Linear Polynomial Research Articles

Application of multiple linear and polynomial regression in the sustainable biodegradation process of crude oil

Statistical regression models have been applied in various biotechnical applications to determine the relationship between response and conditional factors as well as to facilitate prediction. This research focuses on sustainable biodegradation process of crude oil using native and recombinant microbial strains to alleviate the significant environmental threat posed by crude oil contamination. This sustainable process is energy and cost-efficient compared to the traditional measures adopted in the extermination of the contaminated soil due to crude oil. The reaction of the wild and recombinant microbial strains to biodegradation rate was detected in the experimental study. These experimental data were used to develop multiple linear regression (MLR) and polynomial regression models (PR). The coefficient of determination, or R2 value, was used to validate the constructed models. The PR model had a high R2 of 0.863, whereas the MLR model had a low value of 0.495. The PR model provided the best match, and it also explains the impact of conditioning factors on the biodegradation rate. To summarize, the recombinant microbial strain yielded a better biodegradation rate with increasing incubation days at lower crude oil contents.

Convective Heat and Mass Transport in Casson Fluid Flow in Curved Corrugated Cavity with Inclined Magnetic Field.

Convection in fluids produced by temperature and solute concentration differences is known as thermosolutal convection. It has valuable utilization in wide industrial and technological procedures such as electronic cooling, cleaning, and dying processes, oxidation of surface materials, storage components, heat exchangers, and thermal storage systems. In view of such prominent physical significance, focus is made to explicate double (thermal and solutal)-diffusive transport in viscoelastic fluid characterized by the Casson model enclosed in a curved enclosure with corrugations. An incliningly directed magnetic field is employed to the flow domain. A uniformly thermalized and concentrated circular cylinder is installed at the center of the enclosure to measure transport changes. Dimensionally balanced governing equations are formulated in 2D, representing governed phenomenon. Finite element-based open-sourced software known as COMSOL is utilized. The domain of the problem is distributed in the form of triangular and quadrilateral elements. Transport distributions are interpolated by linear and quadratic polynomials. The attained non-linear system is solved by a less time and computation cost consuming package known as PARDISO. Convergence tests for grid generation and validation of results are executed to assure credibility of work. The influence of involved physical parameters on concerned fields are revealed in graphical and tabular manner. Additionally, heat and mass fluxes, along with, kinetic energy variation are also evaluated.

STOCK MARKET PREDICTION AND EFFICIENCY ANALYSIS

Stock is an unpredictable curve. Prediction in the stock market is covered with complexity and instability. The main aim for the persuasion of the topic is to predict the stability in the future market stocks. Many researchers have performed their research on the movement of future market evolution. In the recent trend of Stock Market Prediction Technologies machine learning has integrated itself in the picture for deployment and prediction of training sets and data models. Machine Learning employs different predictive models and algorithms to predict and automate things of requirement. We are using the Nifty 50 dataset for our project. It consists of six attributes and 4000 records spanning from the year 2004 till 2020. For the implementation of our project we are utilizing the machine learning techniques such as Linear Regression, Polynomial Regression, Knn algorithm and Decision tree. Performance of the algorithms will be measured using precision accuracy.

Prediction of weld area based on image recognition and machine learning in laser oscillation welding of aluminum alloy

Laser oscillation welding is an advanced aluminum alloy welding technology which can effectively reduce weld porosity induced by physical and chemical properties of aluminum alloy. Weld area is often as an evaluation index of geometric characteristics to evaluate the welding quality since it has great effect on the mechanical properties of welded joints. In this paper, a prediction method of weld area based on process parameters is proposed for laser oscillation welding of 6061 aluminum alloy. From the metallographic micrographs of welding experiments, the cross-sectional area of weld is calculated by image recognition technology and the error of recognized weld area is less than 8.8%. Additionally, various prediction models for weld area under different process conditions are established by machine learning algorithms including linear regression, polynomial regression and back propagation neural network (BPNN). The established prediction models are compared by the mean square error (MSE) and coefficient of determination (R2). The results show that the BPNN prediction model indicates the highest accuracy and robustnessand can be adopted to predict the cross-sectional area of weld. The proposed method can be used for selecting the optimal process condition for the ideal welded joints with the desired weld geometry to improve the quality of laser oscillation welding.

