Functional Form Research Articles

Estimation of some AM2 model parameters from a derived empirical logistic function of methane production

Because of its capability to convert organic wastes into renewable energy and into some components useful for agriculture, the anaerobic digestion technology can reduce greenhouse gas emissions in the atmosphere and the pollution. Thus, anaerobic digestion can contribute to achieving some of sustainable development goals. Consequently, many theoretical and empirical approaches are proposed for estimating, predicting and optimizing the methane produced by anaerobic digestion. In this context, the logistic function is a mathematical model that can be used to approximate empirical data of the temporal methane production in anaerobic digestion. In a previous paper, under some appropriate approximations, we have derived from AM2 model a single analytical expression in a form of a logistic function for describing the evolution of methane production in batch bioreactors. In the present paper, by comparing the three standard parameters associated with the classical empirical logistic function with that of the derived one from AM2 model; some relationships between them have been established. These relations are exploited for estimating some coefficients and parameters of AM2 model with respect to empiric logistic function parameters and vice-versa. Moreover, this possibility enables more qualitative insight about the evolution of the methane production and the influence of AM2 parameters and coefficients as well as their interaction over its processes.

Composing Serverless Azure Functions in NodeJS with MySQL Database Integration

This paper delves into the concept and implementation of serverless computing, particularly focusing on Azure Functions as a platform for deploying serverless applications. It introduces the notion of a Function app, a container that amalgamates functions into a single logical unit, thereby simplifying management, deployment, and resource sharing. Serverless computing is elucidated as Function as a Service (FaaS), a paradigm where business logic is executed in the form of functions without the need for manual infrastructure management. Azure Functions enables developers to host and execute business logic seamlessly, without the concerns of provisioning infrastructure. The platform supports a multitude of programming languages, including C#, Java, JavaScript, TypeScript, and Python, offering versatility in development approaches. The paper further explores the utilization of triggers, specifically HTTP triggers, for executing code in response to HTTP requests. It highlights the development process within Visual Studio Code, facilitated by the Azure Functions extension, which allows for the comprehensive creation and deployment of projects. Additionally, the distinction between Consumption service plans and App Service Plans is examined, along with the prerequisite of linking every function app to a storage account. Deployment methodologies, both locally and through the Azure portal, are outlined, along with the capabilities for monitoring logs via the Azure portal’s Monitor section. This comprehensive overview provides insights into leveraging Azure Functions for efficient, scalable, and manageable serverless application development.

Semi-empirical model for Henry’s law constant of noble gases in molten salts

Henry’s law constant, which describes the proportionality of dissolved gas to partial pressure of free gas in liquid–gas equilibrium systems, can also be applied to mass transport applications. In this work, we investigated an approach for determining the solubility of noble gases in a molten salt liquid utilizing the equilibrium concept of Henry’s gas constant. Henry’s gas constant is described as a mathematical function dependent on the van der Waals radius of the noble gas and the temperature of the molten salt. The alteration in Gibbs free energy encompasses contributions from both surface and volume energies. Enthalpy and entropy are deduced from these surface and volume energies in the Gibbs free energy formulation. A comparative analysis was conducted between the conventional method and our proposed model. Moreover, useful chemical properties can be determined from examination of surface and volume energies. Our findings provide an accurate and general theory of Gibbs free energy that can be validated experimentally based on the model proposed herein. This work unifies the prediction of Henry gas constant and subsequently the entropy and enthalpy calculation for noble gases in a molten salt solution to a single functional form using van der Waals radius of the gas and temperature of the system. This functional form is then used to perform a multiple regression method to find two parameters corresponding to the surface energy and volume energy. These two parameters are consistent between all combinations of noble gas and molten salt.

High pressure melt line of nickel using a generalized embedded atomic method potential

