Parameters Of Equation Research Articles

Testing in smoothed GMM quantile models with an application to quantile Euler equation

Within the framework of smoothed generalized method of moments for quantile models, including instrumental variables quantile regression as a special case, a distance metric hypothesis test and an overidentification test are proposed. The asymptotoic validity including the consistency of the distance metric hypothesis test are established. Simulations show reasonable finite-sample performance of both proposed tests in terms of size and power. In an empirical example, the proposed tests are applied to test the discount factor and elasticity of intertemporal substitution parameters in quantile Euler equations and overall the quantile Euler equation itself.

Improved reference condition independent method for output performance estimation of PV modules under varying operating conditions

Traditional methods for estimating output property of the photovoltaic (PV) modules are strongly influenced by the selection of reference condition and transforming equations, which determine the calculated physical parameters under real operating conditions. The differences in the carrier transport properties of PV cells under varying operating conditions, such as the number and velocity of minority carriers at the junction edge and their recombination speed, lead to large deviations in the estimation of the output characteristics, especially under low irradiance conditions. To enhance the accuracy of performance estimation, we propose an improved method that is independent of reference condition. This method eliminates the impact of reference conditions and improves the transformation equations under all irradiance levels. Transformation equations of single diode model are established in different irradiance intervals based on the dependence of physical parameter on irradiance and temperature. Especially in the low irradiance range, all effects of irradiance and temperature are considered for each physical parameter in improved transformation equations. To optimize the unknown parameters in the transformation equations, the artificial hummingbird algorithm is used to fit experimental I–V data. The experimental results of six different types PV modules under a wide range of operating conditions are used to verify the effectiveness of the proposed method. The proposed method offers immediate benefits, including independence from reference condition and a more precise relationship between physical parameters and environmental factors in the estimation of PV output properties. Comparing the results to the traditional method by Laudani, the proposed method demonstrates superior capability in estimating I–V characteristics and accurately identifies the maximum power point under various operating conditions, which is of significant value for engineering applications.

Spatial quadric calibration method for multi-line laser based on diffractive optical element

The traditional multi-line laser calibration method relies primarily on calibrating the spatial plane equations of multiple laser lines and reconstructing the multi-line laser in three dimensions through the plane equation and camera parameters. In traditional methods, the multi-line laser is projected as a straight line by default, but in reality, the laser line projected by the multi-line laser is not a plane due to the Diffractive Optical Element (DOE). Instead, it is a surface with a certain curvature in space. During the production process, the multi-line laser experiences significant distortion because of the DOE projecting at a large angle. Consequently, if traditional methods are used, accurate calibration of the multi-line laser cannot be achieved. To address this issue, this paper introduces a new calibration algorithm for multi-line laser based on a spatial quadric equation. By calibrating the spatial quadric equation of the multi-line laser, the spatial characteristics of the laser can be accurately captured. The algorithm involves projecting a crossed 7-line laser onto a calibration plate and changing the position of the calibration plate while capturing images. This allows for obtaining the spatial three-dimensional coordinates of each laser line in the camera coordinate system. Next, spatial quadric equations are fitted for each laser line based on the three-dimensional coordinates. Finally, 3D reconstruction is performed using the quadratic surface parameters of the multi-line laser and camera parameters. The results from 3D reconstruction demonstrate that, compared to traditional laser calibration methods based on planes, the proposed algorithm achieves higher calibration accuracy. It also improves the number of successful binocular multi-line laser matches and overall accuracy.

Predicting parameters of airway dynamics generated from inspiratory and expiratory plethysmographic airway loops, differentiating subtypes of chronic obstructive diseases

BackgroundThe plethysmographic shift volume–flow loop (sRaw-loop) measured during tidal breathing allows the determination of several lung function parameters such as the effective specific airway resistance (sReff), calculated from the ratio...

