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Bisphosphonate (BP) medications can be applied to prohibit the damage of bone density and the remedy of bone illnesses such as osteoporosis. As the metal chelating of phosphonate groups are nearby large with six O atoms possessing the high negative charge, these compounds are active toward producing the chelated complexes through drug design method. BP agents have attracted much attention for the clinical treatment of some skeletal diseases depicted by enhancing of osteoclast-mediated bone resorption.

In this work, it has been accomplished the CAM-B3LYP/6–311+G(d, p)/LANL2DZ to estimate the susceptibility of SWCNT for adsorbing alendronate, ibandronate, neridronate and pamidronate chelated to two metal cations of 2Mg²⁺, 2Ca²⁺, 2Sr²⁺ through nuclear magnetic resonance and thermodynamic parameters. Therefore, the data has explained that the feasibility of using SWCNT and BP agents becomes the norm in metal chelating of drug delivery system which has been selected through alendronate → 2X, ibandronate → 2X, neridronate → 2X and pamidronate → 2X (X = Mg²⁺/Ca²⁺/Sr²⁺) complexes.

The thermodynamic results have exhibited that the substitution of 2Ca²⁺ cation by 2Sr²⁺ cation in the structure of bioactive glasses can be efficient for treating vertebral complex fractures. However, it has been observed the most fluctuation in the Gibbs free energy for BPs → 2Sr²⁺ at 300 K. Furthermore, Monte Carlo simulation has resulted by increasing the dielectric constant in the aqueous medium can enhance the stability and efficiency of BP drugs for preventing the loss of bone density and treating the osteoporosis.

According to this research, by incorporation of chelated 2Mg²⁺, 2Ca²⁺ and 2Sr²⁺ cations to BP drugs adsorbed onto (5, 5) armchair SWCNT, the network compaction would increase owing to the larger atomic radius of Sr²⁺ cation rather than Ca²⁺ and Mg²⁺, respectively.

The purpose of this paper is to assess the feasibility of analytical models, specifically the radial basis function method, Akbari–Ganji method and Gaussian method, in conjunction with the finite element method. The aim is to examine the impact of processing parameters on temperature history.

Through analytical investigation and finite element simulation, this research examines the influence of processing parameters on temperature history. Simufact software with a thermomechanical approach was used for finite element simulation, while radial basis function, Akbari–Ganji and Gaussian methods were used for analytical modeling to solve the heat transfer differential equation.

The accuracy of both finite element and analytical methods was validated with about 90%. The findings revealed direct relationships between thermal conductivity (from 100 to 200), laser power (from 400 to 800 W), heat source depth (from 0.35 to 0.75) and power absorption coefficient (from 0.4 to 0.8). Increasing the values of these parameters led to higher temperature history. On the other hand, density (from 7,600 to 8,200), emission coefficient (from 0.5 to 0.7) and convective heat transfer (from 35 to 90) exhibited an inverse relationship with temperature history.

The application of analytical modeling, particularly the utilization of the Akbari–Ganji, radial basis functions and Gaussian methods, showcases an innovative approach to studying directed energy deposition. This analytical investigation offers an alternative to relying solely on experimental procedures, potentially saving time and resources in the optimization of DED processes.

A semiparametric stochastic frontier model is proposed for panel data, incorporating several flexible features. First, a constant elasticity of substitution (CES) production frontier is considered without log-transformation to prevent induced non-negligible estimation bias. Second, the model flexibility is improved via semiparameterization, where the technology is an unknown function of a set of environment variables. The technology function accounts for latent heterogeneity across individual units, which can be freely correlated with inputs, environment variables, and/or inefficiency determinants. Furthermore, the technology function incorporates a single-index structure to circumvent the curse of dimensionality. Third, distributional assumptions are eschewed on both stochastic noise and inefficiency for model identification. Instead, only the conditional mean of the inefficiency is assumed, which depends on related determinants with a wide range of choice, via a positive parametric function. As a result, technical efficiency is constructed without relying on an assumed distribution on composite error. The model provides flexible structures on both the production frontier and inefficiency, thereby alleviating the risk of model misspecification in production and efficiency analysis. The estimator involves a series based nonlinear least squares estimation for the unknown parameters and a kernel based local estimation for the technology function. Promising finite-sample performance is demonstrated through simulations, and the model is applied to investigate productive efficiency among OECD countries from 1970–2019.