Uniqueness of meromorphic functions sharing sets with its linear difference polynomials

Uniqueness of meromorphic functions sharing sets with its linear difference polynomials

Adaptive stabilized mixed formulation for phase field fracture modeling of nearly incompressible finite elasticity

The recently proposed mixed displacement-pressure-phase field formulation characterized by damage-mitigating incompressibility constraints excels in fracture modeling of nearly incompressible hyperelastic materials. However, such formulations generally call for mixed finite element (FE) allocations that satisfy the inf-sup condition, denying the popular lower equal-order linear FE pairs, like linear polynomial (P1) interpolation for all fields. To overcome this drawback, we develop a stabilized mixed formulation (P1/P1S) by resorting to a pressure projection technique. The lure of this formulation lies in its simplicity and versatility, allowing low-order P1 interpolation for all field variables. With this trait in mind, an efficient adaptive meshing strategy is designed, thereby speeding up computation by more than 15 times. For better coping with the adaptive scenarios involving crack nucleation, we also propose a novel energy-based mesh refinement criterion. The numerical treatment of the stabilized mixed FE formulation is elaborated, as well as the core operations of the adaptive meshing technique. The accuracy, efficiency, and robustness of the proposed formulation are validated by several representative numerical examples. Remarkably, a mixed I/II fracture test thereof is in good agreement with the experiment and thus promises to be a new benchmark.

Linear Regression Machine Learning Algorithms for Estimating Reference Evapotranspiration Using Limited Climate Data

A linear regression machine learning model to estimate the reference evapotranspiration based on temperature data for South Korea is developed in this study. FAO56 Penman–Monteith (FAO56 P–M) reference evapotranspiration calculated with meteorological data (1981–2021) obtained from sixty-two meteorological stations nationwide is used as the label. All study datasets provide daily, monthly, or annual values based on the average temperature, daily temperature difference, and extraterrestrial radiation. Multiple linear regression (MLR) and polynomial regression (PR) are applied as machine learning algorithms, and twelve models are tested using the training data. The results of the performance evaluation of the period from 2017 to 2021 show that the polynomial regression algorithm that learns the amount of extraterrestrial radiation achieves the best performance (the minimum root-mean-square errors of 0.72 mm/day, 11.3 mm/month, and 40.5 mm/year for daily, monthly, and annual scale, respectively). Compared to temperature-based empirical equations, such as Hargreaves, Blaney–Criddle, and Thornthwaite, the model trained using the polynomial regression algorithm achieves the highest coefficient of determination and lowest error with the reference evapotranspiration of the FAO56 Penman–Monteith equation when using all meteorological data. Thus, the proposed method is more effective than the empirical equations under the condition of insufficient meteorological data when estimating reference evapotranspiration.

Efficient reconstruction of directed networks from noisy dynamics using stochastic force inference.

We consider coupled network dynamics under uncorrelated noises that fluctuate about the noise-free long-time asymptotic state. Our goal is to reconstruct the directed network only from the time-series data of the dynamics of the nodes. By using the stochastic force inference method with a simple natural choice of linear polynomial basis, we derive a reconstruction scheme of the connection weights and the noise strength of each node. Explicit simulations for directed and undirected random networks with various node dynamics are carried out to demonstrate the good accuracy and high efficiency of the reconstruction scheme. We further consider the case when only a subset of the network and its node dynamics can be observed, and it is demonstrated that the directed weighted connections among the observed nodes can be easily and faithfully reconstructed. In addition, we propose a scheme to infer the number of hidden nodes and their effects on each observed node. The accuracy of these results is illustrated by simulations.

A Uniform Accuracy High-Order Finite Difference and FEM for Optimal Problem Governed by Time-Fractional Diffusion Equation

In this paper, the time fractional diffusion equations optimal control problem is solved by 3−α order with uniform accuracy scheme in time and finite element method (FEM) in space. For the state and adjoint state equation, the piecewise linear polynomials are used to make the space variables discrete, and obtain the semidiscrete scheme of the state and adjoint state. The priori error estimates for the semidiscrete scheme for state and adjoint state equation are established. Furthermore, the 3−α order uniform accuracy scheme is used to make the time variable discrete in the semidiscrete scheme and construct the full discrete scheme for the control problems based on the first optimal condition and ‘first optimize, then discretize’ approach. The fully discrete scheme’s stability and truncation error are analyzed. Finally, two numerical examples are denoted to show that the theoretical analysis are correct.

