Approximate Values Research Articles

Pointwise superconvergence of block finite elements for the three-dimensional variable coefficient elliptic equation

<p>This study investigated the point-wise superconvergence of block finite elements for the variable coefficient elliptic equation in a regular family of rectangular partitions of the domain in three-dimensional space. Initially, the estimates for the three-dimensional discrete Greens function and discrete derivative Greens function were presented. Subsequently, employing an interpolation operator of projection type, two essential weak estimates were derived, which were crucial for superconvergence analysis. Ultimately, by combining the aforementioned estimates, we achieved superconvergence estimates for the derivatives and function values of the finite element approximation in the point-wise sense of the $ L^\infty $-norm. A numerical example illustrated the theoretical results.</p>

Learning-based augmentation of physics-based models: an industrial robot use case

Abstract In a Model Predictive Control (MPC) setting, the precise simulation of the behavior of the system over a finite time window is essential. This application-oriented benchmark study focuses on a robot arm that exhibits various nonlinear behaviors. For this arm, we have a physics-based model with approximate parameter values and an open benchmark dataset for system identification. However, the long-term simulation of this model quickly diverges from the actual arm’s measurements, indicating its inaccuracy. We compare the accuracy of black-box and purely physics-based approaches with several physics-informed approaches. These involve different combinations of a neural network’s output with information from the physics-based model or feeding the physics-based model’s information into the neural network. One of the physics-informed model structures can improve accuracy over a fully black-box model.

Model Predictive Bang-Bang Controller Synthesis via Approximate Value Functions

In this paper, we propose a novel method for addressing Optimal Control Problems (OCPs) with input-affine dynamics and cost functions. This approach adopts a Model Predictive Control (MPC) strategy, wherein a controller is synthesized to handle an approximated OCP within a finite time horizon. Upon reaching this horizon, the controller is re-calibrated to tackle another approximation of the OCP, with the approximation updated based on the final state and time information. To tackle each OCP instance, all non-polynomial terms are Taylor-expanded about the current time and state and the resulting Hamilton-Jacobi-Bellman (HJB) PDE is solved via Sum-of-Squares (SOS) programming, providing us with an approximate polynomial value function that can be used to synthesize a bang-bang controller.

Nectarine powder of Bulgarian origin: Physicochemical composition, antioxidant activity, microbiological and sorption characteristics

One way to improve the quality of food products is by conducting more thorough research on regional foods. This approach has several benefits, such as promoting human health, supporting the local economy, and preserving cultural food traditions. In this regard, our study investigated the potential of nectarine powder as a regional fruit product that could be developed into a global innovation. The present study examined: the physicochemical composition, antioxidant activity, microbiological load, and adsorption and desorption characteristics of the nectarine powder. The fruit powder was acquired through the use of a heat pump dryer, where drying took place at 42 °C for a duration of 8 h until achieving a moisture content ranging from 13.5 % to 14.5 %. The approximate physicochemical values are as follows: proteins, total carbohydrates, crude fiber, ash content and total lipids. Microbiological parameters, namely the total count of mesophilic aerobic and facultative anaerobic microorganisms, yeasts and molds, Escherichia coli, Salmonella spp., coagulase-positive staphylococci, and coliforms were checked and found to be within the acceptable limits as stipulated by the relevant state standards. Antioxidant activity was demonstrated through the utilization of various methods, including DPPH (33.19 ± 0.09mMTE/g extract), ABRS (2.55 ± 0.05mMTE/g extract), FRAP (1.43 ± 0.03mMTE/g extract) and CUPRAC (0.83 ± 0.01mMTE/g extract) methods. Investigation of the mass transfer sorption characteristics is performed using the gravimetric-static method. The conditions of the experiment were selected according to the usual conditions in which the food products are found in the commercial depot. The equilibrium and monolayer moisture data are investigated at 10 °C, 25 °C and 40 °C and relative air humidity in the wide range from 11 % to 87 %, achieved by the salts saturated solutions. To depict the adsorption and desorption isotherms, the modified models of Halsey, Chung-Pfost, Henderson, and Oswin were selected.

