Flow Analysis of a Trihybrid Nanofluid using Local Linearization Method

We generalize the double smoothing local linear regression method to nonparametric regression of time series. Under a strong mixing condition for the dependence of the time series, we show that after another round of smoothing based on the local linear regression estimates, the double smoothing local linear estimate will have reduced asymptotic bias, while keeping the variance at the same asymptotic order. The asymptotic bias reduces from the order of h 2 for the local linear estimates to h 4 for the double smoothing local linear estimates, where h is the bandwidth. Hence the double smoothing local linear method produces more optimal estimates in terms of mean squared error. Simulation studies and real time series data analysis confirm the advantages of the double smoothing method compared to the local linear method.

The study of this theoretical problem enables sparse or dense functional data, including educational information evaluation data. The choice of different weights is subjected to principal component analysis. The evaluation of music education informatization level mainly evaluates the status quo of music education informatization development, provides a basis for formulating and adjusting music education informatization development policies, and provides support for educational decision‐making, to promote the sustainable and balanced development of music education informatization. The evaluation of music education informatization has become the key promotion work of music education informatization at this stage. This paper studies the convergence rate of functional principal components based on the local linear method under general weighting conditions. First, we introduce the related research on the estimation of mean and covariance function under general weighting. Secondly, for principal functional components under general weighting, namely, eigenvalues and eigen functions, the text gives the corresponding estimated values and derives its strong uniform convergence rate. Finally, the convergence rate was verified by simulation research. The estimation methods and conclusions of this article enrich the research of functional linear regression models and will help analyze the complex and changeable problems encountered in the application of music education information.

The theory of large deviations is applied to the study of the asymptotic properties of the stochastic approximation algorithms (1.1) and (1.2). The method provides a useful alternative to the currently used technique of obtaining rate of convergence results by studying the sequence {(Xn-.)/θan} (for (1.1)), where θ is a 'stable' point of the algorithm. Let G be a bounded neighborhood of θ, which is in the domain of attraction of θ for the 'limit ODE'. The process xn(θ) is defined as a 'natural interpolation' of {Xj,j≥n} with xn(0) = Xn, and interpolation intervals {aj,j≥n}. Define τG n = min{t:xn(t)τG}. Then it is shown (among other things) that Px{τG n ≥ T} ~ exp-nqV, where q depends on {an,cn}, and V depends on the b(.) cov τn, and G. Such estimates imply that the asymptotic behavior is much better than suggested by the 'local linearization methods', and they yield much new insight into the asymptotic behavior. The technique is applicable to related problems in the asymptotic analysis of recursive algorithms, and requires weaker conditions on the dynamics than do the 'linearization methods'. The necessary basic background is provided and the optimal control problems associated with getting the V above are derived.

Based on the Bayesian information criterion, this paper proposes the improved local linear prediction method to predict chaotic time series. This method uses spatial correlation and temporal correlation simultaneously. Simulation results show that the improved local linear prediction method can effectively make multi-step and one-step prediction of chaotic time series and the multi-step prediction performance and one-step prediction accuracy of the improved local linear prediction method are superior to those of the traditional local linear prediction method.

As a maritime country strategically located along the world's leading transportation routes, Indonesia often faces increased ship accidents. Based on the Basarnas Statistics Book, ship accidents handled by Basarnas from 2021 to 2023 increased by 3%. This condition requires an effective forecasting method to carry out SAR operations to predict ship accidents in the Indonesian region in the future and assess the readiness and needs of Basarnas resources. This study compares the forecasting results obtained using the Singular Spectrum Analysis (SSA) and the Local Linear methods. Both methods do not require parametric assumptions. The data used in this study are divided into training data and test data. This data is secondary data obtained from the Basarnas Statistics Book. The training data in this study is the number of SAR operations from January 2021 to December 2022, while the testing data is from January 2023 to December 2023. From the analysis results, it is known that the method with the smallest MAPE is the Local Linear method with a MAPE of test data of 18.67% (good forecasting category), optimal bandwidth (h) = 4.299, and CV (h) = 231.39 where bandwidth is used to determine the level of smoothness of the estimate, while the CV (h) value is used to select the optimal bandwidth that minimizes the estimation error. At the same time, the SSA method has a MAPE of 40.27% (fair forecasting category). This shows that the Local Linear method provides a more accurate forecast of the number of SAR operations related to ship accidents in Indonesia. This research contributes to the SDGs to make Basarnas an effective and accountable institution and improve the planning and decision-making process in SAR operations through accurate forecasting research is relevant to accurate forecasting.