Image Analysis to Determine Length-Weight and Area-Weight Relationships, and Color Differences in Scaled Carp and Mirror Carp Grown in Fiberglass and Concrete Tanks

Sixty scaled carp Cyprinus carpio and sixty mirror carp Cyprinus carpio carpio were raised in fiberglass and concrete tanks. Fish pictures were taken by a digital camera in a lightbox. Image analysis was used to determine length-weight and view area-weight relationships. Length-weight data were fitted to a power equation: (Weight W) = A (Length L)B. R2 ranged from 0.838 to 0.959. Based on the B values, scaled and mirror carps reared in the fiberglass tank showed a negative allometric growth while this was positive for the fish in the concrete tank. For the view area (V)-weight relationship, linear (W = A + BV), and second order polynomial equations were used in addition to the power equation. The R2 values for these equations ranged from 0.916 to 0.995. Skin color was measured by image analysis. Both scaled and mirror carp reared in concrete tanks had L*, a* and b* values significantly higher than those reared in fiberglass tanks (P < .05). Also, the fish reared in fiberglass tanks tended to have less weight for the same view area, compared to those reared in concrete tanks.

Two remarks on Narkiewicz’s property (P)

Due to Narkiewicz a field F has property (P) if for no polynomial fin F[x] of degree at least two there is an infinite f-invariant subset of F. We present a new example of an algebraic extension of {mathbb {Q}} satisfying (P). This is the first example in which we can find points of arbitrarily small positive Weil-height. Moreover, we study the possibility of property (P) for the field generated by all symmetric Galois extensions of {mathbb {Q}}. In particular we prove that there are no infinite backward orbits of non linear polynomials in this field.

The Stock Price Prediction Based on Time Series Model, Multifactorial Regression, Machine Learnings

In general, it is hard to forecast the prices the stock prices due to the stochastic fluctuations. This research aims to describe the process to use time series models, multifactorial regression, and machine learning to predict stock prices. ARIMA and EGARCH models are frequently used time series models to predict stock prices. Least-squares linear regression model, Lasso, and Polynomial Linear Regression model predict well in statistical regression methods. RNN and LSTM have higher prediction accuracy. Overall, time series models, statistical regression, and machine learning all can predict stock prices. Summarizing the different methods or models to forecast stock market trending can help investors to prepare relevant investing strategies. These results shed light on guiding further exploration of

Methodology for multidimensional approximation of current velocity fields around offshore aquaculture installations

Consistent growth of the marine aquaculture industry over the past decades calls for potential deployments of large-scale aquaculture structures to produce finfish, shellfish and macroalgae in varying inshore and offshore environments. Numerical simulations for engineering design applications become more challenging with increase of scale since current velocity fields are no longer uniform, complicating accurate hydrodynamic load calculations. Horizontal and vertical velocity profiles in this case are spatially (depth and particular location within the deployment site) and temporary (date and time) dependent. Thus, proper representation of the current velocity field in numerical models becomes crucial for accurate predictions of structural performance of aquaculture installations. In this paper, an advanced multidimensional approximation method based on discrete current velocity data is formulated. The approach implies presenting the continuous current velocity function as a superposition of weighted radial basis functions extended by a linear polynomial. To address overfitting issues, the thin plate regularization is applied in the method. The approximation is then constrained in order to fit the velocity values on the domain boundaries. The method is implemented in finite element software Hydro-FE and its performance is compared to other approximation methods on the example of a kelp grow line deployed at the Wood Island research site, Maine, USA. It was found that the difference between regular (mean or linearly interpolated) velocity profiles and the velocity profiles approximated with the radial basis function method can reach up to 34–38 % in terms of grow line mooring tensions, and 6–18% in terms of grow line displacement.

Removing membrane locking in quadratic NURBS-based discretizations of linear plane Kirchhoff rods: CAS elements

NURBS-based discretizations of the Galerkin method suffer from membrane locking when applied to primal formulations of curved thin-walled structures. We consider linear plane curved Kirchhoff rods as a model problem to study how to remove membrane locking from NURBS-based discretizations. In this work, we propose continuous-assumed-strain (CAS) elements, an assumed strain treatment that removes membrane locking from quadratic NURBS for an ample range of slenderness ratios. CAS elements take advantage of the C1 inter-element continuity of the displacement vector given by quadratic NURBS to interpolate the membrane strain using linear Lagrange polynomials while preserving the C0 inter-element continuity of the membrane strain. To the authors’ knowledge, CAS elements are the first NURBS-based element type able to remove membrane locking for a broad range of slenderness ratios that combines the following distinctive characteristics: (1) No additional degrees of freedom are added, (2) No additional systems of algebraic equations need to be solved, and (3) The nonzero pattern of the stiffness matrix is preserved. Since the only additional computations required by the proposed element type are to evaluate the derivatives of the basis functions and the unit tangent vector at the knots, the proposed scheme barely increases the computational cost with respect to the locking-prone NURBS-based discretization of the primal formulation. The benchmark problems show that the convergence of CAS elements is independent of the slenderness ratio up to 104 while the convergence of quadratic NURBS elements with full and reduced integration, local B̄ elements, and local ANS elements depends heavily on the slenderness ratio and the error can even increase as the mesh is refined. The numerical examples also show how CAS elements remove the spurious oscillations in stress resultants caused by membrane locking while quadratic NURBS elements with full and reduced integration, local B̄ elements, and local ANS elements suffer from large-amplitude spurious oscillations in stress resultants. In short, CAS elements are an accurate, robust, and computationally efficient numerical scheme to overcome membrane locking in quadratic NURBS-based discretizations.

