Unknown Variables Research Articles

Analysis of a diffusive chemical reaction model in three space dimensions

This article proposes an implicit operator splitting nonstandard finite difference (OS-NSFD) scheme for numerical treatment of two species in three space dimensions reaction-diffusion glycolysis model. Since, the unknown state variables exhibiting the concentrations of species in glycolysis models and they cannot be negative and obtaining their positive solutions is a challenging task. The established theoretical result ensures that our proposed OS-NSFD scheme is unconditionally convergent at equilibrium point and fulfills the condition of positivity of solutions on contrary to other methods. Further, we analyze the existence and uniqueness of the solution obtained for the underlying system. To highlight the effectiveness of OS-NSFD scheme we compare the simulation results of OS-NSFD scheme with three well-known existing operators splitting finite difference (FD) schemes, namely, forward Euler explicit, backward Euler implicit and Crank Nicolson splitting schemes. Many existing techniques provide with the restricted positive solutions which do not work always. These techniques are only applicable if certain conditions on the discretized parameters are considered otherwise; they produce negative solutions, which is not the physical feature of the real system. The current work bridges this gap by catering the unconditional positive solutions to the reaction diffusion models.

Ultrasound-assisted synthesis of novel undecylenic estolides: Modeling and Tribological characterization

Abstract To overcome the issues related to low-temperature characteristics and thermal degradation of fatty acid based lubricant base stocks, chemical modification is essential. To mitigate these shortcomings, considering unsaturated undecylenic acid, the formation of estolides is one of the best transformations considering application in lubricants. Ultrasonic-assisted sulfuric acid-catalyzed synthesis of estolides of undecylenic was modeled using response surface methodology (RSM) and subsequently validated using artificial neural network (ANN) for known and unknown input variables. At optimal reaction conditions of reaction temperature of 56°C, catalyst loading of 0.63 mole-equivalent, and reaction time of 1.61 hours, estolides with estolide number (EN) of 2.58, extraordinary low pour point (PP) of −52°C and better resistance to thermal degradation was obtained. The thermal degradation was evaluated using thermogravimetric analysis (TGA) to find improved resistance toward degradation due to the formation of estolides. Further, tribological properties like wear characteristics, load carrying capacity, and oxidative stability were studied for 5% blends in SN 70 base oil. The anti-wear ability of the estolides was found to be superior to undecylenic acid, with a lower coefficient of friction, scar diameter, depth, and volume. The blend containing estolide was found to have load carrying capacity as high as 800 kgf. Moreover, owing to the double bond migration during the reaction, the oxidative stability of estolides was found to be inferior to the terminally unsaturated undecylenic acid.

A high-order upwind compact difference scheme for solving the streamfunction-velocity formulation of the unsteady incompressible Navier–Stokes equations

In this paper, we propose an upwind compact difference method with fourth-order spatial accuracy and second-order temporal accuracy for solving the streamfunction-velocity formulation of the two-dimensional unsteady incompressible Navier–Stokes equations. The streamfunction and its first-order partial derivatives (velocities) are treated as unknown variables. Three types of compact difference schemes are employed to discretize the first-order partial derivatives of the streamfunction. Specifically, these schemes include the fourth-order symmetric scheme, the fifth-order upwind scheme, and the sixth-order symmetric scheme derived by combining the two parts of the fifth-order upwind scheme. As a result, the fourth-order spatial discretization schemes are established for the Laplacian term, the biharmonic term, and the nonlinear convective term, along with the Crank–Nicolson scheme for the temporal discretization. The unconditional stability characteristic of the scheme for the linear model is proved by discrete von Neumann analysis. Moreover, six numerical experiments involving three test problems with the analytic solutions, and three flow problems including doubly periodic double shear layer, lid-driven cavity flow, and dipole-wall interaction are carried out to demonstrate the accuracy, robustness, and efficiency of the present method. The results indicate that the present method not only has good numerical performance but also exhibits quite efficiency.