DIRECT AND INVERSE THEOREMS FOR APPROXIMATION OF FUNCTIONS BY SUMMATORS

Abstract Approximations of functions by singular integrals have numerous applications in various fields of mathematics. Approximations of functions by singular integrals are studied intensively along with other issues in theory of functions. In their papers P.L. Butzer and R.G. Mamedov study convergence order of singular integrals in generating functions at separate characteristic points and metric in the space p L on bounded and unbounded domains. Important theorems on asymptotic value of approximation of functions by singular integrals are obtained in these papers. Numerical investigations of different authors were devoted to convergence and convergence of singular integrals, approximation of functions by linear operators.

The Effect of Information Entropy Analysis in Computer-Assisted English Translation on Improving Translation Naturalness

Abstract This paper borrows the concept of entropy and refers the information entropy to the computer-aided English translation to build up the information entropy assessment and evaluation model and the information entropy-based English translation optimization model. The information entropy operation formula is used to calculate the fuzziness between the original text and the target translated text, and at the same time, the segmentation function is utilized to find the approximation value of the information entropy value obtained in a sufficiently fine segmentation of the translated text. Obtain the rectangular window function of semantic Gaussian marginalization, project the information entropy data, add the semantic correlation factors of words, identify the features of semantic information, and realize the optimization of English translation. Simulation experiments are carried out to verify the performance of the model. The information entropy evaluation and analysis model in this paper can achieve convergence after 45 iterations. In contrast, the word error rate and the cut-off error rate of the English translation optimization model are both lower than 10%, and the feature recognition and classification are higher than 80%. The fuzzy statements in Chinese writer Lao She’s work “Teahouse” are selected to explore the naturalness of translation. The information entropy value of the translation optimization model in this paper is closer to the original text, and the English translation’s naturalness is better than that of the GLR model.

Characteristics of convergence and stability of some methods for inverting the Laplace transform

The problem of inversion of the integral Laplace transform, which belongs to the class of ill-posed problems, is considered. Integral equations are reduced to ill-conditioned systems of linear algebraic equations, in which the unknowns are either the coefficients of the series expansion in terms of special functions, or the approximate values of the desired original at a number of points. Various inversion methods are considered and their characteristics of accuracy and stability are indicated, which must be known when choosing an inversion method for solving applied problems. Quadrature inversion formulas are constructed, which are adapted for the inversion of long-term and slow processes of linear viscoelasticity. A method of deformation of the integration contour in the Riemann-Mellin inversion formula is proposed, which leads the problem to the calculation of certain integrals and allows obtaining error estimates.

Enhancing Energy Efficiency in Greenhouses: Gas-Radiant Heating with Preheated Ventilation

This paper presents an engineering methodology for calculating the heating system of a cultivation facility, employing ceiling-mounted infrared radiators as the primary heat source. The methodology addresses the challenge of maintaining consistent soil surface temperature amidst fluctuating weather conditions. Gas-fired air heaters supplement the system, preheating incoming air to achieve the desired thermal regime within the space. This approach enables designers to swiftly estimate the required heating equipment capacity and water consumption for soil irrigation under specified conditions. However, for more precise calculations encompassing the full spectrum of microclimate parameters and heat fluxes within the facility, advanced computational tools are necessary. The article details the essential input data for the engineering calculations (including approximate values where applicable) and analyzes the key findings. A case study of the “Farmer 7.5” industrial greenhouse in Moscow, Russia, demonstrates the application. The calculated results for the gas-radiant heating system capacity (34.0 kW), preheating energy consumption (38.9 kW), and irrigation water requirement (32.0 kg/h) were validated through computational analysis.