Retention prediction of monoamine neurotransmitters in gradient liquid chromatography.

Retention prediction of monoamine neurotransmitters has been compared for the generally applied linear solvent-strength model and quadratic polynomial three-parameter model. The design of experiments protocol has been applied to plan linear gradients within the experimental space with altered gradient time, mobile phase flow rate, and column temperature. Relative prediction errors increased at elevated temperature, which is more significant for the linear solvent-strength model when compared to the polynomial model. On the other hand, the predefined design of experiments space controls the retention time errors, as predictions for LC conditions that are outside of the plan are much less accurate and should be avoided. The final part of the work deals with the effect of extracolumn band dispersion on the peak capacity of linear gradients at various gradient times, mobile phase flow rates, and column temperature. The peak capacity determined for corrected experimental data were consistent with the published results dealing with the optimization of peak capacity in gradient elution.

On the Constrained Solution of RBF Surface Approximation

In this contribution, a scattered data approximation problem, chosen from the literature and using the Radial Basis Function (RBF) approach, is considered for the application of point cloud modelling. Three solutions are investigated for the approximation problem. First, a technique known from the literature is investigated using a linear combination of thin-plate splines and linear polynomials, with additional constraint equations. Then, using the same approximation function as before, a technique is developed for a rigorous consideration of the constraint equations. Finally, a technique is presented in which the approximation function consists only of a linear combination of thin-plate splines, without the introduction of linear polynomials and constraint equations. In addition, some interpolation problems with the RBF approach are discussed to present the differences between an interpolation with thin-plate splines only and an interpolation with thin-plate splines together with linear polynomials and constraint equations. Numerical examples are given to illustrate and discuss the solutions from the different techniques.

Reliable Aerial Mobile Communications with RSRP & RSRQ Prediction Models for the Internet of Drones: A Machine Learning Approach.

The unmanned aerial vehicle (UAV) industry is moving toward beyond visual line of sight (BVLOS) operations to unlock future internet of drones applications, including unmanned environmental monitoring and long-range delivery services. A reliable and ubiquitous mobile communication link plays a vital role in ensuring flight safety. Cellular networks are considered one of the main enablers of BVLOS operations. However, the existing cellular networks are designed and optimized for terrestrial use cases. To investigate the reliability of provided aerial coverage by the terrestrial cellular base stations (BSs), this article proposes six machine learning-based models to predict reference signal received power (RSRP) and reference signal received quality (RSRQ) based on the multiple linear regression, polynomial, and logarithmic methods. In this regard, first, a UAV-to-BS measurement campaign was conducted in a 4G LTE network within a suburban environment. Then, the aerial coverage was statistically analyzed and the prediction methods were developed as a function of distance and elevation angle. The results reveal the capability of terrestrial BSs in providing aerial coverage under some circumstances, which mainly depends on the distance between the UAV and BS and flight height. The performance evaluation shows that the proposed RSRP and RSRQ models achieved RMSE of 4.37 dBm and 2.71 dB for testing samples, respectively.