Designing an Information Technology Platform for Imparting Entrepreneurship Values in Social-Emotional Learning for Kindergarten Children Using EFA and CFA

Kindergarten is crucial for today's education. Kindergarten helps kids develop in all areas. Students work in groups on a simple project task in this study. The work includes topic-related activities. Kids should learn early on that being an entrepreneur will shape their identity & future. This condition makes someone realize that their long-term desire to be an entrepreneur comes from their academic success. This study investigated how the 35 questions are assembled & what improves them. 195 kindergarten teachers participated in the study. The sample was analyzed using EFA & CFA. Exploratory factor analysis revealed twelve unknown variables. The above variables explained 80% of the variation. Various factors explained the remaining 20%. All Cronbach's alpha values exceed requirements. CR >.7 & AVE >.5, indicating credible & tested constructs. The EFA showed that 195 research samples were sufficient because the KMO was above 0.50. This allowed more research. Six-factor solutions explained over 80.71% of the variation, so the EFA liked them. These factors kept the results consistent with those of previous studies. These traits facilitate legislator-educator dialogue rather than kindergarten teacher business observation. Researchers can use these properties for cluster analysis or multivariate linear regression. This subject requires more research because students develop a structured approach. Furthermore, experts should examine the research on what is making kindergarten entrepreneurship instruction popular.

Integral Sliding Mode Output Feedback Control for Unmanned Marine Vehicles Using T–S Fuzzy Model with Unknown Premise Variables and Actuator Faults

This paper addresses integral sliding mode output feedback fault-tolerant control (FTC) of unmanned marine vessels (UMVs) with unknown premise variables and actuator faults. Due to the complexity of the marine environment, the presence of uncertainties in the yaw angle renders the premise variables in the Takagi–Sugeno (T–S) fuzzy model of UMVs unknown. Consequently, traditional integral sliding mode techniques become infeasible. To address this issue, a control strategy combining integral sliding mode based on output feedback with a compensator utilizing switching mechanisms is proposed. First, a radial basis function neural network is used to approximate the nonlinear terms in the UMV T–S fuzzy model. In addition, an integral sliding mode surface is constructed based on fault estimation information and membership function estimation. On this basis, an FTC scheme based on integral sliding mode output feedback is developed to ensure that the UMV system is asymptotically stable and satisfies the prescribed H∞ performance index. Finally, simulation results are provided to demonstrate the effectiveness of the presented control strategy.

Neural adaptive dynamic surface control for position tracking of electrohydraulic servo systems based on extended state observer

High-performance motion tracking of electro-hydraulic servo systems plays an important role in developing industrial technology. However, the system itself has parameter uncertainty, uncertain nonlinearity, and measurement noise, significantly decreasing the performance of conventional controllers designed based on nominal models. To improve the tracking performance of electro-hydraulic servo systems, an adaptive dynamic surface control method combining extended state observer and radial basis function neural network is proposed. Firstly, an extended state observer combining neural network output and parameter adaptation technology is designed without the need for speed and pressure feedback to observe the system’s unknown state variables and nonlinear matched disturbance. The design of neural networks is used to approximate mismatched disturbance with significant nonlinearity online. Then, the proposed extended state observer is introduced into the neural adaptive backstepping design, effectively compensating for simultaneous matched and mismatched disturbances, thereby suppressing most of the uncertain nonlinearity of the system. Meanwhile, online update of uncertain parameters further improves the tracking performance of the controller. In addition, the introduction of dynamic surface overcomes the “explosion of complexity” issue in backstepping design. The rigorous stability of the closed-loop system is proved by the Lyapunov stability theory. Finally, the effectiveness of the proposed controller is validated through comparative experiments on valve-controlled hydraulic cylinder.

Plant-Based Meat Analogues in the Human Diet: What Are the Hazards?

