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The purpose of this study is to develop stable, convergent and accurate numerical method for solving singularly perturbed differential equations having both small and large delay.

This study introduces a fitted nonpolynomial spline method for singularly perturbed differential equations having both small and large delay. The numerical scheme is developed on uniform mesh using fitted operator in the given differential equation.

The stability of the developed numerical method is established and its uniform convergence is proved. To validate the applicability of the method, one model problem is considered for numerical experimentation for different values of the perturbation parameter and mesh points.

In this paper, the authors consider a new governing problem having both small delay on convection term and large delay. As far as the researchers' knowledge is considered numerical solution of singularly perturbed boundary value problem containing both small delay and large delay is first being considered.

This study aims to develop an experimentally validated three-dimensional numerical model for predicting different flow patterns produced with a gas dynamic virtual nozzle (GDVN).

The physical model is posed in the mixture formulation and copes with the unsteady, incompressible, isothermal, Newtonian, low turbulent two-phase flow. The computational fluid dynamics numerical solution is based on the half-space finite volume discretisation. The geo-reconstruct volume-of-fluid scheme tracks the interphase boundary between the gas and the liquid. To ensure numerical stability in the transition regime and adequately account for turbulent behaviour, the k-ω shear stress transport turbulence model is used. The model is validated by comparison with the experimental measurements on a vertical, downward-positioned GDVN configuration. Three different combinations of air and water volumetric flow rates have been solved numerically in the range of Reynolds numbers for airflow 1,009–2,596 and water 61–133, respectively, at Weber numbers 1.2–6.2.

The half-space symmetry allows the numerical reconstruction of the dripping, jetting and indication of the whipping mode. The kinetic energy transfer from the gas to the liquid is analysed, and locations with locally increased gas kinetic energy are observed. The calculated jet shapes reasonably well match the experimentally obtained high-speed camera videos.

The model is used for the virtual studies of new GDVN nozzle designs and optimisation of their operation.

To the best of the authors’ knowledge, the developed model numerically reconstructs all three GDVN flow regimes for the first time.

The paper proposes an efficient and insightful approach for solving neutral delay differential equations (NDDE) with high-frequency inputs. This paper aims to overcome the need to use a very small time step when high frequencies are present. High-frequency signals abound in communication circuits when modulated signals are involved.

The method involves an asymptotic expansion of the solution and each term in the expansion can be determined either from NDDE without oscillatory inputs or recursive equations. Such an approach leads to an efficient algorithm with a performance that improves as the input frequency increases.

An example shall indicate the salient features of the method. Its improved performance shall be shown when the input frequency increases. The example is chosen as it is similar to that in literature concerned with partial element equivalent circuit (PEEC) circuits (Bellen et al., 1999). Its structure shall also be shown to enable insights into the behaviour of the system governed by the differential equation.

The method is novel in its application to NDDE as arises in engineering applications such as those involving PEEC circuits. In addition, the focus of the method is on a technique suitable for high-frequency signals.

To reduce the heat load of a gas turbine blade, its surface is covered with an outer layer of ceramics with high thermal resistance. The purpose of this paper is the selection of ceramics with such a low heat conduction coefficient and thickness, so that the permissible metal temperature is not exceeded on the metal-ceramics interface due to the loss ofmechanical properties.

Therefore, for given temperature changes over time on the metal-ceramics interface, temperature changes over time on the inner side of the blade and the assumed initial temperature, the temperature change over time on the outer surface of the ceramics should be determined. The problem presented in this way is a Cauchy type problem. When analyzing the problem, it is taken into account that thermophysical properties of metal and ceramics may depend on temperature. Due to the thin layer of ceramics in relation to the wall thickness, the problem is considered in the area in the flat layer. Thus, a one-dimensional non-stationary heat flow is considered.

The range of stability of the Cauchy problem as a function of time step, thickness of ceramics and thermophysical properties of metal and ceramics are examined. The numerical computations also involved the influence of disturbances in the temperature on metal-ceramics interface on the solution to the inverse problem.

The computational model can be used to analyze the heat flow in gas turbine blades with thermal barrier.

A number of inverse problems of the type considered in the paper are presented in the literature. Inverse problems, especially those Cauchy-type, are ill-conditioned numerically, which means that a small change in the inputs may result in significant errors of the solution. In such a case, regularization of the inverse problem is needed. However, the Cauchy problem presented in the paper does not require regularization.