As the second most abundant metal in the Earth's core, nickel plays an important role in determining the structure and temperature of the Earth's core. Yet, the melt line of Ni at pressures corresponding to the Earth's core has not been explored in the literature. Many previous experimental and simulation efforts have reported the melting point of Ni at pressures below 100 GPa, but there exist large discrepancies, most of which have persisted due to various experimental and simulation bottlenecks in handling extreme pressure and temperature conditions. We adopted the generalized embedded atom method, which overcomes the limitations of existing interatomic potentials, to probe phase stability and phase boundaries of Ni at pressures between 50 and 500 GPa. The potential was validated by comparing the cold curves, phonon dispersion curves, and enthalpies of fusion with ab initio density functional theory calculations. Our analysis shows that face centered cubic (FCC) is stable, and the hexagonal close packed (HCP) and body centered cubic (BCC) phases are metastable close to the melt line. Melting temperatures at different pressures were obtained from two-phase co-existence simulations and take the following functional form: Tm=1969.23+19.15P−0.012P2. In contrast to iron, differences between the melting points of the stable and metastable phases of Ni are less than 250 K at 300 GPa, and the difference in melting points of the metastable BCC and HCP phases changes sign at 500 GPa, which implies that the phase transition mechanisms during solidification can be very complex.

A Parametric Cox Proportional Hazard Model with Application

Survival analysis has become integral to clinical studies, especially in emerging diseases and terminal ailments. This study focused on improving the popular Cox PH model. The new method developed is a parametric type, incorporating the hazard rate of the exponential distribution. It was noted that though the functional form of the Cox PH model was altered, the assumptions were upheld. Additionally, the new model parameters were estimated using the same maximum partial likelihood as the Cox model. Data on the survival times of 137 patients who underwent bone marrow transplants were deployed, and the proposed parametric Cox PH model proved superior to the Cox PH model.

A Modified Ideal Rank Index Number Formula

This paper proposes an index number method called Asanya-Jibasen-Mbaga index, the method satisfied Laspeyre’s and Paasche’s bounding test which is unbiased compared to existing methods. The proposed index methods used expenditure/quantity and rank as weights and it satisfied all the tests of consistency of elementary index formulae. The proposed method was found to approximate the Fisher’s Ideal Price index (PF). The proposed method is an improvement on Jibasen –Gazali-Asanya rank price index. Numerical analyses conducted at low and high levels of aggregation revealed that the Jibasen-Gazali-Asanya rank price Index is biased and also failed Laspeyre’s and Paasche's bounding test. Thus, based on the results of the findings, Asanya-Jibasen-Mbaga index method is recommended as the appropriate functional form of the elementary index method among other existing elementary index methods

Neural network optimizer of proportional-integral-differential controller parameters

Wide application of proportional-integral-differential (PID)-regulator in industry requires constant improvement of methods of its parameters adjustment. The paper deals with the issues of optimization of PID-regulator parameters with the use of neural network technology methods. A methodology for choosing the architecture (structure) of neural network optimizer is proposed, which consists in determining the number of layers, the number of neurons in each layer, as well as the form and type of activation function. Algorithms of neural network training based on the application of the method of minimizing the mismatch between the regulated value and the target value are developed. The method of back propagation of gradients is proposed to select the optimal training rate of neurons of the neural network. The neural network optimizer, which is a superstructure of the linear PID controller, allows increasing the regulation accuracy from 0.23 to 0.09, thus reducing the power consumption from 65% to 53%. The results of the conducted experiments allow us to conclude that the created neural superstructure may well become a prototype of an automatic voltage regulator (AVR)-type industrial controller for tuning the parameters of the PID controller.

A hybrid approach to remote sensing image classification based on pixel density distribution and adaptive neural networks

<span lang="EN-US">The proposed study employed a method for identifying the main contents (category/class) that a Remote Sensing Image (RSI) belongs to, as well as the percentage contribution if the image comprises a significant number of different content types. Histogram based approach has been used to extract the pixel density distribution and its normalized form helps to make solution independent from image physical characteristics. A multilayer feedforward Artificial Neural Network (ANN) design has been used to address the classification problem. The architecture included an adaptive form of transfer function, whose slope characteristics changes along with weights as learning progresses. The approach of solution design is computation efficient because it doesn’t apply extensive pre-processing.</span>

On multiplicative generators of the unified form of 0-overlap and 1-grouping functions

Recently, Qiao introduced a unified form for 0-overlap and 1-grouping functions, called Θ−Ξ functions. With more relaxed boundary conditions, Θ−Ξ functions can be served as a generalization of overlap and grouping functions. As a result, the flexibility and generality of Θ−Ξ functions allow for a wider range of applications, with a potential for application that exceeds that of overlap and grouping functions. This paper focuses on the study of the multiplicative generator pairs (MGPs) of Θ−Ξ functions. Firstly, we propose two concepts of an MGP for a Θ−Ξ function, which are based on the correlation between the value of boundary elements ℓ and ℘, specifically, ℓ<℘ and ℓ>℘. And then, for each of the two cases in turn, we provide the conditions for deriving a Θ−Ξ function from the MGP and determine its block structures. Moreover, we discuss such multiplicatively generated Θ−Ξ functions with neutral elements and examine the actions of (ℓ,℘)-pseudo-automorphisms on them. Finally, we establish two equivalent relationships between MGPs of Θ−Ξ functions with ℓ<℘ and those with ℓ>℘.