Applicability of Numerical Simulation by Particle Method to Unconfined Compression Tests on Geomaterials

This study emphasizes the importance of accurate input parameters for ensuring the precision and reliability of simulations by conducting a sensitivity analysis to determine the calculation and material parameters. The aim is to determine the exact material parameters, for two different soil samples in a rigid state, by comparing the results of a sensitivity analysis with the unconfined compression test benchmark data for each sample. The moving particle semi-implicit (MPS) method, one of the particle methods, was chosen to reproduce the unconfined compression test simulation. The soil particles were assumed to be in the rigid state of the Bingham fluid bi-viscosity model. The first part of the study focuses on a sensitivity analysis of the basic simulation parameter values inputted during the simulation setup for the calculation procedure and the selection of the criteria for the calculation method, and then recommends the optimum values for a higher degree of accuracy based on the results. The second part of the study uses the results to analyze the sensitivity of each influencing parameter of the bi-viscosity Bingham fluid. In the final section, this study will provide a general guideline for selecting the optimum values for the MPS parameters and will recommend approximate values for other soil samples in future research with properties similar to those used in this study. Doi: 10.28991/CEJ-2024-010-01-01 Full Text: PDF

Numerical method for restoring the initial condition for the wave equation

The inverse problem of restoring the initial condition for the time derivative for the one-dimensional wave equation is considered. As an additional condition, the solution of the wave equation at a finite time is given. First, the discretization of the derivative with respect to the spatial variable is carried out and the initial problem is reduced to a differential-difference problem with respect to functions depending on the time variable. To solve the resulting differential-difference problem, a special representation is proposed, with the help of which the problem splits into two independent differentialdifference problems. As a result, an explicit formula is obtained for determining the approximate value of the desired function for each discrete value of a spatial variable. The finite difference method is used for the numerical solution of the obtained differentialdifference problems. The presented results of numerical experiments conducted for model problems demonstrate the effectiveness of the proposed computational algorithm.

A Novel Model for Forecasting Production Performance in Waterflood Oil Reservoirs

The importance of production performance forecasting in reservoir development and economic evaluation cannot be overstated. Previous models have shown deficiencies in accurately predicting production performance, necessitating the development of a new semianalytical model to enhance its application scope and prediction accuracy. This study proposes a novel semianalytical model based on the Buckley–Leverett (BL) equation and a newly proposed linear relationship between outlet water saturation and average water saturation, as well as Willhite’s formula of oil/water relative permeability. The results demonstrate the universality of this new model, as it can generate three equivalent log‐linear relations, including the previously proposed model. Sensitivity analysis confirms the applicability of the model in various reservoirs. In addition, both model and field case studies highlight the advantages of this technique in forecasting water cut and cumulative oil production, with an extensive application scope covering over 90% of the water cut range. A comparison of oil production prediction results from six different predictive methods reveals that the proposed semianalytical model exhibits the lowest error rate of −0.01%. Moreover, the semianalytical model can be utilized to directly solve for the approximate values of the exponents in Willhite’s oil/water relative permeability equations. In summary, this novel semianalytical forecasting model demonstrates a robust ability to forecast water cut, cumulative oil production, and recovery efficiency.

Conirmatory Factor Analysis of Depression, Anxiety and Stress 21 (DASS 21) scale in a study on Occupational Health Psychology in Health Care Professionals from Anand, Gujarat

Introduction: Confirmatory factor analysis (CFA) is a statistical technique to verify the factor structure of a set of observed variables. Objective: The study was conducted with an objective to study the psychometric properties of DASS 21 scale by Confirmatory factor analysis Method: This study used a Multi Method Design (Multiple approach Design), one was a cross sectional study of 228 participants and the other was a Solomon 4 group Design with total 64 participants. Four groups of health care professionals viz Allopathic doctors, Physiotherapists, Nursing professionals and Community Health Officers (CHOs) were chosen for the study. Convenience sampling was done at two stages. Results: Confirmatory factor analysis was used to evaluate the construct validity of DASS 21 scale. The model was overidentified as the estimated parameters were less than the number of observed variances and covariances. CMIN/DF(Chi square (minimum discrepancy function) /Degree of freedom) value was 2.021 which was < 5. Goodness of Fit Index (GFI) value (0.892) was near to .9. Root Mean square Residuals (RMR) and Root Mean Square Error of Approximation (RMSEA) value were 0.031 and 0.063 respectively which were less than 0.08. Average variance extracted (AVE) for the three constructs were less than the squared interconstruct correlation. Conclusion: DASS-21 scale demonstrated a good convergent validity, but in this study, discriminant validity was found to be poor as determined by average variance extracted in comparison to squared Interconstruct correlation.