Local regressions for decomposing CO2 and CH4 time-series in a semi-arid ecosystem

This paper proposes a new local linearization method which approximates a nonlinear stochastic differential equation by a linear stochastic differential equation. Using this method, we can estimate parameters of the nonlinear stochastic differential equation from discrete observations by the maximum likelihood technique. We conduct the numerical experiments to evaluate the finite sample performance of identification of the new method, and compare it with the two known methods: the original local linearization method and the Euler methods. From the results of experiments, the new method shows much better performance than the other two methods particularly when the sampling interval is large

Distribution-free prediction regions of multivariate response PLS models with applications to NIR datasets

A symmetrical airfoil has been constructed by local linearization method. A single-point objective function is defined to check the convergence of the method. As an example, the nose and tail zone of supercritical airfoil is fixed and a flat line is placed between them. The optimizable element of the airfoil contour was conjoined with the nose and tail elements of fixed shape at the sections with coordinates xs1= 0.11 and xs2= 0.66, respectively. The optimizable part of airfoil (the fixed chord line) is divided into N=55 segments. The convergence of this method has been shown with the airfoil constructed with higher critical Mach number rather than the initial airfoil. Finally, this airfoil has been compared with the supercritical airfoil NASA SC (2)-0012 at M∞=0.76. At the second part, several airfoils have been constructed and simulated over different Subsonic and Transonic Mach numbers. Finally, the drag coefficient on constructed airfoils have been compared with supercritical airfoil.

This study deals with the transfer of mass and heat of nanofluid flow over three different geometries of the non‐Darcy permeable vertical cone/wedge/vertical plate. Influence of the Brownian motion and thermophoresis takes place due to the nanofluid. Boundary condition on the temperature is introduced at the surface where the thermal conductivity of the fluid obeys a linear relation with the temperature. The local linearization method is introduced for solving the governing equations, and is based on spectral discretization. To verify the numerical scheme, we compared our results with those in the existing literature. The impact of the governing parameters on the fluid velocity, temperature distribution, and concentration distribution of nanoparticles along with the Nusselt number and Sherwood number is discussed. Some important outcomes of the present study are that the Nusselt number is higher for the plane plate than that for the vertical cone and it significantly decreases with introduction of the radiation parameter. The nanofluid Lewis number decreases the diffusivity of mass of the nanofluid, and as a result it helps enhance the Sherwood number.

This research proposes a new model for nonlinear time series called the Secant Double AR model of order k, SecDAR(k), which is based on the double autoregressive model with an augmented secant function. In 2007, Ling introduced this family of double autoregressive models, with the prototype model named DAR(P), where p is the order of the model. This approach addresses data volatility that leads to heteroscedasticity .Using dynamic principles and local linear methods, this research analyzes the stability conditions of the model. First, we approximate the previously mentioned model to a linear difference equation using a local linear strategy. Secondly, the roots of the characteristic equation are used to assess stability . In the end, the stability conditions for the above model are applied using data showing the average monthly closing price of heating oil in US dollars from 1990 to 2024. To evaluate the accuracy and quality of the models' fit on the actual data, we use the Bayesian Information Criterion (BIC) and the Akaike Information Criterion (AIC). In the application section, we use the stability condition to evaluate the stability for each order of SecDAR(k) from 1 to 6.

Re-Weighted Functional Estimation of Diffusion Models

This study is designed to i) apply chaotic approach in predicting Carbon Monoxide (CO) data series and ii) improve the method in determining number of k–nearest neighbor. Chaotic approach is one alternative approach to predict any data series. Prediction through chaotic approach is made after three important parameters which are delay time τ, embedding dimension m and numbers of nearest neighbor k were determined. Therefore, the chaotic approach is applied. In this study, predictions are done to Carbon Monoxide time series observed at Shah Alam in Malaysia. Parameters τ and m are determined through average mutual information and Cao method respectively. While for k, most of the past researches frequently used try and error method. In this study an improvement of the method in determining the number of k is introduced. This improved method is done through plotting the graph of k versus the correlation coefficient (cc) of prediction model. Parameter cc is obtained through the prediction of data series using local mean approximation method (LMAM), local linear approximation method (LLAM) and improved local linear approximation method (ILLAM). Result shows that the cc value of LMAM is 0.9821 with k = 7, LLAM is 0.9873 with k = 3 and ILLAM is 0.9913 with k = 13. Therefore, the improved methods suggest that the optimal value of k is ranged from 3 ≤ k ≤ 13. It is hoped that the improved method can be used for future research in developing a better prediction model for chaotic data series.

A novel local stochastic linearization method via two extremum entropy principles

Regression methods have been successfully applied to the area of reflectance estimation. The local linear methods show better generalization performance than the global nonlinear methods in this problem. However, the local linear models which treat every neighbor equally would lose some nonlinear information. To improve the learning ability for the nonlinear structure and reserve the generalization ability of the linear method at the same time, we propose the locally weighted linear regression method for reflectance estimation. The proposed method assigns weights to the neighbors with kernel functions and solves the weighted least squares problem to reconstruct the spectral reflectance. Experiment results show that our approach has better recovery precision and generalization performance than both the global kernel methods and the local linear methods.