Research regarding meat analogues is mostly based on formulation and process development. Information concerning their safety, shelf life, and long-term nutritional and health effects is limited. This article reviews the existing literature and analyzes potential hazards introduced or modified throughout the processing chain of plant-based meat analogues via extrusion processing, encompassing nutritional, microbiological, chemical, and allergen aspects. It was found that the nutritional value of plant-based raw materials and proteins extracted thereof increases along the processing chain. However, the nutritional value of plant-based meat analogues is lower than that of e.g., animal-based products. Consequently, higher quantities of these products might be needed to achieve a nutritional profile similar to e.g., meat. This could lead to an increased ingestion of undigestible proteins and dietary fiber. Although dietary fibers are known to have many positive health benefits, they present a hazard since their consumption at high concentrations might lead to gastrointestinal reactions. Even though there is plenty of ongoing research on this topic, it is still not clear how the sole absorption of metabolites derived from plant-based products compared with animal-based products ultimately affects human health. Allergens were identified as a hazard since plant-based proteins can induce an allergic reaction, are known to have cross-reactivities with other allergens and cannot be eliminated during the processing of meat analogues. Microbiological hazards, especially the occurrence of spore- and non-spore-forming bacteria, do not represent a particular case if requirements and regulations are met. Lastly, it was concluded that there are still many unknown variables and open questions regarding potential hazards possibly present in meat analogues, including processing-related compounds such as n-nitrosamines, acrylamide, and heterocyclic aromatic amino acids.

A Co-Localization Algorithm for Underwater Moving Targets with an Unknown Constant Signal Propagation Speed and Platform Errors.

Underwater mobile acoustic source target localization encounters several challenges, including the unknown propagation speed of the source signal, uncertainty in the observation platform's position and velocity (i.e., platform systematic errors), and economic costs. This paper proposes a new two-step closed-form localization algorithm that jointly estimates the angle of arrival (AOA), time difference of arrival (TDOA), and frequency difference of arrival (FDOA) to address these challenges. The algorithm initially introduces auxiliary variables to construct pseudo-linear equations to obtain the initial solution. It then exploits the relationship between the unknown and auxiliary variables to derive the exact solution comprising solely the unknown variables. Both theoretical analyses and simulation experiments demonstrate that the proposed method accurately estimates the position, velocity, and speed of the sound source even with an unknown sound speed and platform systematic errors. It achieves asymptotic optimality within a reasonable error range to approach the Cramér-Rao lower bound (CRLB). Furthermore, the algorithm exhibits low complexity, reduces the number of required localization platforms, and decreases the economic costs. Additionally, the simulation experiments validate the effectiveness of the proposed localization method across various scenarios, outperforming other comparative algorithms.

Free vibration analysis of laminated anisotropic doubly-curved shell structures reinforced with three-phase polymer/CNT/fiber material

The present work investigates the vibrational response of laminated anisotropic doubly-curved shell structures reinforced with Carbon Nanotubes (CNTs) short fibers. The fundamental equations are derived from a curvilinear reference system of principal coordinates, employing the Equivalent Single Layer (ESL) methodology. Furthermore, a general variation in laminate thickness is considered. The unknown field variable is described using higher order theories through the unified formulation, taking into account a general interpolation of the unknown variables with Lagrange polynomials across the physical domain. The Hamiltonian Principle is adopted for the derivation of the dynamic equilibrium equations, which arediscretized numerically by using the Generalized Differential Quadrature (GDQ) method. In addition, an efficient isogeometric NURBS-based mapping is adopted for the distortion of the physical domain. The boundary conditions of the differential problem are modelled through a general distribution of linear elastic springs along the lateral surfaces of the three-dimensional doubly-curved solid. The theory is then applied to study the vibrational modes of structures with different curvatures and lamination schemes, taking into account a general distribution of CNTs along the thickness direction. The homogenized properties of CNTs layers are obtained from the Mori-Tanaka procedure, which accounts for the agglomeration effects of the dispersed nanofibers within the matrix. Unlike previous studies focusing on doubly-curved shells reinforced with composite materials and CNTs, the present formulation enables to derive the vibration characteristics of structures made of generally anisotropic materials with general orientations. Furthermore, the calibration of the parameters for the linear elastic springs’ distribution leads to general external constraints within a single element, thus reducing the computational cost of the problem.