A Numerical Technique for Solving Optimization Problems

The aim of this paper is to calculate a better approximation value (whether it is maximize or minimize ) for one- and two-dimensional nonlinear equations using the best numerical optimization algorithms, which is Newton's method. The idea of this technique is based on approximating the function by expanding the Taylor series expansion and iteratively updating the estimate of the optimal solution. we have obtained good results in terms of accuracy and speed of approach, as shown in the examples mentioned. We also mentioned the applications of Newton’s method in multiple disciplines, including engineering, physics, economics, finance, computer graphics, machine learning, image processing, and other applications.

A new aspect of the ApEn application to improve the PSO-ANFIS model to forecast Caspian Sea levels

Short-term forecasting of sea levels at the Caspian Sea plays an important issue for coastal planning. Therefore, a new aspect of the Approximate Entropy (ApEn) method application is studied to improve the Combined Particle Swarm Optimization and the Adaptive Network-based Fuzzy Inference System (PSO-ANFIS), Auto-Regressive Integrated Moving Average (ARIMA) models and Back Propagation Neural Networks (BP-NN). To evaluate the idea, seawater levels from 1961 to 2021 are categorized as training, validation (from 1961 to 2007 at Anzali station), and testing data (from 2008 to 2021 at Amirabad station). Results show the PSO-ANFIS model performance for forecasting the seawater level changes for four randomly selected time intervals and three critical periods. In addition, it is concluded that there are no considerable changes in the PSO-ANFIS model accuracy for embedding dimensions greater than 13 in forecasting of sea water level in the Caspian Sea. At the same time, the employed ApEn shows that there are no significant changes in approximate entropy values for block numbers more than 13 for the Caspian Sea levels. This shows the ApEn method performance to determine embedding dimensions for the forecaster models of time series. In addition, it resulted that the Caspian Sea water levels are on a decreasing trend on average by 5.495 cm every year until 2024 and the PSO-ANFIS model is reliable for 36 months as a short-term forecaster model. Comparing the developed PSO-ANFIS model with Long Short-Term Memory (LSTM) networks shows the PSO-ANFIS model significant superiority to the LSTM.

A complete solution for anti-jaming radio data-link of an unmanned aerial vehicle

The effectiveness of an unmanned aerial vehicle's flight mission over a given distance depends on many factors. However, one of the key factors in the successful completion of a flight mission is the availability of high-quality management and control of telemetry by an unmanned aerial vehicle, which in turn is determined by a reliable radio communication between the ground control station and the unmanned aerial vehicle. The current stage of use of unmanned aerial vehicles is characterised by the use of active jammers of various types and purposes, the purpose of which is to disable control channels, navigation channels, telemetry channels and data transmission channels of FPV unmanned aerial vehicles in order to prevent the successful completion of the flight mission of the vehicle. The article considers conceptual issues of implementing a guaranteed interference-free radio data transmission and control of an unmanned aerial vehicle in the conditions of active jamming interference when combining various technological solutions. These solutions include the selection and justification of a special frequency range, the use of structural circuit solutions for interference protection of the radio data transmission and control line; the use of a specific scheme for organising communication with an unmanned aerial vehicle; the use of a transceiver and portable and light antennas for the radio channel that meet reasonable technical requirements; the implementation of the possibility of real-time monitoring of the interference situation on board the unmanned aerial vehicle and detection of the type of interference; ensuring flight in the sector. The requirements were justified and options for selecting a transceiver and antenna were proposed. A structural diagram of the radio line is developed and options for its use as a data transmission and control radio line for an unmanned aerial vehicle are proposed. Examples of real-time tracking of the interference situation on board an unmanned vehicle and detection of the type of interference are given. A flight option in the sector without the use of antenna tracking is calculated and justified. The approximate values of the signal at the receiver input of the unmanned vehicle are calculated.

