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This paper aims to focus on the accurate analysis of the fractional heat transfer in a two-dimensional (2D) rectangular monolayer tissue with three different kinds of lateral boundary conditions and the quantitative evaluation of the degree of thermal damage and burn depth.

A symplectic method is used to analytically solve the fractional heat transfer dual equation in the frequency domain (s-domain). Explicit expressions of the dual vector can be constructed by superposing the symplectic eigensolutions. The solution procedure is rigorously rational without any trial functions. And the accurate predictions of temperature and heat flux in the time domain (t-domain) are derived through numerical inverse Laplace transform.

Comparison study shows that the maximum relative error is less than 0.16%, which verifies the accuracy and effectiveness of the proposed method. The results indicate that the model and heat source parameters have a significant effect on temperature and thermal damage. The pulse duration (Δt) of the laser heat source can effectively control the time to reach the peak temperature and the peak slope of the thermal damage curve. The burn depth is closely correlated with exposure temperature and duration. And there exists the delayed effect of fractional order on burn depth.

A symplectic approach is presented for the thermal analysis of 2D fractional heat transfer. A unified time-fractional heat transfer model is proposed to describe the anomalous thermal behavior of biological tissue. New findings might provide guidance for temperature prediction and thermal damage assessment of biological tissues during hyperthermia.

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 present the methodology that was used to perform system identification of a dynamically unstable tilt-rotor from flight test data. The method incorporated wavelet transform into the maximum likelihood principle formulation, emphasizing both time and frequency responses. Using wavelets allowed to additionally filter noise in the data, and this increased the estimation quality. This approach did not require measurement and process noise modeling in contrast to the Kalman filter usage for parameter estimation.

In the study, lateral-directional stability and control derivatives of an unstable tiltrotor in hover were estimated. This was performed by applying the maximum likelihood output error method. The estimated model response was decomposed using the Mallat pyramid and matched to wavelet coefficients obtained directly from measurements. In addition, a coherence-based weighting function was used to put more emphasis on the most reliable data. For comparison, the same set of data was used to identify a model with the same structure using the maximum likelihood principle with an incorporated Kalman filter.

It was found that maximum likelihood principle and wavelet transform allowed for estimating aerodynamic coefficients of a dynamically unstable aircraft. The estimation was performed with high accuracy.

The designed method can be used for system identification of unstable aircraft and when additional noise is present (e.g. when noise due to turbulence was observable during the flight test or higher noise levels were present in the sensors data).

The paper presents verification of a wavelet-based maximum likelihood principle output error method using flight test data.

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 $x(t+1) = A x(t) + C v(t)$.

An optimal control model is built considering the private sector's opportunistic effort diversion and reciprocal effort improvement, while a numerical study is conducted to draw some managerial implications.

In infrastructure PPP projects, private sectors may opportunistically divert part of their effort from the current projects to other projects to allocate their limited human resources. Nevertheless, this effort diversion can be inhibited by dynamic incentives since the private sectors reciprocally exert greater effort into the current projects when receiving the dynamic incentives. This article investigates how the government specifies the output standard that the private sector should meet and offers dynamic incentives to mitigate the private sector's opportunistic effort diversion.

The output standard for the private sector to acquire the dynamic incentives should be specified as the output level corresponding to the private sector's optimal long-run stationary equilibrium (OLSE) effort level, which decreases with its reciprocal preference level but increases with its effort-diverting level. The optimal dynamic incentives comprise an initial incentive and a periodic OLSE incentive, which declines with the reciprocal preference level but improves with the effort-diverting level. Besides, the numerical study reveals that the government should distinguish whether the bidders have high effort-diverting levels and, if so, should focus on their reciprocal preference levels and decline the bidders with low reciprocal preference to avoid utility loss.

This article provides a theoretical model combining opportunistic behavior with reciprocal preference through an optimal control lens, thus embedding the problem of incentive design into a broader socioeconomic framework.

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.

The existence of the advertising delay effect and its impact on supply chain operations have been demonstrated in the current study. Therefore, this study develops a timely inventory control strategy for the fresh produce supply chain to address the advertising delay effect in the fresh produce supply chain.

This study proposes a game model based on the Nerlove-Arrow time delay differential equation and Pontryagin's maximum principle. Through comparative analyses of the optimal equilibrium strategies, the authors compare the optimal equilibrium strategies, product goodwill and optimal inventory trajectories for suppliers and retailers under secondary replenishment decisions and decentralized decisions.

The authors find that (1) Only when the sales cycle meets certain conditions can the overall profit of the supply chain under the secondary replenishment decision be greater than that under the decentralized decision. As the price markup coefficient increases, the total profit of the supply chain first increases and then decreases. (2) With the increase in the delay time, the replenishment quantity during the initial period gradually decreases. After the delay time elapses, the inventory depletion rate under secondary replenishment decisions is faster than that under decentralized decision-making. (3) Although there is a continuously increasing maximum value of product goodwill with the increase in delay time, it becomes difficult to achieve this value for longer delays.

The authors’ findings provide a theoretical basis for supply chain members of fresh agricultural products to select replenishment and inventory control strategies when adopting different levels of delay in advertising marketing.

Firstly, this paper explains the impact of advertising delay effect on fresh produce supply chain from a dynamic perspective, and secondly, it provides guidance on advertising formulation and inventory replenishment for fresh produce retailers under the influence of advertising delay effect.

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.