The purpose of this paper is to present a fast and bare bones implementation of a numerical method for quickly simulating turbulent thermal flows on GPUs. The work also validates earlier research showing that the lattice Boltzmann method (LBM) method is suitable for complex thermal flows.

A dual lattice hydrodynamic (D3Q27) thermal (D3Q7) multiple-relaxation time LBM model capable of thermal DNS calculations is implemented in CUDA.

The model has the same computational performance compared to earlier publications of similar LBM solvers. The solver is validated against three benchmark cases for turbulent thermal flow with available data and is shown to be in excellent agreement.

The combination of a D3Q27 and D3Q7 stencil for a multiple relaxation time -LBM has, to the authors’ knowledge, not been used for simulations of thermal flows. The code is made available in a public repository under a free license.

This paper aims to introduce a non-invasive and convenient method to detect a life-threatening disease called aortic dissection. A Bayesian inference based on enhanced multi-sensors impedance cardiography (ICG) method has been applied to classify signals from healthy and sick patients.

A 3D numerical model consisting of simplified organ geometries is used to simulate the electrical impedance changes in the ICG-relevant domain of the human torso. The Bayesian probability theory is used for detecting an aortic dissection, which provides information about the probabilities for both cases, a dissected and a healthy aorta. Thus, the reliability and the uncertainty of the disease identification are found by this method and may indicate further diagnostic clarification.

The Bayesian classification shows that the enhanced multi-sensors ICG is more reliable in detecting aortic dissection than conventional ICG. Bayesian probability theory allows a rigorous quantification of all uncertainties to draw reliable conclusions for the medical treatment of aortic dissection.

This paper presents a non-invasive and reliable method based on a numerical simulation that could be beneficial for the medical management of aortic dissection patients. With this method, clinicians would be able to monitor the patient’s status and make better decisions in the treatment procedure of each patient.

This paper aimed a fractional-order sliding mode-based lateral lane-change control method that was proposed to improve the path-tracking accuracy of vehicle lateral motion.

In this paper the vehicle presighting and kinematic models were established, and a new sliding mode control isokinetic convergence law was devised based on the fractional order calculus to make the front wheel turning angle approach the desired value quickly. On this basis, a fractional gradient descent algorithm was proposed to adjust the radial basis function (RBF) neuron parameter update rules to improve the compensation speed of the neural network.

The simulation results revealed that, compared to the traditional sliding mode control strategy, the designed controller eliminated the jitter of the sliding mode control, sped up the response of the controller, reduced the overshoot of the system parameters and facilitated accurate and fast tracking of the desired path when the vehicle changed lanes at low speeds.

This paper combines the idea of fractional order calculus with gradient descent algorithm, proposed a fractional-order gradient descent method applied to RBF neural network and fast adjustment the position and width of neurons.

The purpose of the study is to obtain and analyze vibro-acoustic characteristics.

A unified analysis model for the rotary composite laminated plate and conical–cylindrical double cavities coupled system is established. The related parameters of the unified model are determined by isoparametric transformation. The modified Fourier series are applied to construct the admissible displacement function and the sound pressure tolerance function of the coupled systems. The energy functional of the structure domain and acoustic field domain is established, respectively, and the structure–acoustic coupling potential energy is introduced to obtain the energy functional. Rayleigh–Ritz method was used to solve the energy functional.

The displacement and sound pressure response of the coupled systems are acquired by introducing the internal point sound source excitation, and the influence of relevant parameters of the coupled systems is researched. Through research, it is found that the impedance wall can reduce the amplitude of the sound pressure response and suppress the resonance of the coupled systems. Besides, the composite laminated plate has a good noise reduction effect.

This study can provide the theoretical guidance for vibration and noise reduction.

Despite the sophisticated regulatory regime established in Solvency II, analysts should be able to consider other less complex indicators of the soundness of insurers. The Z-score measure, which has traditionally been used as a proxy of individual risk in the banking sector, may be a useful tool when applied in the insurance sector. However, different methods for calculating this indicator have been proposed in the literature. This paper compares six different Z-score approaches to examine which one best fits insurance companies. The authors use a final dataset of 183 firms (1,382 observations) operating in the Spanish insurance sector during the period 2010–2017.