In the present work, we focus on developing an in-house parallel meshless local Petrov-Galerkin (MLPG) code for the analysis of heat conduction in two-dimensional and three-dimensional regular as well as complex geometries.

The parallel MLPG code has been implemented using open multi-processing (OpenMP) application programming interface (API) on the shared memory multicore CPU architecture. Numerical simulations have been performed to find the critical regions of the serial code, and an OpenMP-based parallel MLPG code is developed, considering the critical regions of the sequential code.

Based on performance parameters such as speed-up and parallel efficiency, the credibility of the parallelization procedure has been established. Maximum speed-up and parallel efficiency are 10.94 and 0.92 for regular three-dimensional geometry (343,000 nodes). Results demonstrate the suitability of parallelization for larger nodes as parallel efficiency and speed-up are more for the larger nodes.

Few attempts have been made in parallel implementation of the MLPG method for solving large-scale industrial problems. Although the literature suggests that message-passing interface (MPI) based parallel MLPG codes have been developed, the OpenMP model has rarely been touched. This work is an attempt at the development of OpenMP-based parallel MLPG code for the very first time.

This study aims to propose and numerically assess different ways of discretising a very weak formulation of the Poisson problem.

We use integration by parts twice to shift smoothness requirements to the test functions, thereby allowing low-regularity data and solutions.

Various conforming discretisations are presented and tested, with numerical results indicating good accuracy and stability in different types of problems.

This is one of the first articles to propose and test concrete discretisations for very weak variational formulations in primal form. The numerical results, which include a problem based on real MRI data, indicate the potential of very weak finite element methods for tackling problems with low regularity.

The purpose of this study is to investigate the interaction between magnetotactic bacteria and Fe₃O₄–water nanofluid (NF) in a wavy enclosure in the presence of 2D natural convection flow.

Uniform magnetic field (MF), Brownian and thermophoresis effects are also contemplated. The dimensionless, time-dependent equations are governed by stream function, vorticity, energy, nanoparticle concentration and number of bacteria. Radial basis function-based finite difference method for the space derivatives and the second-order backward differentiation formula for the time derivatives are performed. Numerical outputs in view of isolines as well as average Nusselt number, average Sherwood number and flux density of microorganisms are presented.

Convective mass transfer rises if any of Lewis number, Peclet number, Rayleigh number, bioconvection Rayleigh number and Brownian motion parameter increases, and the flux density of microorganisms is an increasing function of Rayleigh number, bioconvection Rayleigh number, Peclet number, Brownian and thermophoresis parameters. The rise in buoyancy ratio parameter between 0.1 and 1 and the rise in Hartmann number between 0 and 50 reduce all outputs average Nusselt, average Sherwood numbers and flux density of microorganisms.

This study implies the importance of the presence of magnetotactic bacteria and magnetite nanoparticles inside a host fluid in view of heat transfer and fluid flow. The limitation is to check the efficiency on numerical aspect. Experimental observations would be more effective.

In practical point of view, in a heat transfer and fluid flow system involving magnetite nanoparticles, the inclusion of magnetotactic bacteria and MF effect provide control over fluid flow and heat transfer.

This is a scientific study. However, this idea may be extended to sustainable energy or biofuel studies, too. This means that a better world may create better social environment between people.

The presence of magnetotactic bacteria inside a Fe₃O₄–water NF under the effect of a MF is a good controller on fluid flow and heat transfer. Since the magnetotactic bacteria is fed by nanoparticles Fe₃O₄ which has strong magnetic property, varying nanoparticle concentration and Brownian and thermophoresis effects are first considered.