Joint identification of groundwater pollution source information, model parameters, and boundary conditions based on a novel ES-MDA with a wheel battle strategy

Groundwater pollution source identification (GPSI) is an important prerequisite for pollution remediation and risk assessment. However, an accurate GPSI is usually difficult to achieve due to the need to simultaneously consider practical problems and theoretical research. For practical problems, the boundary conditions, especially the concentration boundary, are often given as known constants through prior information. However, in most practical situations, the boundary conditions are complex and cannot be accurately estimated in advance, which leads to the distortion of the final identification results. Therefore, this study focused on the concentration boundary, and first proposed to jointly identify three types of unknown variables (source information, model parameters, and boundary conditions) to ensure that the identification results had more practical value. For theoretical research, as the number of unknown variable types increases, the difficulty of solving the inverse problem often increases, which may lead to inaccurate inversion results. Thus, a novel ensemble smoother with multiple data assimilation (ES-MDA) with a wheel battle strategy was proposed, enhancing the identification accuracy. We designed two cases to verify the effectiveness and practicality of the above ideas: a low-dimensional Case 1 (including four different synthetic scenarios: three scenarios with unknown boundary conditions under three concentration boundary modes and a scenario with known boundary conditions) and a high-dimensional complex Case 2. Identifying the boundary conditions in GPSI was found to be of great significance. Compared to the standard ES-MDA method, the ES-MDA with a wheel battle strategy proposed here could improve the inversion accuracy, and had certain effectiveness and practicality.

Bidirectional machine learning-assisted sensitivity-based stochastic searching approach for groundwater DNAPL source characterization.

In this study, we designed a machine learning-based parallel global searching method using the Bayesian inversion framework for efficient identification of dense non-aqueous phase liquid (DNAPL) source characteristics and contaminant transport parameters in groundwater. Swarm intelligence organized hybrid-kernel extreme learning machine (SIO-HKELM) was proposed to approximate the forward and inverse input-output correlation with a high accuracy using the DNAPL transport numerical simulation model. An adaptive inverse-HKELM was established for preliminary estimation of the source characteristics and contaminant transport parameters to correct prior information and generate high-quality initial starting points of parallel searching. A local accurate forward-HKELM surrogate of the numerical model was embedded in the searching system for avoiding repetitive CPU-demanding likelihood evaluations. A sensitivity-based Metropolis criterion (MC), incorporating the dynamic particle swarm optimization (SD-PSO) algorithm, was developed for improving the search ergodicity and realizing precise inversion of all the unknown variables with drastic variations in sensitivity to the likelihood function. Results showed that the generalization capability and robustness of SIO-HKELM were superior to those of the traditional machine learning methods, including KELM and support vector regression (SVR), and it sufficiently approximated the forward and inverse input-output mapping of the numerical model with testing determination coefficients of 0.9944 and 0.6440, respectively. With high-quality prior information and initial starting points generated by the adaptive inverse-HKELM feed approach, the uncertainty in the inversion outputs was reduced, and the searching process rapidly converged to reasonable posterior distributions in around 60 iterations. Compared with the widely used multichain Markov chain Monte Carlo (MCMC) approach, the parallel searching lines generated by SD-PSO-MC adequately covered the searching space, and the "equifinality" effect was more effectively restrained by reducing the relative errors of all the point estimations to less than 8%. Therefore, the real source information reflected by the statistical characteristics of the SD-PSO-MC inversion outputs was more precise than that obtained using the multichain MCMC approach.

Projectively and affinely invariant PDEs on hypersurfaces

Abstract In Communications in Contemporary Mathematics24 3, (2022),the authors have developed a method for constructing G-invariant partial differential equations (PDEs) imposed on hypersurfaces of an $(n+1)$ -dimensional homogeneous space $G/H$ , under mild assumptions on the Lie group G. In the present paper, the method is applied to the case when $G=\mathsf{PGL}(n+1)$ (respectively, $G=\mathsf{Aff}(n+1)$ ) and the homogeneous space $G/H$ is the $(n+1)$ -dimensional projective $\mathbb{P}^{n+1}$ (respectively, affine $\mathbb{A}^{n+1}$ ) space, respectively. The main result of the paper is that projectively or affinely invariant PDEs with n independent and one unknown variables are in one-to-one correspondence with invariant hypersurfaces of the space of trace-free cubic forms in n variables with respect to the group $\mathsf{CO}(d,n-d)$ of conformal transformations of $\mathbb{R}^{d,n-d}$ .

