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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.

In this paper, the authors study the nonlinear matrix equation Xp=Q±A(X-1+B)-1AT, that occurs in many applications such as in filtering, network systems, optimal control and control theory.

The authors present some theoretical results for the existence of the solution of this nonlinear matrix equation. Then the authors propose two iterative schemes without inversion to find the solution to the nonlinear matrix equation based on Newton's method and fixed-point iteration. Also the authors show that the proposed iterative schemes converge to the solution of the nonlinear matrix equation, under situations.

The efficiency indices of the proposed schemes are presented, and since the initial guesses of the proposed iterative schemes have a high cost, the authors reduce their cost by changing them. Therefore, compared to the previous scheme, the proposed schemes have superior efficiency indices.

Finally, the accuracy and effectiveness of the proposed schemes in comparison to an existing scheme are demonstrated by various numerical examples. Moreover, as an application, by using the proposed schemes, the authors can get the optimal controller state feedback of $x(t+1) = A x(t) + C v(t)$.

The theoretical findings serve as a foundation for further research into understanding sulfide-based solid-state electrolytes, ultimately advancing the progress of all-solid-state batteries.

The electronic properties of Li₇P₃S₁₁ are thoroughly explored through first-principles calculations.

This investigation encompasses the intricate atom-dominated valence and conduction bands, spatial charge density distribution and the breakdown of atom and orbital contributions to van Hove singularities. Additionally, the compound’s wide and discrete energy spectra reflect the substantial variations in bond lengths and its highly anisotropic geometric structure. The complex and nonuniform chemical environment indicates the presence of intricate hopping integrals.

This study provides valuable insights into the critical multiorbital hybridizations occurring in the Li-S and P-S chemical bonds. To validate the theoretical predictions, experimental techniques can be employed. By combining theoretical predictions with experimental data, a comprehensive understanding of the geometric and electronic characteristics of Li₇P₃S₁₁ can be achieved.

In this chapter, we consider the possibility that a firm may use costly resources to improve its technical efficiency. Results from static analyses imply that technical efficiency is determined by the configuration of factor prices. A dynamic model of the firm is developed under the assumption that managerial skill contributes to technical efficiency. Dynamic analysis shows that the firm can never be technically efficient if it maximizes profits, the steady state is always inefficient, and it is locally stable. In terms of empirical analysis, we show how likelihood-based methods can be used to uncover, in a semi-non-parametric manner, important features of the inefficiency-management relationship using a flexible functional form accounting for the endogeneity of inputs in a production function. Managerial compensation can also be identified and estimated using the new techniques. The new empirical methodology is applied in a data set previously analyzed by Bloom and van Reenen (2007) on managerial practices of manufacturing firms in the UK, US, France and Germany.

This paper applies a volume-price probability wave differential equation to propose a conceptual theory and has innovative behavioral interpretations of intraday dynamic market equilibrium price, in which traders' momentum, reversal and interactive behaviors play roles.

The authors select intraday cumulative trading volume distribution over price as revealed preferences. An equilibrium price is a price at which the corresponding cumulative trading volume achieves the maximum value. Based on the existence of the equilibrium in social finance, the authors propose a testable interacting traders' preference hypothesis without imposing the invariance criterion of rational choices. Interactively coherent preferences signify the choices subject to interactive invariance over price.

The authors find that interactive trading choices generate a constant frequency over price and intraday dynamic market equilibrium in a tug-of-war between momentum and reversal traders. The authors explain the market equilibrium through interactive, momentum and reversal traders. The intelligent interactive trading preferences are coherent and account for local dynamic market equilibrium, holistic dynamic market disequilibrium and the nonlinear and non-monotone V-shaped probability of selling over profit (BH curves).

The authors will understand investors' behaviors and dynamic markets through more empirical execution in the future, suggesting a unified theory available in social finance.

The authors can apply the subjects' intelligent behaviors to artificial intelligence (AI), deep learning and financial technology.

Understanding the behavior of interacting individuals or units will help social risk management beyond the frontiers of the financial market, such as governance in an organization, social violence in a country and COVID-19 pandemics worldwide.

It uncovers subjects' intelligent interactively trading behaviors.

The purpose of this article is to treat the nonlinear optimal control problem in EV traction systems which are based on 5-phase induction motors. Five-phase permanent magnet synchronous motors and five-phase asynchronous induction motors (IMs) are among the types of multiphase motors one can consider for the traction system of electric vehicles (EVs). By distributing the required power in a large number of phases, the power load of each individual phase is reduced. The cumulative rates of power in multiphase machines can be raised without stressing the connected converters. Multiphase motors are also fault tolerant because such machines remain functional even if failures affect certain phases.

A novel nonlinear optimal control approach has been developed for five-phase IMs. The dynamic model of the five-phase IM undergoes approximate linearization using Taylor series expansion and the computation of the associated Jacobian matrices. The linearization takes place at each sampling instance. For the linearized model of the motor, an H-infinity feedback controller is designed. This controller achieves the solution of the optimal control problem under model uncertainty and disturbances.

To select the feedback gains of the nonlinear optimal (H-infinity) controller, an algebraic Riccati equation has to be solved repetitively at each time-step of the control method. The global stability properties of the control loop are demonstrated through Lyapunov analysis. Under moderate conditions, the global asymptotic stability properties of the control scheme are proven. The proposed nonlinear optimal control method achieves fast and accurate tracking of reference setpoints under moderate variations of the control inputs.

Comparing to other nonlinear control methods that one could have considered for five-phase IMs, the presented nonlinear optimal (H-infinity) control approach avoids complicated state-space model transformations, is of proven global stability and its use does not require the model of the motor to be brought into a specific state-space form. The nonlinear optimal control method has clear implementation stages and moderate computational effort.