Numerical simulation of thermal flows and entropy generation of magnetized hybrid nanomaterials filled in a hexagonal cavity

The current study addresses the features of entropy generation and thermal flows regarding magnetized hybrid nanofluid in the presence of a cylinder in a closed hexagonal domain. The hexagonal cavity comprises two heated horizontal walls, and two are insulated while the other walls are cold. The whole system has been modeled as coupled non-linear partial differential equations. Also, normalized the governing coupled equation by utilizing a proper pair of variables and are computed with a finite element approach. For the approximation of velocity profiles, a finite element space involving the quadratic polynomial (P2) is selected whereas the pressure and temperature estimation is accomplished through a space of linear polynomial (P1). An analogy is handed with published findings at confining instance. The degree of freedom and grid convergence test is considered for the kinetic energy (KE) and Bejan number (Be). The study reveals a major role in enhancing the heat transfer rate due to hybrid nano-particles. The results show that the increase of magnetic field effect considers the reduction of the heat transfer because the conduction motion occupies the motion of the fluid flow. When the Hartmann number is increased, the magnetic entropy is raised, too. For intensified the Hartmann numbers, the highest ratio of heat transfer occurs for the case of the hybrid nanoparticles, and then MgO-water, followed by the Ag-water. The nature of thermal flow parameters has been scrutinized.

Dietary lysine requirement of juvenile Pacific white shrimp, Litopenaeus vannamei (Boone, 1931) reared in inland saline water of 10 ppt salinity

A feeding trial of 60 days was conducted to assess the dietary lysine requirement of juvenile Litopenaeus vannamei reared in inland saline water. Seven isonitrogenous (~ 360 g crude protein/kg feed), isolipidic (~ 60 g crude lipid/kg feed) and isocaloric (~ 18 MJ gross energy/kg feed) semi-purified test diets with graded lysine levels viz., 13.7 (L1), 16.3 (L2), 18.7 (L3), 21.4 (L4), 23.8 (L5), 26.3 (L6) and 28.9 g/kg (L7) were formulated and prepared. Three hundred and seventy-eight L. vannamei juveniles (2.75 ± 0.01 g) were randomly distributed (60 no/m3 or 33 no/m2) into seven test groups in triplicates following a completely randomized design. L. vannamei juveniles were fed to the apparent satiation level four times daily. At the end of the feeding trial, the results indicated that dietary lysine levels have significantly (P < 0.05) affected the growth and nutrient utilization parameters in juvenile L. vannamei. An increase (P < 0.05) in final body weight, weight gain percentage (WG%), thermal growth coefficient (TGC), protein efficiency ratio and protein productive value were observed with the increasing dietary lysine levels from 13.7 to 23.8 g/kg after which a decreasing trend was observed. The relative feed intake and feed conversion ratio showed a decreasing trend from lower dietary lysine levels to higher levels. Survival rates of experimented shrimp were not significantly different (P > 0.05) among the treatment groups. The whole body crude protein and crude lipid content of L. vannamei showed significantly (P < 0.05) increasing and decreasing trends, respectively towards the increasing dietary lysine levels. The hepatopancreatic and muscle protein metabolic enzyme activities, haemocyanin and serum total protein content of L. vannamei varied significantly among the treatment groups. The broken-line linear and second-order polynomial regression analysis of WG% and TGC against the dietary lysine levels indicated that the optimal dietary lysine level with confidence interval (CI) for juvenile L. vannamei reared in inland saline water of 10 ppt salinity is 23.46 (22.59–24.88 g/kg, 95% CI) to 25.24 g/kg (24.27–26.53 g/kg, 95% CI) and 23.26 (22.70–24.15 g/kg, 95% CI) to 25.25 g/kg (24.27–26.53 g/kg, 95% CI) of the diet, respectively.

Impact of ocean fronts on the reconstruction of vertical temperature profiles from sea surface measurements

Temperature structures in the ocean interior are fundamental to interpret ocean dynamics. Yet their measurements are still limited, despite the increasing effort to deploy in-situ instruments over the last decades. Reconstruction of the vertical temperature profiles from sea surface variables is thus widely adopted to bridge this gap. Most of the studies deal with the reconstruction in a uniform manner without taking the presence of ocean processes into account. In this study, we evaluate the effects of ocean fronts on the reconstruction performances of vertical temperature profiles over the Northwest Pacific Ocean. Four mapping models based on linear and second-order polynomial regressions are trained by inputting the sea surface temperature (SST) and sea level anomaly (SLA). Model validations in terms of the mean bias and standard deviation (STD) are conducted based on an independent dataset excluded from the training process. The model of best performance is with inputs of SST and SLA using the polynominal regression. The spatial distribution of the bias and STD is then linked with the SST gradient to assess the front impacts. We found that the regions of high bias and STD are geographically consistent with that of large SST gradient. Both biases and STDs exhibit a quasi-linear increase trend relative to the SST gradient with slopes varying for depths. The bias reaches its maximum at around 300 m depth and decreases towards both deeper and shallower levels. These results suggest the necessity to consider fronts influence on the reconstruction of vertical temperature profiles, which shall improve the mapping accuracy.