Buoyancy effects on very-large-scale motions and amplitude modulation in convective atmospheric surface layers

A large amount of high-Reynolds-number experimental data was obtained from long-term observations of the atmospheric surface layer in the Qingtu Lake Observation Array under different thermal stability conditions. To reveal the thermal effects, the variations of the scales of turbulent coherent structures, energy distribution and amplitude modulation as a function of thermal stability are investigated. Results show that in the convective atmospheric surface layer, the superposition of buoyancy and shear drives leads to a large enhancement of turbulent kinetic energy, an increase in the scales of coherent structures, and in particular, a more significant enhancement of the very-large-scale motions kinetic energy. This results in an increased energy proportion of very-large-scale motions, and thus enhancing the amplitude modulation effect on small scales. Moreover, the variations in the coherent structure scale, energy proportion of the very-large-scale motions, amplitude modulation coefficient and the corresponding modulating and carrier signal scales with the thermal stability parameter can all be characterized by the same parametric equation form. This study contributes to a better understanding of turbulence dynamics driven by both buoyancy and shear.

АНАЛИЗ ВЛИЯНИЯ КОНСТРУКТИВНЫХ ПАРАМЕТРОВ НА МАНЕВРЕННОСТЬ ТРАКТОРА СО ВСЕМИ УПРАВЛЯЕМЫМИ КОЛЕСАМИ

The results of a theoretical analysis are presented to assess the influence of the longitudinal base and track of a tractor with all steerable wheels on its basic geometric and kinematic characteristics in curved motion, characterizing its maneuverability. The maximum abscissa and ordinate of the trajectory of the entrance to the turn and the minimum theoretical radius of the steady-state stage of a circular loop-free turn are taken as estimated indicators. A comparison is given with the calculation results obtained in the study of a tractor with front steerable wheels under identical design parameters and operating conditions. To determine the necessary desired parameters describing the trajectory of the curved movement of the tractor, parametric equations are obtained. Analysis of the calculation results showed that with an alternate increase in the length of the longitudinal base from 2.2 m to 3.0 m and the track width from 1.2 m to 2.2 m, with the remaining unchanged design and operational characteristics, the minimum radius increases, respectively, by 18.5% and 16.3%, and the maximum ordinate of the trajectory of entry into the turn – by 3.9% and 16.6 %, while the maximum abscissa of this section of the trajectory decreases by 20.4 % and 40.4%. A comparison of the turning method, which is the subject of research in this paper, with the method of turning the front steerable wheels, all other things being equal, showed the effectiveness of the first of them. An increase in the maximum abscissa by 1.75 times was revealed, but a decrease in the maximum ordinate by 1.05 times and the minimum turning radius by 1.69 times. This gives reason to talk about the best maneuverability of a tractor with all steerable wheels.

Observation constraints on scalar field cosmological model in anisotropic universe

In this study, we have explored a scalar field cosmological model in the axially symmetric Bianchi type-I universe. In this study, our aim is to constrain the scalar field dark energy model in an anisotropic background. For this purpose, the explicit solution of the developed field equations for the model is determined and analyzed. Constraints on the cosmological model parameters are established utilizing Markov Chain Monte Carlo (MCMC) analysis and using the latest observational datasets of OHD, BAO, and Pantheon. For the combined dataset (OHD, BAO, and Pantheon), the best-fit values of Hubble and density parameters are estimated as [Formula: see text], [Formula: see text] [Formula: see text] and [Formula: see text]. The model shows a flipping nature and redshift transition occurs at [Formula: see text], and the present value of decelerated parameter is computed to be [Formula: see text] for the combined dataset. We have explored characteristics like the universe’s age, particle horizon, deceleration parameter, and jerk parameter. The dynamical properties, such as energy density [Formula: see text], scalar field pressure [Formula: see text], and equation of state parameter [Formula: see text], are analyzed and presented. We have also described the behavior of the scalar potential [Formula: see text] and scalar field. Furthermore, the authors also described the behavior of energy conditions in scalar-tensor cosmology. The scenario of the present accelerated expansion of the universe is described by the contribution of the scalar field.