Standard Post-Keynesian investment functions and their demand regime: a comprehensive empirical estimation for France

The aim of this article is twofold. In a first step, we estimate a large variety of standard Post-Keynesian investment functions for France over the period 1979–2020 by rigorously following the original features of a theoretical macro-model of growth and distribution. In a second step, for each of these investment functions, we also assess the corresponding demand regime contributing to the current profit-led/wage-led debate. Our results show that the French economy seems to be wage-led. Besides, the intensity of the regime varies greatly with the specific form of the investment function under consideration.

Linear redshift parametrization of deceleration parameter in [formula omitted] gravity

In this study, we investigate the linear redshift parametrization of q(z) within the framework of f(R,Lm) gravity, using constraints derived from H(z)/Pantheon samples. We consider a non-linear functional form for f(R,Lm), specifically given by f(R,Lm)=R2+Lmn, where n represents a free parameter in the model. Subsequently, we derive the solution for the Hubble parameter by investigating the parametrization of q(z) and then apply this solution to the modified Friedmann equations. Our analysis focuses on exploring the behavior of the EoS parameter across different stages of the universe’s evolution, including radiation, matter, and dark energy eras. Furthermore, our results confirm the quintessence nature of the universe’s current accelerated expansion phase (−1<ω<−13), supporting the role of quintessence in driving the universe’s current acceleration. We also explore the redshift dependence of the deceleration parameter, statefinder, Om(z) diagnostics, energy density, pressure, and energy conditions to determine the universe’s accelerating behavior. Importantly, our findings suggest that the linear redshift parametrization of q(z), supported by additional terms in f(R,Lm) gravity, provides a compelling alternative to the cosmological constant.

Konsep Evaluasi Dalam Pembelajaran

Abstract. This article is a theoretical study of the importance of the learning evaluation process. This article was written through library research, namely collecting information that is relevant to the topic or problem that is the object of discussion. The data sources for this research are books, journals, articles related to the topic of the concept of evaluation in learning. Data analysis techniques are reading, studying, analyzing and then concluding. The results of this article provide an important message for teachers or educators to review and re-understand the concept of evaluation, evaluation principles, forms of evaluation, objectives and functions of evaluation, evaluation procedures and techniques, uses and benefits of evaluation.

Fermion-soliton scattering in a modified CP1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb{C}\\mathbb{P}^{1}$$\\end{document} model

The scattering of fermions in the background field of a topological soliton of the modified (2+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(2 + 1)$$\\end{document}-dimensional CP1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb{C}\\mathbb{P}^{1}$$\\end{document} model is studied here both analytically and numerically. Unlike the original CP1\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbb{C}\\mathbb{P}^{1}$$\\end{document} model, the Lagrangian of the modified model contains a potential term. Due to this, a dilatation zero mode of the topological soliton disappears, which results in stability of the fermion-soliton system. The symmetry properties of the fermion-soliton system are established, and the asymptotic forms of fermionic radial wave functions are studied. Questions related to the bound states of the fermion-soliton system are then discussed. General formulae describing the scattering of fermions are presented. The amplitudes of the fermion-soliton scattering are obtained in an analytical form within the framework of the Born approximation, and their symmetry properties and asymptotic forms are studied. The energy levels of the fermionic bound states and the partial phase shifts of fermionic scattering are obtained by numerical methods, and the ultrarelativistic limits of the partial phase shifts are found.

A note on a q-difference equation related to Riccati equations

In this paper, we consider the existence of analytic solutions of associated with q-Airy equation y ( q 2 t ) + qty ( qt ) − y ( t ) = 0. By the position of q, we study the existence of analytic solutions of the form of power functions, the convergence radius of the formal solutions for some cases is also given.