There is growing empirical evidence that firm heterogeneity is technologically non-neutral. This chapter extends the Gandhi, Navarro, and Rivers (2020) proxy variable framework for structurally identifying production functions to a more general case when latent firm productivity is multi-dimensional, with both factor-neutral and (biased) factor-augmenting components. Unlike alternative methodologies, the proposed model can be identified under weaker data requirements, notably, without relying on the typically unavailable cross-sectional variation in input prices for instrumentation. When markets are perfectly competitive, point identification is achieved by leveraging the information contained in static optimality conditions, effectively adopting a system-of-equations approach. It is also shown how one can partially identify the non-neutral production technology in the traditional proxy variable framework when firms have market power.

Ensuring the early detection of structural issues in aircraft is crucial for preserving human lives. One effective approach involves identifying cracks in composite structures. This paper employs experimental modal analysis and a multi-variable Gaussian process regression method to detect and locate cracks in glass fiber composite beams.

The present study proposes Gaussian process regression model trained by the first three natural frequencies determined experimentally using a roving impact hammer method with crystal four-channel analyzer, uniaxial accelerometer and experimental modal analysis software. The first three natural frequencies of the cracked composite beams obtained from experimental modal analysis are used to train a multi-variable Gaussian process regression model for crack localization. Radial basis function is used as a kernel function, and hyperparameters are optimized using the negative log marginal likelihood function. Bayesian conditional probability likelihood function is used to estimate the mean and variance for crack localization in composite structures.

The efficiency of Gaussian process regression is improved in the present work with the normalization of input data. The fitted Gaussian process regression model validates with experimental modal analysis for crack localization in composite structures. The discrepancy between predicted and measured values is 1.8%, indicating strong agreement between the experimental modal analysis and Gaussian process regression methods. Compared to other recent methods in the literature, this approach significantly improves efficiency and reduces error from 18.4% to 1.8%. Gaussian process regression is an efficient machine learning algorithm for crack localization in composite structures.

The experimental modal analysis results are first utilized for crack localization in cracked composite structures. Additionally, the input data are normalized and employed in a machine learning algorithm, such as the multi-variable Gaussian process regression method, to efficiently determine the crack location in these structures.

The authors propose to estimate a varying coefficient panel data model with different smoothing variables and fixed effects using a two-step approach. The pilot step estimates the varying coefficients by a series method. We then use the pilot estimates to perform a one-step backfitting through local linear kernel smoothing, which is shown to be oracle efficient in the sense of being asymptotically equivalent to the estimate knowing the other components of the varying coefficients. In both steps, the authors remove the fixed effects through properly constructed weights. The authors obtain the asymptotic properties of both the pilot and efficient estimators. The Monte Carlo simulations show that the proposed estimator performs well. The authors illustrate their applicability by estimating a varying coefficient production frontier using a panel data, without assuming distributions of the efficiency and error terms.

Fused deposition modeling (FDM) is an extensively used additive manufacturing method with the capacity to build complex functional components. Due to the machinery and environmental factors during manufacturing, the FDM parts inevitably demonstrated uncertainty in properties and performance. This study aims to identify the stochastic constitutive behaviors of FDM-fabricated polylactic acid (PLA) tensile specimens induced by the manufacturing process.

By conducting the tensile test, the effects of the printing machine selection and three major manufacturing parameters (i.e., printing speed S, nozzle temperature T and layer thickness t) on the stochastic constitutive behaviors were investigated. The influence of the loading rate was also explained. In addition, the data-driven models were established to quantify and optimize the uncertain mechanical behaviors of FDM-based tensile specimens under various printing parameters.

As indicated by the results, the uncertain behaviors of the stiffness and strength of the PLA tensile specimens were dominated by the printing speed and nozzle temperature, respectively. The manufacturing-induced stochastic constitutive behaviors could be accurately captured by the developed data-driven model with the R² over 0.98 on the testing dataset. The optimal parameters obtained from the data-driven framework were T = 231.3595 °C, S = 40.3179 mm/min and t = 0.2343 mm, which were in good agreement with the experiments.

The developed data-driven models can also be integrated into the design and characterization of parts fabricated by extrusion and other additive manufacturing technologies.

Stochastic behaviors of additively manufactured products were revealed by considering extensive manufacturing factors. The data-driven models were proposed to facilitate the description and optimization of the FDM products and control their quality.