Transient Dynamics of a Fractional Fisher Equation

We investigate the transient dynamics of the Fisher equation under nonlinear diffusion and fractional operators. Firstly, we investigate the effects of the nonlinear diffusivity parameter in the integer-order Fisher equation, by considering a Gaussian distribution as the initial condition. Measuring the spread of the Gaussian distribution by u(0,t)−2, our results show that the solution reaches a steady state governed by the parameters present in the logistic function in Fisher’s equation. The initial transient is an anomalous diffusion process, but a power law cannot describe the whole transient. In this sense, the main novelty of this work is to show that a q-exponential function gives a better description of the transient dynamics. In addition to this result, we extend the Fisher equation via non-integer operators. As a fractional definition, we employ the Caputo fractional derivative and use a discretized system for the numerical approach according to finite difference schemes. We consider the numerical solutions in three scenarios: fractional differential operators acting in time, space, and in both variables. Our results show that the time to reach the steady solution strongly depends on the fractional order of the differential operator, with more influence by the time operator. Our main finding shows that a generalized q-exponential, present in the Tsallis formalism, describes the transient dynamics. The adjustment parameters of the q-exponential depend on the fractional order, connecting the generalized thermostatistics with the anomalous relaxation promoted by the fractional operators in time and space.

Smooth Time-Varying Feedback Control of Nonholonomic Systems with Applications to the Attitude Control of Underactuated Spacecraft

This paper studies the control of chained nonholonomic systems by using smooth time-varying feedback. First, by using a time-varying state transformation, the chained nonholonomic system is transformed into a linear time-varying system. Second, with the aid of some properties of a class of parametric Lyapunov equations and time-varying systems theory, smooth time-varying state feedback controller is developed to ensure the exponential convergence of both the system states and controls. Different from existing results, the design parameters in the proposed control strategy are independent of the initial conditions of the system. Third, as an application of the proposed smooth time-varying feedback, the attitude control problem for underactuated axisymmetric spacecraft is addressed. Finally, a numerical simulation is presented to validate the effectiveness of the proposed method.

Technical note: Workload and transmission data for mobile C-arm fluoroscopy in gastrointestinal endoscopy.

Mobile C-arms may be used in fixed locations, and it is recommended that qualified experts evaluate structural shielding. To assess clinical workload distributions for mobile C-arms used in gastrointestinal endoscopy and determine the Archer equation parameters for the C-arm beam spectra. Consecutive (30 months) gastrointestinal endoscopic procedures on two Cios Alpha systems (Siemens) were retrospectively analyzed. X-ray tube voltage, tube current-time product, reference point air kerma (Ka,r), air kerma-area product (PKA), and fluoroscopic time were examined. The primary beam half-value layer (HVL) was measured with an ionization chamber and aluminum 1100 plates. Stray radiation fraction at 1m from a scattering source (ACR R/F phantom) was directly measured. Monte Carlo (Geant4) simulation was performed to calculate the transmission of broad X-ray beams through lead, concrete, gypsum, and steel, with X-ray HVLs matching those of the C-arm X-ray beam. The transmission data were fitted to the Archer equation. The number of procedures (3509) was equivalent to 13.48 procedures per room per week. Dose quantities were 54.8 mGy (Ka,r), 18.3Gy∙cm2 (PKA), and 7.8 min (fluoroscopic time) per procedure. X-ray beam irradiation events were recorded for 2906 (82.8%) procedures with 160,009 events, whose mA-minute weighted tube voltage was 91.0kV and the workload was 0.68mA-minute per procedure. The two rooms had a significant difference in the number of procedures per week, 17.3 (29) [mean (maximum)] and 9.6 (16), respectively. The stray radiation fraction was 9.7×10-4 (80kV) and 1.25×10-3 (120kV). Transmission fitting parameters were provided for the tube voltage (on average, 90kV; high end, 120kV) of the C-arm. This work provides workload and transmission data for mobile C-arm fluoroscopy in gastrointestinal endoscopy, which indicates a need for structural shielding evaluation of the procedure rooms.

Dimensionless Policies Based on the Buckingham π Theorem: Is This a Good Way to Generalize Numerical Results?