In the first stage, the authors opt for a root mean squared error (RMSE) criterion to evaluate which of the various mean and SD estimates that are used to compute the Z-score best fits the data. In the second stage, the authors estimate and compare the explanatory power of the six Z-score measures that are considered by using an ordinary least squares (OLS) regression model. Finally, the authors report the results of the baseline equation using the system-GMM estimator developed by Arellano and Bover (1995) and Blundell and Bond (1998) for dynamic panel data models.

The authors find that the best formula for calculating the Z-score of insurance firms is the one that combines the current value of the return on assets (ROA) and capitalization with the SD of the returns calculated over the full sample period.

The main limitation of the research is that it addresses only the Spanish insurance sector, and consequently, the implications of the findings must be framed in this institutional context. However, the authors think that the results could be extrapolated to other countries. Future research should consider including different countries and analyzing the usefulness of aggregated insurer-level Z-scores for macroprudential monitoring.

The Z-score may be a useful early warning indicator for microprudential supervision. In addition to being an indicator of the soundness of insurers simpler than those established in the current regulation, the information provided by this accounting-based measure may help analysts and investors obtain a better understanding of insurance firms' risk factors.

To the best of the authors’ knowledge, this study is the first to examine and compare different approaches to calculating Z-scores in the insurance sector. The few available results on the predictive power of the Z-score are mixed and focus on the banking sector.

雖然在償付能力標準II 內已建立了精密的監管制度，但分析人員應可以考慮以不太複雑的指標，來分析保險公司的穩健程度。Z-分數的估量在銀行業一向作為是個體風險的代理而使用，而Z-分數如應用於保險業，或許會成為有用的工具。唯在文獻裏，學者和研究人員提出了不同的方法來計算這個指標。本文比較六個不同的Z-分數估量方法，以研究出最適合保險公司的方法。我們使用一個最終數據集，包括在2010年至2017年期間在西班牙保險業界營運的183間公司（1382 個觀察）。

在首個階段，我們選擇使用一個方均根誤差(RMSE) 標準來衡量用來計算Z-分數的各個平均值和標準差估量中哪個最適合使用於有關的數據。在第二個階段， 我們以普通最小平方 (OLS) 迴歸模型，去估計並比較被考慮的六個Z-分數估量的解釋力。最後，我們以Arellano與Bover (1995), 以及Blundell與Bond (1998) 為動態追蹤資料模型而發展出來的系統-廣義動差估計推定量，來發表我們基線方程式的結果。

我們發現，計算保險公司Z-分數的最佳公式是把資產收益率及資本總額的現值，和在整個樣本期間計算出來的囘報的標準差結合起來的公式。

我們研究主要的局限為：研究只涉及西班牙的保險業；因此，研究結果的含意，必須在這個體制的背景框架下來闡釋。唯我們相信研究結果或許可外推至其它國家。未來的研究，應考慮納入不同國家作為研究對象，並分析保險公司層面的集成Z-分數的功用，以求達到宏觀審慎監控的目的。

Z-分數或許就微觀審慎監管而言是一個有用的早期警告器。這些以會計為基礎的估量而提供的資訊，除了較現時規例内已建立顯示保險公司穩健程度的各個指標更簡單外，還會幫助分析人員和投資者更了解保險公司的風險因素。

據我們所知，本研究為首個研究，去探討並比較保險業內的Z-分數的計算方法。以前關於Z-分數預測能力的，為數不多並可供取閱的研究結果均不統一；而且，這些研究都聚焦探討銀行業。

This paper focuses on the unconditionally optimal error estimates of a linearized second-order scheme for a nonlocal nonlinear parabolic problem. The first step of the scheme is based on Crank–Nicholson method while the second step is the second-order BDF method.

A rigorous error analysis is done, and optimal L² error estimates are derived using the error splitting technique. Some numerical simulations are presented to confirm the study’s theoretical analysis.

Optimal L² error estimates and energy norm.

The goal of this research article is to present and establish the unconditionally optimal error estimates of a linearized second-order BDF finite element scheme for the reaction-diffusion problem. An optimal error estimate for the proposed methods is derived by using the temporal-spatial error splitting techniques, which split the error between the exact solution and the numerical solution into two parts, that is, the temporal error and the spatial error. Since the spatial error is not dependent on the time step, the boundedness of the numerical solution in L∞-norm follows an inverse inequality immediately without any restriction on the grid mesh.