СИНТЕЗ ТИПОВИХ ЦИФРОВИХ АСТАТИЧНИХ РЕГУЛЯТОРІВ ПРОМИСЛОВИХ ЕЛЕКТРОПРИВОДІВ

The paper is devoted to the clarification and generalization of the analytical methodology for the synthesis of typical digital astatic regulators of industrial electric drives, which can be presented in the form of discrete transfer functions in the Z-transformation, according to the given speed quality factor, and the development of recommendations for determining the setting parameters of such regulators. It is proposed to determine the coefficient of the integral component according to the given speed quality factor, and determine the other setting parameters in such a way as to compensate for two (for PID-regulators) or one (for PI-regulators) poles of the discrete transfer function of the control object. The ranges of speed quality factor values for a number of electric drives that are optimal in terms of dynamic performance indexes have been determined. It has been proven that to increase the speed in systems with PI controllers, it is necessary to compensate for the larger of the two poles. References 10, figures 5.

Comparing researchers' degree of dichotomous thinking using frequentist versus Bayesian null hypothesis testing.

A large amount of scientific literature in social and behavioural sciences bases their conclusions on one or more hypothesis tests. As such, it is important to obtain more knowledge about how researchers in social and behavioural sciences interpret quantities that result from hypothesis test metrics, such as p-values and Bayes factors. In the present study, we explored the relationship between obtained statistical evidence and the degree of belief or confidence that there is a positive effect in the population of interest. In particular, we were interested in the existence of a so-called cliff effect: A qualitative drop in the degree of belief that there is a positive effect around certain threshold values of statistical evidence (e.g., at p = 0.05). We compared this relationship for p-values to the relationship for corresponding degrees of evidence quantified through Bayes factors, and we examined whether this relationship was affected by two different modes of presentation (in one mode the functional form of the relationship across values was implicit to the participant, whereas in the other mode it was explicit). We found evidence for a higher proportion of cliff effects in p-value conditions than in BF conditions (N = 139), but we did not get a clear indication whether presentation mode had an effect on the proportion of cliff effects. PROTOCOL REGISTRATION: The stage 1 protocol for this Registered Report was accepted in principle on 2 June 2023. The protocol, as accepted by the journal, can be found at: https://doi.org/10.17605/OSF.IO/5CW6P .

A geometric framework for distributed frequency models

Geometric control theory, developed by Basile and Marro, and independently, by Wonham and Morse in the 1970s revolves around characterizing the properties of finite dimensional, linear and time-invariant systems using geometry. Some examples of these properties are invariance, controllability and observability. The task addressed in this paper is to develop the geometric tools for fractional systems using the diffusive representation (also known as the distributed frequency) model. The mathematics involved in this approach is different from the classical case as fractional systems are inherently infinite dimensional. Unlike the integer order derivative, the fractional derivative is a non-local operator, and so the evolution of the so-called pseudo-state depends on not just its current value but also its past history. Thus, the notion of an initial condition for a fractional system can come in different forms. This leads to different kinds of fractional derivative operators. With some of these operators, the semigroup property is lost. With the distributed frequency model, the initial condition comes in the form of an initialization function. This takes care of the infinite dimensional nature of fractional systems. Furthermore, the distributed frequency model retains the semigroup property. This is useful in developing invariance and controlled invariance for fractional systems. Moreover, these properties of fractional systems are verified numerically using a higher order finite-dimensional approximation, which retains all the geometric properties of the distributed frequency model.

A simple method for mechanical analysis of pressurized functionally graded material thick-walled cylinder

The complex function method is employed to establish a mechanical model for pressurized thick-wall cylinders made of functionally graded materials (FGM). This model is applicable to all radial varying modes of material properties, including both continuous and discontinuous variations in Young’s modulus and Poisson’s ratio. The main concept behind this mechanical model involves dividing the thick-walled cylinder into concentric thin cylinders, each equipped with a pair of analytical functions representing stress functions. By imposing continuity conditions between adjacent thin cylinders and considering the stress boundary conditions of the entire structure, all unknown forms of analytical functions can be determined. Subsequently, by establishing the correspondence relationship between these analytical functions and stress or displacement, it becomes possible to solve for the stress or displacement at any radial position within the thick-walled cylinder. Through comparison and verification against the numerical simulation results, it can demonstrate that as long as the differential scale is sufficiently small, high accuracy can be achieved in the final result. In other words, solutions obtained for multi-layered hollow cylinder converge toward those obtained for continuously graded thick-walled cylinder. Notably, by starting from the level of stress function and avoiding complex differential and integral equations, a linear equation system can provide information on stress and displacement distributions along the radial direction. Therefore, compared to other solving methods available, this proposed approach offers simplicity and applicability.