The answer to the question posed in the title is yes if the context (the list of variables defining the motion control problem) is dimensionally similar. This article explores the use of the Buckingham π theorem as a tool to encode the control policies of physical systems into a more generic form of knowledge that can be reused in various situations. This approach can be interpreted as enforcing invariance to the scaling of the fundamental units in an algorithm learning a control policy. First, we show, by restating the solution to a motion control problem using dimensionless variables, that (1) the policy mapping involves a reduced number of parameters and (2) control policies generated numerically for a specific system can be transferred exactly to a subset of dimensionally similar systems by scaling the input and output variables appropriately. Those two generic theoretical results are then demonstrated, with numerically generated optimal controllers, for the classic motion control problem of swinging up a torque-limited inverted pendulum and positioning a vehicle in slippery conditions. We also discuss the concept of regime, a region in the space of context variables, that can help to relax the similarity condition. Furthermore, we discuss how applying dimensional scaling of the input and output of a context-specific black-box policy is equivalent to substituting new system parameters in an analytical equation under some conditions, using a linear quadratic regulator (LQR) and a computed torque controller as examples. It remains to be seen how practical this approach can be to generalize policies for more complex high-dimensional problems, but the early results show that it is a promising transfer learning tool for numerical approaches like dynamic programming and reinforcement learning.

Methyl α-D-galactopyranosyl-(1→3)-β-D-galactopyranoside and methyl β-D-galactopyranosyl-(1→3)-β-D-galactopyranoside: Glycosidic linkage conformation determined from MA'AT analysis.

MA'AT analysis has been applied to two biologically-important O-glycosidic linkages in two disaccharides, α-D-Galp-(1→3)-β-D-GalpOMe (3) and β-D-Galp-(1→3)-β-D-GalpOMe (4). Using density functional theory (DFT) to obtain parameterized equations relating a group of trans-O-glycosidic NMR spin-couplings to either phi (ϕ') or psi (ψ'), and experimental 3JCOCH, 2JCOC, and 3JCOCC spin-couplings measured in aqueous solution in 13C-labeled isotopomers, probability distributions of ϕ' and ψ' in each linkage were determined and compared to those determined by aqueous 1-μs molecular dynamics (MD) simulation. Good agreement was found between the MA'AT and single-state MD conformational models of these linkages for the most part, with modest (approximately <15°) differences in the mean values of ϕ' and ψ', although the envelope of allowed angles (encoded in circular standard deviations or CSDs) is consistently larger for ϕ' determined from MA'AT analysis than from MD for both linkages. The MA'AT model of the α-Galp-(1→3)-β-Galp linkage agrees well with those determined previously using conventional NMR methods (3JCOCH values and/or 1H-1H NOEs), but some discrepancy was observed for the β-Galp-(1→3)-β-Galp linkage, which may arise from errors in the conventions used to describe the linkage torsion angles. Statistical analyses of X-ray crystal structures show ranges of ϕ' and ψ' for both linkages that include the mean angles determined from MA'AT analyses, although both angles adopt a wide range of values in the crystalline state, with ϕ' in β-Galp-(1→3)-β-Galp linkages showing greater-than-expected conformational variability.

Generalized ghost dark energy in [formula omitted] gravity

In this manuscript, we use the correspondence principle to construct the generalized ghost dark energy f(Q) model, where Q is the non-metricity. For this purpose, we use the Friedman–Robertson–Walker universe model with power-law scale factor. The energy density in this model linearly depends on the Hubble parameter, with a sub-leading term of H2, resulting in an energy density ρD=ξH+ζH2, where ξ and ζ are arbitrary constants. We reconstruct interacting fluid scenario of this dark energy with dark matter. The reformulated f(Q) gravity model shows how different epochs of the cosmic history can be reproduced by this modified gravity model. The physical characteristics of the model are discussed through the equation of state parameter with the planes of ωD−ωD′ and r−s. We also explore the stability criteria for the interacting model using the squared speed of sound. The equation of state parameter indicates phantom phase of the universe and the squared speed of sound represents stability of the interacting model. The (ωD−ωD′)-plane indicates freezing region, while the (r−s)-plane corresponds to the Chaplygin gas. We conclude that our findings coincide with the latest observational data.