Трещинообразование натуральной и модифицированной прессованием древесины березы повислой (Betula pendula Roth): эффект показателя внутреннего трения под влиянием внешних возмущений

Obtaining information about the presence of cracks in raw materials, blanks and wood products is neces-sary to make a decision on the purposes of its subsequent processing and operation. The method for diagnosing cracks in wood is based on measuring internal friction. For prepared samples of natural and modified wood, sawn from the stem part of drooping birch (Betula pendula Roth) trees growing in Khlevensky Forestry, Lipetsk region. (52.184130, 39.110463, ASL 157m), exposed to radial and tangential directions with ultrasound (frequency 24.5 kHz, exposure 0-20 minutes, step 5 minutes) and pulsed magnetic field (strength - 0.3 T, exposure 0-2 minutes, step 0.5 minutes). Next, the internal friction of the samples was studied on an experimental setup by measuring the logarithmic damping decrement based on free-bending vibrations. The absolute values of the dimensionless coefficient of internal friction Q-1, as the main structural parameter for samples of natural and modified wood, were obtained at a significance level of p=0.95: for humidity, in the presence of one crack, Q-1 decreased by 7.04% (D=0.08), in the presence of two cracks - by 8.4% (D=0.15), in the presence of three cracks - by 9.06% (D=0.15); for ultrasound in the presence of one crack Q-1 decreased by 7.17% (D=0.05), in the presence of two cracks - by 8.46% (D=0.05), in the presence of three cracks - by 9.12% (D=0.09); for a pulsed magnetic field in the presence of one crack Q-1 decreased by 7.14% (D=0.05), in the presence of two cracks - by 8.39% (D=0.09), in the presence of three cracks - by 9.02% (D=0.09). When testing the samples of natural wood and pressure-modified drooping birch (Betula pendula Roth) wood, we obtained an asymptotic equation was obtained for ap-proximating the dependence of the decrease in Q-1 on the number of cracks, with the approximation value R2=0.994. The study of the dependence of internal friction on the process of crack formation in various types of wood provides preparation for the next stage - the construction of a prototype system for non-destructive testing of defects.

First-principles calculation of the structural, electronic and mechanical properties of β′ phase in Mg-RE binary systems

Rare-earth magnesium alloys (Mg-RE) are gaining growing prominence across multiple industries due to their superior mechanical properties and enhanced formability compared to conventional magnesium alloys. β′ phase of Mg-RE alloys exhibits remarkable behavior in strengthening and enhancing corrosion resistance. However, the mechanical behaviors of some β′ phases themselves remain unexplored. Therefore, our objective is to identify the mechanical and thermomechanical properties of β′ phases. Herein, a theoretical study to investigate the structural, electronic, elastic and anisotropic properties of β′–Mg7RE phase from first-principle calculations is described. Besides, the melting temperature and Debye temperature of these intermetallic compounds are also predicted. The calculated results confirm the thermodynamic and mechanical stability of all β′–Mg7RE phases. Additionally, the calculated value of bulk modulus for all β′–Mg7RE phase exhibit similarity, with an approximate value of 38 GPa. The degree of anisotropy in the bulk modulus of the β′–Mg7RE phase is relatively lower compared to the shear and Young’s moduli. Among the β′ phase, β′–Mg7Lu exhibits the most pronounced anisotropy. Furthermore, the highest degree of Young’s and shear moduli anisotropy for all β′ phases are observed in the (001) plane. The value of the electron localization function between Mg and RE atoms ranges from 0.48 to 0.56. In more detail, the density of states (DOS) reveals that hybridization arises from strong interaction between the Mg–p states and RE–d states below the Fermi level. Indeed, the results will offer valuable insights into the influential factors on the mechanical properties of the β′ phase, contributing to a more comprehensive understanding of its performance and potential applications.