Noether symmetries of F(T,X,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(T,X,\\phi )$$\\end{document} cosmology

This article explores an analysis via the Noether symmetry approach to investigate an extended teleparallel F(T,X,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(T,X,\\phi )$$\\end{document} gravity model in the context of a Friedmann–Robertson–Walker spacetime. The model incorporates the torsion scalar T, scalar field ϕ\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\phi $$\\end{document} and the kinetic term X of the scalar field. This approach allows us to select physically interesting models by restricting arbitrariness in the F(T,X,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(T,X,\\phi )$$\\end{document} function. Thus we focus on two types of the function F(T,X,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(T,X,\\phi )$$\\end{document}, namely models involving the generalized teleparallel dark energy and the nonlinear function of the kinetic term and analyze the Noether symmetry properties and demonstrate the presence of non-vanishing Noether vectors. In the first model, by specifically considering the X4\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathbf{X_{4}}$$\\end{document} Noether symmetry, representing a scaling symmetry, we simplify the field equations and introduce a cyclic variable to enable a more workable formulation. Furthermore, we present a comprehensive graphical analysis, showcasing the time evolution of the scale factor and the scalar field by using the solutions obtained through these new variables. Additionally, we examine some fundamental cosmological parameters. For the second model, which includes the nonlinear form of the kinetic term, Noether symmetry results in obtaining simple power-law solutions for the dynamic variables. Our findings clearly show that the considered models represent an accelerating expansion of the Universe, which is consistent with observations. This study highlights the efficacy of the Noether symmetry approach in defining the functional form of F(T,X,ϕ)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$F(T,X,\\phi )$$\\end{document} and obtaining precise cosmological solutions. The analytical solutions and graphical analysis offer valuable insights into the dynamic behavior of the models, contributing to understanding the evolving nature of the Universe.

#376 Self-efficacy, social support and hemodiafiltration are independently associated with better Self-Reported Health Status over time

Abstract Background and Aims Patients with kidney disease receiving dialysis are a highly vulnerable population. Psychosocial determinants of Self-Efficacy (SE) and Social Support (SS) have been suggested as potentially important outcomes for people with end stage kidney disease. We investigated whether these variables could explain differences in Health-Related Quality of Life (HRQL) outcome domains over time independently or in interaction with treatment modality of high-flux hemodialysis (HD) versus high-dose hemodiafiltration (HDF). Method HRQL in 1264 participants from the international multi-centre, prospective, randomized, open label, controlled CONVINCE trial were assessed, using screening and quarterly follow-up data up to 24 months. Measures included the MOS Social Support Scale, General Self-Efficacy Scale, and PROMIS short forms for fatigue, physical function, pain interference and intensity, sleep disturbance, anxiety, cognitive function, depression, ability to participate in social roles. SE, SS and interactions with modality were included as independent variables and HRQL domains as dependent variables in a linear mixed effects model with random intercept and slope for SE and SS. Results Participants were 20-92 (M=62.33, SD=13.50) years old, 62.9% were male. Linear mixed effect regression models showed significant main effects for self-efficacy (β = −0.15-1.09, all p &amp;lt; .0001) on all HRQL domains. Significant SE × time interactions were found for all variables (β = −0.02-0.04, all p &amp;lt; .01) but pain intensity. Main effects for SS were found for cognition (β = 0.31, p = .00) and sleep disturbance (β = −0.21, p = .00). A significant SS × time interaction was found for anxiety (β = 0.01, p = .02) and sleep disturbance (β = 0.02, p = .00). Plots for these associations can be found in Figs 1 and 2. Marginal means were plotted and 25%, 50% and 75% quantiles were used to separate the different levels of SE and SS. There were no significant interactions between treatment modality (HDF vs. HD) and SE/SS. Conclusion Our results indicate that higher SE and better SS are independently associated with higher HRQL of dialysis patients over time, showing no significant interactions with HDF. SE had the largest effects on HRQL. This bears the chance to develop targeted psychosocial interventions to improve health outcomes when introducing new therapy options for patients. However, patients achieving higher HRQL over the course of the treatment may also experience higher SE and SS over time. Future research should include longitudinal assessments on these psychosocial determinants to evaluate their effect further.