Modified Friedmann equations and fractal Black Hole thermodynamics

The general relativity unification and quantum theory is a significant open problem in theoretical physics. This problem arises from the fact that these two fundamental theories, which describe gravity and the behavior of particles at the microscopic level, respectively, are currently incompatible. The unification of these theories is crucial for a complete comprehension of the fundamental forces and the nature of the universe. In this regard, the quantum properties of a Black Hole result in fundamental importance. By analyzing such properties in quantum field theory, in the first step, the gravity enters as a classical background. In semi-classical approximation, Black Holes will emit Hawking radiation with an almost thermal spectrum, while Black Hole’s entropy is proportional to the Black Hole’s horizon. Besides, Hawking’s temperature and Black Hole entropy should follow the first law of Black Hole thermodynamics. Also, Jacobson [Thermodynamics of spacetime: The Einstein equation of state, Phys. Rev. Lett. 75 (1995) 1260, doi:10.1103/PhysRevLett.75.1260] showed shown that there is a connection between Black Hole thermodynamics and Einstein’s equation that opens the root of a potential thermodynamic nature of gravity. This issue opened a new impressive research framework in which the Einstein field equation can be expressed as a form of the first law of thermodynamics and vice versa. In this study, it is assumed that the universe has a fractal structure. Accordingly, modified Friedmann’s equations and the Black Holes thermodynamics in a fractal universe have been examined. The fractal framework shows what features and changes occur in the description of the universe, particularly in studying the thermodynamics of a Black Hole. However, the paper strategy is organized as follows: in the beginning, we consider the first thermodynamic law in a fractal universe. Then, we investigate the Friedmann equation of the fractal universe in the form of the entropy balance, this means [Formula: see text], where [Formula: see text] and [Formula: see text] are the thermal energy and horizon temperature. We consider the entropy [Formula: see text] have two terms; (1) obeys the usual area law and (2) the entropy production term due to the non-equilibrium thermodynamics of a fractal universe. Therefore, in a fractal universe, a term with non-equilibrium thermodynamics of spacetime may be needed. Also, we study the generalized second law of thermodynamics in a fractal universe. When the temperature of the apparent horizon and the temperature of the matter fields inside the horizon are equal, i.e. [Formula: see text], the second law of generalized thermodynamics can be obtained according to the state parameter range equation, which is consistent with the recent observations. Finally, in Sec. 6, based on the mathematical calculations, we study the various cosmological parameters such as the Hubble parameter, scale factor, deceleration parameter and equation of state parameter.

On the Exact Solution of a Scalar Differential Equation via a Simple Analytical Approach

The existence of the advance parameter in a scalar differential equation prevents the application of the well-known standard methods used for solving classical ordinary differential equations. A simple procedure is introduced in this paper to remove the advance parameter from a special kind of first-order scalar differential equation. The suggested approach transforms the given first-order scalar differential equation to an equivalent second-order ordinary differential equation (ODE) without the advance parameter. Using this method, we are able to construct the exact solution of both the transformed model and the given original model. The exact solution is obtained in a wave form with specified amplitude and phase. Furthermore, several special cases are investigated at certain values/relationships of the involved parameters. It is shown that the exact solution in the absence of the advance parameter reduces to the corresponding solution in the literature. In addition, it is declared that the current model enjoys various kinds of solutions, such as constant solutions, polynomial solutions, and periodic solutions under certain constraints of the included parameters.

Active Acoustic Metamaterial Based on Helmholtz Resonators to Absorb Broadband Low-Frequency Noise.

The aim of the present work is to design active acoustic metamaterial consisting of an array of Helmholtz resonators and fabricating them using an additive manufacturing technique in order to assist in a reduction in noise levels in aerospace applications. To this aim, initially, a passive metamaterial consisting of an array of 64 Helmholtz resonator unit cells is designed and tested to establish the effectiveness and region of performance. The selected design variable for change is identified as the resonator cavity depth through the frequency response for each parameter of the Helmholtz resonance equation and randomized to achieve a broadband frequency range of the passive metamaterial. An active model of this design (actuated by a stepper motor) is fabricated and tested. The metamaterials are tested under two acoustic set-ups: a closed system aimed at recreating the environment of a soundproof room and an open-system aimed to recreate the condition of an active liner. For the case of passive system, the metamaterial gave sound attenuation of 18 dB (for f = 150 Hz) in open system configuration and 33 dB (f = 350 Hz) in closed system configuration. The attenuation obtained for the active model was 10-15 dB over the mean line performance for the case of closed system and 15-20 dB for the case of open system. The closed system was also tested for performance at multiple cavity depths by setting two wall depths at 10 mm and three walls at 50 mm. This test yielded an attenuation of 15 dB at 180 Hz, the frequency corresponding to 50 mm cavity depth, and 10 dB at 515 Hz, corresponding to 10 mm cavity depth.

