding impulse functions is also proposed.

The Smoluchowski equation, including the Derjaguin–Landau–Verwey–Overbeek potential energy, is solved to simulate colloidal deposition on a planar wall. The performance of different types of entangling layers and over-parameterization is evaluated.

Colloidal transport can be modelled adequately with variational quantum simulations. Full circular entangling layers with real-amplitude ansätze lead to higher-fidelity solutions. In most cases, the proposed graphical mapping technique requires only a single bit-flip with a parametric gate. Over-parameterization is necessary to satisfy certain physical boundary conditions, and higher-order time-stepping reduces norm errors.

Variational quantum simulation can solve partial differential equations using near-term quantum devices. The proposed graphical mapping technique could potentially aid quantum simulations for certain applications.

This study shows a concrete application of variational quantum simulation methods in solving practically relevant partial differential equations. It also provides insight into the performance of different types of entangling layers and over-parameterization. The proposed graphical mapping technique could be valuable for quantum simulation implementations. The findings contribute to the growing body of research on using variational quantum simulations for solving partial differential equations.

The purpose of this paper is to show that the environmental income drives economic growth of a large open country.

The authors detect that the relative environmental income has double effect of “conspicuous consumption” on the international renewable resource stock changes when a new social norm shapes to environmental-friendly behaviors by using normal macroeconomic approaches.

Every unit of extra demand for renewable resource consumption increases the net premium of domestic capital asset. Even if the technology spillovers are inefficient to the substitution of capital to labor force in a real business cycle, the relative income with scale effect increases drives savings to investment. In this case, the renewable resource consumption promotes both the reproduction to a higher level and saving the potential cost of environmental improvement. Even if without scale effects, the loss of technology inefficient can be compensated by net positive consumption externality for economic growth in a sustainable manner.

It implies how to earn the environment income determines the future pathway of China’s rural conversion to the era of eco-urbanization.

We test the tax incidence to demonstrate an experimental taxation for environmental improvement ultimately burdens on international consumption side.

This paper considers a broader concept of economic integration in order to analyze the impact of integration on economic growth within the context of the knowledge-driven endogenous economic growth model. The equilibrium growth rate derived from the model implies that while increasing the flow of ideas from integration speeds up the long-run rate of growth, impact of trade liberalization is complicated and not decisive. The overall impact of economic integration on • economic growth depends on various aspects of the economy which are related to its R&D investment such as knowledge spillovers, and industrial and market structures. The results of this paper suggest that policy makers need to consider international economic policy, market structure and industrial policy all at once, with special emphasis on the effect affirms' R&D activities when making decisions on economic integration.

The purpose of this research is to systematically review the properties of supply chains demonstrating that they are complex systems, and that the management of supply chains is best achieved by steering rather than controlling these systems toward desired outcomes.

The research study was designed as both exploratory and explanatory. Data were collected from secondary sources using a comprehensive literature review process. In parallel with data collection, data were analyzed and synthesized.

The main finding is the introduction of an inductive framework for steering supply chains from a complex systems perspective by explaining why supply chains have properties of complex systems and how to deal with their complexity while steering them toward desired outcomes. Complexity properties are summarized in four inter-dependent categories: Structural, Dynamic, Behavioral and Decision making, which together enable the assessment of supply chains as complex systems. Furthermore, five mechanisms emerged for dealing with the complexity of supply chains: classification, modeling, measurement, relational analysis and handling.

Recognizing that supply chains are complex systems allows for a better grasp of the effect of positive feedback on change and transformation, and also interactions leading to dynamic equilibria, nonlinearity and the role of inter-organizational learning, as well as emerging capabilities, and existing trade-offs and paradoxical tensions in decision-making. It recognizes changing dynamics and the co-evolution of supply chain phenomena in different scales and contexts.