In the transportation sector, there is progressive transition to EVs. The use of five-phase IMs in EVs exhibits specific advantages, by achieving a more balanced distribution of power in the multiple phases of the motor and by providing fault tolerance. The study’s nonlinear optimal control method for five-phase IMs enables high performance for such motors and their efficient use in the traction system of EVs.

Nonlinear optimal control for five-phase IMs supports the deployment of their use in EVs. Therefore, it contributes to the net-zero objective that aims at eliminating the emission of harmful exhaust gases coming from human activities. Most known manufacturers of vehicles have shifted to the production of all-electric cars. The study’s findings can optimize the traction system of EVs thus also contributing to the growth of the EV industry.

The proposed nonlinear optimal control method is novel comparing to past attempts for solving the optimal control problem for nonlinear dynamical systems. It uses a novel approach for selecting the linearization points and a new Riccati equation for computing the feedback gains of the controller. The nonlinear optimal control method is applicable to a wider class of dynamical systems than approaches based on the solution of state-dependent Riccati equations.

This paper aims to provide a comprehensive analysis of the state of the art in energy efficiency for autonomous mobile robots (AMRs), focusing on energy sources, consumption models, energy-efficient locomotion, hardware energy consumption, optimization in path planning and scheduling methods, and to suggest future research directions.

The systematic literature review (SLR) identified 244 papers for analysis. Research articles published from 2010 onwards were searched in databases including Google Scholar, ScienceDirect and Scopus using keywords and search criteria related to energy and power management in various robotic systems.

The review highlights the following key findings: batteries are the primary energy source for AMRs, with advances in battery management systems enhancing efficiency; hybrid models offer superior accuracy and robustness; locomotion contributes over 50% of a mobile robot’s total energy consumption, emphasizing the need for optimized control methods; factors such as the center of mass impact AMR energy consumption; path planning algorithms and scheduling methods are essential for energy optimization, with algorithm choice depending on specific requirements and constraints.

The review concentrates on wheeled robots, excluding walking ones. Future work should improve consumption models, explore optimization methods, examine artificial intelligence/machine learning roles and assess energy efficiency trade-offs.

This paper provides a comprehensive analysis of energy efficiency in AMRs, highlighting the key findings from the SLR and suggests future research directions for further advancements in this field.

The purpose of this paper is to propose a novel nonlocal fractal calculus scheme dedicated to the analysis of fractal electrical circuit, namely, the generalized nonlocal fractal calculus.

For being generalized, an arbitrary kernel function has been adopted. The condition on order has been derived so that it is not related to the γ-dimension of the fractal set. The fractal Laplace transforms of our operators have been derived.

Unlike the traditional power law kernel-based nonlocal fractal calculus operators, ours are generalized, consistent with the local fractal derivative and use higher degree of freedom. As intended, the proposed nonlocal fractal calculus is applicable to any kind of fractal electrical circuit. Thus, it has been found to be a more efficient tool for the fractal electrical circuit analysis than any previous fractal set dedicated calculus scheme.

A fractal calculus scheme that is more efficient for the fractal electrical circuit analysis than any previous ones has been proposed in this work.

This paper aims to present a set of processes for obtaining the global spraying trajectory of a cold spraying robot on a complex surface.

The complex workpiece surfaces in the project are first divided by triangular meshing. Then, the geodesic curve method is applied for local path planning. Finally, the subsurface trajectory combination optimization problem is modeled as a GTSP problem and solved by the ant colony algorithm, where the evaluation scores and the uniform design method are used to determine the optimal parameter combination of the algorithm. A global optimized spraying trajectory is thus obtained.

The simulation results show that the proposed processes can achieve the shortest global spraying trajectory. Moreover, the cold spraying experiment on the IRB4600 six-joint robot verifies that the spraying trajectory obtained by the processes can ensure a uniform coating thickness.

The proposed processes address the issue of different parameter combinations, leading to different results when using the ant colony algorithm. The two methods for obtaining the optimal parameter combinations can solve this problem quickly and effectively, and guarantee that the processes obtain the optimal global spraying trajectory.

This paper analytically models and numerically investigates two operating levers, namely optimization of product price and optimization of product quality in the context of a manufacturer that sells the products directly in the marketplace. The study attempts to identify how optimizing product quality and product price can fulfill a manufacturer's economic aims such as maximization of the manufacturer's profit and market demand. Anchored to the extant literature, the demand is modeled as a parametric joint multiplicative function of price and quality. Further, price is modeled as a function of product quality.

First, the authors evolve the analytical expression for the manufacturer's profit. Thereafter, following the mathematical principles of unconstrained optimization, the authors arrive at the conditions for optimal product quality and product price. The authors further perform numerical experiments to understand the behavior of economic dimensions such as profit and demand with respect to sensitivities associated with cost, quality and price.

The authors find that under product quality optimization, the optimal product quality is a unique solution in that a highest possible theoretical manufacturer's profit is obtained. However, in the case of product price optimization, the optimal product price is non-unique and is a function of product quality. The authors further find that in the context of functional quality-level expectations, product quality optimization as an operating lever gives a better dividend. However, in the case of higher product quality expectations, product price optimization performs better than product quality optimization. Further, several novel findings are also obtained from numerical experimentations.

The findings of the authors' study have implications for types of industries characterized by relatively low as well as relatively high competitive intensity. Further, as opposed to several extant studies that have often carried out joint optimization of quality and price, the authors' study is one of the first to study the impact of product price and product quality on the manufacturer's economic objective in a disparate and focused manner, thus capturing individual effects.