Stability analysis of anisotropic stellar structures in [formula omitted] gravity

The article explores the dynamics and stability of compact stars in the field of f(R) gravity by investigating the empirical data of different significant compact star candidates. We used the corrections offered by Karmarkar and Tolman to examine the properties of these specific compact stars. For different values of the curvature term, we analyzed the behavior of material variables, energy conditions, equations of state parameters, anisotropy measurements, and the Tolman–Oppenheimer–Volkoff equation in the modeling of stellar structures We provided illustrations with their graphical representations that depict the configuration of the compact stars. For this purpose, we utilized known f(R)-gravity models to express these results as graphical representations to provide evidence supporting the authenticity and stability of the stars.

Finite-time semi-global stabilisation of polynomial growth nonlinear systems by linear time-varying feedback

The paper studied the finite-time semi-global stabilisation problems for a class of nonlinear systems with a novel polynomial growth condition. By using some key properties of a class of parametric Lyapunov equations and constructing time-varying Lyapunov-like functions, two time-varying high-gain controllers, where scalar time-varying functions are generated by differential equations, are designed. Both state feedback and observer-based output feedback are considered. It is shown that the proposed methods can achieve finite-time semi-global stabilisation for closed-loop systems and the controls are bound. Two numerical examples verify the effectiveness of the established results.

Generative adversarial reduced order modelling

In this work, we present GAROM, a new approach for reduced order modeling (ROM) based on generative adversarial networks (GANs). GANs attempt to learn to generate data with the same statistics of the underlying distribution of a dataset, using two neural networks, namely discriminator and generator. While widely applied in many areas of deep learning, little research is done on their application for ROM, i.e. approximating a high-fidelity model with a simpler one. In this work, we combine the GAN and ROM framework, introducing a data-driven generative adversarial model able to learn solutions to parametric differential equations. In the presented methodology, the discriminator is modeled as an autoencoder, extracting relevant features of the input, and a conditioning mechanism is applied to the generator and discriminator networks specifying the differential equation parameters. We show how to apply our methodology for inference, provide experimental evidence of the model generalization, and perform a convergence study of the method.

Individually optimized estimation of energy expenditure in rescue workers using a tri-axial accelerometer and heart rate monitor.

Objectives: This study aimed to provide an improved energy expenditure estimation for heavy-load physical labor using accelerometer data and heart rate (HR) measured by wearables and to support food preparation and supply management for disaster relief and rescue operations as an expedition team. Methods: To achieve an individually optimized estimation for energy expenditure, a model equation parameter was determined based on the measurements of physical activity and HR during simulated rescue operations. The metabolic equivalent of task (MET), which was measured by using a tri-axial accelerometer and individual HR, was used, where two (minimum and maximum) or three (minimum, intermediate, and maximum) representative reference points were selected for each individual model fitting. In demonstrating the applicability of our approach in a realistic situation, accelerometer-based METs and HR of 30 males were measured using the tri-axial accelerometer and wearable HR during simulated rescue operations over 2days. Results: Data sets of 27 rescue operations (age:34.2 ± 7.5years; body mass index (BMI):22.9 ± 1.5kg/m2) were used for the energy expenditure estimation after excluding three rescue workers due to their activity type and insufficient HR measurement. Using the combined approach with a tri-axial accelerometer and HR, the total energy expenditure increased by 143% for two points and 133% for three points, compared with the estimated total energy expenditure using only the accelerometer-based method. Conclusion: The use of wearables provided a reasonable estimation of energy expenditure for physical workers with heavy equipment. The application of our approach to disaster relief and rescue operations can provide important insights into nutrition and healthcare management.