DEVELOPMENT OF LAND-USE REGRESSION MODELS FOR PARTICULATE MATTER ESTIMATION IN NATIONAL CAPITAL REGION, PHILIPPINES

Abstract. Regression models are commonly used to estimate unknown variables, such as environmental parameters. Multiple Linear Regression (MLR) is one of the techniques used to model air quality and measure air pollutant concentrations. Specifically, a technique called Land-Use Regression (LUR) enables the user to generate air pollutant models using geographical layers as input parameters. The study aims to generate models for fine and coarse particulate matter (PM2.5 and PM10, respectively) using LUR for the National Capital Region in 2019. Independent variables considered in this study are road network, traffic count, Normalized Difference Vegetation Index (NDVI), population density, and elevation. The final model results showed significant estimates based on the model parameters. For PM2.5, the model resulted in high values of R2 and adjusted R2 and an RMSE of 0.77 μg/m3. For PM10, model parameters showed that the generated final model for PM10 was significant with a 55% R2 value. Maps were then generated using the final LUR models of PM2.5 and PM10. The models can be improved by adding more types of input variables and longer observation periods.

Predict Unknown Properties of Elements of Periodic Table with Machine Learning

The periodic table of elements includes 92 elements with many unknown properties like melting point, boiling point, heat of vaporization, and molar heat capacity of some specific elements such as Curium, Berkelium, Californium, and Einsteinium. Physicists, chemists, and other scientists have done many successful experiments to predict these mysterious features using the first principal methods. But still many properties have been unclear. In this project we apply Machine Learning models such as linear and logistic regression to predict this unknow values. The known values split to train and test data to find and confirm the model. Then the model will be run over unknown variables.

Efficient energy stable numerical schemes for Cahn–Hilliard equations with dynamical boundary conditions

In this paper, we propose a unified framework for studying the Cahn–Hilliard equation with two distinct types of dynamic boundary conditions, namely, the Allen–Cahn and Cahn–Hilliard types. Using this unified framework, we develop a linear, second-order, and energy-stable scheme based on the multiple scalar auxiliary variables (MSAV) approach. We design efficient and decoupling algorithms for solving the corresponding linear system in which the unknown variables are intricately coupled both in the bulk and at the boundary. Several numerical experiments are shown to validate the proposed scheme, and to investigate the effect of different dynamical boundary conditions on the dynamics of phase evolution under different scenarios.

Effect of Supervision on Performance Employees at Regional Technical Implementation Unit (RTIU) Senaken Penyembolum Market, Paser District

The aim of this research is to determine the effect of supervision on employee performance at the Regional Technical Implementation Unit (RTIU) Penyembolum Senaken Market, Paser Regency. From the results of the validity test, all 10 statement items were declared valid because they were greater than the rtable value of 0.2006 for each statement in this study. From the results of the reliability test, a value of 0.959 was obtained, which means there is a very strong relationship between the independent variable and the dependent variable. From the results of multiple linear regression analysis, it can be seen that the results of the regression equation are Y = 40.597 + 0.535X1 + 0.361X2. Based on the calculation results, an R value (Correlation Coefficient) of 0.915 is obtained which is at an interpretation level between 0.80-1.00, which means that there is a very strong influence from the supervision variable (X) which consists of direct supervision (X1), and supervision indirectly (X2), on employee performance (Y). The value of the Adjusted R Square Determination Coefficient (????2) is 0.833 or 83.3%. These results show that 83.3% of the direct supervision variables (X1) and indirect supervision (X2) have had an influence on the employee performance variable (Y). The remaining 16.7% is influenced by other unknown variables. From the results of the F test carried out, the supervision variable (X) consists of direct supervision (X1) and indirect supervision (X2), together they have an influence on employee performance. This is proven by the Fcount result of 238.507 with a significance level of 0.000, which means it is greater than Ftable 3.09. The results of the t test showed that the t-count value of direct supervision (X1) was 5.646 with a significant level of 0.000 and the t-count value of indirect supervision (X2) was 3.637 with a significance level of 0.000. Of the two independent variables studied, it is known that the direct supervision variable (X1) is the variable that has the dominant influence on employee performance (Y). This is proven by the results of direct supervision (X1) > indirect supervision (X2) or (5.646 > 3.637) so H0 is rejected and Ha is accepted.