First order asymptotics of the sample average approximation method to solve risk averse stochastic programs

We investigate statistical properties of the optimal value of the Sample Average Approximation of stochastic programs, continuing the study (Krätschmer in Nonasymptotic upper estimates for errors of the sample average approximation method to solve risk averse stochastic programs, 2023. Forthcoming in SIAM J. Optim.). Central Limit Theorem type results are derived for the optimal value. As a crucial point the investigations are based on a new type of conditions from the theory of empirical processes which do not rely on pathwise analytical properties of the goal functions. In particular, continuity or convexity in the parameter is not imposed in advance as usual in the literature on the Sample Average Approximation method. It is also shown that the new condition is satisfied if the paths of the goal functions are Hölder continuous so that the main results carry over in this case. Moreover, the main results are applied to goal functions whose paths are piecewise Hölder continuous as e.g. in two stage mixed-integer programs. The main results are shown for classical risk neutral stochastic programs, but we also demonstrate how to apply them to the Sample Average Approximation of risk averse stochastic programs. In this respect we consider stochastic programs expressed in terms of absolute semideviations and divergence risk measures.

DEEP LEARNING-BASED FEATURE FUSION AND TRANSFER LEARNING FOR APPROXIMATING pIC VALUE OF COVID-19 MEDICINE USING DRUG DISCOVERY DATA

The pandemic disease Coronavirus 2019 (COVID-19) caused thousands of infections and deaths globally. It is important to introduce new medicines to address the critical situation in the medical system. The determination of approximate pIC value is necessary for designing medicines based on molecular compounds. Generally, the approximation of pIC value is a lengthy process, so it is difficult and time-consuming. Hence it is essential to introduce a new technique for automatic approximation. In this research, a Convolutional Neural Network-based transfer learning (CNN-TL) is designed for approximating the pIC value. Initially, Simplified Molecular Input Line Entry System (SMILES) notation is extracted from SMILES string symbols using an entropy-based one-hot encoding matrix and the molecular formula-based encoding. The molecular features are then extracted from the input data using Lorentzian similarity and Deep Residual Network (DRN). The pIC value approximation is performed using the CNN-TL model, where the Visual Geometry Group Network-16 (VGGNet-16) is used to fetch hyperparameters used to initialize the CNN. The experimental results proved that the designed CNN-TL technique achieved minimum error rates with normalized values of 0.406 for R2, 0.516 for Root Mean Square Error (RMSE), 0.267 for Mean Square Error (MSE), and for 0.277 Mean Absolute Percentage Error (MAPE).

Development of Poly(sorbitol adipate)-g-poly(ethylene glycol) Mono Methyl Ether-Based Hydrogel Matrices for Model Drug Release.

Hydrogels were prepared by Steglich esterification and by crosslinking pre-synthesized poly(sorbitol adipate)-graft-poly(ethylene glycol) mono methyl ether (PSA-g-mPEG) using different-chain-length-based disuccinyl PEG. PSA and PSA-g-mPEG were investigated for polymer degradation as a function of time at different temperatures. PSA-g-mPEG hydrogels were then evaluated for their most crucial properties of swelling that rendered them suitable for many pharmaceutical and biomedical applications. Hydrogels were also examined for their Sol-Gel content in order to investigate the degree of cross-linking. Physical structural parameters of the hydrogels were theoretically estimated using the modified Flory-Rehner theory to obtain approximate values of polymer volume fraction, the molecular weight between two crosslinks, and the mesh size of the hydrogels. X-ray diffraction was conducted to detect the presence or absence of crystalline regions in the hydrogels. PSA-g-mPEG hydrogels were then extensively examined for higher and lower molecular weight solute release through analysis by fluorescence spectroscopy. Finally, the cytotoxicity of the hydrogels was also investigated using a resazurin reduction assay. Experimental results show that PSA-g-mPEG provides an option as a biocompatible polymer to be used for pharmaceutical applications.