Minimizing electric fields and increasing peripheral nerve stimulation thresholds using a body gradient array coil.

To demonstrate the performance of gradient array coils in minimizing switched-gradient-induced electric fields (E-fields) and improving peripheral nerve stimulation (PNS) thresholds while generating gradient fields with adjustable linearity across customizable regions of linearity (ROLs). A body gradient array coil is used to reduce the induced E-fields on the surface of a body model by modulating applied currents. This is achieved by performing an optimization problem with the peak E-field as the objective function and current amplitudes as unknown variables. Coil dimensions and winding patterns are fixed throughout the optimization, whereas other engineering metrics remain adjustable. Various scenarios are explored by manipulating adjustable parameters. The array design consistently yields lower E-fields and higher PNS thresholds across all scenarios compared with a conventional coil. When the gradient array coil generates target gradient fields within a 44-cm-diameter spherical ROL, the maximum E-field is reduced by 10%, 18%, and 61% for the X, Y, and Z gradients, respectively. Transitioning to a smaller ROL (24 cm) and relaxing the gradient linearity error results in further E-field reductions. In oblique gradients, the array coil demonstrates the most substantial reduction of 40% in the Z-Y direction. Among the investigated scenarios, the most significant increase of 4.3-fold is observed in the PNS thresholds. Our study demonstrated that gradient array coils offer a promising pathway toward achieving high-performance gradient coils regarding gradient strength, slew rate, and PNS thresholds, especially in scenarios in which linear magnetic fields are required within specific target regions.

Exact computation of projected sphere centres in cone beam x-ray projections

A method is presented for fitting the projected centres of spheres in cone beam x-ray imaging. By using a suitable coordinate system, the method allows direct and exact calculation of the sphere centre without fitting the projection shape with an ellipse and correcting from the ellipse centre to the sphere centre. Advantages in numerical implementation result from the number of unknown variables being reduced compared to ellipse fits. Additionally, the orientation of the detector relative to the x-ray source can be obtained from fitting the shapes of projections of multiple spheres without knowledge of the positions or dimensions of the spheres. The accuracy of the method is compared to other techniques using simulated x-ray projections.

Solving rician data analysis problems: theory and numerical modeling using computer algebra metods in Wolfram Mathematica

This paper considers theoretical foundations and mathematical methods of data analysis under the conditions of the Rice statistical distribution. The problem involves joint estimation of the signal and noise parameters. It is shown that this estimation requires the solution of a complex system of essentially nonlinear equations with two unknown variables, which implies significant computational costs. This study is aimed at mathematical optimization of computer algebra methods for numerical solution of the problem of Rician data analysis. As a result of the optimization, the solution of the system of two nonlinear equations is reduced to the solution of one equation with one unknown variable, which significantly simplifies algorithms for the numerical solution of the problem, reduces the amount of necessary computational resources, and enables the use of advanced methods for parameter estimation in information systems with priority of real-time operation. Results of numerical experiments carried out using Wolfram Mathematica confirm the effectiveness of the developed methods for two-parameter analysis of Rician data. The data analysis methods considered in this paper are useful for solving many scientific and applied problems that involve analysis of data described by the Rice statistical model.

Uniform extension–torsion of helical birods

An analytical formulation is presented to study uniform extension–torsion behavior of helical birods. The uniformity in extension and compression reduces the set of governing nonlinear differential equations of birod theory to a set of nonlinear algebraic equations for the relevant unknown variables of a birod. Upon normalizing the algebraic equations, we note that the birod’s coupled extension–torsion behavior in its natural state can be tuned by changing the birod’s constituent strand’s intrinsic curvature and twist, Poisson’s ratio and the birod’s stiffness parameters corresponding to inter-strand separation and rotation. Analytical expressions of the birod’s extensional stiffness, torsional stiffness, extension–torsion coupling stiffness, effective Poisson’s ratio, overwinding/unwinding effect etc. in the birod’s natural state are obtained. In particular, we show that depending on the parameters chosen, a torsionally relaxed birod can undergo non-intuitive slow overwinding followed by rapid unwinding during its stretching as observed during pulling of a torsionally relaxed DNA.